In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

1,3,5-Tris-(α-naphthyl)benzene is an organic non-electrolyte with notable stability of an amorphous phase. Its glassy and supercooled liquid states were previously studied by spectroscopic and calorimetric methods. However, the thermodynamic parameters of phase transitions available from the literature are inconsistent. In this work, the heat capacities of crystalline and liquid phases, the temperature dependence of the saturated vapor pressures, fusion and vaporization enthalpies were determined using differential and fast scanning calorimetry and verified using the estimates based on solution calorimetry. The structural features of 1,3,5-tris-(α-naphthyl)benzene are discussed based on the computations performed and the data on the molecular refractivity. The consistency between the values obtained by independent techniques was demonstrated. The deviations in the previously published data were attributed to possible polymorphism.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

This paper develops feasible control strategies and associated system responses to bring an autonomous front-axle bicycle robot from specified initial conditions to final conditions such that a specific performance index is minimized. To solve the problem, the following approach is used: The feasible controls derived from the normal equations of optimality are substituted into the state and the costate systems and form a combined control-free state-costate system which is vectorized to enable and ease the application of a numerical method. A computer program written in Matlab computer programming language, codes a fourth-order Runge-Kutta numerical method and then solve the combined state-costate system of ordinary differential equations. The obtained results are the feasible bicycle robot trajectory, the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations are designed and provided to persuade on the effectiveness and the reliability of the approach.

The critical period (CP) phenomenon in language development ranks among the 125 conundrums facing scientists in the 21st century, according to Science. While the phenomenon itself has been noncontroversial in first language acquisition, it still warrants an adequate explanation. Predicated on language acquisition as a complex process, questions among the first to be raised include: How do children accomplish this remarkable feat in such a short amount of time? And how do nature and nurture come together to influence language learning? In second language acquisition, however, both the notion of CP, albeit popular, and its empirical evidence have remained contested to this date - among the questions, whether the observed evidence counts as CP-specific and/or whether or not it warrants an isomorphic attribution to maturational constraints. Entwined in this debate are two well-established facets of inter-learner differential attainment. The first is that there exists a stark difference in ultimate attainment between younger and older learners. A second facet is the vast differences in ultimate attainment among older learners. In this article, adopting a social physics approach, we mathematically establish both the relationship between nature and nurture contributions and the presence of a critical period, and, at once, tender a parsimonious and probable theory for the twin phenomena of inter-learner differential attainment.

Background: The liver is involved in disseminated tuberculosis in more than 80% of the cases while primary liver involvement is rare, representing < 1% of all cases. Hepatic tuberculosis (TB) can be treated by conventional anti-TB therapy, however, diagnosing this disease still remains a challenge. The diagnosis might be particularly difficult in patients with a single liver lesion that could be misdiagnosed as a tumor or other focal liver lesions. While computed tomography and magnetic resonance imaging findings have been described, there is a paucity of literature on contrast-enhanced ultrasound (CEUS) features of hepatic TB. Case Summary: herein, we describe a case of a patient with tuberculous lymphadenopathy and chronic HCV-related liver disease who developed a single macronodular hepatic TB lesion. Due to the finding of a hepatocellular carcinoma (HCC) highly suggestive CEUS pattern, specifically a LR5 category according to the Liver Imaging Reporting and Data System (LI-RADS), and a good response to antitubercular therapy, a non-invasive diagnosis of HCC was made, and the patient underwent liver resection. We also review the published literature on imaging features of hepatic TB and discuss the diagnostic challenge represented by hepatic TB when occurs as a single focal liver lesion. Conclusions: this report shows for the first time that CEUS pattern of hepatic TB might be misinterpreted as HCC and specific imaging features are lacking. Personal history and epidemiological data are mandatory in interpreting CEUS findings of a focal liver lesion even when the imaging pattern is highly suggestive of HCC.

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

The screen-printed carbon nanofibers electrodes (SPCNFE) represent an alternative with great acceptance due to their results, as well as their low impact for the environment. In order to improve their performance, in the present work they were modified with silver nanoparticles (Ag-NPs) and electrochemically characterized by using anodic stripping voltammetry. From the Ag-NPs synthesis, silver seeds (Ag-NS) and silver nanoprisms (Ag-NPr) were obtained. The Ag-NPs formation was confirmed by micrographs where Ag-NPs with diameters of 12.20±0.04 nm for Ag-NS, and 20.40±0.09 nm for Ag-NPr were observed. The electrodes were modified by using three different deposition methods: drop-casting, spin-coating and in-situ approaches. It was observed that the last methodology showed a low amount of Ag-NS deposited on the electrode surface and a deep alteration of this surface. Those facts suggested that the in situ synthesis methodology were not appropriate for the determination of heavy metals and it was discarded. The incorporation of the nanoparticles by spin-coating and drop-casting strategies showed different spatial distribution on the electrode surface as proved by scanning electron microscopy. The electrodes modified by these strategies, were evaluated for the cadmium(II) and lead(II) detection using differential pulse anodic stripping voltammetry, obtaining detection limit values of 2.1 and 2.8 µg L^-1, respectively. The overall results showed that the incorporation route does not change directly the electrocatalytic effect of the nanoparticles, but the shape of these nanoparticles (spherical for seeds and triangular for prisms) has a preferential electrocatalytical enhancement over Cd(II) or Pb(II).

This paper explores the relationships between differential topology and general relativity, examining the classical framework's applicability in modelling gravitational fields and the limits encountered with topological defects such as cosmic strings. By illustrating smooth metric structures, holonomy, and geodesic completeness, we reveal the foundational role of differential topology in describing spacetime curvature without quantum corrections. The Einstein field equations and global topological invariants are discussed in contexts where continuous manifolds hold, while highlighting how phenomena like cosmic strings challenge these assumptions. We propose that such topological defects introduce singular behaviours where traditional differential topology reaches its boundaries, potentially necessitating quantum gravitational models for a complete description. Visualizations of Schwarzschild curvature, holonomy in spherical surfaces, and geodesic paths provide insights into gravitational field variability and topological constraints in classical models, underscoring the mathematical and physical principles at play.This paper explores the relationships between differential topology and general relativity, examining the classical framework's applicability in modelling gravitational fields and the limits encountered with topological defects such as cosmic strings. By illustrating smooth metric structures, holonomy, and geodesic completeness, we reveal the foundational role of differential topology in describing spacetime curvature without quantum corrections. The Einstein field equations and global topological invariants are discussed in contexts where continuous manifolds hold, while highlighting how phenomena like cosmic strings challenge these assumptions. We propose that such topological defects introduce singular behaviours where traditional differential topology reaches its boundaries, potentially necessitating quantum gravitational models for a complete description. Visualizations of Schwarzschild curvature, holonomy in spherical surfaces, and geodesic paths provide insights into gravitational field variability and topological constraints in classical models, underscoring the mathematical and physical principles at play.

This paper explores a novel approach to modeling the positional dynamics of stars using discrete dynamical systems. We define star evolution through discrete-time update rules based on right ascension, declination, and distance, incorporating chaotic behavior via nonlinear functions and external perturbations. By applying Ricci flow and Riemannian metrics, we provide new insights into the positional dynamics of stars. Theoretical computations of Perelman entropy are used to assess system complexity, with high-precision Runge-Kutta methods ensuring accurate solutions for our chaotic model. We quantify chaos using Lyapunov exponents and perform bifurcation analysis to study how parameter variations affect the dynamics. Comparing our model to the Lorenz attractor reveals both similarities and unique characteristics in stellar dynamics. Our results show that entropy increases exponentially, indicating that predicting star positions with precision becomes increasingly challenging over time. This study advances the understanding of chaos in celestial systems and contributes to dynamical systems theory by integrating chaos theory with astronomical modeling.

Effective sports training should be attuned to the athlete's specific conditionings and characteristics. In motor learning research, two often neglected factors that influence this resonance are the learner's athletic background and the structural diversity of exercises (e.g., relative similarity). This study examines the effects of three learning approaches (i.e., contextual interference (CI), differential learning (DL), and free-play control condition (CO)) on the parallel learning of Handball (HB), Volleyball (VB), and Basketball (BB) skills, considering participants' prior sport backgrounds. Forty-five males (15 HB, 15 VB, and 15 BB players) with a mean age of 22±1.4 years and at least 6 years of experience in the mastered discipline voluntarily participated in this study. A pre-post-retention test design including a 6-week-intervention program was employed. In terms of short-term (pre-post) gain, only the DL- group significantly improved their performance in both non-mastered disciplines (p=0.03 for the BB free-throw and p=0.05 for the HB shooting tests), with a trend (ES=0.53) towards an improvement in the performance of the mastered VB underarm-pass skill. In terms of relatively permanent gains, the CI group significantly improved their performances from pre- to retention-test only in the non-mastered BB free-throw skill (p=0.018). In contrast, the DL group significantly improved their performance at retention compared to the pre-test in both non-mastered BB (p=0.004) and HB (p=0.003) skills, with a trend (ES=0.4) towards improvement in the mastered VB test. In both short, and relatively permanent terms, higher composite score gains were observed in DL compared to CI (p=0.001 and 0.002) and CO (p=0.001 and <0.0001). In conclusion, the present findings provide additional support for the potential advantages of the DL model over those of CI. These findings can serve as the basis for tailored training and intervention strategies and provide a new perspective for addressing various issues related to individual and situational learning.

FACTS devices provide significance to enhance the functioning of both static and dynamic power systems. The type, size, and location of FACTS devices determine how well they achieve the goals of enhancing voltage stability, loadability, and loss minimization simultaneously. The aim of the function in this study includes voltage stability, line loadings, and loss minimization, which are expected to obtain the most benefits from their installation and other weights allocated to them. It has been determined how installing TCSC, and SVC will improve loadability under situations of continuously increasing load. In this study, a novel optimization technique known as differential evolution invasive weed optimization (DEIWO) is utilized to locate the optimal location for FACTS devices within the IEEE 14 bus system by considering valve point effects. DEIWO was a recently developed, dominant, and simple metaheuristic algorithm for genuine parameter optimization. DEIWO was inspired by the natural process of weed colonization and dissemination, and it is highly effective at addressing broad multi-dimensional, linear and nonlinear optimization problems. The proposed method was implemented in the IEEE 14 bus testing system. Different methods from the research papers have been used to compare and analyze the results. The results demonstrate the DEIWO algorithm's capability and show how it may be used in practice to locate FACTS devices in deregulated electricity networks in the most advantageous place. A comparison of the proposed process to existing algorithms found in the literature and implemented using traditional techniques reveals that it performs better in terms of precision and convergence

Expression analysis of small noncoding RNA (sRNA), including microRNA, piwi-interacting RNA, small rRNA-derived RNA, and tRNA-derived small RNA, is a novel and quickly developing field. Despite a range of proposed approaches, selecting and adapting a particular pipeline for transcriptomic analysis of sRNA remains a challenge. This paper focuses on the identification of the optimal pipeline configurations for each step of human sRNA analysis, including reads trimming, filtering, mapping, transcript abundance quantification and differential expression analysis. Based on our study, we suggest the following parameters for analysis of human sRNA in relation to categorical analyses with two groups of biosamples: (1) trimming with the lower length bound = 15 and the upper length bound = \(Read\ length - 40\% Adapter\ length\); (2) mapping on a reference genome with bowtie aligner with one mismatch allowed (-v 1 parameter); (3) filtering by mean threshold > 5; and (4) analyzing differential expression with DESeq2 with adjusted p-value < 0.05 or limma with p-value < 0.05 if there is very little signal and few transcripts.

This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

This paper develops a methodology to control the navigation of an autonomous ship robot from an initial state to a final. To solve the problem the following approach is used: The ship robot system is modelled as a control system of six ordinary differential equations involving six state variables and three control variables. After having computed the system Hamiltonian, the feasible controls for optimality are derived from the normal equations of optimality as functions of the state and costate variables. Such controls are substituted into the state and the costate equations and give a combined control-free state-costate system of ordinary differential equations which is solved numerically by using a developed Matlab computer program. Associated computational simulations are designed and provided to show the reliability of the approach.

This article is a big picture of how electrical noise or conducted Electromagnetic Interference (EMI) is generated and mitigated in power converters. It gives an overview of what EMI in power converters is – from generation through to conduction and mitigation. It is meant to cover the complete subject as a summary so that the reader will have an outline of how to control conducted EMI by design (where possible) and how to mitigate by filtering. A clear distinction is made between Differential Mode (DM) and Common Mode (CM) EMI generation and mitigation. By using a boost converter as an example the trade-offs for DM noise control are discussed. It is shown how CM EMI is generated in a boost converter using the concept of the “Imbalance Difference Model” (IDM). Practical measurements for an in-line power filter is given showing the effect of the filter on the total EMI of a boost converter. Measurements for the CM current produced due to the imbalance difference for different values of the boost conductor are also shown. The main contribution of this study is linking CM noise generation to DM EMI. It is shown that CM noise is a direct consequence of DM noise (although circuit imbalance and coupling to a common ground also play a role). This paper will be useful to designers seeking the “bigger picture” of how EMI is generated in power converters and what can be done to mitigate the noise.

This paper is a slightly modified, abridged version of a previous work ``Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference ``Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

This paper is a slightly modified, abridged version of a previous work "Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference "Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

Breast cancer is the most commonly diagnosed cancer in women in both developed and developing countries. Due to the increasing alarms in the detection of cases every year, it is considered a priority to evaluate new molecules as potential antitumoral agents. Among these molecules, cationic peptides have emerged as promising therapeutic agents with a membrane-based mechanism of action very hard to counteract by the cancer cells. This biophysical study seeks to offer preliminary insights into how NA-CATH:ATRA-1-ATRA-1, a synthetic cationic peptide derived of the peptide NA-CATH, isolated from the species Natra aja or Chinese cobra, is a potential antitumoral compound at the membrane level on breast cancer cell lines. The interaction of the NA-CATH-ATRA-1-ATRA-1 with two lipid systems representative of tumoral and non-tumoral membranes was followed by differential scanning calorimetry and Fourier-transform infrared spectroscopy. The results showed a strong interaction of NA-CATH-ATRA-1-ATRA-1 with the lipids present in the eukaryotic membranes, especially phosphatidylserine, suggesting a mechanism based on the electrostatic interaction of the peptide with the anionic lipids of the tumoral cancer membranes. The biophysical studies are essential to understand the mechanism of action of a potential pharmaceutics.

In the present study, we introduce the two dimensional Chlodovsky type Bernstein operators based on (p, q)−integer. We examine approximation properties of our new operator by the help of Korovkin-type theorem. Further, we present the local approximation properties and establish the rates of convergence by means of the modulus of continuity and the Lipschitz type maximal function. Also, we give a Voronovskaja type theorem for this operators. And, we investigate weighted approximation properties of these operators and estimate rate of convergence in the same space. Finally, with the help of Maple, illustrative graphics show the rate of convergence of these operators to certain functions . The optimization of approximation speeds by operators during system control provides significant improvements in stability and performance. As a result, the control and modeling of dynamic systems become more efficient and effective through innovative methods. These advancements in the fields of modeling fractional differential equations and control theory offer substantial benefits to both modeling and optimization processes, expanding the range of applications in these areas.

Using Drone Cells to optimize Radio Access Networks is an exemplary way to enhance the capabilities of terrestrial Radio Access Networks. Drones fitted with communication and relay modules can act as Drone Cells. The multi Drone Cell placement problem is solved using an adapted Dispersive Flies Optimization alongside with other meta-heuristic algorithms such as Particle Swarm Optimization and Differential Evolution. A home-brewed simulator has been used to test the effectiveness of the different implemented algorithms. Specific environment respective parameter tuning have been explored to better highlight possible advantages of one algorithm over other in any particular environment. Algorithmic diversity has been explored, leading to several modifications and improvements in the implemented models. The results show that using tuned parameters there is a performance uplift in coverage probability when compared to the default meta-heuristic parameters while still remaining within the constraints implied by the problem’s requirements and resource limitation. The paper concludes by offering a study between multiple meta-heuristic approaches and comparison between the methods, investigating the impact of parameter-tuning as well as analyzing the impact of intermittent restart for algorithms persistent diversity.

The structural evolution and phase composition of multi-block thermoplastic polyurethanes, with different nature of the soft segments based on poly(butylene adipate) (PBA), were analyzed during in-situ thermal treatments. A combination of synchrotron small- and wide-angle X-ray scattering, differential scanning calorimetry, thermogravimetric analysis, and FTIR spectroscopy was used to determine the influence of macrodiol nature and crystallization conditions on the polymorphic behavior of PBA. Using a new synthesis scheme, a relatively high degree of crystallinity for urethane blocks was achieved, which depends on the diisocyanate type in the structure of the soft segment. The hard segment domains impose geometrical constraints on PBA, thereby altering its crystallization process compared to the neat oligomer. Thus, crystallization after annealing at a low temperature (80 °C) is fast, predominantly yielding a metastable β-phase. When heated to 180 °C, which is higher than the hard-segment melting temperature, a phase-separated structure is observed. Subsequent crystallization is slower, favoring the formation of the stable α-PBA modification. The phase separation can be observed even after the hard block melting. A notably slow crystallization from an isotropic melt was documented after the disruption of phase separation at 230 °C.

In this study, 12 organic waste materials were subjected to TG/DTG thermogravimetric analysis and DSC calorimetric analysis. These analyses provided basic information about thermochemical transformations and degradation rates during organic waste pyrolysis. Waste materials were chosen to cover the most abundant waste that can be found in the municipal solid waste stream. Based on TG results, kinetic parameters according to Coats–Redfern method were determined. The pyrolysis activation energy was the highest for cotton 134.5 kJ∙(mol∙K)-1 and the lowest for leather 25.2 kJ∙(mol∙K)-1. The DSC analysis showed number of transformations occurred during pyrolysis for each material. For each transformation, normalized energy required for transformation, or released during transformation were determined and then summarized to present energy balance. The study found that only for three waste materials: PET (-220.1 J⸱g-1), leather (-66.9 J⸱g-1), and chicken meat (-130.3 J⸱g-1) energy balance was negative, while the highest positive balance value was found for potato peelings (367.8 J⸱g-1). The obtained results may be applied for the modelling of energy and mass balance of municipal solid waste pyrolysis.

This theoretical article provides a brief description of the model of living systems' functioning by defining them as resource flows patterns. It reviews the living systems growth limitation between their development cycles by the Fibonacci sequence. Besides, there are presented systems resource base criteria, necessary for accumulating the resources and their investment. The article also considers the conditions for the formation of various systems strategies. Then we reviewed the principles of elemental analysis of information by a person as a living system according to the considered model. The study also shows the possibility of forming priorities in analyzing information for 16 combinations as maximum. At that, it remains crucial to divide a human's information analysis between the two hemispheres of the brain. The described combinations of priorities in a person's information analysis are compared with the existing differential personality models, such as the big five personality traits, the Myers-Briggs type indicator, temperaments model and Honey and Mumford Learning styles.

The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses extensions of invariance alignment and Haberman linking concerning the choice of linking functions for comparisons of many groups. Robust linking functions are proposed for invariance alignment and robust Haberman linking that are particularly suited to item response data under partial invariance. In a simulation study, it is shown that both linking approaches have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment.

This study demonstrates a global, non-parametric, non-iterative optimization of time-mean value of a kind of index vibrated by time-varying forcing. It is based on the fact that the (steady) forced vibration of non-autonomous ordinary differential equation systems is well approximated by an analytical solution when the amplitude of forcing is sufficiently small and its base state without forcing is linearly stable and steady. It is applied to optimize a time-averaged heat-transfer rate on a two-dimensional thermal convection field in a square cavity with horizontal temperature difference, and the globally optimal way of vibrational forcing, i.e. the globally optimal, spatial distribution of vibrational heat and vorticity sources, is first obtained. The maximized vibrational thermal convection corresponds well to the state of internal gravity wave resonance. In contrast, the minimized thermal convection is weak, keeping the boundary layers on both sidewalls thick.

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

Taste signaling is a complex process that is linked to obesity and its associated metabolic syndromes. The sweet taste is mediated through a heterodimeric G protein coupled receptor (GPRC) in a species-specific manner and at multi-tissue specific levels. The sweet receptor recognizes a large number of ligands with structural and functional diversities to modulate different amplitudes of downstream signaling pathway(s). The human sweet-taste receptor has been extremely difficult to study by biophysical methods due to inadequate methods for producing large homogeneous quantities of the taste-receptor protein and a lack of reliable in vitro assays to precisely measure productive ligand binding modes leading to activity upon their interactions with the receptor protein. We report a multimodal high throughput assays to monitor ligand binding, receptor stability and conformational changes to model the molecular interactions between ligand-receptor. We applied saturation transfer difference nuclear magnetic resonance spectroscopy (STD-NMR) complemented by differential scanning calorimetry (DSC), circular dichroism (CD) spectroscopy, and intrinsic fluorescence spectroscopy (IF) to characterize binding interactions. Our method using complementary NMR and biophysical analysis is advantageous to study the mechanism of ligand binding and signaling processes in other GPCRs.

The paper explores the features of numerical simulation to analyze the dynamic behavior of drives controlled by pulse-width modulators. Modern motor control systems widely use pulse width modulation. Effective numerical modeling of such systems has specific features because the models employed are continuous-event and have hybrid behavior due to the presence of nonlinear links with discontinuities of the first kind. Therefore, it is essential to have special integration methods with variable steps, which should be factored in when developing the model. The paper shows how these problems are solved when modeling an electric drive with a DC motor in the SimInTech software.

This paper presents a comprehensive investigation into the applicability and performance of two prominent growth models, namely the Verhulst model and the Montroll model, in the context of modeling tumor cell growth dynamics. Leveraging the power of Physics-Informed Neural Networks (PINNs), we aim to assess and compare the predictive capabilities of these models against experimental data obtained from the growth patterns of tumor cells. We employ a dataset comprising detailed measurements of tumor cell growth to train and evaluate the Verhulst and Montroll models. By integrating PINNs, we not only account for experimental noise but also embed physical insights into the learning process, enabling the models to capture the underlying mechanisms governing tumor cell growth. Our findings reveal the strengths and limitations of each growth model in accurately representing tumor cell proliferation dynamics. Furthermore, the study sheds light on the impact of incorporating physics-informed constraints on the model predictions. The insights gained from this comparative analysis contribute to advancing our understanding of growth models and their applications in predicting complex biological phenomena, particularly in the realm of tumor cell proliferation.

This study aims to categorize the morphological changes during cabbage (B. oleracea ssp. capitata) development: seedling, rosette, folding, and heading and to elucidate the cellular mechanisms of leaf curvature, essential for the formation of the leafy head. We followed the growth of two cabbage morphotypes with distinct head shapes (round and pointed); we phenotyped the size and volume of the whole-plant as well as the size, shape, and curvature of the leaves during growth. By integrating these phenotypic data, we determined the four vegetative stages for both cabbages. Cytological phenotypes of microtome sections from five distinct leaf positions of the rosette, folding, and heading leaves at two timepoints during leaf growth were quantified and revealed variations in cellular parameters among leaf types, between leaf positions, and between the adaxial and abaxial sides. We identified two synergistic cellular mechanisms contributing to the curvature of heading leaves: differential growth across the leaf blade, with increased growth at the leaf's centre relative to the margins; and increased expansion of the spongy parenchyma layer compared to the palisade parenchyma layer, resulting in the direction of the curvature, which is inwards. These two processes together contribute to the typical leafy heads of cabbages.

Summary: Studying biological systems generally relies on computational modeling and simulation, e.g., for model-driven discovery and hypothesis testing. Progress in standardization efforts led to the development of interrelated file formats to exchange and reuse models in systems biology, such as SBML, the Simulation Experiment Description Markup Language (SED-ML), or the Open Modeling EXchange format (OMEX). Conducting simulation experiments based on these formats requires efficient and reusable implementations to make them accessible to the broader scientific community and to ensure the reproducibility of the results. The Systems Biology Simulation Core Library (SBSCL) provides interpreters and solvers for these standards as a versatile open-source API in Java™. The library simulates even complex bio-models and supports deterministic Ordinary Differential Equations (ODEs); Stochastic Differential Equations (SDEs); constraint-based analyses; recent SBML and SED-ML versions; exchange of results, and visualization of in silico experiments; open modeling exchange formats (COMBINE archives); hierarchically structured models; and compatibility with standard testing systems, including the Systems Biology Test Suite and published models from the BioModels and BiGG databases. Availability and implementation: SBSCL is freely available at https://draeger-lab.github.io/SBSCL/.

Whenever vegetated areas are monitored over time, phenological changes in land cover should be decoupled from changes in acquisition conditions, like atmospheric components, sun and satellite heights, and imaging instrument. This especially holds when the multispectral (MS) bands are sharpened for spatial resolution enhancement by means of a panchromatic (Pan) image of higher resolution, a process referred to as pansharpening. In this paper, we provide evidence that pansharpening of visible/near-infrared (VNIR) bands takes advantage from a correction of the path radiance term introduced by the atmosphere, during the fusion process. This holds whenever the fusion mechanism emulates the radiative transfer model ruling the acquisition of the Earth’s surface from space, that is, for methods exploiting a multiplicative, or contrast-based, injection model of spatial details extracted from the panchromatic (Pan) image into the interpolated multispectral (MS) bands. The path radiance should be estimated and subtracted from each band before the product by Pan is accomplished. Both empirical and model-based estimation techniques of MS path radiances are compared within the framework of optimized algorithms. Simulations carried out on two GeoEye-1 observations of the same agricultural landscape at different dates highlight that the de-hazing of MS before fusion is beneficial for an accurate detection of seasonal changes in the scene, as measured by the normalized differential vegetation index (NDVI).

Multivariate Time Series Classification (MTSC) is one of most important tasks in time series analysis, aiding in activities such as human motion recognition and medical diagnostics. Existing methods for MTSC do not explicitly model temporal differences and generalize the idea of temporal difference into a efficient temporal module. Additionally, existing methods are not yet able to capture cross-variable relationships well during network training. As a result, they are unable to achieve convincing feature representation, leading to suboptimal classification accuracy. In this paper, we propose a novel MTSC model called Temporal Difference and Cross-variate Fusion Network (TDCFN), which integrates a two-stream differential LSTM network and a cross-variate feature extraction network to enhance feature representation. TDCFN achieves superior classification accuracy by capturing dynamic temporal evolution and inter-variable relationships. The experimental results show that TDCFN can achieve competitive performance with state-of-the-art multivariate time series classification approaches.

The method for quantitative analysis is based on the direct measurement of the analyte using differential pulse voltammetry (DPV), exploiting its oxidation peak. Calibration curves are set up to evaluate the figures of merit of the analytical method (LOD, LOQ, linear range). The application of the sensor for the dosing of GA in real matrices is carried out by analyzing non-alcoholic and alcoholic beverages and comparing the results with those reported in the literature and with the content of total polyphenols determined by the Folin-Ciocalteu method. In all cases, concentrations of GA align with those previously found in the literature for the beverages examined. Moreover, the values are always lower than the total polyphenols content; this demonstrates the good selectivity of the sensor that can discriminate the target molecule from other polyphenols present.

The differential-equation of second order for space-time oscillation in flat tangential-spacetime of Minkowski-type can be written as an energy-equation. For this energy-equation the analogon of damping energy in two coupled Minkoswki-spacetimes with ftl can be calculated and formulated over Lamberts W-function or via Euler-equation.

The thymus hosts the development of a specific type of adaptive immune cells called T cells. T cells orchestrate the adaptive immune response through recognition of antigen by the highly variable T-cell receptor (TCR). T-cell development is a tightly coordinated process comprising lineage commitment, somatic recombination of Tcr gene loci and selection for functional, but non-self-reactive TCRs, all interspersed with massive proliferation and cell death. Thus, the thymus produces a pool of T cells throughout life capable of responding to virtually any exogenous attack while preserving the body through self-tolerance. The thymus has been of considerable interest to both immunologists and theoretical biologists due to its multiscale quantitative properties, bridging molecular binding, population dynamics and polyclonal repertoire specificity. Here, we review mathematical modelling strategies that were reported to help understand the flexible dynamics of the highly dividing and dying thymic cell populations. Furthermore, we summarize the current challenges to estimating in vivo cellular dynamics and to reaching a next-generation multiscale picture of T-cell development.

Fear extinction requires coordinated neural activity within the amygdala and medial prefrontal cortex (mPFC). Any behavior has a transcriptomic signature that is modified by environmental experiences, and specific genes are involved in functional plasticity and synaptic wiring during fear extinction. Here, we investigated the effects of optogenetic manipulations of prelimbic (PrL) pyramidal neurons on amygdala gene expression to analyze the specific transcriptional pathways involved in adaptive and maladaptive fear extinction. To this aim, transgenic mice were (or not) fear-conditioned and during the extinction phase they received optogenetic (or sham) stimulations over PrL pyramidal neurons. At the end of behavioral testing, electrophysiological (neural cellular excitability and Excitatory Post-Synaptic Currents) and morphological (spinogenesis) correlates were evaluated in the PrL pyramidal neurons. Furthermore, transcriptomic cell-specific RNA-analyses (differential gene expression profiling and functional enrichment analyses) were performed in amygdala pyramidal neurons. Our results show that the optogenetic activation of PrL pyramidal neurons in fear-conditioned mice induces fear extinction deficits, reflected in an increase of cellular excitability, excitatory neurotransmission, and spinogenesis of PrL pyramidal neurons, and in strong modifications of the transcriptome of amygdala pyramidal neurons. Understanding the electrophysiological, morphological and transcriptomic architecture of fear extinction may facilitate the comprehension of fear-related disorders.

Sensory Processing Sensitivity (SPS) is a trait describing inter-individual differences in sensitivity to environments, both positive and negative ones. SPS has attracted growing societal interest. However, (neuro)scientific evidence is lagging behind. We critically discuss how to measure SPS, how it relates to other theories of Environmental Sensitivity and other temperament and personality traits, how SPS interacts with environments to influence (a)typical development, what the underlying aetiologies and mechanisms are, and its relation to mental disorders involving sensory sensitivities. Drawing on the diverse expertise of the authors, we set an agenda for future research to stimulate the field. We conclude that SPS is a heritable, evolutionarily conserved trait, linked to increased risk for psychopathology and stress-related problems in response to negative environments, as well as to greater benefits (e.g., intervention responsivity, positive mood) in positive environments. We need advances in objective assessment of SPS, understanding mechanisms, differentiating it from (seemingly) related mental disorders, to exploit the potential of SPS to improve mental health, preserve human capital, and prevent adverse effects.

This work presents results of property researches of fabricated samples of silica few-mode optical fiber (FMF) with induced chirality under twisting 10 and 66 revolutions per meter, core diameter 11 µm, typical “telecommunication” cladding diameter 125 µm and improved height of quasi-step refractive index profile. Proposed FMF supports 4 guided modes over “C”-band. We represent results of computed characteristics, as well as experimentally measured spectral responses of laser-excited optical signals, including researches and analysis of few-mode effects, occurring after fiber Bragg grating writing.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

An innovative approach is utilized in this paper to solve the Fractional Fokker–Planck–Levy (FFPL) equation. A hybrid technique is designed by combining the finite difference method (FDM), Adams numerical technique, and physics-informed neural network (PINN) architecture, namely, the FDM-APINN, to solve the fractional Fokker‒Planck‒Levy (FFPL) equation numerically. Two scenarios of the FFPL equation are considered by varying the value of α (i.e., 1.75,1.85). Moreover, three cases of each scenario are numerically studied for different discretized domains with 100,200 and 500 points in x∈[-1,1] and t∈[0,1]. For the FFPL equation, solutions are obtained via the FDM-APINN technique via 1000,2000, and 5000 iterations. The errors, loss function graphs, and statistical tables are presented to validate our claim that the FDM-APINN is a better alternative intelligent technique for handling fractional-order partial differential equations with complex terms. FDM-APINN can be extended by using nongradient-based bioinspired computing for higher-order fractional partial differential equations.

In this paper we suggest a first ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann-Stieltjes integral with a signed measure, using semigroup theory. The main result is a theorem that provides the exact form of a semigroup for the Riemann-Stieltjes integral with a measure having a countable number of extrema. The article provides examples of semigroups based on integral operators with signed measures and discusses the fractional powers of differential operators with partial derivatives.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

The structure and phenomena arising from charge transfer in cold field emission modus in a single closed carbon nanotube under cold field emission conditions were studied. By studying microphotographs in various microscopes - AFM, SEM, TEM it was found inhomogeneities in the form of two types of superlattices. The conductivity of the emitter section of a nanodiode circuit with an emitter made of an individual closed carbon nanotube (CNT) and arrays of closed CNTs was studied. High values of cold field emission were observed, as well as nonlinearity and anomalies of the current-voltage characteristic (I-V characteristics), which manifested themselves in the form of peaks at low and high current values. Peaks in the CVC have distinct areas of negative differential conductivity. It is argued, that the anomalously high currents in the I–V characteristics of cold field emission of electrons from a nanoemitter made of closed CNTs can be associated with a sharp increase in the density of electron states at energies near the van Hove singularity.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

Protein import into the endoplasmic reticulum (ER) is the first step in the biogenesis of about 10,000 different soluble and membrane proteins in humans. It involves co- or post-translational targeting of precursor polypeptides to the ER and their subsequent membrane insertion or translocation. So far, three pathways for ER targeting of precursor polypeptides plus four pathways for ER targeting of mRNAs were described. Typically, these pathways deliver their substrates to the Sec61 polypeptide-conducting channel in the ER membrane. Next, the precursor polypeptides are inserted into the ER membrane or translocated into the ER lumen, which may involve auxiliary translocation components, such as the TRAP and Sec62/Sec63 complexes, or auxiliary membrane protein insertases, such as EMC and the TMCO1 complex. Recently, the PEX19/PEX3-dependent pathway, which has a well-known function in targeting and inserting various peroxisomal membrane proteins into pre-existent peroxisomal membranes, was also found to act in targeting and, putatively, inserting monotopic hairpin proteins into the ER. These either remain in the ER as resident ER membrane proteins or are pinched off from the ER as components of new lipid droplets. Therefore, the question arose if this pathway may play a more general role in ER protein targeting, i.e. represents a fourth pathway for ER targeting of precursor polypeptides. Thus, we addressed the client spectrum of the PEX19/PEX3-dependent pathway in both PEX3-depleted HeLa cells and PEX3-deficient Zellweger patient fibroblasts by an established approach, which involves label-free quantitative mass spectrometry of the total proteome of depleted or deficient cells and differential protein abundance analysis. The negatively affected proteins included twelve peroxisomal proteins and two hairpin proteins of the ER, thus confirming two previously identified classes of putative PEX19/PEX3-clients in human cells. Interestingly, fourteen collagen-related proteins with signal peptides or N-terminal transmembrane helices and belonging to the secretory pathway were also negatively affected by PEX3-deficiency, which may suggest compromised collagen biogenesis as a hitherto unknown contributor to organ failures in the respective Zellweger patients.

This review explores the intersection of developmental biology and differential topology in understanding vertebrate ontogenetic constraints. We examine how the topological organization of gene regulatory networks (GRNs) influences developmental trajectories and evolutionary possibilities. By analyzing the mathematical frameworks of differential topology and their application to chromatin architecture, we demonstrate how spatial gene arrangements create constraints that both channel and limit morphological evolution. Special attention is paid to the role of topologically associating domains (TADs) and their conservation across vertebrate lineages, suggesting their fundamental importance in maintaining developmental stability. We propose that the hierarchical nature of GRN topology serves as a primary mechanism for establishing evolutionary constraints while simultaneously facilitating phenotypic innovation within defined parameters. This synthesis provides new insights into how physical genome organization shapes the possibilities and limitations of vertebrate body plan evolution.

The structure and physicochemical properties of polyvinyl alcohol (PVA) and PVA/glycerol films have been investigated by Fourier-transform infrared spectroscopy (FT-IR), X-ray Diffraction (XRD), thermogravimetry/differential thermal analysis (TG/DTA), and advanced scanning probe microscopy (SPM). In the pure PVA films, SPM allowed us to observe ribbon-shaped domains with a different frictional and elastic contrast, which apparently originated from a correlated growth or assembly of PVA crystalline nuclei located within individual PVA clusters. The incorporation of 1.0 wt.% glycerol led to modification in shape of those domains from ribbon-like in pure PVA to rounded in PVA/glycerol 1.0 wt.% films; changes in the relative intensities of the XRD peaks and a decrease of the amorphous halo in the XRD pattern were also detected, while the DTA peak corresponding to the melting point remained at almost the same temperature. For higher glycerol content, FT-IR revealed additional glycerol-characteristic peaks presumably related to the formation of glycerol aggregates, and XRD, FT-IR, and DTA all indicated a reduction in crystallinity. For more than 2.0 wt.% glycerol, the plasticization of the films complicated the acquisition of SPM images without tip-induced surface modification. Our study contributes to the understanding of crystallinity in PVA and how it is altered by a plasticizer such as glycerol.

Polyvinyl Alcohol (PVA)/ Graphene Quantum Dots (GQDs) polymer nanocomposite films have been prepared, and the relationship between their structural, thermal and nanoscale morphologi-cal properties, and their photoluminescent response, has been investigated. Although according to X-ray Diffraction (XRD), Fourier-Transform Infrared Spectroscopy (FT-IR) and Differential Thermal Analysis (DTA) the incorporation of GQDs does not significantly affect the percentage crystallinity of the PVA matrix, for a range of added GQD concentrations, Atomic Force Micros-copy (AFM) showed the formation of islands with apparent crystalline morphology on the surface of the PVA/GQD films, with GQD presumably acting as a nucleating agent for island growth. The incorporation of GQD also led to the formation of characteristic surface pores with increased stiffness and frictional contrast, according to Ultrasonic Force Microscopy (UFM) and Frictional Force Microscopy (FFM) data. The photoluminescence (PL) spectra of the films were found to de-pend both on the amount of GQD incorporated and on the film morphology. For GQD loads > 1,2wt%, a GQD-related band was observed at ~ 1650 cm-1 in FT-IR, along with an increase in the PL band at lower energy. For a load of ~2wt% GQD, the surface morphology was characterized by extended cluster aggregates with lower stiffness and friction than the surrounding matrix, and the PL signal decreased.

The requirement for developing tools capable of detecting and monitoring heavy metals (HMs) has recently taken on more significance due to worries about their toxic effect on human health and aquatic habitats. In this study, a simple electrochemical sensing carbon paste electrode (CPE) based on composite of Zinc/Iron layered double hydroxide (LDH) and polyaniline (PANI) was developed for the determination of lead ions in aquatic solutions. For this purpose, Zn-Fe LDH/PANI was prepared and characterized by Fourier transform infrared (FTIR), X ray diffraction (XRD), and scanning electron microscopy (SEM). Modified carbon electrode based Zn-Fe LDH/PANI was electrochemically characterized compared with unmodified electrode in FCN as a redox probe using cyclic voltammetry (CV). Thus, Zn-Fe LDH/PANI was utilized as sensing material for the electrochemical determination of lead ions using differential pulse voltammetry (DPV). Zn-Fe LDH/PANI/CPE show limits of detection (LOD) and quantification (LOQ) of 167.8 nM and 559.4 nM, respectively. Zn/Mg/Fe LDH was prepared using co-precipitation method and characterized by XRD, FTIR, SEM and BET, used for removal of Pb+2 ions. Removal process was investigated at different conditions as pH, metal ion concentrations, starting adsorbent dose at first and contact time. Zn/Mg/Fe LDH was evaluated as an effective adsorbent material for lead ions elimination in aquatic solutions, with capacity of adsorption 700 mg/g. The elimination of lead ions on Zn/Mg/Fe LDH fitted the pseudo first-order kinetics model and the isotherm was matched with Langmuir model. Studies revealed that the ideal removal conditions were pH = 5.0, an adsorbent mass of 0.05 g, and 20 ml of 50 ppm metal ion concentration at 60 min. The Zn-Fe LDH/PANI composite also showed potential anti-cancer properties against lung cancer cells (A549) while maintaining safety for normal lung fibroblast cells (WI-38). Collectively, advancements in electrochemical sensors offer promising solutions for lead ion detection, with wide-reaching applications in wastewater treatment and cytotoxicity assessment. These innovations have the potential to enhance environmental monitoring and public health safety.

The zero offset voltage in anti-aliasing low-pass filters (LPF) included at the ADC input has a significant effect on the effective bit rate of the ADC. The article discusses methods for minimizing the systematic component of the zero offset voltage (V_OS) of operational amplifiers (Op-Amp) in the structure of the LPF, due to the degradation of the current gain of the base (b) of bipolar transistors for an extremely common subclass of Op-Amp with one high-impedance node. The methods of matching a high-impedance Op-Amp node and a buffer amplifier with the help of special correcting SCM^p and SCMⁿ multipolars are proposed. Methods of description and formation of the given coefficients of weak current asymmetry of typical Op-Amp functional units (current mirrors, input DS, buffer amplifiers, SRC, etc.) are presented. As an example, the results of computer simulation of GaAs Op-Amp with small V_OS performed on JFET field and p-n-p bipolar transistors are given.

This study proposes a methodology for identifying time intervals in which time-of-use (ToU) energy tariffs can be set. This is achieved by analyzing the variability in electric power demand and esti-mating the potential for demand flexibility. The proposed methodology is as follows: first, data preprocessing is performed, focusing on the organization and cleaning of individual consumption records. Subsequently, the data are processed and classified by using consumption variability analysis and clustering techniques. Then, representative clusters are selected and time intervals are analyzed to identify periods of high electric power consumption variability. This methodology was tested with real data from smart meters in the Colombian electrical system, in which time intervals with potential for settinh ToU tariffs were ultimately identified. This work promotes the implementation of demand response strategies that enhance sustainability and facilitate the transition to a more resilient energy landscape both nationally and internationally. The findings are expected to contribute to the formulation of tariff schemes that encourage con-scious changes in electric energy consumption patterns.

A controlled ammonia (NH₃) release experiment was performed at a grassland site to quantify the effect of dry deposition, at the field scale between the source and the receptors (NH₃ measurement locations), on the estimates of emission rates by means of inverse dispersion modelling. NH₃ was released for 3 hours at a constant rate of Q = 6.29 mg s⁻¹ from a grid of 36 orifices spread over an area of 250 m². The increase in line-integrated NH₃ concentration was measured with open-path optical miniDOAS devices at different locations downwind of the artificial source. Using a backward Lagrangian stochastic (bLS) dispersion model (bLSmodelR), the fraction of the modelled release rate to the emitted NH₃ (Q_bLS/Q) was calculated from the measurements of the individual instruments. Q_bLS/Q was found to be systematically lower than 1, on average between 0.69 and 0.91, depending on the location of the receptor. We hypothesized that NH₃ dry deposition to grass and soil surfaces was the main factor responsible for the observed depletion of NH₃ between source and receptor. A dry deposition algorithm based on a deposition velocity approach was included in the bLS modelling. Model deposition velocities were evaluated from a ‘big‑leaf’ canopy resistance analogy. Canopy resistances (generally termed Rc) that provided Q_bLS/Q = 1 ranged from 75 to 290 s m⁻¹, showing that surface removal of NH₃ by dry deposition can plausibly explain the original underestimation of Q_bLS/Q. The inclusion of a dry deposition process in dispersion modelling is crucial for emission estimates, which are based on concentration measurements of depositing tracers downwind of homogeneous area sources or heterogeneously distributed hot spots, such as e.g. urine patches on pastures in the case of NH₃.

Background: Ultrasonography (US) represents the gold standard imaging method for the assessment of testicular lesions (TL). The gray-scale (GSUS) and color-Doppler (CDUS) ultrasound examination allow sonographers to investigate size, margins, echotexture and vascular features of TL, with the effort to differentiate benign from malignant lesions. Recently, the use of contrast-enhanced US (CEUS) and sonoelastography (SE) led to further improvements in the differential diagnosis of TL. Although GSUS and CDUS are often sufficient to suggest the benign or malignant nature of TL, CEUS can be decisive in the differential diagnosis of unclear findings, while SE can help to strengthen the diagnosis. The contemporary combination of GSUS, CDUS, CEUS and SE led to a new diagnostic paradigm named multiparametric US (mp-US), able to provide a more detailed characterization of TL than the single techniques alone. This narrative and pictorial review is aimed to describe the mp-US appearance of several TL. Methods: An extensive Medline search was performed identifying studies in the English language focusing on mp-US evaluation of TL. Results: a practical mp-US “identity card” and iconographic characterization of several benign and malignant TL is provided herein. Conclusions: the mp-US characterization of TL reported herein can be useful in daily clinical practice.

The National Institute of Justice reported that current methods for processing sexual assault samples have a high failure rate, with 60 to 80 percent of tested kits unable to produce usable DNA profiles. Even when samples test positive for male DNA, 34 percent of sexual assault kits (SAK) do not yield recovered male DNA after differential extraction. Less than 30% recovery of available sperm DNA contributes to this low success rate. The SpermX™ method (SX) has been shown to recover 80 percent or more of sperm DNA from sexual assault samples. An interlaboratory evaluation compared SX to standard differential extraction (DE) protocols. Mock samples with known ratios of female epithelial cells and sperm cells were processed using both methods. Results revealed that SX consistently provided CODIS up-loadable DNA profiles, even with as few as 25 sperm cells, whereas DE failed to produce usable results. On average, SX yielded a seven-fold increase in the recovery of unshared male alleles compared to DE. In conclusion, SX outperformed DE in recovering higher quantities of male DNA with minimal female carryover in sexual assault-type samples. This improved success rate in obtaining usable DNA profiles can significantly aid in solving sexual assault cases. Keywords: Differential extraction, Sexual Assault Kit (SAK), Sperm DNA, STRmix™, Combined DNA Index System (CODIS), Forensic DNA analysis, Low Sperm Samples, DNA Mixtures, Autosomal STR Analysis, SpermX.

The paper examines rational Darboux-Crum transforms (RDCTs) of the Jacobi-reference (JRef) potential on the line, with an emphasis on the transformations using only normalizable seed solutions. The Cooper-Ginocchio-Khare (CGK) potential constitutes the simplest example of this rich family of exactly solvable one-dimensional (1D) potentials. It was explicitly confirmed that that an arbitrary Darboux-Crum transformation (DCT) of the given Sturm-Liouville equation (SLE) can be represented as a chain of sequential Darboux deformations of the associated Liouville potentials. If the rational SLE (RSLE) under consideration is exactly solvable and the transformation function (TF) used at each step is nodeless then each RSLE constructed in such a way was proven being exactly solvable itself. The exact solvability of RDCTs of the JRef canonical SLE (CSLE) was also confirmed for the DCTs using pairs of juxtaposed eigenfunctions (an extension of the renowned Adler theorem to the RCSLEs of our interest). By re-expressing the reference polynomial fraction (RefPF) of the transformed CSLE in terms of the Krein determinant (KD), instead of Crum Wronskian (CW), it was shown that the eigenfunctions under consideration are expressible in terms of polynomial solutions of a generalized Heun equation with positions of the most poles dependent on the exponent parameters. The outlined technique was extended to two isospectral SUSY partners of the JRef potential (as well as to its third sibling with the inserted new lowest-energy level) which, by analogy with the CGK potential, are quantized by polynomial solutions of the 2-Heun equation with all four poles at some fixed positions on the real axis.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

The sexual reproduction of ascomycetes is controlled by the mating-type(MAT) locus. (Pseudo)homothallic reproduction has been hypothesized based on genetic data from Hirsutella sinensis (Genotype #1 of Ophiocordyceps sinensis). In this study, the differential occurrence of the mating-type genes in the MAT1-1 and MAT1-2 idiomorphs, which constitute the genetic control of O. sinensis reproduction, was analyzed in 237 strains and 5 genomes of H. sinensis. The mating-type genes were differentially transcribed in H. sinensis Strain L0106, and the MAT1-2-1 transcript in H. sinensis Strain 1229 was alternatively spliced, with an unspliced intron I containing stop codons; these findings constitute O. sinensis reproduction controls at the transcriptional and coupled transcriptional-translational levels. The occurrence of the mating-type genes and a-/α-pheromone receptor genes differed among the 5 H. sinensis genomes. The differential occurrence and transcription of these genes are inconsistent with self-fertilization under (pseudo)homothallism but suggest self-sterility of H. sinensis, which therefore needs a mating partner to achieve sexual outcrossing under heterothallism or hybridization. Consistent occurrence and transcription of the mating-type genes of both the MAT1-1 and MAT1-2 idiomorphs have been reported in natural and cultivated Cordyceps sinensis, but these findings are insufficient to determine the reproduction mode(s) because of the co-occurrence of >90 fungal species and multiple genomically independent genotypes of O. sinensis. The mutant MAT1-1-1 and α-pheromone receptor transcripts in natural C. sinensis result in the N-terminus or middle-truncated proteins, with changes in hydrophobicity and secondary structures of the proteins, suggesting heterogeneous fungal source(s) of the proteins and hybridization reproduction.

In the present paper, the effect of the non-linear thermal radiation on the neutral gas mixture in the unsteady state is investigated for the first time. The unsteady BGK technique of the Boltzmann kinetic equations for a neutral non-homogenous gas is solved. The solution of the unsteady case makes the problem more general significance than the stationary one. For this purpose, the moments' method, together with the traveling wave method, is applied. The temperature and concentration are calculated for each gas component and mixture for the first time.Furthermore, the study is held for aboard range of temperatures ratio parameter and a wide range of the molar fraction. The distribution functions are calculated for each gas component and the gas mixture. The significant non-equilibrium irreversible thermodynamic characteristics the entire system is acquired analytically. That technic allows us to investigate the consistency of Boltzmann's H-theorem, Le Chatelier principle, and thermodynamics laws. Moreover, the ratios among the different participation of the internal energy alteration are evaluated via the Gibbs formula of total energy. The final results are utilized to the argon-helium non-homogenous gas at different magnitudes of radiation force strength and molar fraction parameters. 3D-graphics are presented to predict the behavior of the calculated variables, and the obtained results are theoretically discussed.

This work introduces the mathematical framework of the novel “First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (1st-CASAM-NODE)” which yields exact expressions for the first-order sensitivities of NODE decoder-responses to the NODE parameters, including encoder initial conditions, while enabling the most efficient computation of these sensitivities. The application of the 1st-CASAM-NODE is illustrated by using the Nordheim-Fuchs reactor dynamics/safety phenomenological model, which is representative of physical systems that would be modeled by NODE while admitting exact analytical solutions for all quantities of interest (hidden states, decoder outputs, sensitivities with respect to all parameters and initial conditions, etc.). This work also lays the foundation for the ongoing work on conceiving the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-CASAM-NODE)” which aims at yielding exact expressions for the second-order sensitivities of NODE decoder-responses to the NODE parameters and initial conditions while enabling the most efficient computation of these sensitivities.

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

The extent of micro-phase separation in polyurethanes (PUs) depended on the molecular weight, the chemical nature and the structure of the polyol/soft segments. Balanced properties in PUs were obtained by using blends of polyols during synthesis. No previous studies have been devoted to understand the interactions between the soft segments that affect the properties of the PUs. In this study, different blends of two polyols of different nature (polyester – PE - and polycarbonate diol - CD) and similar molecular weight were prepared and their structural, thermal, surface, viscoelastic and self-adhesion properties were assessed. PE showed larger number of structural repeating units and higher number of polar groups than CD, but the carbonate-carbonate interactions in CD were stronger than the ester-ester interactions in PE. The blending of CD and PE imparted synergic structural properties, particularly in the ones containing less than 50 % PE, they were associated to the disrupt of carbonate-carbonate interactions in CD and the formation of new ester-carbonate and hydroxyl-carbonate interactions. Therefore, higher glass transition temperatures, a new diffraction peak at 2θ = 24°, one additional thermal degradation at 426-436 °C, and less steeper decline of the storage moduli to lower temperature were found in CD+PE blends with less than 50 wt.% PE. Furthermore, the different interactions between the polyol chains in the blends were also evidenced on their surface properties, and all CD+PE blends showed self-adhesion property which seemed related to the existence of ester-carbonate and carbonate-carbonate interactions.

This work introduces the mathematical framework of the novel “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations” (1st-FASAM-NODE). The 1st-FASAM-NODE methodology produces and computes most efficiently the exact expressions of all of the first-order sensitivities of NODE-decoder responses with respect to the parameters underlying the NODE’s decoder, hidden layers, and encoder, after having optimized the NODE-net to represent the physical system under consideration. Building on the 1st-FASAM-NODE, this work subsequently introduces the mathematical framework of the novel “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-FASAM-NODE).” The 2nd-FASAM-NODE methodology yields and computes most efficiently the exact expressions of the second-order sensitivities of NODE decoder-responses with respect to the NODE parameters. Since the physical system modeled by the NODE-net necessarily comprises imprecisely known parameters that stem from measurements and/or computations subject to uncertainties, the availability of the first-and second-order sensitivities of decoder responses to the parameters underlying the NODE-net are essential for performing sensitivity analysis and quantifying the uncertainties induced in the NODE-decoder responses by uncertainties in the underlying uncertain NODE-parameters.

The morphology of virgin reactor powder (RP) of high-density polyethylene HDPE with MW = 160,000 g/mol was investigated with the help of DSC, SEM, SAXS and WAXS methods. The morphological SEM analysis showed, that the main morphological units of RP are macro- and micro-shish kebab structures with significantly different geometric dimensions, as well as individual lamellae of folded chain crystals. Quantitative analysis of an asymmetric SAXS reflection made it possible to reveal the presence of several periodic morphoses in the RP with long periods from 20 nm to 60 nm and to correlate them with the observed powder morphology. According to the DSC crystallinity data, the thickness of the lamellae in each long period was estimated. Their surface energy was calculated in the framework of the Gibbs-Thompson theory. The presence of regular and irregular folds on the surface of the different shish-kebab lamellae is discussed. The percentage of identified morphoses in the RP was calculated. It has been suggested that the specific structure of HDPE RP is due to the peculiarity of polymer crystallization during suspension synthesis in a quasi-stationary regime, in which local overheating and inhomogeneous distribution of shear stresses in a chemical reactor are possible.

In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and an inversion formula for the Stirling numbers of the first and second kinds, the authors establish meaningfully and significantly two identities which simplify coefficients in a family of ordinary differential equations associated with higher order Bernoulli numbers of the second kind.

This work presents an illustrative application of the newly developed “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-FASAM-NODE)” methodology to determine most efficiently the exact expressions of the first- and second-order sensitivities of NODE-decoder responses to the neural net’s underlying parameters (weights and initial conditions). The application of the 2nd-FASAM-NODE methodology will be illustrated using the Nordheim-Fuchs phenomenological model for reactor safety, which describes a short-time self-limiting power transient in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted. The representative model responses that will be analyzed in this work include the model’s the time-dependent total energy released, neutron flux, temperature and thermal conductivity. The 2nd-FASAM-NODE methodology yields the exact expressions of the first-order sensitivities of these decoder responses with respect to the underlying uncertain model parameters and initial conditions, requiring just a single large-scale computation per response. Furthermore, 2nd-FASAM-NODE methodology yields the exact expressions of the second-order sensitivities of a model response requiring as few large-scale computations as there are features/functions of model parameters, thereby demonstrating its unsurpassed efficiency for performing sensitivity analysis of NODE-nets.