The developments of confirmed daily Sars-CoV-2 infections can be modeled a posteriori in a comparatively simple and satisfactory way by means of a special exponential function: its exponential coefficient varies exponentially with time itself. This property enables the function to directly simulate the „daily case“ curve fragments observed for the first waves of the current epidemics in a number of counties and countries. Linear combinations of two or more of the functions allow for the modeling of the complete curves observed in the vast majority of all regions for which case number developments have been tabulated.

Despite great advances in understanding the dynamics of viral epidemics, the emergence of rapidly spreading, highly pathogenic viruses remains a realistic and catastrophic possibility, which current health systems may not be able to fully contain. An intriguing feature in many recent zoonotic viral outbreaks is the presence of superspreaders, which are infected individuals that cause dramatically more new cases than the average. Here I study the effect of superspreaders on the early dynamics of emerging viruses that have not gained the capacity for efficient human-to-human transmission, i.e viruses with R0 < 1. I show that superspreaders have a higher chance of rapid extinction, but under crowded conditions can lead to outbreaks, causing far more cases than regular viruses. I suggest that outbreaks of highly pathogenic superspreaders are more likely when they coincide in time and space with an unrelated outbreak leading to increased hospital admission rates. These superspreader outbreaks may be difficult to detect, especially in the context of a different epidemic in progress, and can significantly affect mortality patterns observed in affected areas.

Social networking applications such as Twitter have increasingly gained significance in terms of socio-economic, political, and religious as well as entertainment sectors. This in turn, has witnessed a wide gamut of information explosion in the social networking realm that can tend to be both useful as well as misleading at the same point of time. Spam detection is one such solution that caters to this problem through identification of irrelevant users and their data. However, existing research has so far laid primary focus on user profile information through activity detection and relevant techniques that may underperform when these profiles exhibit characteristics of temporal dependency, poor reflection of generated content from the user profile, etc. This is the primary motivation for this paper that addresses the aforementioned problem of user profiles by focusing on both profile information and content-based spam detection. To this end, this work delivers three significant contributions. Firstly, exhaustive use of Natural language processing (NLP) techniques has been rendered towards creation of a new comprehensive dataset with a wide range of content-based features. Secondly, this dataset has been fed into a customized state-of-art hybrid machine learning model that has been exclusively built using a combination of both machine learning and deep learning techniques. Extensive simulation based analysis not only records over 98% accuracy but also establishes the practical applicability of this proposal by proving that modeling based on the mixed profile and content-generated data is more capable of spam detection in contrast to each of these standalone approaches. Finally, a novel methodology based on logistic regression is proposed and supported by analytical formulations. This paves the way for the custom-built dataset to be analyzed and corresponding probabilities to be obtained that differentiate legitimate users from spammers. The obtained mathematical outcome can henceforth be used for future prediction of user categories through appropriate parameter tuning for any given dataset. This makes our method a truly generic one capable of identifying and classifying different user categories.

: Arboviruses transmitted by Aedes aegypti and Ae. albopictus have been introduced to Florida on many occasions. Infrequently, these introductions lead to sporadic local transmission and, more rarely, sustained local transmission. Both mosquito species are present in Florida, with spatio-temporal variation in population composition. We developed a 2-vector compartmental, deterministic model to investigate factors influencing Chikungunya virus (CHIKV) establishment. The model includes a non-linear, temperature-dependent mosquito mortality function based on minimum mortality in a central temperature region. Latin Hypercube sampling was used to generate parameter sets used to simulate transmission dynamics, following the introduction of one infected human. The analysis was repeated for 3 values of the mortality function central temperature. Mean annual temperature was consistently important in the likelihood of epidemics, and epidemics increased as the central temperature increased. Ae. albopictus recruitment was influential at the lowest central temperature while Ae. aegypti recruitment was influential at higher central temperatures. Our results indicate that the likelihood of CHIKV establishment may vary, but overall Florida is permissive for introductions. Model outcomes were sensitive to the specifics of mosquito mortality. Mosquito biology parameters are variable, and improved understanding of this variation will improve our ability to predict the outcome of introductions.

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order, on the quotient space of isomorphism classes of finite groups, that is well behaved with respect to cardinality. If $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G\leq\mathbb Z_{p_1}^{n_1}\oplus\mathbb Z_{p_2}^{n_2}\oplus\cdots\oplus\mathbb Z_{p_k}^{n_k}$ where $n=p_1^{n_1}p_2^{n_2}\cdots p_{k}^{n_k}$ is the prime factorization of $n$. We find a canonical order for the objects of $G$ and define equivalent objects of $G$, thus finding the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and we are provided with a minimal set of independent equations that define the group. We show how to find all groups of order $n$, and order them. We give examples using all groups with order smaller than $10$, and we find the canonical block form of the symmetry group $\Delta_4$. In the next section, we extend our results to the infinite case, which defines a real number as an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational aspects of these representations.

Academic publishing appears to be the most important key of the academic functions (academic research, excellence in teaching and learning and community services). Selecting the right journal to publish research results is a challenge to academics. Yet, there is inadequate knowledge about a model specifically directed at the topic of the journal selection process with a mathematical certainty. The objectives of this research are: to identify the main factors that an author or researchers consider when selecting an academic journal for submitting a manuscript, and, to develop a mathematical algorithm of journal selection that provide the best journal choice with a mathematical certainty based on difficulty of each factor. Quantitative research through questionnaires has been applied as an appropriate instrument base to address the researcher’s identification of the factors that should be considered when selecting a journal. Questionnaire developed and emailed to academics in 31 public and private universities in the developing countries. Academics reported that the most important publication difficulty factors were publishing in reputable journals, and publishing in a journal that has an impact factor. However, the most least publication difficulty factors were found to be: number of issues per year and if the journal is an open access. The proposed mathematical algorithm of journal’s publication difficulty factors was developed and tested.

This economic evaluation aims to support policy-making on the combined use of pre-exposure prophylaxis (PrEP) with HIV vaccines by evaluating the potential cost-effectiveness of implementation that would support the design of clinical trials for assessment of combined product safety and efficacy. The target study population is a cohort of men who have sex with men (MSM) in the United States. Policy strategies considered include standard HIV prevention, daily oral PrEP, HIV vaccine, and their combination. We constructed a Markov model based on clinical trial data and published literature. We used a payer perspective, monthly cycle length, a lifetime horizon, and a 3% discount rate. We assumed a price of $500 per HIV vaccine series in the base case. HIV vaccines dominated standard care and PrEP. At current prices,PrEP was not cost-effective alone or in combination. A combination strategy had the greatest health benefit but was not cost-effective (ICER=$463,448/QALY) as compared to vaccination alone. Sensitivity analyses suggest a combination may be valuable for higher-risk men with good adherence. Vaccine durability and PrEP drug prices were key drivers of cost-effectiveness. Results suggest that boosting potential may be key to HIV vaccine value.

Vaccination is an important method of immunological preventive care required for health management of all animal including fish. More particularly, immunization is important in in-land fisheries for the management of diseases in fish brood stocks and healthy seed production. According to the latest statistics in 2020, 90.3 million tonnes of captured fish production was achieved from the aquaculture sector. Out of the above, 78.8 million tonnes from marine and 11.5 million tonnes from inland waters aquaculture sectors. About 4% decline in fish production was achieved in 2020 than 2018 from inland fisheries sectors. On the other hand, the digestive protein content, healthy fats and nutritional values of fish products are comparitively more affordable as compared to other meat sources. In 2014, about 10% aquatic cultured animals were lost (costing &gt; 10 billion $ global annual loss) due to infectious diseases. Therefore, vaccination in fish especially in brood stocks is one of the most important approaches to stop such losses in the fisheries sector. Fish vaccines consist of either whole killed pathogens, subunit of a protein, a recombinant protein, DNA vaccines or live attenuated vaccines. Challenges existing are adaption of vaccination in fisheries sector, route of administration, use of effective adjuvants and most importantly lack of effective results. Use of autogenous vaccines, vaccination via intramuscular, intraperitoneal or oral routes, and most importantly adding vaccines in feed using top dressing methods or as a constituent in fish feed are now in emerging. These method shall lower the risk of using antibiotics in cultured water which in turn will reduce the environmental contamination.

Parkinson's disease (PD) is the second most common neurodegenerative disorder, entailing several motor-related symptoms that contribute to a reduced quality of life in affected subjects. Recent advances in wearable technologies and computing resources have shown great potential for the assessment of PD-related symptoms. However, the potential applications (e.g., early diagnosis, prognosis and monitoring) and key features of digital biomarkers for motor symptoms of PD (DB-MS-PD) have not been comprehensively studied. This study aims to provide a state-of-the-art review of current digital biomarker definitions for PD, focusing on the use of wearable devices. This review systematically examines research articles from 2012 to 2024, focusing on key features and recent technologies in PD research. A total of 22 studies were included and thoroughly analyzed. Results indicate that DB-MS-PD can accurately distinguish patients with PD (PwPD) from healthy controls (HC), assess disease severity or treatment response, and detect motor symptoms. Large sample sizes, proper validation, non-invasive devices, and ecological monitoring make DB-MS-PD promising for improving PD management. Challenges include sample and method heterogeneity and lack of public datasets. Future studies can leverage evidence of the current literature to provide more effective and ready-to-use digital tools for monitoring PD.

In this study, a new diphosphate compound, Ag0.2Na0.6FeP2O7, was synthesized using a solid-state reaction method and extensively studied using various techniques. The compound's structure was confirmed through X-ray diffraction analysis, revealing a single-phase monoclinic structure with the P21/C space group. The electrical behavior of the compound was investigated, and its conductivity followed Jonscher's universal law. The correlated barrier hopping (CBH) model explained the temperature-dependent ac conductivity and parameter "s" well. The study also explored the contribution of single-polaron and bipolaron hopping to the a.c. conductivity and discussed the ionic conductivity in relation to the structural characteristics of the sample. Overall, this investigation significantly enhances our comprehension of the distinctive electrical properties of Ag0.2Na0.6FeP2O7 and its potential practical applications.

Exploring therapeutic options is crucial in the ongoing COVID-19 pandemic caused by SARS-CoV-2. Nirmatrelvir, a potent inhibitor targeting the SARS-CoV-2 Mpro, shows promise as an antiviral treatment. Additionally, Ivermectin, a broad-spectrum antiparasitic drug, has demonstrated effectiveness against the virus in laboratory settings. However, its clinical implications are still debated. Using computational methods such as molecular docking and 100 ns molecular dynamics simulations, we investigated how Nirmatrelvir and Ivermectin interact with SARS-CoV-2 Mpro(A). Calculations using density functional theory have been instrumental in elucidating the behavior of isolated molecules, primarily by analyzing the frontier molecular orbitals. Our analysis revealed distinct binding patterns: Nirmatrelvir formed strong interactions with amino acids like MET49, MET165, HIS41, HIS163, HIS164, PHE140, CYS145, GLU166, and ASN142, showing stable binding with a root mean square deviation (RMSD) of around 2.0 Å. On the other hand, Ivermectin interacted with THR237, THR239, LEU271, LEU272, and LEU287, displaying an RMSD of 1.87 Å, indicating enduring interactions. Both ligands stabilized Mpro(A), with Ivermectin showing stability and persistent interactions despite forming fewer hydrogen bonds. These findings offer detailed insights into how Nirmatrelvir and Ivermectin bind to the SARS-CoV-2 main protease, providing valuable information for potential therapeutic strategies against COVID-19.

Seeds from several Ribes taxa were surveyed for phenolic compounds and in vitro antiproliferative activity against HT-29 colorectal cancer cells. Total phenolic compounds were analysed through the Folin-Ciocalteu procedure, while phenolic profiles were analysed by LC coupled to a single mass spectrometer Orbitrap using an electrospray interface (ESI). Antitumor effects were established using the MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay. Total phenolics ranged from 11.4 in R. alpinum to 94.8 mg of caffeic acid equivalents (CAE)/g in R. nigrum 'Koksa'. Concerning phenolic compounds, four were hydroxylated benzoic acids, four cinnamic acid derivatives, eight flavonoids, and nine flavonoid glycosides. The growth inhibition against HT-29 cancer cells was exercised much better by R. nigrum 'Koksa' and Ribes 'Erkeeni' (GI50 37 and 42 µg/ml). All Ribes extracts, except R. nigrum 'Hara katarlik', showed higher activity than that of R. rubrum (GI50 at 72 h: 99 µg/ml). Interestingly, the highly bioactive extract from Ribes 'Erkeeni' contains all detected phenolics, while R. nigrum 'Koksa' lacks only populnin. Therefore, the high bioactivity found for such extracts could be due to a synergy due to all detected compounds. This work constitutes a comprehensive action for expanding knowledge on the phenolic profiles and antitumor activity of GLA-rich Ribes seeds.

A mechanical ventilation system is a big support for breathing complications, in which an external solution is quite necessary to keep oxygen compensation in the patients. Its knowledge is well widespread and different equipment has been developed. However, they are very expensive and their quantity in medical centers is not sufficient, especially in Peru. Hence, it has been required to develop new methods to provide oxygen by a low cost equipment; Protofy, a research group from Spain, designed one of the first low cost mechanical ventilation systems which was medically validated by its government. In this sense, a redesign of the mechanical ventilation system was carried out according to the local requirements and available technology, a different airbag resuscitator with different properties and geometry, but maintaining its working concept based on a cam compression mechanism. Sensors and a display were added to improve the performance with a control algorithm for the rotation frequency and to show the ventilation curves over time to the medical staff. It was necessary to develop a mathematical model to relate the behavior between ventilation curves for a patient and physical variables of the design, especially in the epidemic COVID 19, that many countries are dealing with at the time research is being conducted. The mechanical ventilation system was redesigned, fabricated, and tested measuring its ventilation curves over time. Results indicate that this redesign provides a sturdy equipment able to work during a longer lifetime than the original. The replicability of the ventilation curves behavior is assured, while the mechanism dimensions are adapted for a particular airbag resuscitator. The mathematical model of the whole system can predict satisfactorily the ventilation curves over time and was used to provide the air pressure, volume, and flow as a function of the rotation angle measured by sensors.

The managers’ strategic behavior of commercial real estate in a competitive environment is discussed. The means of this research are methods of mathematical and experimental game theory. Illustrates an example of a decision-theoretic game problem with two players engaged in the management of competing shopping centers. The strategies of these players are determined by the costs of the development. Since the number of visitors is constantly and changing the quality of shopping centers, managers actually pull visitors from each other, the game-theoretical formulation of the problem of management of shopping centers corresponds to the zero-sum game. The model example shows that with the help of mathematical modeling it is possible to determine the theoretical expected behavior of agents. The model of the software module created specifically for experimental research is described. The experiments are designed to compare the theoretically predicted behavior with the real actions of people. The novelty is that at significant costs of the Manager for the development and promotion of shopping and entertainment centers, the strategies of managers are resistant to each other's actions, in contrast to changes in the external environment is shown.

Based on the minimum conduction band edge caused by the minimum channel potential resulting from the quasi-3D scaling theory and the 3D density of state (DOS) accompanied by the Fermi-Dirac distribution function on the source and drain sides, a unified semiconductor-device-physics-based ballistic model is developed for the threshold voltage of modern multiple-gate (MG) transistors, including FinFET, W-gate MOSFET, and Nanosheet (NS) MOSFET. It is shown that the thin silicon, thin gate oxide, and high work function will alleviate the ballistic effects and resist the threshold voltage degradation. Besides, as the device dimension is further reduced to give rise to the 2D/1D DOS, the lowest conduction band edge is hence increased to resist the threshold voltage degradation. The nanosheet MOSFET exhibits the largest threshold voltage among the three transistors due to the smallest minimum conduction band edge caused by the quasi-3D minimum channel potential. Compared to P-type MOSFET (P-FET), the N-FET shows more threshold voltage because the electron has a more effective mass than the hole

Polycystic ovary syndrome (PCOS) is a complex disorder that impacts both the endocrine and metabolic systems. The gut microbiota plays a crucial role in in metabolism regulation and immune responses through its interaction with the external environment. This article explores the intricate interplay between intestinal flora and the pathogenesis of PCOS, focusing on the pivotal role of microbial metabolites, specifically short-chain fatty acids (SCFAs). SCFA levels in fecal and blood samples from women with PCOS (n=69) and healthy controls (n=18) were analyzed using Gas Chromatography-Mass Spectrometry (GC/MS) for precise measurement. The results revealed that women with PCOS exhibited a significant reduction in beneficial bacteria alongside a notable overgrowth of opportunistic microorganisms. An overproduction of acetic acid (AA) and valeric acid (VA) in fecal samples suggests a link between elevated SCFAs and the development of obesity and PCOS. Interestingly, AA in the bloodstream might offer a protective effect against PCOS by ameliorating key symptoms such as high body mass index (BMI), insulin resistance (IR), and chronic inflammation. This finding points to the potential therapeutic value of maintaining optimal AA levels in the blood. Although serum SCFA levels showed non-significant changes following metformin treatment, the normalization of AA in the gut underscores that metformin exerts a more pronounced effect locally within the gastrointestinal tract. This treatment also led to an increase in beneficial gut bacteria and a reduction in opportunistic pathogens, suggesting a restoration of gut microbial balance. Furthermore, the study identified the most effective model for predicting the success of metformin therapy, based on serum concentrations of butyric acid (BA) and VA, achieving a 91% accuracy rate, 100% sensitivity, and 80% specificity. These promising findings highlight the potential for developing targeted interventions and personalized treatments, ultimately improving clinical outcomes for women with PCOS.

The assessment of soil contamination in the vicinity of integrated siderurgical plants is of outmost importance for agroecosystems and human health, and sensitive techniques should be employed for accurate assessment of chemical elements (metals, potential toxic elements, rare earths, radioelements) in soil and further evaluation of potential ecological and safety risk. In this paper a total of 45 major, minor and trace elements (Al, As, Au, Ba, Br, Ca, Cd, Ce, Co, Cr, Cs, Cu, Dy, Eu, Fe, Hf, Hg, I, K, La, Mg, Mn, Mo, Na, Nd, Ni, Pb, Rb, Sb, Sc, Sm, Sn, Sr, Ta, Tb, Th, Ti, Tm, U, V, W, Y, Yb, Zn and Zr) were quantified in soils located around a large siderurgical works (Galati, SE Romania) using instrumental neutron activation analysis (INAA) in combination with X-ray fluorescence (XRF) and inductively coupled plasma mass spectrometry (ICP-MS). The statistical analysis results and vertical distribution patterns for three depths (0-5 cm, 5-20 cm, 20-30 cm) indicate inputs of toxic elements in the sites close to the ironmaking and steelmaking facilities and industrial wastes dumping site. For selected elements, a comparison with historical, legislated and world reported concentration values in soil was performed and depth migration, contamination and toxic risk indices were assessed. The distribution of major, rock forming elements was closer to the Upper Continental Crust (UCC), and to the Dobrogea loess, finding confirmed by the ternary diagram of the incompatible trace elements Sc, La and Th, as well as by the La to Th rate. At the same time, the La/Th vs. Sc and Th/Sc vs. Zr/Sc bi-plots suggested a felsic origin and a weak recycling of soils mineral components.

Byers Peninsula is considered one of the largest ice-free areas in Maritime Antarctica. Since 2006, the Spanish Polar Program has taken part in a large number of environmental studies involving effects of climate changes in lives cycles, limnology and microbiology. Soils from maritime Antarctica are generally weakly developed and have chemical, physical and morphological characteristics strongly influenced by the parent material. However, biological activity during the short Antarctic summer promotes intense transference of nutrients and organic matter in areas occupied by different species of birds and marine mammals. To mapping and monitoring those areas with high biological occupation, could be very useful to have models of edaphic properties prepared from satellite images. In this approach, Deep Learning and Linear Regression models of soil properties and spectral indexes as explicative variables were performed. We training models of soil properties closely related to biological activity such as Dissolved Organic Carbon (DOC) and the iron fraction associated with organic matter (Fe). We tested the best approach to model the spatial distribution of DOC, Fe and pH by training models of Linear Regression and Deep Learning over Sentinel2 and WorldView2 images. The most robust models were used to track possible areas with ornithogenic soils as well as areas of the Byers Peninsula that could support the highest biological development.

The mathematical structure underlying a sentence is made of two independent processing units in series. The conditional probability density function of sentence length (measured in words) recordable in the extended short–term memory (E–STM) buffer made of CF cells is Gaussian. The number of sentences that authors of Italian and English Literatures have written is compared to that theoretically available to them. The multiplicity factor α describes this comparison. α&gt;1 is more likely than α&lt;1 and often α≫1, therefore the same sentence pattern is reused many times. These texts are easier to read. Very few novels show α&lt;1. In these cases, there are enough diverse sentence patters to convey meaning, but most of them are not used. Texts are more difficult to read, as measured by a universal readability index GU. A mismatch index IM synthetically describes the process. α, GU. and IM increase with year of publication. Future work will concern other literatures – including ancient ones as Greek and Latin – to confirm what, in our opinion, is general feature of human mind.

A new generation of nano-technologies is expanding solid propulsion capabilities and increasing their relevance for versatile and manoeuvrable micro-satellites with safe high-performance propulsion. We propose the innovative concept, connected with application of new synergistic effect of the energetic materials performance enhancement and reaction zones programming for the next generation small satellite multimode solid propulsion system. The main idea of suggested concept is manipulating by the self-organized wave patterns excitation phenomenon, by the properties of the energetic materials reaction zones and by localization of the energy release areas. This synergistic effect can be provided through application of the functionalized carbon-based nanostructured metamaterials as a nano-additives along with simultaneous manipulating by their properties through the electrostatic field. Mentioned effect will be controlled through predictive programming both by the spatial structure and physics-chemical properties of the functionalized carbon-based nano-additives and through the electromagnetic control of the self-organized wave pattern excitation and micro- and nano- scale oscillatory networks in the energetic material reaction zones. Suggested new concept makes it possible to increase the energetic material regression rate and increase the thrust of the solid propulsion system with minimal additional energy consumption.

In our recent publications pertaining to 4G model of final unification and based on strong and electroweak interactions, we have developed a completely new formula for estimating nuclear binding energy. With reference to currently believed Semi Empirical Mass Formula (SEMF), we call our formula as ‘Strong and Electroweak Mass Formula’ (SEWMF). Our formula constitutes 4 simple terms and only one energy coefficient of magnitude 10.1 MeV. First term is a volume term, second term seems to be a representation of free nucleons associated with electroweak interaction, third term is a radial term and fourth one is an asymmetry term about the mean stable mass number. Considering this kind of approach, nuclear structure can be understood in terms of strong and weak interactions and cold nuclear fusion like complicated concepts can be understood in a theoretical approach positively. In this paper, by considering the accountability of we are making an attempt to improve the applicability and effectiveness of SEWMF. Number 0.00125 being a workable electroweak coefficient for Z=6 to 132 and A=2Z to 3.5Z, number of free nucleons assumed to be associated with electroweak interaction can be expressed as Improved asymmetry term can be expressed as, where represents the light house like stable mass number. With reference to old version, our improved binding energy formula can be expressed as, We are working on its possible modification for mass numbers less than the stable mass numbers. Following this approach, it is possible to show that nuclear binding energy scheme is associated with strong and weak interactions and is practically independent of Coulombic repulsions. Proceeding further, currently believed cold nuclear fusion assumed be associated with hydrated metals can be understood and can be confirmed with strong and weak interactions independent of coulombic repulsions. We are very confident to say that our approach will certainly motivate modern science community in this new direction.

This note first summarizes the history of the manuscript "On a Continuum Model for Avalanche Flow and Its Simplified Variants" by Grigorian and Ostroumov―published in the Special Issue on snow avalanche dynamics of Geosciences―since the early 1990s and explains the guiding principles in editing it for publication. The changes are then detailed and some explanatory notes given for the benefit of readers who are not familiar with the early Russian work on snow avalanche dynamics. Finally, the editor's personal views as to why he still considers this paper of relevance for avalanche dynamics research today are presented in brief essays on key aspects of the paper, namely the role of simple and complex models in avalanche research and mitigation work, the status and possible applications of Grigorian's stress-limited friction law, and non-monotonicity of the dynamics of the Grigorian–Ostroumov model in the friction coefficient. A comparison of the erosion model proposed by those authors with two other models suggests to enhance it with an additional equation for the balance of tangential momentum across the shock front. A preliminary analysis indicates that continuous scouring entrainment is possible only in a restricted parameter range and that there is a second erosion regime with delayed entrainment.

Monitoring and protecting flowing watercourses is a complex and challenging task that requires the collaboration and coordination of various stakeholders such as governments, industries, farmers, consumers and environmental groups. The study of the dynamics of the concentration of polluting factors and especially the concentrations of heavy metals and highlighting a seasonal variation is a necessary element from this point of view. In this article, we present the results of our analyzes carried out in two measurement campaigns executed in 10 monitoring points along the Danube River, between Braila city and Isaccea city in the pre-deltaic area, during the summer season and autumn season 2022. The importance of this area is given by the fact that the Dan-ube Delta is part of the UNESCO heritage and the monitoring of polluting factors is a necessity in the desire to protect this area. The data measured during the July and August 2022 campaign co-vers a wide range of chemical species: Phosphate, CCO, CBO5, NH4+, N-NO2, N-NO3-, N-Total, P-PO4 3-, SO42-, Cl-, phenols, as well as metals with a harmful effect: Aluminum, Arsenic, Cad-mium, Chromium, Iron. The study includes an evaluation based on the statistical approach of the results to highlight the significant correlations and differences identified between the two data sets. Next, to highlight the obtained results, a numerical model was considered using HEC-RAS and ESRI ArcGis applications in a two-dimensional unsteady flow model in order to get the non-homogenous concentrations’distributions in the studied area. These two-dimensional models have been less studied in the specialized literature. In this way, interesting results could be ob-tained and prediction methods regarding the dynamics of metal concentrations could be struc-tured. The data obtained was used for the terrain model from the USGS service and the flows of the Danube and its two tributaries were simulated using the data provided by the national ser-vices. In this work, we present the results obtained for the dynamics of the concentrations of the metals Aluminum, Arsenic, Cadmium, Chromium and Iron and the evaluation of the specific ab-sorption coefficients for the explanation and correlation with the results of the measurements. The study is part of a more complex project in which the spatio-temporal distribution of the polluting factors in the water was evaluated and the habitats in the study area were inventoried - especially those of community interest. the aspects related to the influence of the distribution of polluting factors on the state of health will be the subject of another article.

Depth-sensing technology has led to broad applications of inexpensive depth cameras that can capture human motion and scenes in 3D space. Background subtraction algorithms can be improved by fusing color and depth cues, thereby allowing many issues encountered in classical color segmentation to be solved. In this paper, we propose a new fusion method that combines depth and color information for foreground segmentation based on an advanced color-based algorithm. First, a background model and a depth model are developed. Then, based on these models, we propose a new updating strategy that can eliminate ghosting and black shadows almost completely. Extensive experiments have been performed to compare the proposed algorithm with other, conventional RGB-D algorithms. The experimental results suggest that our method extracts foregrounds with higher effectiveness and efficiency.

The search for materials with exceptional properties has led to significant advances in the field of non-carbon diamond-like conductive thin films (DLC-CTFs). These films, synthesized by chemical vapor deposition (CVD) and other techniques, are being actively researched for their potential in high-tech applications. This literature review discusses the synthesis methods, material properties, and applications of DLC-CTFs, highlighting the role of non-carbon dopants in enhancing electrical conductivity. This literature review aims to provide a comprehensive overview of the historical development, synthesis techniques, material properties, characterization methods, and applications of DLC-CTFs, with a focus on the impact of non-carbon doping on their conductive properties. By reviewing the literature. The review also addresses the challenges faced and suggests future research directions.

A tritium resistant coating on the surface of materials is one of the main methods to reduce tritium permeability. In actual operating processes, mechanical damage such as spalling and scratches will occur on the surface of tritium resistant coatings. These mechanical damages will affect the hydrogen permeability resistance of the coatings. It is an important engineering problem that evaluate the effect of these damage on the tritium resistance of the coating. In this experiment, the mechanical damage of FeAl/Al2O3 tritium resistant coating on 316L stainless steel was simulated by scratching, debonding and thermal shock, and the gas hydrogen isotope permeation (GDP) test was carried out. The influence of mechanical damage degree on the tritium permeation behaviour of the coating was evaluated and discussed.

The “Crisis of Reproducibility” has received considerable attention both within the scientific community and without. While factors associated with scientific culture and practical practice are most often invoked, I propose that the Crisis of Reproducibility is ultimately a failure of generalization with a fundamental scientific basis in the methods used for biomedical research. The Denominator Problem describes how limitations intrinsic to the two primary approaches of biomedical research, clinical studies and pre-clinical experimental biology, lead to an inability to effectively characterize the full extent of biological heterogeneity, which compromises the task of generalizing acquired knowledge. Drawing on the example of the unifying role of theory in the physical sciences, I propose that multi-scale mathematical and dynamic computational models, when mapped to the modular structure of biological systems, can serve a unifying role as formal representations of what is conserved and similar from one biological context to another. This ability to explicitly describe the generation of heterogeneity from similarity addresses the Denominator Problem and provides a scientific response to the Crisis of Reproducibility.

High-precision, ultra-thin angular detectable imaging upon a single pixel holds significant promise for light field detection and reconstruction, thereby catalyzing advancements in machine vision and interaction technology. Traditional light-direction angle sensors relying on optical components like gratings and lenses face inherent constraints from diffraction limits in achieving device miniaturization. Recently, angle sensors via coupled double nanowires have demonstrated prowess in attaining high-precision angle perception of incident light at sub-wavelength device scales, which may herald a novel design paradigm for ultra-compact angle sensors. However, the current approach to measure the three-dimensional (3D) incident light direction is unstable. In this paper, we propose a flexible segmented concentric nanorings structure capable of discerning the 3D light-direction based on its sensitivity character to both elevation (θ) and azimuth (ϕ) angles at a micrometer device scale. Through deep learning (DL) analysis and prediction, our simulations reveal that for angle scanning with a step size of 1o, the device can still achieve a detection range of 0∼360o for azimuth and 45o∼90o for elevation, with an average accuracy of 0.19o, and DL can further solve some data aliasing problems to expand the sensing range. Our design broadens the angle sensing dimension based on mutual resonance coupling among nanorings segments, and through waveguide implementation or sensor array arrangements, the detection range can be flexibly adjusted to accommodate diverse application scenarios.

This paper presents an original method of additive manufacturing of cylindrical parts with variable circumference thickness, which allows the control of the deposition of molten material using an algorithm for decomposing the part geometry into volumetric elements with known dimensional configuration. In the absence of a post-processor capable of controlling additive manufacturing on a 5-axis numerical control machine, control of the deposition of molten material is done using parameterized programs, which can control both the feed speeds of the machine tool axes and the specific functions of the printing equipment. Additive manufacturing can make a positive contribution to sustainable development compared to traditional manufacturing technologies, thus making a positive contribution for a sustainable future. The aim of the work is to make it possible to 3D print parts with variable wall thickness using a CNC machining centre. To obtain the variable thickness layer we have implemented an original method of deposition with molten material (FDM), the coordination of the system composed of physical elements respectively programmable elements, is realized through control functions materialized in parameterized part programs, the generated outputs being the variable speed of the machine axes on a circular trajectory, the angular positioning, the filament advance.

Scholars of the English Literature unanimously say that J.R.R. Tolkien and C.S. Lewis influenced each other writings. For the first time we have investigated this issue mathematically by using an original multi–dimensional analysis of linguistic parameters, based on surface deep–language variables and linguistic channels. To set our investigation in the framework of the English Liter-ature, we have considered some novels written by earlier authors, such as C. Dickens, G. Mac-Donald and others. The deep–language variables and the linguistic channels, discussed in the paper, are likely due to writers’ unconscious design and have revealed connections between texts far beyond writers’ awareness. In summary, the capacity of the extended short–term memory required to readers, the universal readability index of texts, the geometrical representation of texts and the fine tuning of linguistic channels within texts – all tools largely discussed in the paper – have revealed strong connections between The Lord of the Rings (Tolkien), The Chronicles of Narnia, The Space Trilogy (Lewis) and novels by MacDonald, therefore in agreement with what scholars of the English Literature say.

The development of synthetic biology has enabled us to make massive progress on biotechnology and to approach research questions from a brand new perspective. In particular, the design and study of gene regulatory networks in vitro, in vivo and in silico, have played an increasingly indispensable role in understanding and controlling biological phenomena. Among them, it is of great interest to understand how associative learning is formed at the molecular circuit level. Noticeably, mathematical models have been increasingly used to predict the behaviors of molecular circuits. The Fernando’s model, which is thought to be one of the first works in this line of research using the Hill equation, attempted to design a synthetic circuit that mimics Hebbian learning in the neural network architecture. In this article, we carry out in-depth computational analysis of the model and demonstrate that the reinforcement effect can be achieved by choosing the proper parameter values. We also construct a novel circuit that can demonstrate forced dissociation, which was not observed in the Fernando’s model. Our work can be readily used as reference for synthetic biologists who consider implementing the circuits of this kind in biological systems.

The result of the multidisciplinary collaboration of researchers from different areas of knowledge to validate a solar radiation model is presented. The MAPsol is a 3D local-scale adaptive solar radiation model that allows to estimate direct, diffuse and reflected irradiance for clear sky conditions. The model includes the adaptation of the mesh to complex orography and albedo, and considers the shadows cast by the terrain and buildings. The surface mesh generation is based on surface refinement, smoothing and parameterisation techniques and allows the generation of high quality adapted meshes with a reasonable number of elements. Another key aspect of the paper is the generation of a high-resolution digital elevation model (DEM). This high-resolution DEM is constructed from LiDAR data and its resolution if two times more accurate than the publicly available DEMs. The validation process uses direct and global solar irradiance data obtained from pyranometers at the University of Salamanca located in an urban area affected by systematic shading from nearby buildings. This work provides an efficient protocol for studying solar resources, with particular emphasis on areas of complex orography and dense buildings where shadows can potentially make solar energy production facilities less efficient.

In this paper, we make an attempt to estimate the famous Avogadro number with programming logics written in Python associated with advanced nuclear binding energy formulae. Average rest mass of nucleon, nuclear binding energy per nucleon and electron rest mass seem to play a vital role in estimating the unified atomic mass unit and Avogadro number. Interesting point to be noted is that, Avogadro number seems to be the inverse of the Unified atomic mass unit. With further study, it seems possible to estimate the unified atomic mass unit and Avogadro number accurately. Our interesting observation is that, short range strong nuclear force seems to have a vital role in deciding the accuracy of Avogadro number. For that purpose one may consider AI techniques along with newly observed atomic nuclides and their nuclear binding energies. For Z=6 to 118 and A_low=2Z and A_upper=3.5Z, estimated average value of Avogadro number is $N_{Average} \cong 6.01938 \times 10 ^{26}$. Considering the saturation of nuclear binding energy, at Z=26, $N_{Z=26} \cong \left(6.02229 \textrm{to} 6.02285\right) \times 10 ^{26}$. At academic level, our proposal can be given a chance as a case study. It is planned to develop a web application for this purpose.

Solar pasteurization, as a means of treating milk in remote rural areas without electrical power, is based on using solar energy to thermally inactivate pathogenic microorganisms at temperatures below the boiling point to maintain or improve milk quality. A solar milk pasteurizer of flat‐plate water‐heating glass acting as the solar collector, connected to a stainless-steel cylindrical milk vat, was constructed and evaluated in Navrongo, in the tropical savanna zone of Ghana, West Africa. The novel approach taken in this project is to integrate the solar collection and heat exchanger into a single unit using materials and fabrication techniques readily available in the developing world. The vat comprises a 1.5 mm thick stainless steel cylindrical tank, a 2.2 cm wide hot water jacket, and an outer layer of 5.0 mm thick aluminium foil insulation. Hot water produced by the collector was used for pasteurizing milk. The optimum quantity of milk that this device could pasteurize under the study conditions was 8 L. The device could pasteurize raw milk to a maximum temperature of 74 °C at 14:00 h GMT. The ambient temperature during the pasteurization ranged from 30 °C to 43 °C. The microbial analysis before and after the pasteurization was done, and the result shows that the total bacteria count before pasteurization was 6.6x10⁶ log CFU/mL per unit volume, and the total bacteria count after pasteurization was 1.0x10² log CFU/mL. By acceptable standards, the total bacteria count after pasteurization is within a safe range for consumption, and coliform counts were negative. The solar milk pasteurization system is cost-effective. Hence, it is appropriate for milk producers in arid pastoral areas without electricity to adopt the solar pasteurizer as an alternative to firewood as a fuel source for milk pasteurization. This approach can potentially create a cottage industry that may also play a crucial role as a water treatment technology that will improve the health of rural populations.

Mathematical modelling is widely used for describing infection transmission and evaluating interventions. The lack of reliable social parameters in the literature has been mentioned by many modelling studies, leading to limitations in the validity and interpretation of the results. Using data from the European MSM Internet survey 2017, we developed a network model to describe sex acts among MSM in Belgium. The model simulates daily sex acts among steady, persistent casual and one-off partners in a population of 10,000 MSM, grouped as low- or high-activity by using three different definitions. Model calibration was used to estimate partnership duration and homophily rates to match the distribution of cumulative sex partners over 12 months. We estimated an average duration between 1065 and 1409 days for steady partnerships, 4-6 and 251-299 days for assortative high- and low-activity individuals and 8-13 days for disassortative persistent casual partnerships, respectively, varying across the three definitions. High quality data on social network and behavioral parameters are scarce in literature. Our study addresses this lack of information by providing a method to estimate crucial parameters for network specification.

Hund's rule of maximum multiplicity is a powerful empirical tool for determining the electron population of electronic shells. It was recently discovered that it is also the rule of minimum Shannon entropy. This study extends these findings to the Aufbau rule and discusses them from the perspective of emergent dimensionality, providing a monotonically increasing entropy function. We observed that some elements that violate the Aufbau rule have the same entropies in the actual and Aufbau electron configurations. On the other hand, lower entropies of all actual elements' configurations are associated with higher or equal numbers of unpaired electrons in these configurations compared to the Aufbau configurations. The only exception to this rule is palladium.

Debris flows have generated major disasters worldwide due to their great destructive capacity, which is associated with their high energy levels and short response times. To achieve an adequate risk management of these events, it is necessary to define as accurately as possible the different hazard levels to which the territory is exposed. This article develops a new methodology to estimate this hazard based on the hydrodynamic characteristics of the flow and the granulometry of the sediments that can be mobilized by the flow. The hydrodynamic characteristics of the flow are determined through a mathematical modeling that considers the rheology of non-Newtonian flows and the different volumes of sediments that could be transported during events corresponding to different return periods. The proposed methodology was implemented in the Jamundí River basin (Colombia). The results obtained indicate that in the upper part of this basin there is a low hazard level, while in the lower part of the basin approximately 15% of the affected territory has a medium hazard level and the remaining 85% has a low hazard level. The methodology developed is simple to implement but technically rigorous since it considers all relevant aspects in the generation of debris flows.

The Oxford English Dictionary includes 17 definitions for the word “model” as a noun and other 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For in-stance, “model railways” refer to replicas of railways and trains at a smaller scale and a “model student” refers to an exemplar individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning of a model. Even if the context is narrowed, specifically to the research related to the tumour microenvironment, a “model” can be understood in a wide variety of ways, from an animal model, to a mathematical expression. This paper presents a review of the different “models” of the tumour microenvironment grouped by the different def-initions of the word into four categories: model organisms, in vitro models, mathematical models, and computational models. Then, the frequency of different meanings of the word “model” related to the tumour microenvironment is measured from the number of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequency of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, in particular xenografts and mouse models are the most common used “models”, the number of entries have been slowly de-creasing. Mathematical models, prognostic and risk models follow in frequency and these have been growing in use.

The article proposes a method for determining the p-value of correlations in compositional data, i.e., those data that arise as a result of dividing the original values by their sum. Data organized in this way are typical for many fields of knowledge, but there is still no consensus on methods for interpreting correlations in such data. In a space closed by normalizing quantity, correlation coefficients behave differently than under normal conditions: their probabilities of occurrence do not coincide with those inherent in the standard scale of estimates. In the tens of the new millennium, almost all newly emerging methods for estimating correlation in compositional data began to require mandatory log-transformation of the variable values. In the method proposed here there are no log-transformations. We return to the early stages of attempting to solve the problem and rely on negative shifts in correlations in the multinomial distribution. In modeling the data, we use a hybrid method that combines the hypergeometric distribution with the distribution of any other law. During our work on the calculation method, we found that the number of degrees of freedom in compositional data measures discretely only when all the normalizing sums are equal and that it decreases when the sums are not equal, becoming a continuously varying quantity. Estimation of the number of degrees of freedom and the strength of its influence on the magnitude of the shift in the distribution of correlation coefficients is the basis of the proposed method.

A mathematical model of energy metabolism in erythrocyte-bioreactors loaded with alcohol dehydrogenase and acetaldehyde dehydrogenase was constructed and analyzed. Such erythrocytes can convert ethanol to acetate using intracellular NAD and, thus, can be used to treat an alcohol intoxication. Analysis of the model reveals that the rate of ethanol consumption by the erythrocyte-bioreactors increases proportionally to activity of incorporated ethanol-consuming enzymes until their activity reaches a specific threshold level. When the ethanol-consuming enzyme activity exceeds this threshold, the steady state in the model becomes unstable and the model switches to an oscillation mode caused by a competition of glyceraldehyde phosphate dehydrogenase and ethanol-consuming enzymes for NAD. An amplitude and period of metabolite oscillations first increase with the increase in the activity of e encapsulated enzymes. A further increase in these activities leads to a loss of the glycolysis steady state, and a permanent accumulation of glycolytic intermediates. The oscillation mode and the loss of the steady state can lead to osmotic destruction of erythrocyte-bioreactors due to an accumulation of intracellular metabolites. Our results demonstrate that the interaction of enzymes encapsulated into erythrocyte-bioreactors with erythrocyte metabolism should be taken into account in order to obtain an optimal efficacy of these bioreactors.

Creative thinking is increasingly recognised as an essential ability that should be part of school curricula. Given the move towards online learning and assessment, we investigate whether mathematical creativity can be assessed at-scale in the Numbers game, an arithmetic game in Math Garden, a popular online math practice platform. In the Numbers game, a generalisation of the 24 Game, children are asked to figure out how to compute a target number using basic arithmetic operations and a given set of numbers. We argue that creative thinking is required when the search space is complex, and propose that the base-pattern, i.e., the sequence of the operations needed to solve a Numbers game item, indicates search space complexity. We then demonstrate that items with disordered base-patterns are more likely to require mathematical creativity to figure out. Specifically, our analysis shows that for items with only one solution sequence, those with disordered base-patterns are more difficult and take longer to solve compared to items with ordered base-patterns. For items where multiple solution sequences are possible, nine times out of ten children choose ordered over disordered base-patterns. We conclude that the Numbers game has potential for assessing mathematical creativity at-scale.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

Objective: To use mathematical models to predict the epidemiological impact of lifting the lockdown in London, UK, and alternative strategies to help inform policy in the UK. Methods: A mathematical model for the transmission of SARS-CoV2 in London. The model was parametrised using data on notified cases, deaths, contacts, and mobility to analyse the epidemic in the UK capital. We investigated the impact of multiple non pharmaceutical interventions (NPIs) and combinations of these measures on future incidence of COVID-19. Results: Immediate action at the early stages of an epidemic in the affected districts would have tackled spread. While an extended lockdown is highly effective, other measures such as shielding older populations, universal testing and facemasks can all potentially contribute to a reduction of infections and deaths. However, based on current evidence it seems unlikely they will be as effective as continued lockdown. In order to achieve elimination and lift lockdown within 5 months, the best strategy seems to be a combination of weekly universal testing, contact tracing and use of facemasks, with concurrent lockdown. This approach could potentially reduce deaths by 48% compared with continued lockdown alone. Conclusions: A combination of NPIs such as universal testing, contact tracing and mask use while under lockdown would be associated with least deaths and infections. This approach would require high uptake and sustained local effort but it is potentially feasible as may lead to elimination in a relatively short time scale.

The pennate diatom Phaeodactylum tricornutum is a model organism able to synthesize industrially-relevant molecules. Commercial-scale cultivation currently requires large monocultures, prone to bio-contamination. However, little is known about the identity of the invading organisms. To reduce the complexity of natural systems, we systematically investigated the microbiome of non-axenic P. tricornutum cultures from a culture collection in reproducible experiments. The results revealed a dynamic bacterial community that developed differently in “complete” and “minimal” media conditions. In complete media, we observed an accelerated “culture crash”, indicating a more stable culture in minimal media. The identification of only four bacterial families as major players within the microbiome suggests specific roles depending on environmental conditions. From our results we propose a network of putative interactions between P. tricornutum and these main bacterial factions. We demonstrate that, even with rather sparse data, a mathematical model can be reconstructed that qualitatively reproduces the observed population dynamics, thus indicating that our hypotheses regarding the molecular interactions are in agreement with experimental data. Whereas the model in its current state is only qualitative, we argue that it serves as a starting point to develop quantitative and predictive mathematical models, which may guide experimental efforts to synthetically construct and monitor stable communities required for robust upscaling strategies.

The escalating global demand for clean water has propelled research into sustainable and cost-effective purification methods. Activated carbon (AC) derived from biowaste materials presents an environmentally friendly and economically viable solution for water treatment. This review article provides an extensive overview of the synthesis techniques, characterization methods, and applications of biowaste activated carbon (BAC) for water purification. It discusses the diverse sources of biowaste, such as agricultural residues, food waste, and biomass, and explores various activation methods including physical, chemical, and biological processes. Furthermore, the article examines the adsorption mechanisms, performance factors, regeneration strategies, and emerging trends in BAC synthesis and application. Insights from this review can guide future research endeavors and facilitate the development of sustainable water purification technologies.

Progress in laser-driven proton acceleration requires increasing the proton maximum energy and laser-to-proton conversion efficiency, while reducing the divergence of the proton beam. However, achieving all these qualities simultaneously has proven challenging experimentally, the increase in beam energy often coming at the cost of beam quality. Numerical simulations suggest that coupling multi-PW laser pulses with ultrathin foils could offer a route for such simultaneous improvement. Yet experimental investigations have been limited by the scarcity of such lasers and the need for very stringent temporal contrast conditions to prevent premature target expansion before the pulse maximum. Here, combining the newly commissioned Apollon laser facility that delivers high-power ultrashort (∼24fs) pulses, with a double plasma mirror scheme to enhance its temporal contrast, we demonstrate the generation of up to 35 MeV protons with only 5 J of laser energy. This approach also achieves improved laser-to-proton energy conversion efficiency, reduced beam divergence, and optimized spatial beam profile. Therefore, despite the laser energy losses induced by the plasma mirror, the proton beams produced by this method are enhanced on all accounts compared to those obtained under standard conditions. Particle-in-cell simulations reveal that this improvement results from the intensified electrostatic field caused by a more compact hot-electron distribution.

The Epithelial- Mesenchymal Transition (EMT) is a biological phenomenon associated with explicit phenotypic and molecular changes in cellular traits. Unlike the earlier-held popular belief of it being a binary process, EMT is now thought of as a landscape including diverse hybrid E/M phenotypes manifested by varying degrees of the transition. These hybrid cells can co-express both epithelial and mesenchymal markers and/or functional traits, and can possess the property of collective cell migration, enhanced tumor-initiating ability, and immune/targeted therapy-evasive features, all of which are often associated with worse patient outcomes. These characteristics of the hybrid E/M cells have led to a surge in studies that map their biophysical and biochemical hallmarks that can be helpful in exploiting their therapeutic vulnerabilities. This review discusses recent advances made in investigating hybrid E/M phenotype(s) from diverse biophysical and biochemical aspects by integrating live cell-imaging, cellular morphology quantification and mathematical modeling, and highlights a set of questions that remain unanswered about the dynamics of hybrid E/M states.

Despite the existing effective treatment methods, tuberculosis (TB) is the second most deadly infectious disease globally, its carriers in the latent and active phases accounting for more than 20% of the world population. An effective method to control TB and reduce the mortality is regular population screening and diagnosis of the latent form of TB in order to take preventive and curative measures. Numerous methods allow diagnosing TB and directly detecting Mycobacterium tuberculosis (M.tb) biomarkers, including M.tb DNA, proteins, and specific metabolites, as well as antibodies produced by the host immune system in response to M.tb. PCR, ELISA, immunofluorescence and immunochemical analyses, flow cytometry, and other methods allow the detection of M.tb biomarkers or the host immune response to M.tb by recording the optical signal of fluorescent or colorimetric dyes included in the diagnostic tools. Current research in biosensors is aimed at increasing the sensitivity of detection, which can be achieved by using brighter and more photostable optical tags containing fluorescent quantum dots. Here, we review current methods for detection of M.tb biomarkers using optical sensor systems, primarily quantum dot–based nanosensors, and summarize M.tb biomarkers whose detection can be made significantly more sensitive by using quantum dot–based nanosensors.

A Q-switched Nd:YAG laser was focused on Pb-Ti alloy samples in several Laser Induced Breakdown experiments in order to measure the Stark parameters of several spectral lines (58) of single ionized Titanium including the 3504.89 Å, and the 3510.83 Ålines (where we aported new experimental and theoretical values).Diagnostics of the laser induced plasmas (electron density and electron temperature) was performed using Balmer’s H alpha line (6562.7 Å).Temperatures were obtained by the Boltzmann Plot technique with spectral lines of Pb I (after correction for its evident self-absorption).Subsequently, calculations by the Griem approach of the Stark broadening parameters for several spectral lines were performed using the Gaunt factors proposed by Van Regemorter and those proposed by Douglas H. Sampson. In the latter cases the values obtained were very close to the experimental values. It allows us to assume that the calculations made for the spectral lines of Ti II, without experimental information, are more accurate using the Gaunt factors proposed by Sampson.

Nitric oxide (NO) is a key molecule in cardiovascular homeostasis and its abnormal delivery is highly associated with the occurrence and development of cardiovascular disease (CVD). The assessment and manipulation of NO delivery is crucial to the diagnosis and therapy of CVD, such as endothelial dysfunction, atherosclerotic progression, pulmonary hypertension, and cardiovascular manifestations of Coronavirus (COVID-19). However, due to the low concentration and fast reaction characteristics of NO in cardiovascular system, the clinical applications centered on the NO delivery are challenging. In this tutorial review, we first summarized the methods to estimate the in vivo NO delivery process based on the clinical images and mathematical modeling to assess the endothelial function and vulnerability of atherosclerotic plaque. Then, the emerging bioimaging technologies that have the potential to directly measure the arterial NO concentration were discussed, including the Raman spectroscopy and electrochemical sensor. Aside from the diagnostic methods, therapies aimed at controlling NO delivery to regulate CVD were reviewed, including the inhaled NO therapy to treat the pulmonary hypertension and COVID-19, stem cell therapy and NO-releasing platform to treat endothelial dysfunction and atherosclerosis.

We study how abstract representations emerge in a Deep Belief Network (DBN) trained on benchmark datasets. Our analysis targets the principles of learning in the early stages of information processing, starting from the “primordial soup" of the under-sampling regime. As the data is processed by deeper and deeper layers, features are detected and removed, transferring more and more “context-invariant” information to deeper layers. We show that the representation approaches an universal model – the Hierarchical Feature Model (HFM) – determined by the principle of maximal relevance. Relevance quantifies the uncertainty on the model of the data, thus suggesting that “meaning" – i.e. syntactic information – is that part of the data which is not yet captured by a model. Our analysis shows that shallow layers are well described by pairwise Ising models, which provide a representation of the data in terms of generic, low order features. We also show that plasticity increases with depth, in a similar way as it does in the brain. These findings suggest that DBNs are capable of extracting a hierarchy of features from the data which is consistent with the principle of maximal relevance.

The article presents the results of tests of minor head losses through PVC and PP elbows for a flow of water and mixtures of water and sand with grain sizes of up to 0.5 mm and concentrations of 5.6 g∙L-1, 10.84 g∙L-1, and 15.73 g∙L-1. The tests were carried out at variable flow velocities for three elbow diameters of 63, 75, and 90 mm. The flow rate, pressure difference in the tested cross-sections, and temperature of the fluids were measured and automatically recorded. The results of the measurements were used to develop mathematical models for determining the minor head loss coefficient as a function of elbow diameter, sand concentration in the liquid, and Reynolds number. The mathematical model was developed by cross validation. It was shown that when the concentration of sand in the liquid was increased by 1.0 g∙L-1, the coefficient of minor head loss through the elbows increased, in the Reynolds number range of 4.6∙104 − 2.1∙105, by 0.3−0.01% for PP63, 0.6−0.03 % for PP75, 1.1−0.06 % for PP90, 0.8−0.01 % for PVC63, 0.8−0.02 % for PVC75, and 0.9−0.04 % for PVC90. An increase in Re from 5∙104 to 2∙106 for elbows with diameters of 63, 75 and 90 mm caused a 7.3 %, 6.8 %, and 6.0 % decrease in the minor head loss coefficient, respectively.

The proximal part of the colon offers opportunities to prolong the absorption window following oral administration of a drug. In this work, we used computer simulations to understand how the hydrodynamics in the proximal colon might affect the release from dosage forms designed to target the colon. For this purpose, we developed and compared three different models: a completely-filled colon, a partially-filled colon and a partially-filled colon with a gaseous phase present (gas-liquid model).The highest velocities of the liquid were found in the completely-filled model, which also shows the best mixing profile, defined by the distribution of tracking particles over time. No significant differences with regard to the mixing and velocity profiles were found between the partially-filled model and the gas-liquid model. The fastest transit time of an undissolved tablet was found in the completely-filled model. The velocities of the liquid in the gas-liquid model are slightly higher along the colon than in the partially-filled model. The filling level has an impact on the exsisting shear forces and shear rates, which are decisive factors in the development of new drugs and formulations.

The origin and climate impact of Arctic aerosols, like the Arctic Haze, are not fully understood. Therefore, long-term aerosol observations in the Arctic are performed. In this study we present a homogenised data set from sun and star photometer operated in the European Arctic, in Ny-Ålesund, Svalbard, from 2004 – 2023. Due to polar day and polar night it is crucial to use observations of both instruments. Their data is evaluated in the same way and follows the cloud-screening procedure of AERONET. Additionally, an improved method for the calibration of the star photometer is presented. We found out, that winter months are generally more polluted and have larger particles than summer. While the monthly median Aerosol Optical Depth (AOD) decreases in spring, the AOD increases significantly in autumn months. The Arctic Haze is not characterised by large particles and can not be distinguished from large aerosols in winter months. With autocorrelation analysis we found out, that AOD events usually occur with duration of several hours and are therefore caused by large-scale processes and may have a periodicity of several days. Local processes can be neglected in Ny-Ålesund but long-range transport plays a major role for the Arctic aerosol budget. We also compared AOD events with large-scale processes, like large-scale oscillation patterns, sea ice, weather conditions or wildfires on the Northern Hemisphere but did not find one single cause, which clearly determines the Arctic AOD.

Deep convolutional neural networks (CNNs) have revolutionised computer vision technology by automatically learning hierarchical representations of image data, leading to state-of-the-art performance in visual recognition tasks. This article presents a comprehensive review of deep CNNs, from their evolution and architectures to the current state-of-the-art research. The review also provides the core concepts and building blocks of CNNs and their concise mathematical representations. Furthermore, it explores applications of deep CNNs in three popular domains, including medical diagnosis, remote sensing, and facial recognition. This review will benefit researchers and practitioners in computer vision and artificial intelligence, as well as industry professionals seeking to leverage the latest advancements in deep learning technologies.

Depressions containing partially molten rocks were investigated in Quaternary pebbly sedi-ments in Alpine foreland in Bavaria, Germany. Ruins of limekilns from 18-19th centuries are abundant around Seeshaupt. They are usually associated with earthworks for fuel feeding and protection from wind. Depressions contain partially molten stones from furnace walls, with lime and burnt loam remnants. On the surface of pebbles (typically gneisses), green glass formed with chemical composition possibly affected by moderately volatile components of wood biomass, mainly K and Cu. Thermoplastic deformation of pebbles is limited and the sur-face melt deformation points to slow flow. At Emmerting, on the other hand, two walled circu-lar depressions which lack additional earthworks have been identified as possible impact cra-ters. Thermally affected pebbles show much more intense deformation. Colorless to greenish glass, also K and Cu enriched, usually forms only thin surface coatings, in places covered by younger melt extruded from pebble interior. Burnt loam is missing. At Grabenstätt-Kaltenbach, a depression of unclear origin was investigated. Morphologically, it matches craters rather than limekilns, but anthropogenic contamination (brick-like material) is probable. The rare molten samples do not display extreme deformation features. The thermally affected stones, mainly those from Emmerting, have elevated magnetic susceptibility.

Patients with COVID-19 may develop pneumonia, severe symptoms of acute respiratory distress syndrome, and multiple organ failure. Nevertheless, the variety of forms of this disease, requires further research on the pathogenesis of this disease. Based on the analysis of published data on the concentrations of SARS-CoV-2 in biological fluids of the nasopharynx, lungs and intestines and using a developed modular model of the virus distribution in human tissue and organs, an assessment of the SARS-CoV-2 reproduction in various compartments of the body is presented. Most of viral particles can enter into the esophagus from nasopharynx. Entering viral particles into the gastrointestinal tract will obviously be accompanied by infection of the intestinal epithelium and accumulation of the virus in the intestinal lumen in an amount proportional their secretory and protein-synthetic activities. The relatively low concentration of SARS-CoV-2 in tissues implies an essential role of transport processes and redistribution of the virus from nasopharynx and intestines to lungs. The model simulations also supposes that sanitation of the nasopharynx mucosa at the initial stage of the infectious process considering inhibition of the virus accumulation by means of cellular and humoral responses has prospects for the use in medicine practice.

This work is located in a growing sector within the field of renewable energies, wave energy converters (WECs). Specifically, it focuses on one of the point absorbers wave (PAWs) of the hybrid platform W2POWER. With the aim of maximising the mechanical power extracted from the waves by these WECs and reduce their mechanical fatigue, the design of five different model predictive controllers (MPCs) with hard and soft constraints has been carried out. As contribution of this paper, two of the MPCs have been designed with the addition of an embedded integrator. In order to validate the MPCs, an exhaustive study on performance and robustness is realized through simulations carried out in which uncertainties in the WEC dynamics are considered. Furthermore, looking for realistic in these simulations, an identification methodology for PAWs is proposed and validated by means of real time series of a scale prototype.

Membrane-based sensors (MePSs) exhibit remarkable precision and sensitivity in detecting pressure changes. MePSs are commonly used to monitor catalytic reactions in solution, generating gas products crucial for signal amplification in bioassays. They also allow catalyst quantification by indirectly measuring the pressure generated by the gaseous products. This is particularly interesting to detect enzymes in biofluids associated with disease onset. To enhance the performance of a MePS, various structural factors influence membrane flexibility and response time, ultimately dictating the device's pressure sensitivity. In this study, we fabricated MePSs using polydimethylsiloxane (PDMS) and investigated how structural modifications affect the Young's modulus (E) and residual stress (σ0) of the membranes. These modifications have a direct impact on the sensors' sensitivity to pressure variations, observed as a function of the volume of the chamber (Σ) or of the mechanical properties of the membrane itself (S). MePSs exhibiting the highest sensitivities were then employed to detect catalyst quantities inducing the dismutation of hydrogen peroxide, producing dioxygen as gaseous product. As a result, catalase enzyme was successfully detected using these optimized MePSs, achieving a remarkable sensitivity of (22.7 ± 1.2) µm/nM and a limit of detection (LoD) of 396 pM.

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

Optimization techniques are pivotal across various scientific domains, typically involving solving problems among feasible alternatives based on specific goals, alternatives, or constraints. In mathematical optimization, traditional methods like Simulated Annealing (SA) do not guarantee finding global minima/optima, especially in cases that contain high dimensions in objective functions. This paper introduces a novel approach where a free-energy driven self-adaptive SA algorithm is designed to handle such cases by incorporating free-energy costs within the Metropolis-Hastings framework. This algorithm not only dynamically adjusts to the changing dimensions of the objective function, but it also enhances a faster optimization process. Furthermore, as examples we demonstrate its capability on a convex unimodal function and the non-convex Rastrigin function, revealing faster convergence to search global minima compared to standard SA algorithm. At last, parameter estimation of noisy exponential data has been executed by our Simulated Annealing driven by the Free-Energy (SAFE) algorithm. Our results suggest that this novel approach may significantly improve optimization speed and accuracy, providing a robust tool for complex multidimensional optimization problems.

The mechanism by which the human nose perceives an odor is complex and involves various chemical reactions in the transformation of the odorous molecule into an electrical impulse sent to the brain that returns the sensation of smell. The smell is classified and quantified, and its instrumental detection can be carried out through the “electronic nose”, an interactive device that lends itself to various applications. In the agri-food sector, the development of portable devices makes possible to smell foods and measure their level of deterioration and maturation; this is undoubtedly useful for reducing waste, identifying the best moment for food consumption, and improving the level of food safety. With regard to the environmental compatibility of materials and techniques for packing and laying conglomerates (for example bituminous), the problem of olfactory nuisance for the population residing in the neighborhood is still an unresolved problem. The approach based on electronic noses is very effective. The electronic nose also represents an important resource in the screening of respiratory pathologies, where there is the need to identify a rapid and reliable diagnostic test for pathologies such as pneumonia or seasonal flu. Environmental monitoring of pollutants is of particular relevance today and the electronic nose is an important candidate for the use in this field. The gas sensor market leverages physics, chemistry and materials engineering to develop highly sensitive, reliable and stable sensor platforms, capable of detecting very small amounts of gas molecules in the environment. To develop competitive gas sensing platforms, new materials are being considered, including polymers, nanostructured metal oxides and nanostructured carbon-based materials (CNTs). In addition to the experimental aspects, in particular Raman and electron spectroscopy techniques together with atomic force microscopy, theoretical-mathematical modeling plays an extremely important role in this sector, with particular attention to the case of micro and nanometric dimensions. Many efforts are now aimed in improving the sensitivity of these devices and this is related to the diffusion of carriers in them. The paper also offers an overview of the mathematical models relating to mechanical processes and dynamics at the micro-nanometric scale, lastly focusing on the Drude-Lorentz type models, with related more recent generalizations.

The continuous casting tundish is non-isothermal due to heat losses and temperature variation from the inlet stream generating relevant convection forces. This condition is commonly avoided through qualitative fluid dynamic analysis only. This work searches to establish the conditions for which non-isothermal simulations are mandatory or for which isothermal simulations are enough to accurately describe the fluid dynamics inside the tundish by quantifying the buoyant and inertial forces. The mathematical model, simulated by CFD software, considers the Navier-Stokes equations, the realizable k- model for solving the turbulence, and the Lagrangian discrete face to track the inclusion trajectories. The results show that temperature does not significantly impact the volume fraction percentages or the mean residence time results, nevertheless, bigger velocity magnitudes under non-isothermal conditions than in isothermal conditions and noticeable changes in the fluid dynamics between isothermal and non-isothermal cases in all the zones where buoyancy force dominates over inertial forces were observed. Because of the results, it is concluded that isothermal simulations can accurately describe the flow behavior in tundishes when the flow control devices control the fluid dynamic, but the simulation without control devices or with a weak fluid dynamic dependence on the control devices requires non-isothermal simulations.

In this research work, we present a mathematical model for novel coronavirus -19 (NCOVID-19) which is consisted on three different compartments susceptible, infected and recovered classes abbreviated as under convex incident rate involving and emigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by using various tools of nonlinear analysis. Then by mean of nonstandard finite difference scheme (NSFD), we simulate the results against the data of Wuhan city for the sixty days. By means of simulation, we show how protection, exposure, emigration, death and cure rates affect the susceptible, infected and recovered population with the passage of time involving emigration. On the basis of simulation, we observe the dynamical behavior due to emigration of susceptible and infected classes or one of these two.

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.

The ongoing electrification of the heat and transport sectors is expected to lead to a substantial increase in peak electricity demand over the coming decades, which may drive significant investment in network reinforcement in order to maintain a secure supply of electricity to consumers. The traditional way of security provision has been based on conventional investments such as the upgrade of the capacity of electricity transmission or distribution lines. However, the energy storage technology can also provide security of supply, thereby constituting a cost-efficient alternative to expensive conventional reinforcements. In this context, the current paper presents a methodology for the economic quantification of the security contribution of energy storage. This methodology makes use of mathematical optimization for the calculation of the F-factor metric, which reflects the optimal amount of peak demand reduction as compared to the power capability of the energy storage asset. In this context, a case study is presented in which the security contribution of energy storage is analyzed as a function of its power capability, energy capacity and efficiency as well as of characteristics of load patterns.

Nanocomposites of TiO₂ Degussa P25 nanoparticles/activated carbon (TiO₂/AC ) were prepared at various mass ratios of (4:1), (3:2), (2:3), and (1:4) by a facile process. The effects of TiO₂/AC mass ratios on the structural, morphological, and photocatalytic properties were systematically studied in comparison with bare TiO₂ and bare AC. TiO₂ nanoparticles exhibited dominant anatase and minor rutile phases, and a crystallite size of approximately 21 nm; while AC had XRD peaks of graphite and carbon, and a crystallite size of 49 nm. The composites exhibited tight decoration of TiO₂ nanoparticles on micron-/submicron AC particles, and uniform TiO₂/AC composites were obtained as evidenced by the uniform distribution of Ti, O, and C in an EDS mapping. Moreover, Raman spectra show the typical vibration modes of anatase TiO₂ (e.g., E_1g⁽¹⁾, B_1g⁽¹⁾, E_g⁽³⁾) and carbon materials with D and G bands. The TiO₂/AC with (4:1), (3:2), and (2:3) possessed higher reaction rate constants (k) in photocatalytic degradation of methylene blue (MB) than that of either TiO₂ or AC. Among the investigated materials, TiO₂/AC = 4:1 achieved the highest photocatalytic activity with a high k of 55.2×10^-3 min^-1 and an MB removal efficiency of 96.6% after 30 min treatment under UV-Vis irradiation (120 mW/cm²). The enhanced photocatalytic activity for TiO₂/AC is due to the synergistic effect of the high adsorption capability of AC and the high photocatalytic activity of TiO₂. Furthermore, TiO₂/AC promotes the separation of photoexcited electron/hole (e^-/h⁺) pairs to reduce their recombination rate and thus enhance photocatalytic activity. The optimal TiO₂/AC composite in this study can be used for treating industrial or household wastewater with organic pollutants.

Experiments to measure a single molecule/particle, i.e. an individual molecule/particle, at room temperature or under physiological conditions without immobilization, for example on a surface, or without significant hydrodynamic flow have so far failed. This failure has given impetus to the underlying theory of Brownian molecular motion towards its stochastics due to diffusion. Quantifying the thermodynamic jitter of molecules/particles inspires many and forms the theoretical basis of single-molecule/single-particle biophysics and biochemistry. For the first time, our simulation results for a live cell (cytoplasm) show that the tracks of individual single molecules are localized in Brownian motion, while there is fanning out in fractal diffusion (anomalous diffusion).

Experiments to measure a single molecule/particle, i.e. an individual molecule/particle, at room temperature or under physiological conditions without immobilization, for example on a surface, or without significant hydrodynamic flow have so far failed. This failure has given impetus to the underlying theory of Brownian molecular motion towards its stochastics due to diffusion. Quantifying the thermodynamic jitter of molecules/particles inspires many and forms the theoretical basis of single-molecule/single-particle biophysics and biochemistry. For the first time, our simulation results for a live cell (cytoplasm) show that the tracks of individual single molecules are localized in Brownian motion, while there is fanning out in fractal diffusion (anomalous diffusion).

High average power narrow-linewidth tunable solid-state lasers in the wavelength region between 2 to 3 μm are attractive light sources for many applications. This paper reports a narrow-linewidth widely-tunable laser system based on the polycrystalline Cr2+:ZnSe elements pumped by the repetitively-pulsed 2.1 µm Ho3+:YAG laser operating at the tens of kilohertz pulse rate. An advanced procedure of ZnSe-element doping and surface improvement was applied to increase the laser-induced damage threshold, which resulted in an increase of the output power of the Cr2+:ZnSe laser system. The high-average-power laser system comprised double master-oscillators and power amplifiers: Ho3+:YAG and Cr2+:ZnSe laser oscillators, and Ho3+:YAG and Cr2+:ZnSe power amplifiers. The output wavelength was widely tuned within 2.3-2.7 µm by an acousto-optical tunable filter inside the Cr2+:ZnSe master oscillator cavity. The narrow-linewidth operation at the pulse repetition rate of 20-40 kHz in a high-quality beam with the average output power up to 9.7 W was demonstrated.

The outbreak of coronavirus disease 2019 (COVID-19) was identified in Wuhan, China, in December 2019. As of April 17, 2020, more than 2 million cases of COVID-19 have been reported worldwide. Northern Italy is one of the world’s centers of active coronavirus cases. In this study, we predicted the spread of COVID-19 and its burden on hospital care under different conditions of social distancing in Lombardy and Emilia-Romagna, the two regions of Italy most affected by the epidemic. To do this, we used a Susceptible-Exposed-Infectious-Recovered (SEIR) deterministic model, which encompasses compartments relevant to public health interventions such as quarantine. A new compartment L was added to the model for isolated infected population, i.e., individuals tested positives that do not need hospital care. We found that in Lombardy restrictive containment measures should be prolonged at least until early July to avoid a resurgence of hospitalizations; on the other hand, in Emilia-Romagna the number of hospitalized cases could be kept under a reasonable amount with a higher contact rate. Our results suggest that territory-specific forecasts under different scenarios are crucial to enhance or take new containment measures during the epidemic.

Asparagus shoots are worldwide consumed, although most of such species have a restricted range, and several taxa still remain unstudied. In this work, a total of four taxa from different locations were scrutinized and compared with cultivated A. officinalis. All shoots were screened for saponins by LC-MS, and in vitro antiproliferative activities against the HT-29 colorectal cancer cell line (by MTT assay). The total saponins (TS) contained in the crude extracts ranged from 710.0 (A. officinalis) to 1258.6 mg/100 g dw (A. acutifolius). It stands out the richness of compounds detected in this work: a total of 47 saponins have been detected and quantified in the edible parts (shoots) of 5 taxa of Asparagus. The structure of all the saponins found present skeletons of the furostane and spirostane type. In turn, the structures with a furostane skeleton are divided into unsaturated and dioxygenated, both in the 20-22 position. The sum of dioscin and derivatives varied largely along the studied taxa. It reached the following percentages of TS: 27.11 (A. officinalis), 18.96 (A. aphyllus), 5.37 (A. acutifolius), and 0.59 (A. albus), while in A. horridus such compound remains undetected. Aspachiosde A, D, and M varied largely among samples, while a total of seven aspaspirostanosides were characterized in the analyzed species. Hierarchical cluster analysis of the saponin profiles clearly separated the various taxa and demonstrated that the taxonomic position is more important than the place from which the samples were acquired. Thus, saponin profiles have chemotaxonomic significance in Asparagus taxa. The MTT assay showed dose- and time-dependent inhibitory effects of several saponins extracts on HT-29 cancer cells, standing out the cell growth inhibition exercised by A. albus and A. acutifolius (GI50 of 125 and 175 µg/mL). This work constitutes a whole approach to evaluate the saponins from shoots of different Asparagus taxa and provide arguments for use them as functional foods.

Recent experiments devoted to characterizing the behavior of sessile ferroelectric liquid droplets on ferroelectric solid substrates, showed the existence of a droplet electromechanical Rayleigh-like instability. The instability is induced by the bulk polarization of the ferroelectric fluid which couples to the polarization of the underlying substrate through its fringing field and solid-fluid interface coupling. With the aim of characterizing this phenomenon, namely the coupling between the polarizations of a fluid and a solid material, we studied the behavior of ferroelectric liquid droplets confined between two solid substrates, arranged in different configurations realized so to generate fringing fields with different profiles. Results show that the features of the droplets instability are indeed affected by the specific fringing field shape in a way dominated by the minimization of the electrostatic energy associated to the bulk polarization of the ferroelectric fluid.

The inherent value and use of hydrocarbon from waste plastics and solvents can be extended through open-loop chemical recycling as this process converts plastic to range of non-plastic materials. This process is enhanced by first creating plastic-solvent-combinations from multiple sources which are then streamlined through single process stream. We report on the relevant mechanics for streamlining industrially relevant polymers such as polystyrene (PS), polypropylene (PP), high-density polyethylene (HDPE) and acrylonitrile butadiene styrene (ABS) into chemical slurries mixed with various organic solvents such as toluene, xylene and cyclohexane. The miscibility of the polymer feedstock within the solvent was evaluated using the Relative Energy Difference method, and the dissolution process was evaluated using the “Molecular theories in a continuum framework” model. These models were used to design a batch process yielding 1 tonne/h slurry by setting appropriate assumptions including constant viscosity of solvents, disentanglement-controlled dissolution mechanism and linear increase of the dissolved polymer’s mass fraction over time. Solvent selection was found to be the most critical parameter for the dissolution process. The characteristics of the ideal solvent are high affinity to the desired polymer and low viscosity. This work serves as a universal technical guideline for open-loop chemical recycling of plastics avoiding the growth of waste plastic in a circular economy framework.

Due to its time effective, joint friendly and highly customizable character whole-body-electromyostimulation (WB-EMS) is regarded as a feasible solution for a large variety of training issues particularly in the area of non-athletic application. To identify gaps in research and summarize prevalent evidence we conducted an evidence map on outcomes addressed by WB-EMS trials in middle-aged to older, non-athletic adults. Based on a comprehensive systematic search in five databases and two study registers according to PRISMA, 54 projects published in 80 articles were included. More than 90% of the studies reported outcomes related to the physical fitness or function domain. Body composition parameters were addressed by two thirds of the projects. Health-related outcomes addressed by WB-EMS included cancer/neoplasm (n=7), endocrine regulation (n=8), glucose metabolism (15), nervous system diseases (n=2), cardiovascular system diseases (n=22), non-specific chronic low back pain (n=4), osteopenia (n=5) and diseases of the renal system (n=12). Outcomes related to inflammation were addressed 18 times. Of importance, no studies reported clinically relevant adverse effects related to the WB-EMS intervention. In summary, while considerable evidence on outcomes related to fitness/function and body composition is prevalent, evidence gaps of WB-EMS research were particular evident for diseases of the nervous and cerebrovascular system.

Hepatitis B surface antigen (HBsAg) is not only the biomarker of hepatitis B virus (HBV) infection and expression activity in hepatocytes, but also contributes to viral specific T cell exhaustion and HBV persistent infection. Therefore, anti-HBV therapies targeting HBsAg to achieve HBsAg loss are key approaches for HBV functional cure. In this study, we found that YZH-106, a rupestonic acid derivative, inhibited HBsAg secretion and viral replication. Further investigation demonstrated that YZH-106 promoted the lysosomal degradation of viral L- and M-HBs proteins. Mechanistic study by Biacore and docking analysis revealed that YZH-106 bound directly to PreS2 domain of L- and M-HBsAg, thereby blocking their entry to the endoplasmic reticulum (ER) and promoting their degradation in cytoplasm. Our work thereby provide basis for design of novel compound therapy to target HBsAg against HBV infection.

Gigantic particle accelerators, incredibly complex detectors, an antimatter factory and the discovery of the Higgs boson – this is part of what makes CERN famous. Only a few know that CERN also hosts the world largest Open Access initiative: SCOAP3. The Sponsoring Consortium for Open Access Publishing in Particle Physics (SCOAP3) started operation in 2014 and has since supported the publication of 19,000 Open Access articles in the field of particle physics, at no direct cost, nor burden, for individual authors worldwide. SCOAP3 is made possible by a 3,000-institute strong partnership, where libraries re-direct funds previously used for subscriptions to ’flip’ articles to ’gold Open Access’. With its recent expansion, the initiative now covers about 90% of the journal literature of the field. This article describes the economic principles of SCOAP3, the collaborative approach of the partnership, and finally summarizes financial results after four years of successful operation.

The Sentinel-1 SAR Extra Wide swath mode with its 40 meters pixel size allows accurate lead mapping in Arctic sea ice areas. We present an improved winter lead detection algorithm based on a modified U-Net convolutional neural network. We introduce a preprocessing procedure that balances normalized radar cross section (NRCS) values between sub-swaths. This results in more consistent Sentinel-1 SAR images as input for the classifier, which is especially important for the cross-polarization HV channel. In turn, image consistency is essential for automatic image semantic segmentation. We develop a new lead detection algorithm and compare it with a previously published version. We produce pan-Arctic, 40 meters resolution lead maps and present pan-Arctic lead area fraction on a 12 km grid for January 2019. Within different Arctic regions, the lead area fraction is stable and varies only within the expected natural variability during the one month studied here. The average Arctic-wide lead area fraction is 2.44 % with 0.25 % standard deviation during January 2019. The improved lead detection algorithm leads to a better lead discrimination and extends the applicability area to the entire Arctic.

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

Mathematical modeling is the most important tool for constructing the theory of different kinds of two-phase flows. The review is devoted to the analysis of the advent of the approach of mathematical modeling of two-phase flows, where solid particles act mainly as the dispersed phase. The main problems and features of the study of gas-solid two-phase flows are excluded. The main characteristics of gas flows with solid particles are given and the classification of two-phase flows is developed on their basis. The Lagrangian and Euler approaches to modeling the motion of a dispersed phase (particles) are described. Much attention is paid to the consideration of numerical simulation methods that describe descriptions of turbulent gas flow at different hierarchical levels (RANS, LES, DNS), different levels of description of interphase interactions (one-way coupling (OWC), two-way coupling (TWC) and four-way coupling (FWC)), as well as at different levels of interface resolution (partial-point (PP) and particle-resolved (PR)). Excluded are examples of some studies carried out on the basis of the identified approaches, as well as their exclusion for mathematical modeling of various classes of gas-solid two-phase flows.

Modern medicine adopted four presumptions when it evolved from ancient experienced-based mind-body medicine. To understand its failure in finding cures for chronic diseases, we examined four presumptions, and found that statistical population of health properties does not exist for most research purposes, mathematical models are misused to model intensive properties, synthetic drugs are inherently more dangerous than nature-made medicines under their respective application conditions, and reductionist treatments are inferior and inherently dangerous. We found that clinical trials are valid only for research where treatment effect is much stronger than the total effects of all interfering or co-causal factors or errors introduced by misused mathematical models can be tolerated. In all other situations, clinical trials introduce excessive errors and fail to detect treatment effects, or produce biased, incorrect or wrong results. We further found that chronic diseases are manifestation of small departures in multiple process attributes in distinctive personal biological pathways networks, that modern medicine lacks required accuracy for accurately characterizing chronic diseases, and that reductionist treatments are good at controlling symptoms and safe for short term uses. For all stated reasons, as long as modern medicine continues relying on the flawed presumptions, it can never find predictable cures for chronic diseases. By implication, predictable cures to chronic diseases are adjustments to lifestyle, dietary, emotional, and environmental factors to slowly correct departures in process attributes responsible for chronic diseases.

There are several well-known methods for determining enzyme catalytic activity, including spectral techniques and electrochemical approaches. However, at present, there is no definitive solution to the challenges associated with the fluorescent approach in, for instance, systems of reverse micelles, non-aqueous media, and model biomembranes. We propose the use of the fluorescent resonant energy transfer (FRET) technique, which can enhance the selectivity of fluorescent detection of enzyme activity by shifting the maximum emission wavelength to the longer-wavelength range and reducion the influence of medium components. As fluorescence donors, we have used derivatives of 4-methylumbelliferone (MUmb) and 7-amino-4-methylcoumarin (AMC), which also serve as substrates for hydrolases such as chymotrypsin, phosphatase, and asparaginase. During the catalytic depletion of substrates, an accumulation of a highly fluorescent product is observed. This product can be specifically detected using the fluorescent marker rhodamine 6G (R6G), which emits light in the red region of the spectrum (550–600 nm) with high quantum yield. A significant FRET effect is observed when forming AOT reverse micelles. This is due to the proximity of fluorophores within the hydrophobic core of the micelle, which is shorter than in a buffer solution. This approach have practical implications for visualizing intracellular processes. The FRET technique can be used to determine intracellular enzymatic activity by detection with confocal laser scanning microcopy (CLSM), as demonstrated with L-asparaginase, a clinically important anti-leukemia medication. The approach suggested will allow researchers to study enzyme activity within cells. This has the potential to revolutionize medicine by improving drug development and shedding light on previously unknown aspects of cellular metabolism.

In this paper, the time-resolved model of photoacoustic signal for samples with a complex inner structure is derived including local non-equilibrium of structural elements with multiple degrees of freedom, i.e. structural entropy of the system. The local non-equilibrium is taken into account through the fractional operator. By analyzing the model for two types of time-dependent excitation, a very short pulse and a very long pulse, it is shown that the rates of non-equilibrium relaxations in complex samples can be measured by applying the derived model and time-domain measurements. Limitations of the model and further directions of its development are discussed.

Wide bandgap semiconductors-based photocatalysts are usually limited by their low solar energy conversion efficiency due to their limited absorption solar wavelength, surface’s fast recombination of photoelectron–hole pairs and low charge-carrier mobility. Here we report a new stepwise solution synthesis for making a new photocatalytic core/shell of titanate nanowire/reduced graphene oxide shell (or titanate/rGO) 1D-nanocomposite. The new core/shell nanocomposite maximized the specific surface area, largely reduced the charge transfer resistance and reaction energy barrier, and significantly improved the absorption of the visible light. The core/shell nanocomposites’ large on/off current ratio and rapid photo-responses boosted the photocurrent by 30.0%, the photocatalysis rate by 50.0%, and the specific surface area by 16.4%, when comparing with the pure titanate nanowire core. Our numerical simulations support the effective charge separation on the new core-shell nanostructure, which can help further advance the new photocatalysis.

Silica on Silicon is a major optical integration platform, while the emergent class of integrated Laser written circuits' platform offers additionally high customizability, and flexibility for rapid prototyping. However, the inherent waveguides' low core/cladding refractive index contrast characteristic compared to other photonic platforms in silicon or silicon nitride, sets serious limitations for on-chip efficient coupling with single photon emitters, like semiconductor nanowires with quantum dots limiting the applications in quantum computing. A new light coupling scheme proposed here overcomes this limitation providing means for light coupling >50%. The scheme is based on the incorporation of an optical microsphere between the nanowire and the waveguide, properly optimized and arranged in terms of: size, refractive index, distance of microsphere between nanowire and waveguide. Upon suitable design of the optical arrangement, the photonic nanojet emitted by the illuminated microsphere excites efficiently the guided eigenmodes of the input channel waveguide, thus launching light with high coupling efficiency. The method is tolerant in displacements, misalignments, and imperfections and is fabricationally feasible by current state of the art techniques. The proposed method enables the on-chip multiple single photon emitters' integration thus allowing the development of highly customizable and scalable quantum photonic integrated circuits for quantum computing.

In physics we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands years ago and I discuss some challenges and open questions in quantum foundations and in the standard model. We liberated nuclear energy, landed on the Moon and built ‘quantum computers’. Encouraged by these successes many believe, that when we reconcile the general relativity with the quantum theory then we will have the correct theory of everything. Perhaps, we should be much more humble. Our perceptions of reality are biased by our senses and by our brain bending them to meet our priors and expectations. Our abstract mathematical models describe only in an approximate way different layers of physical reality. To describe the motion of a meteorite we can use a concept of a material point but the point-like approximation breaks completely, when the meteorite hits the Earth. Similarly, thermodynamic, chemical, molecular, atomic, nuclear, elementary particle layers of physical reality are described using specific abstract mathematical models and approximations. In my opinion, the theory of everything does not exist.

Canine distemper virus (CDV) poses a substantial threat to diverse carnivores, leading to sys-temic and often fatal diseases. Accurate and prompt diagnosis is paramount for effective man-agement and curbing further transmission. This study evaluates the diagnostic efficacy of drop-let digital PCR (ddPCR) in comparison to conventional reverse transcription (RT-PCR) and quantitative reverse transcription real-time PCR (RT-qPCR). Seventy-six clinical samples were collected from dogs with CDV symptoms diagnosed by specialized veterinarians, and sixteen samples from asymptomatic individuals. Conventional PCR, quantitative real-time PCR, and ddPCR were deployed, and their diagnostic capabilities were meticulously assessed. DdPCR ex-hibited heightened analytical sensitivity, reaching a detection limit of 3 copies/μL, whereas RT-qPCR had a detection limit of 86 copies/μL. The comparative analysis between clinical diagnosis and molecular techniques, including RT-PCR and RT-qPCR, demonstrated low concordance, with Kappa coefficients of 0.268 and 0.324, respectively. In contrast, ddPCR, showed a moderate concordance, with a Kappa coefficient of 0.477. Sensitivity was 42.39% for RT-PCR, 57.89% for RT-qPCR and 72.37% for ddPCR, with 100% of specificity for all methods. This study under-scores ddPCR's superior sensitivity and concordance with clinical CDV diagnosis, even at low viral concentrations, suggesting it as a promising alternative for CDV diagnosis.

The development of a Digital Track Model (DTM) within Kazakhstan's railway system presents an innovative approach to enhancing efficiency and safety across the network. This paper investigates the economic viability of DTM implementation, offering a comprehensive mathematical model that highlights potential reductions in maintenance costs and improvements in system accuracy and durability. The findings advocate for DTM's potential to significantly elevate railway operations, suggesting a pivotal step towards modernizing Kazakhstan's transit infrastructure.

The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.

This paper proposes an electric vehicle routing problem with considering states of charging stations and suggests solution strategies. Charging of electric vehicles is a main issue in the field of electric vehicle routing problem. There are many studies to find locations of charging stations, recharging functions for batteries of vehicles, and so on. However, states of charging stations significantly affect the routes of electric vehicles, which is not much explored. The states may include open or close of charging stations, occupied or empty of charging slots, and so on. This paper investigates how the states of charging stations are estimated and routing strategies are determined. We formulate a mixed integer programming model and suggest how to solve the problem with exact method. Numerical examples provide the optimal routing strategies of electric vehicles in the changing environments of the states of charging stations.

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprised of fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed wing aircraft systems. Here the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity techniquesto recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models will enable us to avoid common control design methods, such as gain scheduling, where stability issues can be extremely challenging.

Calcium and magnesium are important not only for human health, but also for reducing problems related to the corrosive and aggressive effects of soft water on drinking water distribution materials. Experimental and mathematical modeling of the recarbonization process aimed at increasing the content of these biogenic elements in water was carried out using the novelty of a continuous laboratory and pilot scale fluidized bed reactors. Water remineralization using half-calcined dolomite (HCD) and carbon dioxide was used. The influence of operating conditions Q(CO2), freshwater inflow and HCD dose on quality indicators of treated drinking water (c(Ca2+), c(Mg2+), c(Ca2++Mg2+) and Ca/Mg) was studied. The results show that the concentration of Mg2+ is more significantly affected by the amount of HCD in the system and the flow of CO2. The influence of freshwater inflow on the Mg2+content is to a lesser extent. At a constant CO2 flow, therefore, as the tap water inflow increases, the Ca2+ content decreases and the Mg2+ content increases, which has results in a decrease in the Ca/Mg molar ratio. However, the Ca/Mg ratio can be effectively controlled by adding an appropriate amount of HCD at certain time intervals. Overproduction of ions is easily controlled by CO2 flow.

Ensuring fire safety is an important condition for the successful operation of industrial enterprises. It is necessary to detect the threat of fire before ignition. An indicator of danger is the appearance of gas, which occurs as a result of unauthorized heating of equipment. Gas sensors make it possible to detect the appearance of gases characteristic of the decomposition of materials at the stage of smouldering and pyrolysis, which cause a change in the composition of the atmosphere. This paper presents a mathematical method for the rational placement of gas analyzers for premises of potentially hazardous industries. It is the rational placement of gas sensors, which ensures safety, taking into account economic feasibility that determines the effectiveness of their use. For the first time, the analysis of gas accumulation during the movement of the flow from the source to the ceil-ing, then propagation to the location of the sensors, is used for the first time to select the placement of gas sensors. Depending on the permissible values of the gas volume, the placement and number of gas sensors are selected. The calculation of the conditions for the rational placement of gas sen-sors for the most common indicators, such as carbon monoxide and hydrogen at different sizes and heights of rooms, is carried out. The method of calculating the location of gas analyzers makes it possible to diagnose and predict fire hazard at technological facilities on the basis of gas control, and compare the obtained values with the maximum permissible values. This method provides cal-culation of the coordinates of the gas source from the coordinates of the triggered sensors. Knowing the coordinates of all sensors, the coordinates of the sensors that gave the alarm, and the formula for determining the volume of the gas cloud under these sensors, it is possible to assess the localization of the source of dangerous gas in the protected room. This increases the efficiency of the fire safety system. The method makes it possible to control the layout of sensors depending on the volume of protected premises, types of production, the creation of new sensors, changes in the composition of hazardous gas in different technological conditions.

Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease that has afiected millions of people worldwide. Initially, basic public health measures were implemented to control specially the spread of such virus. However, vaccination has emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent spread of the disease. In this study, a modeling approach is used to analyze the impact of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical method, the model is solved based on reported cases in Pakistan. A spectral method is employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known as R0, which indicates the potential for disease transmission. The study also includes a detailed stability analysis, examining the invariance properties of the model solution and discussing equilibrium points and their stability in disease-free and endemic states. Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.

A mathematical model is proposed to analyze the spreading dynamics of COVID-19. By using the parameters of the model, namely the basic reproduction number (R0) and the attenuation constant (k), the daily number of infections (DNI) and the cumulative number of infections (CNI) are deduced and shown to be in good agreement with experimental data. This model effectively addresses three key issues: explaining the waveform pattern of DNI, predicting the occurrence of the second wave of infection, and understanding the competitive spread of two viruses in a region. The findings demonstrate that these significant challenges can be comprehensively tackled using a simple mathematical framework. The theoretical insights derived from this model hold potential in guiding the estimation of the severity of an infection wave and formulating effective strategies for the control and mitigation of epidemic outbreaks.

In this paper mathematical analysis of the HIV/AIDS deterministic model exposed in [Espitia, C. et. al. Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia, Journal of Computational Biology 29 (2022) 483–493] is made. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness, calculus of basic reproduction number, stationary points such as disease free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE) are calculated, local stability (LAS) of disease free equilibrium. It research allow to conclude that the best way to reduce contagion and consequently to reach a DFE is thought to be the reduction of homosexual partners rate as they are the most affected population by the virus, and are therefore the most likely to become infected and to spread the infection. Increasing the departure rate of infected individuals, leads to a decrease in untreated infected heterosexual men and untreated infected women.

A compartmental epidemiological model with seven groups is introduced herein, to account for the dissemination of diseases similar to the Coronavirus disease 2019 (COVID-19). In its simplified version, the model contains ten parameters, four of which relate to characteristics of the virus, whereas another four are transition probabilities between the groups; the last two parameters enable the empirical modelling of the effective transmissibility, associated in this study with the cumulative number of fatalities due to the disease within each country. The application of the model to the fatality data (the main input herein) of five countries (to be specific, of those which had suffered most fatalities by April 30, 2020) enabled the extraction of an estimate for the basic reproduction number $R_0$ for the COVID-19 disease: $R_0=4.91(33)$.

Pressure fluctuations beneath hydraulic jumps downstream of Ogee spillways potentially damage stilling basin beds. This paper deals with the extreme pressures underneath free hydraulic jumps along a smooth stilling basin. The experiments were conducted in a laboratory flume. From the probability distribution of measured instantaneous pressures, the pressures with different non-exceedance probabilities (P*a%) could be determined. It was verified that the maximum pressure fluctuations, as well as the negative pressures, are located at the positions closest to the spillway toe. The minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of P*a% related to the characteristic points along the basin, and different Froude numbers. To benchmark, the results, the dimensionless forms of mean pressures, standard deviations, and pressures with different non-exceedance probabilities were assessed. It was found that an existing methodology can be used to interpret the present data, and pressure distribution in similar conditions, by using a new third-order polynomial relationship for the standard deviation (σ*X) with the determination coefficient (R2) equal to 0.717. It was verified that the new optimized adjustment gives more accurate results for the estimation of the maximum extreme pressures than the minimum extreme pressures.

Multiple lines of evidence indicate that CD8$^+$ T cells are important in the control of HIV-1 (HIV) replication. However, CD8$^+$ T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8$^+$ T-cell responses induced during the course of HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8$^+$ T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8$^+$ T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8$^+$ T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8$^+$ T cells in the chronic infection. The breadth of HIV-specific CD8$^+$ T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8$^+$ T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8$^+$ T-cell responses and the presence of intra- and interclonal competition between multiple CD8$^+$ T-cell responses; such competition may limit the magnitude of CD8$^+$ T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8$^+$ T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.

Studies performed at single-cell resolution have demonstrated the physiological significance of cell-to-cell variability. Various types of mathematical models and systems analyses of biological networks have further been used to gain a better understanding of the sources and regulatory mechanisms of such variability. In this work, we present a novel sensitivity analysis method, called molecular density function perturbation (MDFP), for the dynamical analysis of cellular heterogeneity. The proposed analysis is based on introducing perturbations to the density or distribution function of the cellular state variables at specific time points, and quantifying how such perturbations affect the state distribution at later time points. We applied the MDFP analysis to a model of signal transduction pathway involved in TRAIL (tumor necrosis factor-related apoptosis-inducing ligand)-induced apoptosis in HeLa cells. The MDFP analysis showed that caspase-8 activation regulates the timing of the switch-like increase of cPARP (cleaved poly(ADP-ribose) polymerase), an indicator of apoptosis. Meanwhile, the cell-to-cell variability in the commitment to apoptosis depended on mitochondrial outer membrane permeabilization (MOMP) and events following MOMP, including the release of Smac (second mitochondria-derived activator of caspases) and cytochrome-C from mitochondria, the inhibition of XIAP (X-linked inhibitor of apoptosis) by Smac and the formation of apoptosome.