A human eye has about 120 million rod cells and 6 million cone cells. This huge number of light sensing cells inside a human eye will continuously produce a huge quantity of visual signals which flow into a human brain for daily processing. However, the real-time processing of these visual signals does not cause any fatigue to a human brain. This fact tells us the truth which is to say that human-like vision processes do not rely on complicated formulas to compute depth, displacement, and colors, etc. On the other hand, a human eye is like a PTZ camera. Here, PTZ stands for pan, tilt and zoom. We all know that in computer vision, each set of PTZ parameters (i.e., coefficients of pan, tilt and zoom) requires a dedicated calibration to determine a camera’s projection matrix. Since there is an infinite number of PTZ parameters which could be produced by a human eye, it is unlikely that a human brain stores an infinite number of calibration matrices for each human eye. Therefore, it is an interesting question for us to answer, which is to say whether simpler formulas of computing depth and displacement exist or not. Moreover, these formulas must be calibration friendly (i.e., easy process on the fly or on the go). In this paper, we disclose an important discovery of a new solution to 3D projection in a human-like binocular vision system. The purpose of doing 3D projection in binocular vision is to undertake forward and inverse transformations (or mappings) between coordinates in 2D digital images and coordinates in a 3D analogue scene. The formulas underlying the new solution are accurate, easily computable, easily tunable (i.e., to be calibrated on the fly or on the go) and could be easily implemented by a neural system (i.e., a network of neurons). Experimental results have validated the discovered formulas.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

In the broader landscape of cryptocurrency risk management, this study delves into the nuanced estimation of Value at Risk (VaR) for a uniformly weighted portfolio of cryptocurrencies, employing the bivariate Normal Inverse Gaussian distribution renowned for its semi-heavy tails. Utilizing high-frequency data spanning from January 1st, 2017, to October 25th, 2022, with a primary focus on Bitcoin and Ethereum, our research seeks to accentuate the resilience of VaR methodology as a paramount risk assessment tool. The essence of our investigation lies in advancing the comprehension of VaR accuracy by quantitatively comparing observed returns of both cryptocurrencies with their corresponding estimated values, with a central theme being the endorsement of the Normal Inverse Gaussian distribution as a potent model for risk measurement, particularly in the domain of high-frequency data. To bolster the statistical reliability of our results, we adopt a forward test methodology, showcasing not only a contribution to the evolution of risk assessment techniques in Finance but also underscoring the practicality of sophisticated distributional models in econometrics. Our findings not only contribute to the refinement of risk assessment methods but also highlight the applicability of such models in precisely modeling and forecasting financial risk within the dynamic realm of cryptocurrencies, epitomized by the case study of Bitcoin and Ethereum.

Hydroxyapatite and b-tricalcium phosphate have been clinically applied as artificial bone materials due to their high biocompatibility. The development of artificial bones requires the verification of safety and efficacy through animal experiments; however, from the viewpoint of animal welfare, there is necessary to reduce the number of animal experiments. In this study, we utilized machine learning to construct a model that estimates the bone-forming ability of bioceramics from material fabrication conditions, material properties, and in vivo experimental conditions. We succeeded in constructing the two models as follows: ‘Model 1’, which predicts material properties from their fabrication conditions, and ‘Model 2’, which predicts the bone-formation rate from material properties and in vivo experimental conditions. By an inverse analysis of the two models, we proposed candidates for material fabrication conditions to achieve target values of bone-formation rate. Under the proposed conditions, the material properties of the fabricated material were consistent with the estimated material properties. Furthermore, a comparison between bone-formation rates after 12 weeks of implantation in the porcine tibia and the estimated bone-formation rate. This result showed that the actual bone-formation rates existed within the error range of the estimated bone-formation rates, indicating that machine learning consistently predicts the results of animal experiments using material fabrication conditions. We believe that these findings will lead to the establishment of alternative animal experiments to replace animal experiments in the development of artificial bones.

Nanoparticles are of great importance for various scientific and technological applications, drug discovery, ecology, molecular biology, etc. Size is a basic characteristic of any particle, and dynamic light scattering is beyond competition when measuring particle size in dispersions ranging from nanometers to micrometers. Unfortunately, this method has a serious problem in processing and interpreting experimental data. Instrument noise and polydispersity of the sample lead to the situation when one initial autocorrelation function corresponds to several different particle size distributions. Sometimes these different solutions of the inverse task can be found by changing parameters in the software. Sometimes the scientist cannot be suspicious of possible other solutions, having one result from the program. In this article I demonstrate the problem on model and experimental data using three known programs: CONTIN, the Malvern Zetasizer and DynaLS. I also present my own free program Autocor, which allows to test our own hypotheses about the modality and shape of the particle size distribution by optimizing the parameters of our own models with a small number of degrees of freedom.

Mercury (Hg (II)) contamination is indefatigable global hazard which causes severe permanent damages to human health. Extensive research has been carried out to produce mercury adsorbents however they are still facing certain challenges limiting their upscaling. Herein we reported the synthesis of novel amine impregnated inverse vulcanized copolymer for effective mercury removal. Poly(S-MA) was prepared using sulfur and methacrylic acid employing inverse vulcanization method following by functionalization. The polyethylenime (PEI) was impregnated on poly(S-MA) to increase the adsorption active sites. The developed adsorbent was then characterized using Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). FTIR confirmed formation of copolymer and successful impregnation of PEI and SEM revealed composite porous morphology of the copolymer. Amine impregnated copolymer (amine@poly(S-MA)) outperformed poly(S-MA) in mercury as it showed 20 % superior performance with 44.7 mg/g maximum adsorption capacity. The adsorption data best fits the pseudo second order which indicates that the chemisorption is most influential mechanism in this case indicating the involvement of NH2 in mercury removal. The adsorption is mainly monolayer on homogenous surface as indicated by 0.76 value of Redlich-Peterson exponent (g) which describes the adsorption nature advent from R2 value of 0.99.

This article proposes application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using the deep learning. In general, the spots represent vague figures in abstract “information spaces” or crisp figures with lack of in-formation about their shapes and are adequate for representation human mental images and reasoning in Artificial Intelligence (AI). However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, basing on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Also, we defined L4 vectors, L4 matrices, and mathematical operations on them. Developed apparatus can be used in AI, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates application of spot-based inverse Radon algorithm for binary image reconstruction.

Model predictive control (MPC) is a multi-objective control technique that can handle 2 system constraints. However, the performance of an MPC controller highly relies on a proper 3 prioritization weight for each objective, which highlights the need for a precise weight tuning 4 technique. In this paper, we propose an analytical tuning technique by matching the MPC 5 controller performance with the performance of a linear quadratic regulator (LQR) controller. The 6 proposedmethodology derives the transformation of LQRweightingmatrixwith a fixedweighting 7 factor using discrete algebraic Riccati equation (DARE) and designs MPC controller using the 8 idea of discrete time linear quadratic tracking problem (LQT) in the presence of constraints. 9 The proposed methodology ensures the optimal performance between unconstrained MPC and 10 LQR controller and provides a sub-optimal solution while the constraints are active during 11 transient operations. The resultingMPC behaves as the discrete time LQR by selecting appropriate 12 weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. 13 In this paper, the effectiveness of the proposed technique is investigated in the application of 14 a novel vehicle collision avoidance system which is designed in the form of linear inequality 15 constraints within MPC. The simulation results confirm the potency of the proposed MPC control 16 technique in performing a safe, feasible and collision free path while respecting the inputs, states 17 and collision avoidance constraints.

This note addresses a fundamental problem in matrix theory on establishing and characterizing range equalities for matrix expressions that involve generalized inverses. We first establish a group of necessary and sufficient conditions for the matrix range equality ${\rm range}(D_1 - C_1A_1^{\dag}B_1) = {\rm range}(D_2 - C_2A_2^{\dag}B_2)$ to hold, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of matrix. We then give several groups of range equalities with extrusion properties for multiple matrix products associated with two matrices and their conjugate transposes and Moore--Penrose inverses.

Crystallization is a significant procedure in the manufacturing of many pharmaceutical and solid food products. In-situ Electrical Resistance Tomography (ERT) is a novel Process Analytical Tool (PAT) to provide a cheap and quick way to test, visualize, and evaluate the progress of crystallization processes. In this work, the spatial accuracy of the non-conductive phantoms in low conductivity solutions was evaluated. Gauss-Newton, Linear Back Projection, and iterative Total Variation reconstruction algorithms were used to compare the phantom reconstructions for tap water, industrial-grade saturated sucrose solution, and demineralized water. Cylindrical phantom measuring 10 mm in diameter and a cross-section area of 1.5 % of the total beaker area was detected at the center of the beaker. Two phantoms with a 10 mm diameter were visualized separately in non-central locations. The quantitative evaluations were done for the phantoms with radii ranging from 10 mm to 50 mm in demineralized water. Multiple factors such as ERT device and sensor development, FEM mesh density and simulations, image reconstruction algorithms, number of iterations, segmentation methods, and morphological image processing methods were discussed and analyzed to achieve spatial accuracy. The development of ERT imaging modality for the purpose of monitoring crystallization in low conductivity solutions was performed satisfactorily.

This note shows that the well-known reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$ for the Moore--Penrose inverse of matrix product is equivalent to many other equalities for that are composed of multiple products $(AB)^{\dag}$ and $B^{\dag}A^{\dag}$ by means of the definition of the Moore--Penrose inverse and orthogonal projector theory.

In the present work, we evaluate the prediction capability of six Pedotransfer functions (PTFs), reported in the literature, for the saturated hydraulic conductivity estimations (Ks). We used a database with 900 measured samples obtained from the Irrigation District 023, in San Juan del Rio, Queretaro, Mexico. Additionally, six new PTFs were construct for Ks from clay percentage, bulk density and saturation water content data. The results show, for the evaluated models, that one model present an overestimation for Ks>0.5 cm h-1 values, three models have a underestimation for Ks>1.0 cm h-1 and two models have a good correlation (R2>0.98) but are necessary more than three parameters. Nevertheless, the last two models requires from three to four parameters in order to get the optimization. By other hand, the models proposed in this work have a similar correlation with a less number of parameters: the fit is seen to be much better than using the existing ones, achieving a correlation of R2 = 0.9822 with only one variable and a R2 = 0.9901 when we use two.

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

The development and generalization of Digital Volume Correlation (DVC) on X-ray computed tomography data highlight the issue of long term storage. The present paper proposes a new model-free method for pruning the DVC data. The size of the remaining sampled data can be user-defined, depending on the needs concerning storage space. The data pruning procedure is deeply linked to hyper-reduction techniques. The DVC data of a resin-bonded sand tested in uniaxial compression is used as an illustrating example. The relevance of the pruned data is tested afterwards for model calibration. A new Finite Element Model Updating (FEMU) technique coupled with an hybrid hyper-reduction method is used to successfully calibrate a constitutive model of the resin bonded sand with the pruned data only.

We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large and for a range of IMQ exponents. The IMQ functions are, however, advantageous when a small number of functions is used or with a small number of collocation points e.g. when using square collocation.

The active power-assist function greatly expands the potential applications of exoskeleton robots, yet the motion intention estimation (MIE) for active power-assist strategy is quite problematic. Through the analysis of the conduction path and the different stage manifestations of motion intention in human body, we confirmed that the joint torque of human body meets the basic requirements of MIE for the active power-assist that we suggest, namely: (i) it reflects the direction and intensity of the wearer’s efforts; (ii) it precedes the human limb motion; (iii) it generates real-time and continuous output. Thus, an online calculation method of human joint torque was proposed. The sensing system integrated in exoskeleton robots was designed to perceive motion data and foot contact force of a human body. A special inverse dynamics with a parameterized model of the human body was proposed. Contrast experiments were carried out with the motion capture system, which results’ accuracy and similarity were evaluated via the root mean square error and correlation coefficient. The comparative analysis of two synchronous results shows good accuracy of the proposed MIE method, which lays the foundation for the realization of active power-assist.

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

Keywords: Echocardiographic alterations; left ventricle; dog; Trypanosoma cruzi; flow patterns; dilated cardiomyopathy; Chagas disease

Introduction: Venous thromboembolism (VTE), comprising deep vein thrombosis (DVT) and pulmonary embolism (PE), is a common condition associated with high morbidity and mortality. Although patients with heart failure (HF) are known to have an increased risk of PE, there is limited evidence regarding its specific impact on patients with acute PE, both in presentation and outcomes, and its relationship with left ventricular ejection fraction (LVEF). Material and Methods: A prospective observational study was conducted at two tertiary hospitals, including patients with symptomatic acute PE between January 2012 and December 2022. The primary objective of the study was the development of a composite outcome (mortality, major bleeding, and recurrence) within the first 30 days. The secondary objective was the development of early complications in patients with HF and reduced LVEF. Results: Out of 1991 patients included with symptomatic acute PE, 7.13% had a history of HF. Patients with HF were older and had more comorbidities. The HF group showed higher mortality (11.27% vs. 4.33%, p<0.001) and major bleeding (9.86% vs. 4.54%, p=0.005). In multivariate analysis, HF was an independent risk factor for the development of the composite outcome (HR 1.93; 95% CI: 1.35-2.76). Reduced LVEF was independently associated with a higher risk of bleeding (HR 3.44; 95% CI: 1.34-8.81). Conclusion: In patients with symptomatic acute pulmonary embolism, heart failure is independently associated with a higher risk of early complications. Additionally, heart failure with reduced LVEF is an independent risk factor for major bleeding.

Especially in the last two decades, due to the developments in durable mechanical circulatory support (MCS) technology and applications, left ventricular assist (LVAD) implantation has become used in more fragile end-stage heart failure patients with higher risk. Despite advances in technology and patient care processes, right heart failure remains the leading cause of morbidity and mortality after durable LVAD implantation. It is difficult to make decisions about the type and duration of MCS during preoperative evaluation, and many clinical, hemodynamic, biochemical and echocardiographic criteria must be taken into account when evaluating the right ventricle. Complex quantitative scoring systems, including measurements of different risk factors for postimplant right ventricular failure, and composite variables, including the anatomical and functional status of the right ventricle, have been used to decide between left or biventricular assist device implantation. The successful use of artificial intelligence (AI) and machine learning (ML) in various applications in the medical field has paved the way for the idea of using it to better predict possible conditions such as right heart failure after LVAD implantation. This review aims to evaluate the current situation of risk prediction models using AI and ML technology, which have become popular in recent years, and possible future developments in predicting right heart failure after the application of durable MCS systems.

Background The workload of nurses in the intensive care unit (ICU) can affect the quality of nursing services. Aim This study aimed to determine the relationship between the nursing activity score and missed care in patients hospitalized in the ICU in Zanjan, Iran. Methods This observational and prospective study was conducted from April 3 to September 18 in 2021. In this study, the tools used included a patient and nurses' profile questionnaire, Nursing Activity Score (NAS). Missed care was observed in the 301 patients for whom the NAS was calculated. Analysis of variance (ANOVA) was used to investigate the differences in mean levels of missed care. Logistic regression models were used to assess the association between factors and missed nursing care. Results Results show that the Medical ICU's mean NAS was 76.31 (95% CI: -13.06 -14.89). In 9 dimensions of care, the extent of missed care was 40.7%. In the care dimensions of assessment, hand hygiene, and infection control, the mean NAS had a statistically significant increase at higher levels of missed care (P<.5). Furthermore, work experience was identified as a protective factor for missed care (OR =.59, 95% CI: .37–.94, χ2= =4.97, p =.026). Conclusion The study revealed a high incidence of missed care. The study revealed that the mean workload was high in certain dimensions of care such as assessment, hand hygiene, and infection control. The increase in workload for nurses results in lost care. Nonetheless, the utilization of experienced nurses can help mitigate this problem. However, utilizing experienced nurses can help reduce this problem.

Cardiac resynchronization therapy (CRT) via biventricular pacing (BiVP-CRT) is considered a mainstay treatment for symptomatic heart failure patients with reduced ejection fraction and wide QRS. However, up to one third of patients receiving BiVP-CRT are considered non-responders to the therapy. Multiples strategies have been proposed to maximize the percentage of CRT responders including two new physiological pacing modalities that have emerged during the lasts years: His bundle pacing (HBP) and left bundle branch area pacing (LBBAP). Both pacing techniques aim at restoring the normal electrical activation of the ventricles through the native conduction system in opposition to the cell-to-cell activation of conventional right ventricular myocardial pacing. Conduction system pacing (CSP), including both HBP and LBBAP appears to be a promising pacing modality for delivering CRT and has proven to be safe and feasible in this particular setting. This article will review the current state of the art of CSP-based CRT, its limitations and future directions.

Traditional diagnosis of patent foramen ovale (PFO) in the heart has involved the use of transcranial doppler (TCD). However, TCD is essentially a blind test that cannot directly visualize the location of blood vessels. Since TCD relies on qualitative assessments by examiners, there is room for errors, such as misalignment of the ultrasound's angle of incidence with the actual blood vessels. This limitation affects the reproducibility and consistency of the examination. In this study, we presented an alternative approach for assessing right-to-left shunt (RLS) associated with PFO using contrast transcranial color-coded doppler (C-TCCD) with bubble contrast. The patient under consideration had been diagnosed with an ischemic stroke through imaging, but the subsequent cardiac work-up failed to determine the cause. Employing C-TCCD for RLS screening revealed a confirmed RLS of Spencer’s three grades. Subsequently, transesophageal echocardiography (TEE) was conducted to evaluate PFO risk factors, confirming an 8 mm PFO size, a 21 mm tunnel length, a hypermobile interatrial septum, and persistent RLS. The calculated high-risk PFO score was 4 points, categorizing it as a very high-risk PFO. This case underscores the importance of C-TCCD screening in detecting RLS associated with PFO, especially in cryptogenic stroke patients when identifying the underlying cause of ischemic stroke becomes challenging.

A hemispheric asymmetry is known for the processing of global vs. local visual information. In this study, we investigated the existence of a hemispheric asymmetry for visual processing of low vs. high spatial frequency gratings. Event-related potentials were recorded in a group of healthy right-handed volunteers from 30 scalp sites. Six types of stimuli (1.5, 3 and 6 c/deg gratings) were randomly flashed 180 times in the left and right upper hemi-fields. Stimulus duration was 80 ms and ISI ranged between 850-1000 ms. Participants had to pay attention and respond to targets based on their spatial frequency and location, or to passively look at the stimuli. C1 and P1 visual responses, as well as a later Selection negativity and a P300 components of ERPs were quantified and subjected to repeated-measure ANOVAs. Overall, performance was faster for the RVF, thus suggesting a left hemispheric advantage for attentional selection of local elements. Similarly, the analysis of mean area amplitude of C1 (60-110 ms) sensory response showed a stronger attentional effect (F+L+ vs. F-L+) at left occipital areas, thus suggesting the sensory nature of this hemispheric asymmetry.

The correct selection of the value of p is a complex and iterative procedure that requires experience in the interpretation of the obtained interpolated maps. Inverse Distance Weighting is a method applied to the porosities of the K and L hydrocarbon reservoirs, discovered in the Neogene (Lower Pontian) subsurface sandstones in the northern Croatia (Pannonian Basin System). They represent small and large data samples. Also a standard statistical analysis of the data was made, followed by the qualitative-quantitative analysis of the maps, based on the selection of different values of the power distance exponent (p-value) for the K and L reservoirs maps. According to the qualitative analysis, for a small data set, p-value could be set on 1 or 2 giving the most optimal result, while for a large data set, a p value of 3 and 4 could be applied. By quantitative analysis, for the case of small data p=2 is recommended, resulting in a root mean square error value of 0.03458, a mean absolute error of 0.02013 and a median absolute deviation of 0.00546. Oppositely, a p-value of 3 and 4 is selected as appropriate for a large data set, with root mean square errors of 0.02435 and 0.02437, mean square errors of 0.01582 and 0.01509 and median absolute deviations 0.00896 and 0.00444. Eventually for a small data set, it is recommended to use a p-value of 2, and for a large data set, a p-value of 3 or 4.

Applications of gradient method for nonlinear optimization in development of Gradient Neural Network (GNN) and Zhang Neural Network (ZNN) are investigated. Particularly, the solution of the matrix equation AXB=D which changes over time is studied using the novel GNN model, termed as GGNN(A,B,D). The GGNN model is developed applying GNN dynamics on the gradient of the error matrix used in the development of the GNN model. The convergence analysis shows that the neural state matrix of the GGNN(A,B,D) design converges asymptotically to the solution of the matrix equation AXB=D, for any initial state matrix. It is also shown that the convergence result is the least square solution which is defined depending on the selected initial matrix. A hybridization of GGNN with analogous modification GZNN of the ZNN dynamics is considered. The Simulink implementation of presented GGNN models is carried out on the set of real matrices.

Application of the Ramsey Theory to the set of the points placed in the plane is discussed. Consider a set of N points located in the same plane. The straight lines connecting these points are yikx=αikx+βik i,k=1...N. Listed below values of slopes αik are possible: αik&gt;0; αik=0; αik is not defined; αik&lt;0. Following coloring procedure is introduced: we connect the pairs of points for which αik&gt;0, αik=0 or αik is not defined, with the red links, and the pairs of points for which αik&lt;0 place with green links. The suggested coloring procedure enables building of the complete bi-colored graph for any set containing N points located in the same plane. We apply the Ramsey theorem to the complete graph emerging from the suggested coloring. For the set containing N=6 points at least one monochromatic triangle will necessarily appear in the graph. The values of the slopes αik depend on the chosen coordinate system. The rotation of coordinate axes changes the coloring of the graph; however, at least one monochromatic triangle will be present for N=6. The introduced coloring procedure diminishes the order of the symmetry group of the regular hexagon, irrespectively to the orientation of the coordinate axes. We hypothesized that this will be true for arbitrary regular n-polygon, independently on the orientation of coordinate axes. The inverse bi-color Ramsey graphs arise, when we replace red links appearing in the source graph with red ones, and vice versa. The total number of triangles in the “direct” and “inverse” Ramsey graphs is the same. We considered the particular case of the set of points for which αik&gt;0 or αik&lt;0 is true in the given coordinates. In this particular case, the rotation of the Cartesian coordinate axes to the angle θ=π2 yields the inverse complete graph. Generalization of this coloring for an arbitrary number and arbitrary location of the source points is introduced.

In this note we study the computation of the minimum polynomial of a matrix $A$ and how we can use it for the computation of the matrix $A^n$. We also describe the form of the elements of the matrix $A^{-n}$ and we will see that it is closely related with the computation of the Drazin generalized inverse of $A$. Next we study the computation of the exponential matrix and finally we give a simple proof of the Leverrier - Faddeev algorithm for the computation of the characteristic polynomial.

We present an improved algorithm for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithm is much more accurate than the famous fast inverse square root algorithm and has a similar computational cost. The presented modification concern Newton-Raphson corrections and can be applied when the distribution of these corrections is not symmetric (for instance, in our case they are always negative).

In this research, a novel method to investigation the transient heat transfer coefficient in a channel is suggested experimentally, in which the water flow, itself, is considered both just liquid phase and liquid-vapor phase. The experiments were designed to predict the temporal and spatial resolution of Nusselt number. The inverse technique method is non-intrusive, in which time history of temperature is measured, using some thermocouples within the wall to provide input data for the inverse algorithm. The conjugate gradient method is used mostly as an inverse method. The temporal and spatial changes of heat flux, Nusselt number, vapor quality, convection number, and boiling number have all been estimated, showing that the estimated local Nusselt numbers of flow for without and with phase change are close to those predicted from the correlations of Churchill and Ozoe (1973) and Kandlikar (1990), respectively. This study suggests that the extended inverse technique can be successfully utilized to calculate the local time-dependent heat transfer coefficient of boiling flow.

Here are analysed data taken in two hydrocarbon fields ("A" and "B"), located in the western part of Sava Depression (North Croatia). They are in the secondary phase of production. The selected reservoirs "L" (in the “A” Field) and "K" (“B”) are of the Lower Pontian (Upper Miocene) age and belong to Kloštar-Ivanić Formation. Due to strong tectonics, there are numerous tectonic block, relatively rarely sampled with well and laboratory tests. Here are selected two variables for interpolation - reservoirs permeabilities and the injected volumes of field water. The following interpolation methods are described, compared and applied: Nearest Neighbourhood, Natural Neighbour (the first time in the Sava Depression) and Inverse Distance Weighting. The last one has been proven as the most appropriate for datasets with size lower than 20 points.

Different process parameters can alter the temperature during machining. Consequently, selecting process parameters that lead to a desirable cutting temperature would help to increase the tool life, decrease the tensile residual stress, and controls the microstructure evolution of the workpiece. An inverse computational methodology is proposed to design the process parameters for specific cutting temperature. A physics-based analytical model is used to predict the temperature induced by cutting forces. To calculate the temperature induced by the deformation in the shear zone, a moving point heat source approach is used. The shear deformation and chip formation model is implemented to calculate machining forces as functions of process parameters, material properties, and etc. The proposed model uses the analytical model to predict the cutting temperatures and applies a variance-based recursive method to guide the inverse analysis. In order to achieve the cutting process parameters, an iterative gradient search is used to adaptively approach the specific temperature by the optimization of process parameters such that an inverse reasoning can be achieved. Experimental data are used to illustrate the implementation and validate the viability of the computational methodology.

Schrödinger dynamics is a nonlocal process. Not only does local perturbation affect instantaneously the entire space, but the effect decays slowly. When the wavefunction is spectrally bounded, the Schrödinger equation can be written as a universal set of ordinary differential equations, with universal coupling between them, which is related to Euler’s formula. Since every variable represents a different local value of the wave equation, the coupling represents the dynamics’ nonlocality. It is shown that the nonlocal coefficient is inversely proportional to the distance between the centers of these local areas. As far as we know, this is the first time that this inverse square law was formulated.

Background/aims: Prior research identified a significant association between heart disease and metabolic dysfunction-associated liver steatohepatitis (MASLD), but the mechanisms are unclear. This study aims to search predictive biomarkers for grade I left ventricular diastolic dysfunction (LVDD), an early stage of heart failure (HF), in type 2 diabetes mellitus (T2DM) patients. Methods: This single-center, prospective observational study screened 73 T2DM patients for grade 1 LVDD and MASLD using 2D echocardiography, tissue analysis, spectral color Doppler, and Fibromax. Results: The study analyzed 50 patients (mean age 58±11.3 years) with a median diabetes duration of 7 years, abdominal obesity (mean BMI 34.4±5.9 kg/m2), and a mean HbA1c of 7.9±1.5%. The prevalence of grade I LVDD, fibrosis, mild steatosis, moderate to severe liver steatosis, mild MASLD, and moderate MASLD was 54%, 44%, 14%, 80%, 43%, and 34%, respectively. Regression analysis revealed that grade 1 LVDD was positively associated with age, Fibrotest, ɑ2-macroglobulin, epicardiac adipose tissue (EAT), and negatively associated with lateral s`, E wave, E/e`, E/A, medium E`, and septal e` (p&lt; 0.05 for all). ɑ2-macroglobulin &gt; 1.92 g/L (AUROC= 0.782, sensitivity 70.4%, specificity 81.2%) and fibrotest score &gt; 0.11 (AUROC 0.766, sensitivity 92.6%, specificity 56.2%) were significant predictors of grade I LVDD. Conclusion: HF is a multifaceted disorder associated with multisystem organ damage, including nonalcoholic MASLD. Although the underlying mechanisms remain unclear, innovative non-invasive biomarkers, such as ɑ2-macroglobulin or fibrotest, could concurrently indicate liver stiffness and the likelihood of grade I LVDD, an early, asymptomatic HF stage in T2DM patients.

Modified mRNAs (modRNAs) are an emerging delivery method for gene therapy. In particular, the modRNA-based COVID-19 vaccines have proven that modRNA is a safe and effective therapeutic tool. Moreover, modRNA has the potential to treat various human diseases including cardiac dysfunction. Acute myocardial infarction (MI) is a major cardiac disorder that currently lacks curative treatment options. MI is commonly accompanied by fibrosis and impaired cardiac function. Our group previously demonstrated that the matricellular protein CCN5 inhibits cardiac fibrosis (CF) and improves cardiac dysfunction. However, it remains elusive whether the early intervention of CF under stress conditions is beneficial or more detrimental due to potential adverse effects such as left ventricular (LV) rupture. To obtain acute CCN5 expression, we used modRNA-mediated gene transfer in a mouse MI model. To evaluate CCN5 activity, we established two independent experimental schemes: 1) preventive intervention and 2) therapeutic intervention. Cardiac function and structural changes were measured by echocardiography and magnetic resonance imaging. Finally, fibrosis and the underlying molecular pathway were analyzed by western blotting, quantitative real-time polymerase chain reaction, and immunohistochemistry. The modRNA-CCN5 gene transfer successfully ameliorated CF and enhanced cardiac function in both preventive and therapeutic interventions without LV rupture or any adverse cardiac remodeling. Conclusively, early intervention in CF by modRNA-CCN5 gene transfer is an efficient and safe therapeutic modality for treating MI-induced heart failure without adverse structural remodeling.

Cardiomyopathies (CMPs) are a group of myocardial disorders that are characterized by structural and functional abnormalities of the heart muscle. These abnormalities occur in the absence of coronary artery disease (CAD), hypertension, valvular disease, and congenital heart disease. CMPs are an increasingly important topic in the field of cardiovascular diseases due to the complexity of their diagnosis and management. In 2023, the ESC guidelines on cardiomyopathies were first published, marking significant progress in the field. The growth of techniques such as cardiac magnetic resonance imaging (CMR) and genetics has been fueled by the development of multimodal imaging approaches. For the diagnosis of CMPs, a multimodal imaging approach, including CMR, is recommended. CMR has become the standard for non-invasive analysis of cardiac morphology and myocardial function. This document provides an overview of the role of CMR in CMPs, with a focus on tissue mapping. CMR enables the characterization of myocardial tissues and the assessment of cardiac functions. CMR sequences and techniques, such as late gadolinium enhancement (LGE) and parametric mapping, provide detailed information on tissue composition, fibrosis, edema, and myocardial perfusion. These techniques offer valuable insights for early diagnosis, prognostic evaluation, and therapeutic guidance of CMPs. The use of quantitative CMR markers enables personalized treatment plans, improving overall patient outcomes. This review aims to serve as a guide for the use of these new tools in clinical practice.

Critical aortic valve stenosis (CAVS) is a life-threatening cardiac disease of the newborn requiring urgent treatment. First-line therapy is still controversial. The aim of our study was (1) to analyze retrospectively the patients of our institution who underwent balloon aortic valvuloplasty (BAV) due to CAVS, and (2) to describe techniques for improved feasibility of the intervention using microcatheters and retrieval loops. Twelve patients underwent 23 BAVs: 1 BAV was performed in 3 patients, 2 BAVs in 7 patients, and 3 BAVs in 2 patients. Trans-valvular pressure gradient (Δp) and left ventricular shortening fraction (LVSF) improved significantly in the first two interventions; first BAV: Δp from 73.7 ±34.5 mmHg to 39.8 ±11.9 mmHg (p=0.003) and LVSF from 22.3 ± 13.5 % to 31.6 ±10.2 % (p=0.001); second BAV: Δp from 73.2 ±33.3 mmHg to 35.0 ± 20.2 mmHg (p&lt;0.001) and LVSF from 26.7 ±9.6 % to 33.3 ±7.4 % (p=0.004). Cardiac surgery during the neonatal period was avoided for all children; median time to valve surgery was 5.75 years. Few complications occurred: mild to moderate aortic regurgitation, one remediable air embolism, and one intimal injury of the ascending aorta. We conclude that BAV is a successful primary treatment for CAVS resulting in left ventricular relief, stabilization of the neonate, and a time gain until cardiac surgery.

Background: Heart failure is a major cause of morbidity and mortality worldwide; left ventricular diastolic dysfunction plays a leading role in this clinical context. Diastolic dysfunction may be predisposed by increased abdominal fat and, consequently, increased pericardial and epicardial adiposity. This study aimed to determine whether pericardial and epicardial fat are associated with left ventricular diastolic function. Methods: 82 patients had their abdominal circumference measured and underwent transthoracic echocardiography to measure the thickness of pericardial and epicardial fat and assess the left ventricular diastolic function. Two groups were created based on mean pericardial fat thickness (4.644 mm) and were related to abdominal circumference and echocardiographic parameters. Results: Subjects in the PF High group showed a significant decrease in septal e' (p&lt;0.0001), lateral e' (p&lt;0.0001) and E/A ratio (p=0.003) and a significant increase in E/e' ratio (p&lt;0. 0001), E wave deceleration time (p=0. 013), left atrial volume (p&lt;0.0001), LV mass (p=0.003), tricuspid regurgitant jet velocity (p&lt;0.0001) and LV diameter (p=0.014) compared to the PF Low group. Conclusions: Measurement of abdominal circumference, pericardial and epicardial fat is an early indicator of diastolic changes with transthoracic echocardiography being the gold standard exam.

The purpose of the study was to identify factors characterizing a decrease in LV global systolic function in patients with ST-segment elevation myocardial infarction (STEMI) after revascularization using cardiac magnetic resonance imaging (MRI)-based ischemic injury pattern and laboratory parameters sensu left ventricular global systolic function. A total of 109 STEMI patients were examined. The patients underwent contrast-enhanced cardiac MRI with a 1.5 Tesla GE SIGNA Voyager (GE HealthCare, USA) on the 7th-10th days from the onset of the disease. According to cardiac MRI analysis, the patients were divided into the following groups with regard to left ventricular ejection fraction (LVEF) values: group 1 – patients with LVEF ≥50%; group 2 – patients with mildly reduced LVEF 40-49%; group 3 – patients with low LVEF <40%. A predominance of most parameters of the ischemic injury pattern was noted in patients with mildly reduced and low LVEF versus patient group with LVEF ≥50%. Some risk factors for a decrease in LVEF <50% systolic function in STEMI patients after revascularization were revealed: male gender; time from the onset of the anginal attack to revascularization; coronary artery status; several LV parameters; ischemic injury characteristics; natriuretic peptide and troponin I levels.

Background Few data exist on comparative long-term outcomes of severe aortic stenosis (AS) patients with different flow-gradient patterns undergoing transcatheter aortic valve implantation (TAVI). This study sought to evaluate the impact of pre-TAVI flow-gradient pattern on long-term clinical outcomes after TAVI and assess changes in left ventricular ejection fraction (LVEF) of different subtypes of AS patients following TAVI. Methods Consecutive patients with severe AS undergoing TAVI in our institution were screened and prospectively enrolled. Patients were divided in four subgroups according to pre-TAVI flow/gradient pattern: (i) low flow - low gradient (LF-LG): stroke volume indexed (SVi) ≤ 35ml/m2 and mean gradient (MG) < 40mmHg), (ii) normal flow - low gradient (NF-LG): SVi > 35ml/m2 and MG < 40mmHg, (iii) low flow - high gradient (LF-HG) : SVi ≤ 35ml/m2 and MG ≥ 40mmHg and (iv) normal flow - high gradient (NF-HG): SVi > 35 ml/m2 and MG ≥ 40mmHg. Transthoracic echocardiography was repeated at 1-year follow-up. Clinical follow-up was obtained at 12 months, and yearly thereafter until 5-year follow up was complete for all patients. Results A total of 272 patients with complete echocardiographic and clinical follow-up were included in our analysis. Their mean age was 80±7 years and the majority of patients (N=138, 50.2%) were women. 62 patients (22.8% of the study population) were distributed in LF-LG group, 98 patients (36%) were LF-HG patients, 95 patients (34.9%) were NF-HG, while 17 patients (6.3%) were NF-LG. There was a greater prevalence of comorbidities among LF-LG AS patients. One-year all-cause mortality differed significantly between the four subgroups of AS patients (log rank p: 0.022) and was more prevalent among LF-LG patients (25.8%) compared to LF-HG (11.3%), NF-HG (6.3%) and NF-LG patients (18.8%). At 5-year follow-up, global mortality remained persistently higher among LF-LG patients (64.5%) compared to LF-HG (47.9%), NF-HG (42.9%) and NF-LG patients (58.8%) (log rank p: 0.029). At multivariable Cox hazard regression analysis, baseline SVi (HR: 0.951, 95% C.I.; 0.918 – 0.984), the presence of at least moderate tricuspid regurgitation at baseline (HR: 3.091, 95% C.I: 1.645 - 5.809) and at least moderate paravalvular leak (PVL) post-TAVI (HR: 1.456 , 95% C.I.: 1.106 - 1.792 ) were significant independent predictors of late global mortality. LF-LG patients and LF-HG patients exhibited a significant increase in LVEF at 1-year follow-up. A lower LVEF (p<0.001) and a lower Svi (p<0.001) at baseline were associated with LVEF improvement at 1 year. Conclusions Patients with LF-LG AS have acceptable 1-year outcomes with significant improvement in LVEF at 1-year follow-up, but exhibit an exceedingly high 5-year mortality following TAVI. The presence of low transvalvular flow and at least moderate tricuspid regurgitation at baseline and significant paravalvular leak post-TAVI were associated with poorer long-term outcomes in the entire cohort of AS patients. The presence of a low LVEF or a low SVi predicts LVEF improvement at 1-year.

Re-interpretation of the Fermat principle governing propagation of light in media within the Ramsey Theory is suggested. Complete bi-colored graphs corresponding to the light propagation in media are considered. The vertices of the graphs correspond to the points of the real physical space, in which light sources or sensors are placed. Red links in the graphs correspond to the actual optical paths, emerging from the Fermat principle. A variety of optical events: refraction, reflection, etc. may be involved in the light propagation. Green links, in turn, denote the trial/virtual optical paths, which actually do not occur. The Ramsey Theorem states that within the graph containing six points, inevitably, actual or virtual optical cycle will be necessarily present. Implementation of the Ramsey Theorem to the light propagation in metamaterials is discussed. The Fermat Principle states that in metamaterials a light ray in going from point S to point P must traverse an optical path length L that is stationary with respect to variations of this path. Thus, bi-colored graphs built of links corresponding to maxima or minima of optical paths become possible. Graphs, comprising six vertices, inevitably will demonstrate optical cycles, built of the mono-colored links corresponding to the maxima or minima of the optical path. The notion of the “inverse graph” is introduced and discussed. The total number of triangles in the “direct” (source) and “inverse” Ramsey optical graphs is the same, Optical interpretation of the infinite Ramsey Theorem is suggested.

Our image recognition system mainly judges whether the left upper limb in the image is the left upper limb or the right upper limb through our deep learning model in the image. The doctor then could give the correct surgical position. From the experimental results, it could be found that the precision rate and recall rate of the intelligent image recognition system proposed in this paper for preventing the upper limb dislocation surgery could reach 98% and 93%, respectively. It proved that our artificial intelligent image recognition system, AIIRS, could indeed assist orthopedic surgeons to prevent the occurrence of left and right dislocation in upper limb surgery. At the same time, this paper also completes the IRB application approval through the prototype experimental results and will conduct the second phase of human trials in the future. It showed that the research results of this paper will be of great benefit and research value to upper limb orthopedic surgery.

Our image recognition system mainly judges whether the left upper limb in the image is the left upper limb or the right upper limb through our deep learning model in the image. The doctor then could give the correct surgical position. From the experimental results, it could be found that the precision rate and recall rate of the intelligent image recognition system proposed in this paper for preventing the upper limb dislocation surgery could reach 98% and 93%, respectively. It proved that our intelligent image recognition system could indeed assist orthopedic surgeons to prevent the occurrence of left and right dislocation in upper limb surgery. At the same time, this paper also completes the IRB application approval through the prototype experimental results and will conduct the second phase of human trials in the future. It showed that the research results of this paper will be of great benefit and research value to upper limb orthopedic surgery.

Hypoplastic left heart syndrome (HLHS) is a severe congenital heart disease (CHD) affecting 1 in 5,000 newborns. We constructed the interactome of 74 HLHS-associated genes identified from a large-scale mouse mutagenesis screen, augmenting it with 408 novel protein-protein interactions (PPIs) using our High-precision Protein-Protein Interaction Prediction (HiPPIP) model. The interactome is available on a webserver with advanced search capabilities (http://severus.dbmi.pitt.edu/wiki-HLHS). 364 genes including 73 novel interactors were differentially regulated in tissues/iPSC-derived cardiomyocytes of HLHS patients. Novel PPIs facilitated the identification of TOR signaling and endoplasmic reticulum stress modules. 60.5% of the interactome consisted of housekeeping genes that may harbor large-effect mutations and drive HLHS etiology but show limited transmission. Network proximity of diabetes, Alzheimer’s disease, and liver carcinoma-associated genes to HLHS genes suggested a mechanistic basis for their comorbidity with HLHS. Interactome genes showed tissue-specificity for sites of extracardiac anomalies (placenta, liver and brain). The HLHS interactome shared significant overlaps with the interactomes of ciliopathy and microcephaly-associated genes, with the shared genes respectively enriched for genes involved in intellectual disability and/or developmental delay, and neuronal death pathways. This supported the increased burden of ciliopathy variants and prevalence of neurological abnormalities observed among HLHS patients with developmental delay and microcephaly respectively.

Hypertrophic Cardiomyopathy (HCM) is a common inherited disorder characterized by unexplained left ventricular hypertrophy, with or without left ventricular outflow tract (LVOT) obstruction. Single nuclei RNA-sequencing (snRNA-seq) of both obstructive and nonobstructive HCM patient samples have revealed alterations in communication between various cell types but a direct and integrated comparison between the two HCM phenotypes has not been reported. We performed a bioinformatic analysis of HCM snRNA-seq datasets from obstructive and nonobstructive patient samples to identify differentially expressed genes and distinctive patterns of intercellular communication. Differential gene expression analysis revealed 37 differentially expressed genes, predominantly in cardiomyocytes but also in other cell types, relevant to aging, muscle contraction, cell motility and the extracellular matrix. Intercellular communication was generally reduced in HCM, affecting the extracellular matrix, growth factor binding, integrin binding, PDGF binding and SMAD binding, but with increases in adenylate cyclase binding, calcium channel inhibitor activity, and serine-threonine kinase activity in nonobstructive HCM. Increases in neuron to leukocyte and dendritic cell communication, in fibroblast to leukocyte and dendritic cell communication and in endothelial cell communication to other cell types, largely through changes in expression of integrin-b1 and its cognate ligands, were also noted. These findings indicate both common and distinct physiological mechanisms affecting the pathogenesis of obstructive and nonobstructive HCM and provide opportunities for personalized management of different HCM phenotypes.

This article presents raw data of biaxial tensile measurements of rat heart passive myocardium conducted in lab scale environment. The passive myocardium of the rat was divided into three regions, namely: left ventricle, mid-wall and right ventricle. The biaxial dataset of passive rat myocardia is presented as stress vs strain of the passive rat myocardium in various regions. The determination of valid material properties of the heart plays an important role in the development computational models. These computational models are useful in studying various scenarios and mechanisms of heart diseases. In addition, valid and accurate materials are critical in the development of new therapies. The dataset presented here is useful in the area of soft tissue mechanics including studying the mechanisms of heart diseases such as myocardial infarction. Accordingly, the evaluation of stress and strain in left ventricle, mid-wall and right ventricle was performed.

The natural compounds PSK and PSP have antitumor and immunostimulant properties. These pharmacological benefits have been documented in vitro and in vivo, although there is not information in silico which describes the action mechanisms at molecular level. In this study, the inverse docking method was used to identify the interactions of PSK and PSP with two local databases: BPAT with 66 antitumor proteins, and BPSIC with 138 surfaces and intracellular proteins. This led to the identification interactions and coincidences of PSK and AB680 inhibitor in the active site of CD73. It was also found that PSK bonds to CD59 interacting with amino acids APS22 and PHE23, which coincide with the rlLYd4 internalization inhibitor. With the isoform of K-RAS protein, PSK bonded to the TYR32 amino acid at switch 1, while with BAK it bonded to the region of the α1 helix, while PSP bonded to the activation site and the C-terminal and N-terminal ends of that helix. In Bcl-2, PSK interacted at the binding site of the Venetoclax inhibitor, showing coincidences with amino acids ASP111, VAL133, LEU137, MET115, PHE112, and TYR108; while PSP had coincidences with THR132, VAL133, LEU137, GLN118, MET115, APS111, PHE112, and PHE104.

In this paper, we propose a system of nonlinear mixed variational inequality problems, which consists of two elliptic mixed variational inequality problems on Banach spaces. Under suitable assumptions, using the Kakutani-Ky Fan fixed point theorem and Minty techniques, we prove the solution set to the system of nonlinear mixed variational inequality problem is nonempty, weakly compact and unique. Additionally, we suggest a stability result for the system of nonlinear mixed variational inequality problem by perturbing the duality mappings. Furthermore, we present an optimal control problem governed by the system of nonlinear mixed variational inequality problems and establish a solvability result.

Living systems must solve the problem of realizing their environment to act appropriately to maintain external relationships and internal order for survival and reproduction. This problem is a biological version of the philosophical enigma of how the self can escape solipsism. This study develops a comprehensive model to solve this adaptation problem. LSs must be composed of material entities that have the property of detecting their external states. The detection of the outside is conceptualized as “cognition,” a related state change that occurs at three levels of nested hierarchy: physical, chemical, and semiotic cognitions. Any entity that cognizes the surroundings is a “cognizer.” The hierarchical extension of cognition to all levels of the world provides a monistic view that only cognizers exist. Semiotic cognition is essential for the emergence and evolution of life. Living systems invented semiotic cognitions based on physical and chemical cognitions to manage the probability distribution of events that occur to them. This study proposes a theoretical model in which semiotic cognition is an adaptive process in which inverse causality operations produce particular internal states as symbols that signify hidden external states. This operation makes the living systems aware of the external world.

Digital twin, an innovative technology propelled by data and models, plays a seminal role in the digital transformation and intelligent upgrade of ships. This study introduces a digital twin methodology for real-time monitoring of ship structure deformation fields, based on finite discrete strain data, and a visualization tool framework is developed using virtual reality technology. First, the inverse Finite Element Method (iFEM) is employed to derive the deformation field of the ship structure in real time via sensor strain data. Secondly, the deformation field data obtained based on the iFEM algorithm is converted into general visualization data conducive to interpretation within VR applications. Lastly, a digital twin software tool is built to enable synchronous response and interaction between the virtual scene and the physical scene, directly superposing particular virtual objects (data acquired by sensors, CAD virtual models, and deformation field cloud images) onto the physical scene in real-time. The digital twin tool embodies a virtual reality visualization system framework integrating physical data measurement, reconstruction, analysis, expression, storage, rendering and interaction of deformation field data. Through practical application, the flexibility, effectiveness and compatibility of the developed prototype tool are verified. According to the results, the system can enhance the efficiency of scientific communication, model validation, and interdisciplinary sharing during the analysis and evaluation of mechanical properties of ship structures.

Inverse optimal control is a method for recovering the cost function used in an optimal control problem in expert demonstrations. Most studies on inverse optimal control have focused on building the unknown cost function through the linear combination of given features with unknown cost weights, which are generally considered to be constant. However, in many real-world applications, the cost weights may vary over time. In this study, we propose an adaptive online inverse optimal control approach based on a neural-network approximation to address the challenge of recovering time-varying cost weights. We conduct a well-posedness analysis of the problem and suggest a condition for the adaptive goal, under which the weights of the neural network generated to achieve this adaptive goal are unique to the corresponding inverse optimal control problem. Furthermore, we propose an updating law for the weights of the neural network to ensure the stability of the convergence of the solutions. Finally, simulation results for an example linear system are presented to demonstrate the effectiveness of the proposed strategy. The proposed method is applicable to a wide range of problems requiring real-time inverse optimal control calculations

Diffuse optical tomography (DOT) is an optical medical imaging method that can assess the structural properties of tissues and their functional characteristics, such as hemoglobin concentration, water content, as well as lipid concentration, via three-dimensional image reconstruction. This paper presents the theoretical basis and working principle of diffuse optical tomography. The paper explains how the optical properties of tissue can be imaged by photon migration techniques based on diffusion theory. The author presents the reasoning for near-infrared (NIR) imaging as the most effective technique in terms of quantitative recovery of spectroscopic optical parameters. This work also listed various advantages, applications, and challenges of DOT. The paper also briefly discusses current progress in near-infrared medical imaging and its future direction.

One of matrix equalities composed of multiple products of matrices and their generalized inverses is given by $A_1B_1^{-}A_2B_2^{-} \cdots A_kB_k^{-}A_{k+1}= A$ where $A_1$, $B_1$, $A_2$, $B_2$, $\ldots$, $A_k$, $B_k$, $A_{k+1}$, and $A$ are given matrices of appropriate sizes, and $B_1^{-}$, $B_2^{-}$, $\cdots$, $B_k^{-}$ are generalized inverses of matrices. The cases for $k = 1, 2$ and their special forms were properly approached in the theory of generalized inverses of matrices. In this note, the author presents an algebraic procedure to derive explicit necessary and sufficient conditions for the equality with $k = 3$ to always hold using certain rank equalities for the block matrices constructed by the given matrices, and then mention a key step of extending the previous work to a general situation.

Automatic control to any of robot manipulators, some kind of issues are being observed. A numerical method for solution generation to the inverse kinematics problem of redundant robotic manipulators is presented to obtain the smoothest algorithm as possible, leading to a robust iterative method. After the primary objective of the reachability of end-effectors to the target point is achieved, the aim is set to resolve the redundant degrees of freedom of redundant manipulator. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configurations of the manipulator. In addition, this technique is computationally effective and able to apply for serial manipulators with any DOF applications. A planar 3R-DOF serial link redundant manipulator is considered as exemplar problem for solving. Also, the continuum approach for resolving more complex structure with variable DoF is illustrated here and their brief applicability to support surgeries and adaptive use of artificial linkage moments is also calculated.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

Interpolation is procedure that depends on spatial and/or statistical properties of analysed variable(s). It is special challenging task for data that included low number of samples, like dataset with less than 20 data. This problem is especially emphasized in the subsurface geological mapping, i.e. in the cases where data are taken solely from wells. Successful solutions of such mapping problems ask for knowledge about interpolation methods designed primarily for small datasets and dataset itself. Here are compared two methods, namely Inverse Distance Weighting and Modified Shepard’s Method, applied for three variables (porosity, permeability, thickness) measured in the Neogene sandstone hydrocarbon reservoirs (Northern Croatia). The results showed that pure cross-validation is not enough condition for appropriate map selection, but also geometrical features need to be considered, for datasets with less than 20 points.

Based on the Graph Model of Conflict Resolution (GMCR), a two-stage decision framework is developed to reveal the essence of brownfield incidents and facilitate the resolution of brownfield conflicts caused by the incidents. More particularly, the forward GMCR is utilized in Stage I, the negotiation stage, to simulate the evolution of a brownfield conflict (BC) and predict its potential resolution via stability analysis. If no acceptable equilibrium can be obtained, the BC progresses into Stage II, the third-party-intervention stage, where the inverse GMCR is used to assist a third party in intervening the conflict to achieve a desirable outcome. To illustrate the practicality of this framework, a recent BC occurred in Changzhou, China, is taken as a case study. Invaluable insights are provided through the computation and investigation of the corresponding preference relationships.

The article presents a cyber-physical system for acquiring, processing and reconstructing images from measurement data. The technology was based on process tomography, intelligent measurement sensors, machine learning, Big Data, Cloud Computing, Internet of Things as a solution for Industry 4.0. Industrial tomography enables observation of physical and chemical phenomena without the need of internal penetration and allows real-time monitoring of production processes. The application includes specialized intelligent devices for tomographic measurements and dedicated algorithms for solving the inverse problem. The work focuses mainly on electrical tomography and image reconstruction using deterministic methods and machine learning, the reconstruction results were compared, different measurement models were used. The researches were carried out for synthetic data and laboratory measurements. The main advantage of the proposed system is the possibility of spatial data analysis and their high processing speed. The presented research results show that the process tomography gives the possibility to analyse the processes taking place inside the facility without disturbing the production, analysis and detection of obstacles, defects and various anomalies. Knowing the characteristics of a given solution, the application allows you to choose the appropriate method to reconstruct the image.

The article presents a non-destructive test system based on electrical impedance tomography for monitoring flood embankments. The technology of cyber-physical systems and the Internet of Things with the use of electrical impedance tomography enables real-time monitoring of flood embankments. This solution provides a visual analysis of damage and leaks, which allows for quick and effective intervention and possible prevention of danger. A dedicated solution based on the IT structure, dedicated laboratory models and a dedicated measurement system with various types of sensors and machine learning algorithms for image reconstruction has been developed. The system includes specialized intelligent devices for tomographic measurements. The application contains the analysis of anomalies occurring in the structure of the object as a result of damage or danger and breaking the shaft during the flood. The presented solution enables ongoing monitoring of objects by collecting measurement results, forecasts and simulations. The main advantage of the proposed system is the spatial ability to analyse shafts, high accuracy of imaging and high speed of data processing. The use of tomographic techniques in conjunction with image reconstruction algorithms allow for non-invasive and very accurate spatial assessment of humidity and damages of flood embankments. The presented results show the effectiveness of the presented research.

The article presents the results of research on a new method of spatial analysis of walls and buildings moisture. Due to the fact that destructive methods are not suitable for historical buildings of great architectural significance, a non-destructive method based on electrical tomography has been adopted. A hybrid tomograph with special sensors was developed for the measurements. This device enables the acquisition of data, which are then reconstructed by appropriately developed methods enabling spatial analysis of wet buildings. Special electrodes that ensure good contact with the surface of porous building materials such as bricks and cement were introduced. During the research, a group of algorithms enabling supervised machine learning was analyzed. They have been used in the process of converting input electrical values into conductance depicted by the output image pixels. The conductance values of individual pixels of the output vector made it possible to obtain images of the interior of building walls, both flat intersections (2D) and spatial (3D) images. The presented group of algorithms has a high application value. The main advantages of the new methods are: high accuracy of imaging, low costs, high processing speed, ease of application to walls of various thickness and irregular surface. By comparing the results of tomographic reconstructions, the most efficient algorithms were identified.

Right-sided ligamentum teres (RSLT) is a rare anatomic variant in which the fetal umbilical vein connects to the right portal vein. Patients with RSLT frequently have hepatic vasculature and bile duct anomalies, which increase the risk of complications with hepatectomy. Most patients with RSLT undergo open hepatectomy. We describe a patient with RSLT and hepatocellular carcinoma who underwent laparoscopic hepatectomy. The patient was a 69-year-old man with hepatocellular carcinoma located in the left liver based on computed tomography (CT) and magnetic resonance imaging. Imaging also demonstrated RSLT. Three-dimensional CT analysis revealed independent right lateral type anomalies of the portal vein and bile duct. Laparoscopic extended left lateral sectionectomy was performed after careful surgical planning. Ultrasonography was used frequently during surgery to avoid damaging the right hepatic vasculature. The left lateral and partial left median sections were removed as planned. The patient’s postoperative recovery was uneventful. Avoiding injury to the right hepatic vasculature is essential when performing left lobectomy, including left lateral sectionectomy, in patients with RSLT. Laparoscopic hepatectomy can be performed safely in patients with RSLT, provided that careful surgical planning is conducted using preoperative three-dimensional CT analysis and intraoperative ultrasonography is used.

Rationale: The 14-3-3 protein family is known to interact with many proteins in non-cardiac cell types to regulate multiple signaling pathways, particularly those relating to energy and protein homeostasis; and the 14-3-3 network is a therapeutic target of critical metabolic and proteostatic signaling in cancer and neurological diseases. Although the heart is critically sensitive to nutrient and energy alterations, and multiple signaling pathways coordinate to maintain the cardiac cell homeostasis, neither the structure of cardiac 14-3-3 protein interactome, nor potential functional roles of 14-3-3 protein-protein interactions (PPIs) in heart has been explored. Objective: To establish the comprehensive landscape and characterize the functional role of cardiac 14-3-3 PPIs. Methods and Results: We evaluated both RNA expression and protein abundance of 14-3-3 isoforms in mouse heart, followed by co-immunoprecipitation of 14-3-3 proteins and mass spectrometry in left ventricle. We identified 52 proteins comprising the cardiac 14-3-3 interactome. Multiple bioinformatic analyses indicated that more than half of the proteins bound to 14-3-3 are related to mitochondria; and the deduced functions of the mitochondrial 14-3-3 network are to regulate cardiac ATP production via interactions with mitochondrial inner membrane proteins, especially those in mitochondrial complex I. Binding to ribosomal proteins, 14-3-3 proteins likely coordinate protein synthesis and protein quality control. Localizations of 14-3-3 proteins to mitochondria and ribosome were validated via immunofluorescence assays. The deduced function of cardiac 14-3-3 PPIs is to regulate cardiac metabolic homeostasis and proteostasis. Conclusions: Thus, the cardiac 14-3-3 interactome may be a potential therapeutic target in cardiovascular metabolic and proteostatic disease states, as it already is in cancer therapy.

The paper proposes an approach to solving the inverse epidemiological problem, written in terms of the “mean field” theory. Finding the coefficients of the epidemiological SIR mean field model is reduced to solving an optimization problem, for the solution of which only zero-order methods can be used. The Nelder-Mead method was chosen as such a method. The algorithm for solution of the inverse coefficient problem is proposed. Computational experiments were carried out to compare the obtained solutions with respect to synthetic and real data. The results of computational experiments have shown the efficiency of this approach. Ways to further improve the approach have also been determined.

Laboratory experiments and investigations into natural phenomena in this research series have unveiled the presence of a gravitational repulsion force that permeates our environment on both microscopic and macroscopic scales, contingent upon the thermal energy present. This paper presents a study exploring novel properties of gravitational forces among gas molecules, employing principles of thermodynamics. A model has been devised based on the interactions between pairs of gas molecules. While traditional models treat gravitational interaction as a singular force, our experimental approach validates it as the composite of two distinct forces: gravitational repulsion and attraction. By utilizing established experimental data on gas thermodynamics, our model demonstrates robust performance both analytically and experimentally. It verifies the coexistence of gravitational repulsion and attraction forces among gas molecules, showcases their Inverse-Cube relationship with distance, and elucidates the direct proportionality of the repulsion force to absolute temperature. This bridges a crucial gap between energy and fundamental forces. The order of magnitudes of gravitational repulsion and attraction forces are found to be considerably large, contrasting with the low values predicted by classical theory, which results from their amalgamation. Recognizing these forces as substantial in magnitude promises unprecedented outcomes and advancements.

The available direct gas dynamic tables provide the area ratio and the Prandtl-Meyer(P-M) angle of isentropic expansion of gas as functions of the Mach number. But finding the value of the Mach number in terms of area ratio or P-M angle requires an inverse function. Currently, the Mach number is determined by either interpolation from the direct gas dynamics tables, or the application of non-linear equation solvers using numerical methods. Both methods are approximate. In this paper inverse functions for Mach number in the form of Taylor’s series expansions are reported to develop the so-called inverse tables. The advantage of this approach is that the Mach number with a greater accuracy, referred to as nearly exact can be obtained by reading from the inverse table. In the presentation, the necessary equations and new tables that can be used by the scientific community will be disseminated. The data and computer programs are made available on GitHub through https://github.com/anillals/Inverse-gas-dynamic-tables- and-codes. A paper describing the complete mathematical steps in the derivation of the equations can be found at https://rdcu.be/dgrlf

In this paper, we introduce as a pedagogical strategy an internal division-free, straightforward, and symmetrically progressing algorithm in manually computing matrix inverse and solving systems of linear equations by revisiting the application of elementary row operations in the Gauss-Jordan reduction method and connecting it to the determinant method. The proposed cross-multiplication-flip (CMF) algorithm employs cross-multiplication similar to the butterfly movement in computing determinants as a strategic application of elementary row operations to efficiently reduce the rows and then applies flipping of rows and entries to put an upper triangular matrix into lower triangular form to continue the reduction process.

In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.

Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The problem is reduced to a linear algebraic system with a nondegerate matrix.

As an implementation of inverse Radon transform, the Second-order Divided-difference Back Projection (SDBP) technique has been proposed in this paper, by which the accurate CT reconstruction can be theoretically realized. A computational model for CT reconstruction filter expressions has been derived on the basis of SDBP technique. The method reveals the correlation between the convolution kernel for data restoration and the filter expression. By substituting kernel functions into the computational model, the amplitude sequences of a variety of filters can be calculated. On the proposed filter construction method, the decomposition form of filters has been discovered, where a series of basic filters have been acquired. The properties of any filter depend on the decomposed basic filters. Basic filters can be used to compose filters in actual needs.

The nonlocal boundary value problem, dtρu(t)+Au(t)=f(t) (0&lt;ρ&lt;1, 0&lt;t≤T), u(ξ)=αu(0)+φ (α is a constant and 0&lt;ξ≤T), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operator A, is considered. The operator dt on the left hand side of the equation expresses either the Caputo derivative or the Riemann-Liouville derivative; naturally, in the case of the Riemann - Liouville derivatives, the nonlocal boundary condition should be slightly changed. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence of a solution to problems is investigated. Inequalities of coercivity type are obtained and it is shown that these inequalities differ depending on the considered type of fractional derivatives. The inverse problems of determining the right-hand side of the equation and the function φ in the boundary conditions are investigated.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

The application of instrumented indentation to assess material properties like Young’s modulus and micro-hardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e. kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress-strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress-strain-curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-non-destructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

Despite their obvious differences, biological systems at different scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are usually obscured by the parcelled terminology employed by various scientific sub-disciplines. To explore these commonalities, this papers a comparative study of diverse applications of the maximum entropy principle, ranging from amino acids up to societies. By presenting these studies under a common language, this paper establishes a unified view over seemingly highly heterogeneous biological scenarios.

In laser-assisted milling, higher temperature in shear zone softens the material potentially resulting in a shift of mean residual stress, which significantly affects the damage tolerance and fatigue performance of product. In order to guide the selection of laser and cutting parameters based on the preferred mean residual stress, inverse analysis is conducted by predicting residual stress based on guessed process parameters, which is defined as the forward problem, and applying iterative gradient search to find process parameters for next iteration, which is defined as the inverse problem. An analytical inverse analysis is therefore proposed for the mean residual stress in laser-assisted milling. The forward problem is solved by analytical prediction of mean residual stress after laser-assisted milling. The residual stress profile is predicted through the calculation of thermal stress, by treating laser beam as heat source, and plastic stress by first assuming pure elastic stress in loading process, then obtaining true stress with kinematic hardening followed by the stress relaxation. The variance-based recursive method is applied to solve inverse problem by updating process parameters to match the measured mean residual stress. Three cutting parameters including depth of cut, feed per tooth, and cutting speed, and two laser parameters including laser-tool distance and laser power, are updated with respected to the minimization of resulting residual stress and measurement in each iteration. Experimental measurements are referred on the laser-assisted milling of Ti-6Al-4V grade 5 and ELI. The percentage difference between experiments and predictions is less than 5% for both materials, and the selection is completed within 50 loops.

Hypertrophic cardiomyopathy (HCM) is a common form of cardiomyopathy in cats, and heart failure occurs as diastolic dysfunction progresses. HCM in cats is broadly classified as non-obstructive and obstructive hypertrophic cardiomyopathy, depending on the presence or absence of outflow tract obstruction. Measurement of the intraventricular pressure differences (IVPD) using Color M-mode (CMM) has attracted attention as a reliable diastolic index as it correlates with catheterization, the gold standard for assessment of diastolic performance. Since, IVPD is affected by the size of the heart, the intraventricular pressure gradient (IVPG) index, which is unaffected by heart size, is used by dividing IVPD be LV length. In the present study, CMM IVPG was used to non-invasively assess diastolic impairment in cats with obstructive hypertrophic cardiomyopathy. This study was conducted on ten control cats and 18 cats in the HCM group. Although no severe left atrial enlargement was observed in the HCM group, the Basal IVPG was significantly increased in the HOCM group compared to the control group. While IVPD typically suggests impaired diastolic function and reduced ventricular compliance, the significant increase observed in the HOCM group compared to controls may suggest an indirect elevation in left atrial pressure, likely secondary to left ventricular outflow tract obstruction. The increase in IVPG in HOCM, as shown in this study, is a pathological effect of left ventricular outflow tract obstruction that cannot be detected by conventional echocardiographic indices, and evaluating IVPG is useful for evaluating cardiac function from a different perspective than conventional methods.

To clarify the risk factors for aggravation of esophagogastric varices (EGV) after hepatitis C virus (HCV) eradication with direct-acting antiviral (DAA) therapy, we enrolled 167 consecutive patients with HCV-related compensated cirrhosis who achieved a sustained virological response (SVR) after DAA therapy. During a median of 69 months, EGV was aggravated in 42 (25%) patients despite SVR. The cumulative 1, 3, 5, and 10-year aggravated EGV rates were 7%, 23%, 25%, and 27%, respectively. Multivariate analysis identified platelet count <11.0×10⁴/μL, LSM ≥18.0 kPa, total bile acid ≥33.0 μmol/L, and diameter of left gastric vein (LGV) ≥5.0 mm at HCV eradication as independent risk factors for EGV aggravation post-SVR. In groups that meet all of these risks, the cumulative EGV aggravation rates at 1, 3, and 5 years were 27%, 87%, and 91%, respectively. However, none of the patients who had only one or none of the risk factors experienced EGV aggravation. Platelet count, LSM, total bile acid, and diameter of LGV at HCV eradication were associated with aggravated EGV post-SVR. EGV tends to worsen as two or more of these risk factors increase.

The impact of systemic vascular resistance (SVR) in hypertrophic (HCM) and amyloid cardio-myopathies has been seldom investigated. We studied pressure-strain loop derived myocardial work (MW) indices and SVR in patients with either sarcomere HCM or wild type transthyretin cardiac amyloidosis (ATTR), presented with heart failure and preserved left ventricular ejection fraction (HFpEF) at the outpatient cardiology units at Messina and Catania University Hospitals (Italy). Patients were in sinus rhythm and needed to have good transthoracic ultrasound imaging quality to undergo transthoracic strain-echocardiography. Other than conventional parameters, SVR and GWI (global work index) were measured. Based on cross-tabulation (a way to assess the ventricular-arterial coupling), the patients were then classified in 4 classes according to the cut-off values suggested by previous studies of 1,440 dyne/s/cm-5 for SVR (Stefadouros et al., 1973) and 1576 mm Hg% for GWI (Olsen et al., 2022). Sixty patients, 30 in each group, aged 61±16 years, 78% males, were studied. HCM were younger than ATTR patients and in a better clinical status (23% HCM vs 77% ATTR were NYHA class 3, p<0.001). Overall, 51 patients (85%) showed high SVR, of whom 21 were HCM (70%) and 30 ATTR (100%) (p<0.005). Both, SVR and GWI were impaired (the poorest class C) in 43% HCM patients (with greater left ventricular concentric hypertrophy) vs 93% of ATTR patients (in advanced NYHA class) (p<0.001). In conclusion, assessing SVR and GWI in HFpEF patients with HCM or ATTR can help clinicians to interpret the pathophysiological and clinical features of such complex diseases.

Hypoxia can induce pulmonary edema (PE) and inflammation. Furthermore, hypoxia depresses left ventricular (LV) inotropy despite sympathetic activation. Here, we investigated the role of nitrosative stress and cardiovascular dysfunction in hypoxic lung injury. Additionally, we studied effects of adrenergic blockade (AB) on hypoxia-induced pulmonary injury. Eighty-six female rats were exposed for 72 h to normoxia or normobaric hypoxia and received infusions with NaCl, prazosin, propranolol or prazosin-propranolol combination. We evaluated hemodynamic function and performed histological and immunohistochemical analyses of the lung. Hypoxia significantly depressed LV but not right ventricular (RV) inotropic and lusitropic functions. AB significantly decreased LV function both in normoxia and hypoxia. AB effects on RV were weaker. Hypoxic rats showed signs of moderate PE and inflammation. This was accompanied by elevated levels of tumor necrosis factor (TNF)  and nitrotyrosine, a marker of nitrosative stress in the lungs. In hypoxia, all types of AB significantly reduced both TNF and nitrotyrosine to normoxic levels. However, AB did not attenuate PE. Results suggest that hypoxia-induced sympathetic activation contributes to inflammation and nitrosative stress in the lungs but not to PE. We suggest that AB in hypoxia aggravates hypoxia-induced inotropic LV dysfunction and backlog into pulmonary circulation, thus promoting PE.

In this paper, the neural network is developed for solving the inverse photoacoustic problem aiming to estimate thermo-elastic properties and thickness of a semiconductor sample. The idea was that these sample properties be estimated from the phase characteristic because the phase measurements are more sensitive. The neural network has been trained on a large basis of photoacoustic phases calculated from a theoretical Si n-type model in the range of 20Hz to 20kHz, on which random Gaussian noise has been applied. It is shown that high accuracy and precision could be reached in solving of inverse photoacoustic problem using only phase measurement.

The growing expansion of the economy and population has resulted in an increased inclination towards the utilization of groundwater resources. Conducting a geophysical survey is a widely employed method for subsurface mapping and the detection of groundwater. A geophysical study was conducted in Nanshan township, Huarong County, located in the Hunan province of the South-Central region of China. The investigation involved the utilization of a 2D Electrical Resistivity Imaging technique employing forward and inverse pole-dipole electrode array. A total of six survey lines were established, each with an electrode distance from the nearest measuring point to exceeding 800 m. The maximum current electrode separation was utilized in this setup. The spacing between the electrical resistivity sounding points was established at regular intervals. The findings from the exploration indicate the existence of multiple faults within the surveyed region. The study additionally identified two regions of structural failure, which occurred due to the convergence of faults oriented in different directions. This convergence led to the fracturing of rocks, an increase in water content, and a decrease in resistivity. The findings from the exploration were utilized in the formulation of five verification target boreholes. The results of this study offer significant insights that can inform future investigations into groundwater exploration endeavors within the region.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*&gt;0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

Australia is a unique continent surrounded by the ocean and the majority of catchments flow to the coast. Some of these catchments are gauged and others are ungauged. There are 405 gauged catchments covering 2,549,000 km2 across the coastal regions of 12 drainage divisions in Australia. Whereas there are 771 catchments conceptualised as ungauged covering additional 835,000 km2. The mean annual rainfall and PET and its spatial and temporal distribution vary significantly from one drainage division to another. We developed a continuous daily streamflow time series of all gauged and ungauged catchments from 1993 onwards. We applied the GR4J lumped conceptual model to these catchments. The performance of gauged catchments was analysed through (i) visual inspection of daily hydrographs, flow duration curves and daily scatter plots, and (ii) performance metrics including NSE and PBias. Based on the NSE and PBias, performance ratings of 80% and 96% of the models respectively were found 'good'. There was no relationship found between the catchment area and model performance. The ungauged catchments were divided into four categories based on distance from potential donor catchments where observed data are available for GR4J model calibration, and Köppen climate zone. The total ungauged catchments represent 24.7% of the total drainage division areas. The streamflow from ungauged catchments was estimated using GR4J model based on the parameters of their donor catchments. Overall, runoff ratios from ungauged catchments were found to be higher compared to their donor gauged catchments, likely driven by their higher rainfall and less PET. This tendency was particularly evident in two drainage divisions – the Carpentaria Coast (CC) and Tanami-Timor Sea Coast (TTS) where ungauged areas comprised 51% and 43% respectively. The mean gauged annual streamflow varied significantly across drainage divisions – 230 GL from South Australian Gulf (SAG) to 146,150 GL in TTS. The streamflow from all ungauged catchments was estimated at 232,200 GL per year. Overall, the average streamflow from all drainage divisions, including gauged and ungauged areas, across the coastal regions of Australia was estimated at 419,950 GL per year. This nationwide estimate of streamflow dataset could potentially enhance our understanding of coastal processes and improvements of marine modelling systems and tools.

In the broad field of Inverse Analysis and Structural Identification, it is nowadays of a large interest the study of Gaussian Processes, as a reliable and efficient optimisation method, particularly helpful toward the identification of a global optimum point, under the conditions of complicated functions to be optimised. In the present contribution, a specific case study is considered, focusing on a historical road reinforced concrete arched bridge, located in Northern Italy, employing dynamic modal properties, deciphered from in-situ measurements, previously acquired under operational traffic conditions, by a standard wired accelerometer system, placed at the deck level. Aiming at the identification and diagnosis of the bridge structure, three main methodological steps are herein considered: the adoption of a FEM model of the structure (in the linear dynamic framework), the definition of an appropriate discrepancy function, based on measured and numerically computed quantities (natural frequencies and mode shapes of the bridge), and the investigation of such a discrepancy function, toward a consistent selection of an optimisation strategy for the identification of sought parameters (Young’s moduli and mass densities of diverse elements of the structure). The presented developments, within the framework of methodological optimisation approach by Gaussian Processes, and achieved results display a rather efficient perspective, with reference to the considered case study, toward inverse analysis for structural diagnosis, in the context of strategic (historical) infrastructures.

The inverse Finite Element Method (iFEM) is a model-based technique to compute the displacement (and then the strain) field of a structure from strain measurements and a geometrical discretization of the same. Different literature works exploit the error between the numerically reconstructed strains and the experimental measurements to perform damage identification in a Structural Health Monitoring framework. However, only damage detection and localization are performed, without attempting a proper damage size estimation. The latter could be based on machine learning techniques, however, an a priori definition of the damage conditions would be required. To overcome these limitations, the present work proposes a new approach in which the damage is systematically introduced in the iFEM model to minimize its discrepancy with respect to the physical structure. This is performed with a maximum likelihood estimation framework, where the most accurate damage scenario is selected among a series of different models. The proposed approach is experimentally verified on an aluminum plate subjected to fatigue crack propagation, which enables the creation of a Digital-Twin of the structure itself. The strain field fed to the iFEM routine is experimentally measured with an Optical Backscatter Reflectometry fiber and the methodology is validated with independent observations of lasers and the Digital Image Correlation.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

Spiral galaxies and their rotation curves have key characteristics of differentially spinning objects. Oblate spheroid shapes are a consequence of spin and reasonably describe galaxies, indicating that their matter is distributed in gravitationally interacting homeoidal shells. Previously published equations describing differentially spinning oblate spheroids with radially varying density are here applied to 51 galaxies, mostly spirals. A constant volumetric density (rho, kg m-3) is assumed for each thin homeoid in these formulae, after Newton, which is consistent with RC being reported simply as a function of equatorial radius r. We construct parameter-free inverse models that uniquely specify mass inside any given r, and thus directly constrain rho vs. r solely from velocity v(r) and galactic aspect ratios (assumed as 1:10 when data are unavailable). Except for their innermost zones, rho is proven to be closely proportional to rn, where n for all 36 spirals studied equals -1.80±0.40. Our values for interior densities compare closely with independently measured baryon density in appropriate astronomical environments: for example, calculated rho at galactic edges agrees with estimated rho of intergalactic media (IGM). Our finding that central densities increase with galaxy size is consistent with behavior exhibited by diverse self-gravitating entities. Our calculated mass distributions are consistent with visible luminosity and require no non-baryonic component. Empirical luminosity-velocity relationships for galaxies, such as the Tully-Fisher rule, originate in Newtonian physics.

An inverse aeroacoustic problem for a helicopter rotor combined with aerodynamic constraint is proposed based on Ffowcs Williams and Hawkings equation in subsonic. The rotor noise includes thickness noise and loading noise when quadrupole noise is neglected. Thickness noise is related to geometry and motion conditions. Loading noise is related to the pressure on the wall. Therefore, the equation between pressure on the wall and far-field noise can be established, thus the pressure on the wall can be obtained by solving this equation. Since this equation is an ill-posed, the singular value decomposition combined with the regulation method is applied and the aerodynamic constraint is taken into account. The direct noise prediction is verify firstly and then the inverse problem is solved. The reconstruction pressure is compared to the input data. The result is in good agreement with the input value. At the same time, the influence of interference noise is also considered. Under low signal-to-noise ratio, the reconstruction result is also reasonable.

Transformer models have emerged as frontrunners in the field of natural language processing, primarily due to their adept use of self-attention mechanisms to grasp the semantic linkages between words in sequences. Despite their strengths, these models often face challenges in single-task learning scenarios, particularly when it comes to delivering top-notch performance and crafting strong latent feature representations. This challenge is more pronounced in the context of smaller datasets and is particularly acute for under-resourced languages such as Arabic. In light of these challenges, this study introduces a novel methodology for text classification of Arabic texts. This method harnesses the newly developed Reverse Positional Encoding (RPE) technique. It adopts inductive-transfer learning (ITL) framework combined with a switching self-attention shared encoder, thereby increasing the model's adaptability and improving its sentence representation accuracy. The integration of Mixture of Experts (MoE) and Reverse Positional Encoding (RPE) techniques empowers the model to process longer sequences more effectively. This enhancement is notably beneficial for Arabic text classification, adeptly supporting both the intricate five-point and the simpler ternary classification tasks. The empirical evidence points to its outstanding performance, achieving accuracy rates of 87.20% for the HARD dataset, 72.17% for the BRAD dataset, and 86.89% for the LABR dataset, as evidenced by the assessments conducted on these datasets.

Heart failure with reduced ejection fraction (HFrEF) is considered a major healthcare problem with frequent decompensations, high hospitalization and mortality rates. In severe heart failure (HF), the symptoms are refractory to medical treatment and require advanced therapeutic strategies. Early recognition of HF sub- and decompensation is the cornerstone of the timely treatment intensification and, therefore, improvement of the prognosis. Echocardiography is the gold standard for the assessment of systolic and diastolic functions. It allows to obtain accurate and non-invasive measurements of the ventricular function in HF. In severely compromised HF patients, advanced cardiovascular ultrasound modalities may provide a better assessment of intracardiac hemodynamic changes and subclinical congestion. Particularly, cardiovascular and lung ultrasound allow to make a more accurate diagnosis of subclinical congestion in HFrEF. The aim of this review is to summarize the advantages and limitations of currently available ultrasound modalities in the ambulatory monitoring of patients with HFrEF.

In this paper, we propose the definition of block tensors and the real representation of tensors. Equipped with the simplification method, i.e., the real representation along with the M-P inverse, we demonstrate the conditions that are necessary and sufficient for the system of dual split quaternion tensor equations (A*NX,X*SC)=(B,D) when its solution exists. Furthermore, the general expression of the solution is also provided when the solution of the system exists and we use a numerical example to validate it in the last section. To the best of our knowledge, it is the first time that the aforementioned tensor system has been examined on dual split quaternion algebra. Additionally, we provide its equivalent conditions when its Hermitian solution X=X* and η-Hermitian solutions X=Xη* exist. Subsequently, we discuss two special dual split quaternion tensor equations. Last but not least, we propose an application for encrypting and decrypting two color videos and we validate this algorithm through a specific example.

In this paper, we introduce generalized entropy, the acceleration of its entropy and its the partial entropy. We assume that generalized entropy can be expressed as a second-order polynomial by applying the idea of logistics function to its entropy. In other words, we assume that the acceleration of generalized entropy is a constant. Besides, we show that the negative inverse of the partial entropy can express Newton's gravity, which is an inverse square law. By applying these concepts, we attempt to explain that 1) Gravity is constant within small distances with some conditions. It is possible that gravity have 5-states within small enough distance. There is possible anti-force, which is the opposite of Newtonian gravity Among the 5-states. Furthermore, within small distance, we show the possibility that the gravitational potential and the Coulomb potential can be treated in the same way, that 2) The rotation speed of a galaxy does not depend on its radius if the radius is within the size level of the universe. (The galaxy rotation curve problem), and that 3) The gravitational acceleration toward the center changes at long distances compared to the Newton's gravity. We show that it is an extension of Newton's gravity. Furthermore, we show that the possibility of the existence of some constants which controls gravity and the speed of galaxies, and that gravity may relate on entropy.

This article presents a novel resolution of the Collatz Conjecture, centered on the concept of Generative Completeness of the inverse Collatz function. We introduce and rigorously prove that for all N ∈ ℕ⁺, there exists a minimal generator m_N = 1 such that all positive integers up to N can be generated through successive applications of the inverse Collatz function G. This key property, which we term "Generative Completeness", forms the cornerstone of our proof. Building upon this foundation, we establish several crucial results: The boundedness of all Collatz sequences The existence and uniqueness of cycles in Collatz sequences The nature of the unique cycle as {1, 4, 2} We then present three distinct approaches to resolving the Collatz Conjecture, all fundamentally rooted in the Generative Completeness property. These diverse methods not only prove the conjecture but also provide deep insights into the structure of Collatz sequences.

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of dual-phase-lag heat conduction model with the Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag-Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

The Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and ensure that the predictions are consistent and stable with the physical laws. PINNs opens up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar-Gross-Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts the equilibrium control equations in different discrete velocity directions within SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling inference of the fluid's non-equilibrium characteristics. The third component, a physics informed function translates the outputs of the first two networks into physical infor-mation. By minimizing the residuals of the physical partial differential equations (PDEs), the physics informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models applicable to different dimensions, named PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physical informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into the neural network through the interpretation function. Therefore, PINN-SRT-LBM allows the neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Experimental results confirm the accurate prediction of flow infor-mation at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

In the context of Inverse Analysis in Civil Engineering, parameter identification and model calibration, of a structural system, relying on dynamic measurements, are subjects of a growing research interest. In the present contribution, the topic is tackled with reference both to simplified structural numerical examples and to a specific case study, namely a historical road three-span reinforced concrete arched bridge, with vibrational data previously acquired by standard wired accelerometers on the deck, under operational traffic conditions. In particular, the present work aims at focussing on the identification issues, concerning the definition of a maximum allowable threshold number of sought material parameters (e.g., Young’s moduli and mass densities of different structural components), with respect to the amount of available measurement data, and the investigation of the inverse analysis discrepancy function to be optimised, in order to set the intrinsic issue of multiple “realizations”, in case of a plain use of modal properties, and in view of forming a well–posed optimisation problem. Structural modelling, sensitivity analysis and numerical optimisation approaches are herein combined toward a robust and efficient identification strategy, to be effectively employed in structural assessment and diagnosis, also with respect to originally available or enriched sets of experimental data. The proposed methodology, and collected results, shall outline an efficient identification procedure, in view of automated inverse analysis, practically oriented to the dynamic assessment and structural diagnosis in the Civil Engineering context, as applied e.g. to strategic bridge infrastructures.

Universal gravitation is investigated with principles of foundational classical (Newtonian) physics. The results reveal gravitation an atomic field action; hence, Newton’s law, although absolutely valid, unavoidably misleads in creating the impression of matter rather than waveform action. Six force constants fully define gravitation: (i) a waveform torque field ; (ii) an expansion force field ; (iii) a centripetal force field ; (iv) a matter-wave torque field (the force fields , and constitute gravitational inertial rest frame); (v) a Galilean acceleration field and (vi) nuclear inverse mass-squared centripetal force constant The inertial rest frame force constants sum up to give observational G = 2.266 + 2.61 + 2.61cos46^o) x 10^-11 = 6.689 x 10^-11 m³ kg^-1 s^-2. Notably, the procedure is able to account also for observational inclination of galaxies and their aligned conjunctions. An attempt is made to account for angular momentum quantization and rectilinear, parabolic or elliptic profile of objects in gravitational acceleration. Same quantitative expression, , defines the photon and gravitation thus uniquely unifying gravitation, electricity and magnetism; furthermore, the expression reveals the photon packed with tremendous energy amounting to some . It is argued that: (i) neither mass nor gravitation curves spacetime; (ii) the principles that sustain cosmic time-scale dynamic equilibrium, scale invariance and inertia are incompatible with quantum gravitation; and (iii) the cosmic vacuum field comprises gravitational (photonic) waves, hence the interferometer likely measures shock waves.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

This paper describes a new approach that can be used to determine the mechanical properties of unknown materials and complex material systems. The approach uses inverse finite element modelling (FEM) accompanied with a designed algorithm to obtain the modulus of elasticity, yield stress and strain hardening material constants of an isotropic hardening material model, as well as the material constants of the Drucker-Prager material model (modulus of elasticity, cap yield stress and angle of friction). The algorithm automatically feeds the input material properties data to finite element software and automatically runs simulations to establish a convergence between the numerical loading-unloading curve and the target data obtained from continuous indentation tests using common indenter geometries. A further module was developed to optimise convergence using an inverse FEM analysis interfaced with a non-linear MATLAB algorithm. A sensitivity analysis determined that the dual Spherical and Berkovich (S&B) approach delivered better results than other dual indentation methods such as Berkovich and Vickers (B&V) and Vickers and Spherical (V&S). It was found that better convergence values can be achieved despite a large variation in the starting parameter values and / or material constitutive model and such behaviour reflects the uniqueness of the dual S&B indentation in predicting complex material systems. The study has shown that a robust optimization method based on a non-linear least-squares curve fitting function (LSQNONLIN) within MATLAB and ABAQUS can be used to accurately predict a unique set of elastic plastic material properties and Drucker-Prager material properties. This is of benefit to the scientific investigation of properties of new materials or obtaining the material properties at different location of a part which might be not be similar due to manufacturing processes (e.g. different heating and cooling rates at different locations).

In this paper, some mixed type bounds on the spectral radius $\rho(A\circ B)$ for the Hadamard product of two nonnegative matrices ($A$ and $B$) and the minimum eigenvalue $\tau(C\star D)$ of the Fan product of two $M$-matrices ($C$ and $D$) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several $M$-matrices is also presented: $$ \tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq n}\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\}, $$ where $A_{1},\ldots, A_{k}$ are $n\times n$ $M$-matrices and $P_{1},\ldots, P_{k}>0$ satisfy $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$. Some special cases of the above result and numerical examples show that this new bound improves some existing results.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.