The deep energy method (DEM), a type of physics-informed neural network, is evolving as an alternative to finite element analysis. This method employs the principle of minimum potential energy to predict deformations under static loading conditions. However, the model’s accuracy is contingent upon choosing the appropriate architecture for the model, which can be challenging due to the high interactions between hyperparameters, large search space, difficulty in identifying objective functions, and non-convex relationships with the objective functions. To improve DEM’s accuracy, we first introduce random Fourier feature (RFF) mapping. RFF mapping helps with the training of the model by reducing bias towards high frequencies. The effects of six hyperparameters are then studied under compression, tension, and bending loads in planar linear elasticity. Based on this study, a systematic automated hyperparameter optimization approach is proposed. Due to the high interaction between hyperparameters and the non-convex nature of the optimization problem, Bayesian optimization algorithms are used. The models trained using optimized hyperparameters and having Fourier feature mapping can accurately predict deflections compared to finite element analysis. Additionally, the deflections obtained for tension and compression load cases are more sensitive to variations in hyperparameters than bending.

A multiscale mathematical model is proposed seeking to study the propagation dynamics of the Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through sexual contact without protection, considering the use of antiretroviral therapy (ART) and therapeutic failure. The model consists in a scale-free complex network that follows a power law, coupled with the immunological dynamics of each individual, that is, it considers the infection by the virus in the immune system of each HIV carrier, through a system of non-linear differential equations that govern the infection’s behavior in the immune system. Propagation of the virus in the network is modelled by taking into account information from the immunological status of each person. The study found that for a population to have high HIV prevalence, it is not necessary at the beginning of the simulation time for the virus to propagate rapidly. In addition, the study proves that with a higher number of sexual partners, there will be greater prevalence of HIV in the population and that the use of ART helps to control the propagation of the infection in the population. As an interesting result, it was also found that there is a higher number of HIV carriers who abandon ART than those who have access to it.

G protein-coupled receptor 15 (GPR15, also known as BOB) is an extensively studied orphan GPCR involving HIV infection, colonic inflammation and smoking-related diseases. Recently, GPR15 was deorphanized and its corresponding natural ligand demonstrated an ability of inhibiting cancer cell growth. However, no study reported the potential role of GPR15 in a pan-cancer manner. Using large-scale publicly available data from the Cancer Genome Atlas (TCGA) and the Genotype-Tissue Expression (GTEx) databases, we found that GPR15 expression is significantly lower in colon adenocarcinoma (COAD) than in normal tissues. And among 33 cancer types, GPR15 expression is significantly correlated with the prognoses of COAD, neck squamous carcinoma (HNSC), lung adenocarcinoma (LUAD) positively and stomach adenocarcinoma (STAD) negatively. This study also revealed that commonly upregulated gene set in the high GPR15 expression group (stratified via median) of COAD, HNSC, LUAD and STAD are enriched in immune systems, indicating that GPR15 might be considered as a potential target for cancer immunotherapy. Furthermore, we modelled the 3D structure of GPR15 and conducted the structure-based virtual screening. The top 8 hits compounds were screened and then subjected to molecular dynamics (MD) simulation for stability analysis. Our study provided novel insights into the role of GPR15 in a pan-cancer manner and discovered a potential hit compound for GPR15 antagonists.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

We enhance Frobenius' method for solving linear ordinary differential equations about regular singular points. Key to Frobenius' approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-zero integer. We demonstrate the method on Bessel's equation and derive previously unknown tandem recurrence relations for coefficients of solutions of the second kind, for Bessel equations of all integer and half-integer order.

Purpose – Extend the Blade Element Momentum Theory (BEMT) such that rotors with pronounced cone and axis angle (tilt or yaw) can be calculated. Derive an equation for the speed ratio (lambda) as a function of Tip Speed Ratio (TSR), radius, blade, cone and axis angle. This converts the BEMT into an Unsteady BEMT or UBEMT. Present the Wagner rotor as one such rotor geometry. --- Methodology – Literature review and calculations. --- Findings – The UBEMT can be used to calculate highly unconventional rotor geometries. --- Research Limitations – Although the aerodynamic coefficients used in the UBEMT are from measurements in steady flow conditions, they can be used with success. --- Practical Implications – Also conventional Horizontal Axis Wind Turbines (HAWT) with noticeable cone and axis angle should be calculated with the UBEMT. The accuracy of power calculations of these HAWTs can be slightly improved. --- Originality – Analytic equations for rotors with cone and axis angle have barely been discussed.

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

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

The differential gear train and speed regulating motor constitute the variable ratio transmission for grid-connected wind turbine with differential speed regulation. The synchronous generator in the system can accessing the power grid without frequency converter. The transmission can realize the mode of variable speed constant frequency that the wind rotor speed is varying and the generator rotor speed is constant. The power control method is studied under the different wind speed which is lower or higher than rated wind speed with using the relational expression of utilization rate of wind energy Cp, pitch angle β and the tip speed ratio λ. The SIMULINK software is used to build the 1500 kW wind turbine model with differential speed regulation. Some different wind speed is made as input. The feasibility of power control method for grid-connected wind turbine with differential speed regulation is verified by the comparison between the simulation results and the theoretical value of the key parameters.

Rubbish in a forest environment is a great threat to this ecosystem, but this threat may also apply to the lost benefits for visitors to the forest. Previous studies proved that forest areas have a positive effect on obtaining psychological relaxation in the people visiting them. However, it was not known whether this restorative experience could be disturbed in any way by the presence of an open dump in the forest. To check how the presence of a landfill affects the visitors, an experiment was planned in which the respondents observed a forest area with a landfill and a forest landscape without a landfill for 15 minutes (control). The respondents then assessed the landscape using the semantic differential method and the Perceived Restorativeness Scale (PRS). An analysis of these observations showed that the presence of a landfill in the forest significantly changed the appreciation of the landscape by the respondents, the values of positive experiences decreased, and the negative experiences increased. Restorativeness was also reduced. Based on the results, it can be concluded that the presence of garbage in the forest may interrupt the restorative experience of its visitors.

This research presents the design and characteristics of new wideband polarizer based on the square waveguide with irises. Matching and polarization characteristics of the polarizer have been simulated and optimized. Frequency dependences of the characteristics are presented. Developed polarizer can be applied in satellite information systems.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.

Observation of parity-violating effects in chiral molecules is a long-standing challenge of the molecular spectroscopy community. In the microwave regime, the difference in transition frequencies between enantiomers is predicted to be below the mHz level, which is considerably beyond current experimental capabilities. The most promising future efforts combine vibrational spectroscopy, buffer gas cooling, and carefully chosen molecular candidates with large predicted parity-violating shifts. Here, we demonstrate for the first time high-precision differential microwave spectroscopy, achieving sub-Hz precision by coupling a cryogenic buffer gas cell with a tunable microwave Fabry-Perot cavity. We report statistically limited sub-Hz precision of (0.08±0.72) Hz, observed between enantiopure samples of (R)-1,2-propanediol and (S)-1,2-propanediol at frequencies near 15 GHz. We confirm highly repeatable spectroscopic measurements compared to traditional pulsed-jet methods, opening up new capabilities in probing subtle molecular structural effects at the 10−10 level and providing a platform for exploring sources of systematic error in parity-violation searches. We discuss dominant systematic effects at this level and propose possible extensions of the technique for higher precision.

Image segmentation and classification still represent an active area of research since no universal solution can be identified. Established segmentation algorithms like thresholding are problem specific, treat well the easy cases and mostly relied on single parameter i.e intensity. Machine learning approaches offer alternatives where predefined features are combined into different classifiers. On the other hand, the outcome of machine learning is only as good as the underlying feature space. Differential geometry can substantially improve the outcome of machine learning since it can enrich the underlying feature space with new geometrical objects, called invariants. In this way, the geometrical features form a high-dimensional feature space for each pixel, where original objects can be resolved. Alternatives based on the geometry of the image scale-invariant interest points have been exploited successfully in the field of computer vision. Here, we integrate geometrical feature extraction based on signal processing, machine learning, and input relying on domain knowledge. The approach is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application, we demonstrate powerful image classification functionality based on the same principles, which was applied to the HeLa and HEp-2 data sets. Obtained results demonstrate that feature space enrichment properly balanced with feature selection functionality can achieve performance comparable to deep learning approaches.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

New class of conserved quantities is constructed. These quantities find direct application in mechanics of dissipative (generally non-conservative) dynamical systems. Approach demands formulation in the language of geometric mechanics, providing theoretical framework for situations with energy flow in and out of the system. As a by product, we suggest possibility of existence of Hamiltonian form for every autonomous ODE system, evolution of which is governed by non-potential generator of motion. Various examples are provided, ranging from physics and mathematics, to chemical kinetics and population dynamics in biology. Applications of these ideas in geometric integration techniques (GNI) of numerical analysis are discussed, and as an example of such, new discrete gradient-based numerical method is introduced.

A plant’s early response to pathogen stress is a vital indicator of its disease resistance. In order to study the response mechanism of resistant and susceptible flax cultivars to Fusarium oxysporum f. sp. lini (Foln), we applied RNA-sequencing to analyze transcriptomes of flax with Foln 0.5, 2 and 8 hours post inoculation (hpi). We found a significant difference in the number of differential expression genes (DEGs) between resistant and susceptible flax clutivars. The number of DEGs in the Fusarium-resistant cultivar increased dramatically at 2 hpi, and a large number of DEGs participated in the Fusarium-susceptible cultivar response to Foln infection 0.5 hpi. GO enrichment analysis determined that the up-regulated DEGs of both flax cultivars were enriched such as oxidoreductase activity and oxidation-reduction process. At the same time, the genes involved in diterpenoid synthesis were up-regulated in resistant cultivar, while those involved in extracellular region, cell wall and organophosphate ester transport were down-regulated in susceptible cultivar. KEGG enrichment analysis showed the genes encoded WRKY 22 and WRKY33 which involved in MAPK signaling pathway were up-regulated expressed in S-29 and down-regulated expressed in R-7, negatively regulated the disease resistance of flax; The genes encoded Hsp 90 family which in involved in plant pathogen interaction pathway were up-regulated in R-7 and down-regulated in S-29, which positively regulated the disease resistance of flax; The genes encoded MYC2 transcription factor and TIFY proteins which involved in plant hormone signaling pathway were up-regulated in R-7, and regulated the jasmonic acid metabolism of flax and the signal transduction of plant hormones. Meanwhile seven regulatory genes with the most correlation were screened out, Among Lus10025000.g and Lus10026447.g regulated other genes expressed both in plant hormone signal transduction pathway and MAPK signal pathway. In conclusion, these findings will facilitate further studies on the function of these candidate genes in flax of response to Fusarium stress, and the breeding of disease-resistant flax cultivar.

In the context of the French-German space lidar mission MERLIN dedicated to the determination of the atmospheric methane content, an end-to-end mission simulator is being developed. In order to check whether the instrument design meets the performance requirements, simulations have to count all the sources of noise on the measurements like the optical energy variability induced by speckle. Speckle is due to interference as the lidar beam are quasi monochromatic. Speckle contribution to the error budget has to be estimated but also simulated. In this paper, the speckle theory is revisited and applied to MERLIN double pulsed IPDA lidar and also to the DLR demonstrator CHARM-F. Results show: on the signal path, speckle noise depends mainly on the size of the illuminating area on ground; on the solar flux, speckle is fully negligible both because the pixel size and the optical filter spectral width; on energy monitoring path a decorrelation mechanism is needed to reduce speckle noise on averaged data. Speckle noises for MERLIN and CHARM-F can be simulated by Gaussian noises with only one random draw by shot separately for energy monitoring and signal paths.

Recently, hybrid logic circuits based on magnetic tunnel junctions (MTJs) have been widely investigated to realize zero standby power. However, such hybrid CMOS/MTJ logic circuits suffer from a severe sensing reliability due to the limited tunnel magnetoresistance ratio (TMR≤150%) of the MTJ and the large process variation in the deep sub-micrometer technology node. In this paper, a novel differential sensing amplifier (DSA) is proposed, in which two PMOS transistors are added to connect the discharging branches and evaluation branches. Owing to the positive feedback realized by these two added PMOS transistors, it can achieve a large sensing margin. By using an industrial CMOS 40 nm design kit and a physics-based MTJ compact model, hybrid CMOS/MTJ simulations have been performed to demonstrate its functionality and evaluate its performance. Simulation results show that it can achieve a smaller sensing error rate of 9% in comparison with the previously proposed DSAs with the TMR ratio of 100% and process variation of 10%, while maintaining almost the same sensing delay of 74.5 ps and sensing energy of 1.92 fJ/bit.

A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

In this paper, we define new kind of Daehee numbers, the degenerate Daehee numbers of the third kind, using degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

The hydrodynamic behavior of the air-acetic acid system in a bubble column is studied using a differential pressure transmitter, double probe optical fiber probe, and the electrical resistance tomography (ERT) technique. The superficial gas velocity ranges from 0.016 to 0.094 m/s under ambient temperature and pressure. The influences of viscosity and surface tension on gas holdup, bubble rising velocity, and bubble chord distribution in the column are discussed with different mass fractions of an acetic acid solution. The results show that as the mass fraction of acetic acid increases, the surface tension of the liquid phase decreases, and the viscosity first increases and then decreases. This causes the gas holdup in the column to first increase and then decrease, and reaches the maximum value at an acetic acid mass fraction of 55% to 60%. The rising velocity of the bubbles in the column is high in the central region and has a low-value distribution near the wall. The bubble chord length distribution is concentrated, and the distribution of the bubble chord length in the column becomes narrow with any decrease in surface tension. Studying the hydrodynamic behavior of a bubble column with the air-acid system is of great significance considering the absence of data on air-organic acid systems.

Traditional potential transformers have problems of large volume, difficulty in insulation, iron core saturation, ferroresonance overvoltage and poor transient response characteristics. The voltage sensor based on the principle of electric field coupling and differential input structure does not need to contact the measured object or ground, and can avoid the above problems. However, it requires a sufficiently high capacitance between the differential electrodes to obtain sufficient accuracy and a high voltage division ratio. The existing method of using mutual capacitance between the differential electrodes will cause many problems and fail to meet the practical needs. To solve the above problems, this paper innovatively uses multi-layer ceramic capacitor to replace the mutual capacitance and designs a new type of voltage sensor. In addition, by using single bypass small resistance grounding method to increase the input impedance of the differential signal processing circuit, error of the sensor is further reduced. The experimental results show that the sensor has excellent accuracy and great transient response characteristics. The ratio error under power frequency is within ±0.5% and the phase error is within 1. The ratio error in the range of 500 Hz∼30 kHz is within ±5% and the phase error is within 5. Moreover, it has the advantages of low cost, miniaturization, flexible shape and easy to adjust the voltage division ratio. These characteristics indicate that the sensor has good voltage measurement and sensor network potential.

The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection (a(t)) and recovery (u(t)) rates regulating the transitions from the susceptible to the infected and from the infected to the recovered compartment, respectively. Here approximated SIR-solutions for different time dependencies of the infection and recovery rates are derived which are based on the adiabatic approximation assuming time-dependent ratios k(t)=u(t)/a(t) varying slowly in comparison to the typical time characteristics of the pandemic wave. For such slow variations the available analytical approximations from the KSSIR-model, valid for a stationary value of the ratio k, are used to insert a-posteriori the adopted time-dependent ratio of the two rates. Instead of investigating endless different combinations of the time dependencies of the two rates a(t) and u(t) a suitably parameterized reduced time dependence of the ratio k(tau) is adopted. Together with the definition of the reduced time this parameterized ratio k(tau) allows us to cover a great variety of different time dependencies of the infection and recovery rates. The agreement between the solutions from the adiabatic approximation in its four different studied variants and the exact numerical solutions of the SIR-equations is remarkably good providing strong confidence in the accuracy of the proposed adiabatic approximation.

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix, and the Laplace transform. The fundamental solution is presented in a form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of a RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

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

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, because the necessary mathematical tools have only just began to be developed.

Molybdenum oxides is well-known electro-catalysts in fuel cells systems, they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of Mo as catalysts in the pharmaceutical analysis is not common yet. In this study, bare glassy carbon electrodes were modified by the oxides by means of electrochemical deposition and the modified electrodes were used as catalysts for the electrochemical oxidation of hydrochlorothiazide (HCT). Well-resolved anodic peaks were reported for the analyzed pharmaceuticals when the Mo/GCE was utilized for the analysis of HCT. Analytical performance of the modified electrodes was evaluated based on the following statistical parameters; linearity ranges, correlation coefficients, limits of detection and quantitation, and recovery values. The prepared electrodes were used for the determination of the active ingredients in their pharmaceutical formulations and the reported activity was correlated to influence of the utilized pH on both structures of the used electrodes and the detected analytes.

The study is devoted to the issues of mathematical modeling and simulating the sport differential mechanism (DM) with controllable torque redistribution. The issue is caused by the elaboration of ADAS systems with the automated torque vectoring for transmissions of all-wheel-drive (AWD) vehicles and the inclusion of such devices in the combined autonomous vehicle trajectory control scheme. At the article's beginning, the use of devices for redistributing traction forces is reasoned by analyzing the curvilinear vehicle motion, where they could ensure the accuracy of vehicle steerability. The literature review highlights modern developments in the field of modeling and researching such DMs. Considering the vehicle turn with a minimum radius, the conditions corresponding to passing greater torque over the outrunning rear axle are determined. All the mechanism's components and loads acting between them are described in detail. To form an original method of mathematical description of the mechanism functioning, the system of differential equations, systems of kinematic and force connections are considered separately. The article details the mathematical approach to generalize the way for automating the equation compilation for rotational mechanical systems such as vehicle transmissions. In the simulation section, a Simulink model reflecting the functional components and calculation procedures is presented. A series of testing and simulations on the DM operation with forcible torque distribution is carried out. Modeling data are presented, and the analysis of simulation results is performed. In the completion, conclusions are made regarding the scope and use of this model and the prospects for further developing the method proposed to automate the formation of equation systems.

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

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

An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

Background: Traditional omic analysis relies on p-value and fold change as selection criteria. There is an ongoing debate on their effectiveness in delivering systemic and robust interpretation, due to their dependence on assumptions of conformity with various parametric distributions.Here, we propose a threshold-free selection method based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques based on fixed thresholds. Methods: Our work extends the Rank Products methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP distribution’s entropy to isolate the features of interest by their contribution to the distribution’s information content. The aim is a methodology performing threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under scrutiny. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterisations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and information-rich, indicating phenotypic aspects specific to the tissue and biological phenomenon i nvestigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresholding, thus facilitating the full automation of the analysis.

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

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.

Standard cell culture is routinely performed at supraphysiological oxygen concentrations (~18% O2). Conversely, oxygen levels in most tissues range from 1%–6% (physioxia). Such hyperoxic conditions can alter reactive oxygen species (ROS) production, energy metabolism, mitochondrial network dynamics, and response to drugs and hormones. The aim of this project was to investigate the transcriptional response to different oxygen levels and whether it is similar across cell lines, or cell-line specific. Using RNA-seq, we performed differential gene expression and functional enrichment analyses in four human cancer cell lines, LNCaP, Huh-7, PC-3, and SH-SY5Y cultured at either 5% or 18% oxygen for 14 days. We found that oxygen levels affected transcript abundance of hundreds of genes, with the affected genes having little overlap between cell lines. Functional enrichment analysis also revealed different processes and pathways being affected in each cell line. Interestingly, we found that the top differentially expressed genes are involved in cancer biology. Further, we observed several hypoxia-inducible factor (HIF) targets upregulated at 5% oxygen, suggesting a role of HIF at physiological oxygen conditions. Finally, oxygen strongly induced transcription of mitochondrial genes in most cell lines, in a cell-type specific manner too. We conclude that cellular response to oxygen is widely cell-type specific, emphasizing the importance of maintaining physioxia in cell culture.

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

A diagnosis of typical chronic lymphocytic leukemia (CLL) requires the presence of ≥5000 clonal B-lymphocytes/μL with the coexistence of CD19, CD20, CD5, and CD23 and the restriction of light chain immunoglobulin, and the lack of expression of antigens CD22 and CD79b. Atypical CLL (aCLL) can be distinguished from typical CLL morphologically and immunophenotypically. Atypical CLL cells are defined as prolymphocytes; morphologically, these present as deeply-clefted lymphocytes which are larger than those in typical CLL, with condensed chromatin and without prominent nucleoli. However, current aCLL diagnostics rely more on immunophenotypic characteristics rather than atypical morphology. Immunophenotypically, atypical CLL differs from classic CLL in the lack of expression of one or fewer surface antigens, most commonly CD5 and CD23, and the patient does not meet the criteria for a diagnosis of any other B-cell lymphoid malignancy. Morphologically atypical CLL has more aggressive clinical behavior and worse prognosis than classic CLL. Patients with aCLL are more likely to display markers associated with poor prognosis, including trisomy 12, unmutated IGVH, and CD38 expression compared with classic CLL. However, no standard or commonly-accepted criteria exist for differentiating aCLL from classic CLL and the clinical significance of aCLL is still under debate. This review summarizes the current state of knowledge on the morphological, immunophenotypic and genetic abnormalities of aCLL.

The overwhelming majority of bladder cancers are transitional cell carcinomas. Albeit mostly monotonous, carcinomas in the bladder may occasionally display a broad spectrum of histological features that should be recognized by pathologists because some of them represent a diagnostic problem and/or lead prognostic implications. Sometimes these features are focal in the context of conventional transitional cell carcinomas, but some others are generalized across the tumor making its recognition a challenge. For practical purposes, the review distributes the morphologic spectrum of changes in architectural and cytological. So, nested and large nested, micropapillary, myxoid stroma, small tubules and adenoma nephrogenic-like, microcystic, verrucous, and diffuse lymphoepithelioma-like, on one hand, and plasmacytoid, signet ring, basaloid-squamous, yolk-sac, trophoblastic, rhabdoid, lipid/lipoblastic, giant, clear, eosinophilic (oncocytoid), and sarcomatoid, on the other, are revisited. Key histological and immunohistochemical features useful in the differential diagnosis are mentioned. In selected cases, molecular data associated with the diagnosis, prognosis, and/or treatment are also included.

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

Cell migration is essential for physiological, pathological and biomedical processes such as, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion and inflammation. In light of this, quantifying mechanical properties during the process of cell migration is of great interest in experimental sciences, yet few theoretical approaches in this direction have been studied. In this work, we propose a theoretical and computational approach based on the optimal control of geometric partial differential equations to estimate cell membrane forces associated with cell polarisation during migration. Specifically, cell membrane forces are inferred or estimated by fitting a mathematical model to a sequence of images, allowing us to capture dynamics of the cell migration. Our approach offers a robust and potentially accurate framework to compute geometric mechanical membrane forces associated with cell polarisation during migration and also yields geometric information of independent interest, we illustrate one such example that involves quantifying cell proliferation levels which are associated with cell division, cell fusion or cell death.

Background: The reliability of a recent review of meningiomas in the archeologic record was difficult to assess, given the inverted sex ratio of the report and other contents apparently at variance with anatomical/medical findings in scientifically-identified cases. It therefore seemed appropriate to reexamine the nature of meningiomas and derive improve criteria for their recognition in the archeologic record and distinguish them from hemangiomas and bone marrow hyperplasia (recognized in the form of porotic hyperostosis). Methods: Medically-documented cases of meningiomas, hemangiomas and cranial bone marrow hyperplasia were examined to establish a macroscopic standard that distinguishing among them. Alleged cases in the archeologic record were examined for conformity with those criteria. Results: An en face pattern of uniform mesh with contained whorls appears pathognomonic for meningiomas. This contrasts with the non-uniform marrow expansion displacement of trabeculae in porotic hyperostosis and non-uniform vascular displacement of trabeculae in hemangiomas. Reassessment of past attributions revealed few cases of meningiomas that could be confidently diagnosed. Those identified has sex ratios parsimonious with medical literature reports. Conclusions: Criteria suggested for identifying meningiomas permits distinguishing from hemangiomas, bone marrow hyperplasia (porotic hyperostosis) and from the macroscopically-observable surface spicules characteristic of osteosarcomas. Examination for fulfillment of criteria for meningiomas and hemangiomas seems to provide a picture (including sex ratios) more parsimonious with the clinical literature, concluding that Cook and Danforth’s disparate ratios were related to less fastidious case selection. Additionally, confidence in recognizing porotic hyperostosis may be compromised because of apparent similar macroscopic alterations to those seen with hemangiomas.

Schizophrenia (SCZ) is a severe mental disorder that may result in hallucinations, delusions, and extremely disordered thinking. How each cell type in the brain contributes to SCZ occurrence is still unclear. Here, we leveraged the human dorsolateral prefrontal cortex bulk RNA-seq data, then used the RNA-seq deconvolution algorithm CIBERSORTx to generate SCZ brain single-cell RNA-seq data for a comprehensive analysis to understand SCZ-associated brain cell types and gene expression changes. Firstly, we observed that the proportions of brain cell types in SCZ differed from normal samples. Among these cell types, astrocyte, pericyte, and PAX6 cells were found to have a higher proportion in SCZ patients (astrocyte: SCZ = 0.163, Control = 0.145, P.adj = 4.9×10-4; pericyte: SCZ = 0.057, Control = 0.066, P.adj = 1.1×10-4; PAX6 : SCZ = 0.014, Control = 0.011, P.adj = 0.014), while the L5/6_IT_CAR3 cells and LAMP5 cells are the exact opposite (L5/6_IT_Car3 : SCZ = 0.102, Control = 0.108, P.adj = 0.016; LAMP5 : SCZ = 0.057, Control = 0.066, P.adj = 2.2×10-6). Next, we investigated gene expression in cell types and functional pathways in SCZ. We observed chemical synaptic transmission dysregulation in two types of GABAergic neurons (PVALB and LAMP5), and immune reaction involvement in GABAergic neurons (SST) and non-neuronal cell types (endothelial and oligodendrocyte). Furthermore, we observed that some differential expression genes from bulk RNA-seq displayed cell-type-specific abnormal in the expression of molecules in SCZ. Finally, the cell types with the SCZ-related transcriptomic changes could be considered to belong to the same module since we observed two major similar coordinated transcriptomic changes across these cell types. Together, our results offer novel insights into cellular heterogeneity and the molecular mechanisms underlying SCZ.

The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.

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

In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured.

Pregnancy is a dynamic state with multiple metabolic changes occurring including insulin resistance. Gestational diabetes mellitus (GDM), a form of diabetes that appears during pregnancy, develops if metabolic aberrations occur, in particular, in normal pregnancy-induced insulin resistance. Multi-omics is a powerful approach for uncovering the mechanisms driving metabolic change in different physiologic and pathologic states. A recent study demonstrated that the gestational gut microbiome mediates pregnancy metabolic adaptations through effects on gut indoleamine-2,3 dioxygenase 1 activity and the production of kynurenine. Using the dataset generated from this highly controlled study, we performed a comprehensive analysis of the pregnancy-specific physiological and metabolic profiles, 16S rRNA microbiome, and plasma untargeted LC-MS metabolome data. To facilitate the utilization of these analysis results by other researchers, we developed MOMMI-MP, a database that provides an easy-to-use platform to browse and search differential abundant microbial taxa and metabolites, and to examine metabolic pathways. The datasets consist of data collected from 3 genetically diverse strains of mice (C57BL/6J, CD1, and NIH-Swiss) over 6 time points during the gestational (days 0, 10, 15, and 19 during gestation) and postpartum (days 3 and 20 after delivery) states, totaling 180 samples for each strain. The computational results are presented in various tables and plots, and organized in MOMMI-MP to empower exploratory analyses by other researchers. In conclusion, MOMMI-MP is a resource to facilitate the investigation of novel mechanisms governing metabolic changes during pregnancy.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

The Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

Pursuing "intelligent justice" necessitates an impartial, productive, and technologically driven methodology for judicial determinations. This scholarly composition proposes a framework that harnesses Artificial Intelligence (AI) innovations such as Natural Language Processing (NLP), ChatGPT, ontological alignment, and the semantic web, in conjunction with blockchain and privacy techniques, to examine, deduce, and proffer recommendations for the administration of justice. Specifically, through the integration of blockchain technology, the system affords a secure and transparent infrastructure for the management of legal documentation and transactions while preserving data confidentiality. Privacy approaches, including differential privacy and homomorphic encryption techniques, are further employed to safeguard sensitive data and uphold discretion. The advantages of the suggested framework encompass heightened efficiency and expediency, diminished error propensity, a more uniform approach to judicial determinations, and augmented security and privacy. Additionally, by utilizing explainable AI methodologies, the ethical and legal ramifications of deploying intelligent algorithms and blockchain technologies within the legal domain are scrupulously contemplated, ensuring a secure, efficient, and transparent justice system that concurrently protects sensitive information upholds privacy.

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

In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.

To assess the degree to which it has met its commitments under the Paris Agreement, Morocco is called upon to carry out carbon assessments and transparent evaluations. Within the forestry sector, little is known about the role of Morocco’s forests in contributing to carbon uptake. With this aim, we applied for the first time in literature the 3-PG model to Cedrus atlantica ((Endl.) Manetti ex Carrière, 1855), which represents about 131.800 ha of Morocco’s forest area (i.e. Azrou forest). Through the Differential Evolution - Markov Chains (DE-MC) we tested and assessed the sensitivity and calibrated the 3-PG model. This process-based model provided significant results regarding the carbon sequestration capacity. The results showed the following: i- Parameters related to stand properties, canopy structure, and processes, as well as biomass partitioning, are the most important or sensitive for the performance of the model; ii- The DE-MC method optimized the values of the 3-PG parameters which was confirmed by the means of Gelman-Rubin convergence test; iii- According to the predictions of the calibrated 3-PG, the Net Primary Production in the pure Azrou forest varies between 0.32 and 7.88 tC.ha−1.yr−1, it is equal in average to 4.9 tC.ha−1.yr−1, which given the total area corresponds to 7078 tC.yr−1.

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.

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials

Partial differential equations (PDEs) are used to describe a wide range of phenomena, such as heat transfer, fluid dynamics, and quantum mechanics. By solving PDEs, we can ob- tain insights into the behavior of the system and make predictions about its future evolution. Conventional numerical methods for obtaining the approximate solutions of PDEs may re- quire extensive computational resources and time, especially for complex PDEs and large- scale problems. The recently developed physics-informed neural network (PINN) has shown promise in a variety of scientific and engineering fields by incorporating physical laws into the loss functions of the neural network (NN). In addition, the training of PINN does not require ground truth data, but it has poor generalization ability to unseen domains. On the other hand, a convolutional neural network (CNN) has fast inference and better generalization ability, but it requires a large amount of training data. Taking the advantages of PINN and CNN by using Legendre multiwavelets (LMWs) as basis functions, we introduce a new method to approach the PDEs in this paper, namely Physics-Informed Legendre Multiwavelets CNN (PiLMWs-CNN), in order to continuously approximate a grid-based state representation that can be handled by a CNN. PiLMWs-CNN enable us to train our models using only physics-informed loss functions without any pre- computed training data, simultaneously providing fast and continuous solutions that gener- alize to previously unknown domains. In particular, the LMWs can simultaneously possess compact support, orthogonality, symmetry, high smoothness, and high approximation order. Compared to orthonormal polynomial (OP) bases, the approximation accuracy can be greatly increased and computation costs can be significantly reduced by using LMWs. We applied PiLMWs-CNN to approximate the damped wave equation, incompressible Navier-Stokes (N- S) equation, and two-dimensional heat conduction equation. The experimental results show that this method provides more accurate, efficient, and fast convergence with better stability when approximating the solution of PDEs.

The core reasoning task for datalog engines is materialization, the evaluation of a datalog program over a database alongside its phys- ical incorporation into the database itself. The de-facto method of computing it, is through the recursive application of inference rules. Due to it being a costly operation, it is a must for datalog engines to provide incremental materialization, that is, to adjust the computation to new data, instead of restarting from scratch. One of the major caveats, is that deleting data is notoriously more involved than adding, since one has to take into account all possible data that has been entailed from what is being deleted. Differential Dataflow is a computational model that provides efficient incremen- tal maintenance, notoriously with equal performance between ad- ditions and deletions, and work distribution, of iterative dataflows. In this paper we investigate the performance of materialization with three reference datalog implementations, out of which one is built on top of a lightweight relational engine, and the two others are differential-dataflow and non-differential versions of the same rewrite algorithm, with the same optimizations.

Real-world optimization problems are often gov- erned by one or more constraints. Over the last few decades, extensive research has been performed in Constrained Opti- mization Problems (COPs) fueled by advances in computational power. In particular, Evolutionary Algorithms (EAs) are a preferred tool for practitioners for solving these COPs within practicable time limits. We propose a novel hybrid Evolutionary Algorithm based on the Differential Evolution algorithm and Adaptive Parameter Gaining Sharing Knowledge-based algo- rithm to solve global real-world constrained parameter space. The proposed CHAGSKODE algorithm leverages the power of multiple adaptation strategies concerning the control parameters, search mechanisms, as well as uses knowledge sharing between junior and senior phases. We test our method on the benchmark functions taken from the CEC2020 special session & competition on real-world constrained optimization. Experimental results indicate that CHAGSKODE is able to achieve state-of-the- art performance on real-world constrained global optimization when compared against other well-known real-world constrained optimizers.

In our study we investigated the accelerated aging process of PLA under 253.7 nm UV-C irradiation with the use of GPC, NMR, FTIR, DSC methods and formal kinetic analysis. The results of GPC and DSC indicated a significant degree of destructive changes in PLA macromol-ecules, while spectroscopic methods NMR and FTIR showed maintenance of PLA main structural elements even after a long time of UV exposure. In addition to that, the GPC method displayed the formation of a high-molecular fraction starting from 24 hours of irradiation, and an increase in its content after 144 hours of experiment. It has been showed for the first time that a distinctive feature of prolonged UV exposure is the occurrence of intra- and intermolecular radical recom-bination reactions, leading to the formation of a high-molecular fraction of PLA decomposition products. This causes the observed slowdown of the photolysis process. It was concluded that photolysis of PLA is a complex of physicochemical processes, the mechanism of which depends on morphological changes in a solid phase of the polymer under UV radiation.

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

Frontal Temporal Dementia (FTD) is a neurological disorder known to have less therapeutic options. So far only a few biomarkers are available for FTD that can be used as potential comorbidity targets. To this end, in the present study we aim to identify potential biomarkers or susceptible genes for FTD that show comorbidities with diseases such as COVID-19 and Breast Cancer. Gene expression Omnibus datasets containing FTD expression profiles from African American and white ethnicity background were included in our study. In FTD samples of GSE193391 dataset, we identified 305 DEGs with 168 genes being up-regulated and 137 genes being down-regulated. We conducted comorbidity analysis for COVID-19 and Breast cancer followed by analysis of potential drug interactions, pathogenicity, analysis of genetic variants and functional enrichment analysis. Resulting genes AKT3, GFAP, ADCYAP1R1, VDAC1, and C4A showed significant transcriptomic alterations in FTD and significant comorbidity status with COVID-19 and Breast cancer. Functional pathway analysis revealed that these comorbid genes were significantly enriched in the pathways such as glioma, JAK/STAT signaling, systematic lupus erythematosus, neurodegeneration-multiple diseases and neuroactive ligand-receptor interaction. Overall, from these results, we concluded that these genes could be recommended as potential therapeutic targets for the treatment of comorbidities in FTD.

The present work focuses on developing miniaturized, light weight electrochemical sensors for detection of chemical warfare agents (CWAs) like sarin and tabun simulants, i.e., diisopropyl fluorophosphate (DFP), and O,S-diethyl methyl phosphonothioate (O,S-DEMPT). Differential pulse voltammetry (DPV) was employed to examine the redox properties of capturing molecular probe CE2 with the nerve agent stimulants. Coupling of a portable potentiostat with the drone technology could allow on-situ and remote detection of analytes such CWAs to be realized, which can be crucially important to the national and global securities.

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

We discuss a remote sensing system that is used to simultaneously detect range-resolved differential absorption LIDAR (light detection and ranging; DIAL) signals and integrated path DIAL signals (IP-DIAL) from aerosol targets for ranges up to 22 km. The DIAL/IP-DIAL frequency converter consists of an OPO pumped at 1064 nm to produce light at 1.6 μm and operates at 100 Hz pulse repetition frequency. The probe light is free space coupled to a movable platform that contains one transmitter and two receiver telescopes. Hybrid photon counting/current systems increase the dynamic range for detection by two orders of magnitude. Range resolved and column integrated dry-air CO2 and CH4 mixing ratios are obtained from line shape fits of CO2 and CH4 centered at 1602.2 nm and 1645.5 nm, respectively and measured at 10 different frequencies over ≈ 1.5 cm-1 bandwidth. The signal-to-noise ratios (SNR) of the IP-DIAL returns from cloud aerosols approach 1000:1 and the uncertainties in the mixing ratios weighted according to the integrated counts over the cloud segments range from 0.1 % to 1 %. The range averaged DIAL mixing ratios are in good agreement with the IP-DIAL mixing ratios at the 1 % to 2 % level for both CO2 and CH4. These results can serve as a validation method for future active and passive satellite observational systems.

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

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

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

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

Variable during practice is widely accepted to be advantageous for motor learning and therefor a valuable strategy to effectively reduce high-risk landing mechanics and prevent primary anterior cruciate ligament (ACL) injury. Few attempts have examined the specific effects of variable train-ing in athletes who have undergone ACL reconstruction. Thereby it is still unclear to what extent the variations in different sensor areas lead to different effects. Accordingly, we compared the effects of versatile movement variations (DL) with variations of movements with emphasis on disrupting visual information (VMT) in athletes who had undergone ACL reconstruction. For-ty-five interceptive sports athletes after ACL reconstruction were randomly allocated to a DL group (n= 15), VT group (n= 15) or control group (n= 15). The primary outcome was functional performance (Triple Hop Test). The secondary outcomes included dynamic balance (Star Excur-sion Balance Test (SEBT)), biomechanics during single-leg drop-landing task hip flexion (HF), knee flexion (KF), ankle dorsiflexion (AD), knee valgus (KV), and vertical ground reaction force (VGRF), and kinesiophobia (Tampa Scale of Kinesiophobia (TSK)) assessed before and after the 8-weeks of interventions. Data were analyzed be means of 3×2 repeated measures ANOVA fol-lowed by post hoc comparison (Bonferroni) at the significance level of p≤0.05. Significant group × time interaction effects, main effect of time and main effect of group were found for triple hop test, all eight directions of SEBT, HF, KF, AD, KV, VGRF and TSK. There was no significant main ef-fect of group in HF and triple hop test. Also, significant differences in triple hop test, seven direc-tions of SEBT, HF, KF, KV, VGRF and TSK were found between control group with the DL and VMT groups. Between group differences in AD and medial direction of SEBT were not signifi-cant. Also, there was no significant differences between VMT and control groups in triple hop test and HF variables. Both motor learning (DL and VMT) programs improved outcomes in patients after ACL reconstruction. Findings suggest that DL and VMT training programs lead to compa-rable improvements in rehabilitation.

Micro-expression (ME) is one of the key psychological stress reactions. It is a modest, spontaneous facial mechanism. ME has significant applicability in a variety of psychologically-related sectors because to its precision and unpredictability with regard to psychological manifestations. Nevertheless, the current Micro-expression recognition (MER) algorithms have poor accuracy and a limited quantity of ME data, and this study issue has not been thoroughly investigated. Therefore, we present an approach for deep learning based on a Spatio-temporal capsule network (STCP-Net). STCP-Net has four components: a jitter reduction module, a differential feature extraction module, an STCP module, and a fully linked layer. The first two modules are aimed to extract diversifying differential features more precisely and to limit the influence of head jitter. The STCP module is used to extract Spatio-temporal features layer by layer, taking the temporal and geographical connection between features into account. This research runs sufficient trials using the Leave One Subject Out (LOSO) methodology for cross-validation using the CASMEII dataset. The conclusion and analysis demonstrate that the algorithm is innovative and efficient.

This study focuses on the optimal deployment problem, and determines the optimal size of a military force to send to the battle field. The decision is optimized, based on an objective function, that considers the cost of deployment, the cost of the time it takes to win the battle, and the costs of killed and wounded soldiers with equipment. The cost of deployment is modeled as an explicit function of the number of deployed troops and the value of a victory with access to a free territory, is modeled as a function of the length of the time it takes to win the battle. The cost of lost troops and equipment, is a function of the size of the reduction of these lives and resources. An objective function, based on these values and costs, is optimized, under different parameter assumptions. The battle dynamics is modeled via the Lanchester differential equation system based on the principles of directed fire. First, the deterministic problem is solved analytically, via derivations and comparative statics analysis. General mathematical results are reported, including the directions of changes of the optimal deployment decisions, under the influence of alternative types of parameter changes. Then, the first order optimum condition from the analytical model, in combination with numerically specified parameter values, is used to determine optimal values of the levels of deployment in different situations. A concrete numerical case, based on documented facts from the Battle of Iwo Jima, during WW II, is analyzed, and the optimal US deployment decisions are determined under different assumptions. The known attrition coefficients of both armies, from USA and Japan, and the initial size of the Japanese force, are parameters. The analysis is also based on some parameters without empirical documentation, that are necessary to include to make optimization possible. These parameter values are motivated in the text. The optimal solutions are found via Newton- Raphson iteration. Finally, a stochastic version of the optimal deployment problem is defined. The attrition parameters are considered as stochastic, before the deployment decisions have been made. The attrition parameters of the two armies have the same expected values as in the deterministic analysis, are independent of each other, have correlation zero, and have relative standard deviations of 20%. All possible deployment decisions, with 5000 units intervals, from 0 to 150000 troops, are investigated, and the optimal decisions are selected. The analytical, and the two numerical, methods, all show that the optimal deployment level is a decreasing function of the marginal deployment cost, an increasing function of the marginal cost of the time to win the battle, an increasing function of the marginal cost of killed and wounded soldiers and lost equipment, an increasing function of the initial size of the opposing army, an increasing function of the efficiency of the soldiers in the opposing army and a decreasing function of the efficiency of the soldiers in the deployed army. With stochastic attrition parameters, the stochastic model also shows that the probability to win the battle is an increasing function of the size of the deployed army. When the optimal deployment level is selected, the probability of a victory is usually less than 100%, since it would be too expensive to guarantee a victory with 100% probability. Some of many results of relevance to the Battle of Iwo Jima, are the following: In the deterministic Case 0 analysis, the optimal US deployment level is 66200, the time to win the battle is 30 days and 14000 US soldiers are killed or wounded. If the marginal cost of the time it takes to win a victory doubles, the optimal deployment increases to 75400, the time to win a victory is reduced to 26 days, and less than 12000 soldiers are killed or wounded. In the stochastic Case 0 analysis, the optimal US deployment level is 65000, the expected time to win the battle is 46 days and almost 25000 US soldiers are expected to be killed or wounded. If the cost per killed or wounded soldier increases from 0 to 5 M $US, the optimal deployment level increases to 75000. Then, the victory is expected to appear after 35 days and 19900 US soldiers are expected to be killed or wounded.

The energy-intensive sector of the cement industry needs to find technologically advanced methods to produce cement with as little energy as possible, without polluting the environment and without sacrificing the quality (fineness) of the cement. In addition, the stress on the machines changes the behavior of the data. By combining the k-means method, two (2) feature selection methods, nine (9) machine learning methods, and the differential evolution (DE) method, a dynamic system is created where the user determines the key performance indicators (KPIs) each time. The user has the potential to control the distribution of the data, the input of machine learning models, and the ability to switch the system to the suggested values without damage. The selection of the best-performing models is based on the normalized root mean squared error (NRMSE). The DE method optimizes the dynamic objective function. The optimal values of the manipulated variables are evaluated compared to the value of the objective function from the actual values of the variables. In all experiments, the recommendations are acceptable. The final results show an improvement in the operation of both the cement mill and kiln compared to the current operating condition.

In engineering practice, various types of information data are affected by many factors during the collection process. For example, information data measurement errors are caused by equipment performance and the working environment. During the transmission of detection information, the signal distortion caused by energy loss and signal interference causes unpredictable detection errors in the collected information data. Through the study of fractional calculus theory, it was found that it is suitable for studying nonlinear, non-causal, and non-stationary signals, and has the dual functions of improving detection information and enhancing signal strength. Therefore, under the influence of many factors, we applied the fractional difference algorithm to the field of information data processing. Multi-sensor detection data fusion algorithm based on the fractional partial differential equation was adopted to establish its online detection data. A multi-sensor detection data fusion algorithm based on a fractional partial differential equation is established, which effectively fuses the information data detection errors caused by various influencing factors and greatly improves the detection accuracy of information data. The effectiveness of this method is proved through its application in an experiment.

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

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

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

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

This article describes the choice of an optimization algorithm for solving problems and the optimal design of an unmanned aerial vehicle propeller. To solve the problem using evolutionary algorithms, it was transformed into an unconstrained optimization problem using a penalty function. The airfoil contours were constructed using a Bezier curve. Design variables were divided into two types: those that describe in general terms the propeller geometry or operation, such as propeller diameter, number of blades, and rev/min; and those that vary with propeller radius, such as chord length, effective airfoil angle, and airfoil geometry. The objective function is the calculation of the propeller power required to achieve a given thrust. The differential evolution algorithm was used to solve this problem.

Calculus, as a starting point to everyone's study of mathematics, was developed along with classical mechanics. Though not rigorously formulated, the intuition for differential form and infinitesimal motion makes calculus not hard to understand. And hence it does not require great effort to grasp the principles of classical mechanics. However, the situation becomes quite different when it comes to the quantum world. Given a particle system, what of interest is always the physical quantity of this system, such as energy, position, momentum, entropy, etc. But it is no longer straightforward.

The paper focuses on the different dynamical systems for the prey-predator model for different cases which includes greater depth of the food chain and varying number of preys and predators. We simulate the different postulated models and provide a comparative study for the same.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDE) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, this paper applies the deep learning algorithm to solve a class of high-dimensional nonlinear partial differential equations with jump terms and their corresponding backward stochastic differential equations (BSDE) with jump terms. Using the nonlinear Feynman-Kac formula, the problem of solving this kind of PDE is transformed into the problem of solving the corresponding backward stochastic differential equations with jump terms, and the numerical solution problem is turned into a stochastic control problem. At the same time, the gradient and jump process of the unknown solution are separately regarded as the strategy function and they are approximated respectively by using two multilayer neural networks as function approximators. Thus, deep learning-based method is used to overcome the “curse of dimensionality” caused by high-dimensional PDE with jump, and the numerical solution is obtained. In addition, this paper proposes a new optimization algorithm based on the existing neural network random optimization algorithm, and compares the results with the traditional optimization algorithm, and achieves good results. Finally, the proposed method is applied to three practical high-dimensional problems: Hamilton-Jacobi-Bellman equation, bond pricing under the jump Vasicek model and high-dimensional option pricing model with default risk. The proposed numerical method has obtained satisfactory accuracy and efficiency. The method has important application value and practical significance in investment decision-making, option pricing, insurance and other fields.

(1) Background: Motor neuron diseases (MNDs) are fatal neurodegenerative diseases. Biomarkers could help in defining patients’ prognosis and stratification. Beyond neurofilaments, chitinases are a promising family of possible biomarker, which correlate with neuroinflammatory status. We evaluated plasmatic levels of CHI3L1 in MNDs, MND mimics and healthy controls (HCs); (2) Methods: We used Sandwich ELISA to quantify CHI3L1 in plasma samples from 44 MNDs, 7 HSP, 9 MND mimics and 19 HCs. We collect also ALSFRSr scale, MRC scale, spirometry, mutational status, progression rate (PR), blood sampling, neuropsychological evaluation; (3) Results: Plasma levels of CHI3L1 resulted to be different among groups (p= 0.005). Particularly, MND mimics showed higher CHI3L1 levels compared to MNDs and HCs. CHI3LI levels did not differ among PMA, PLS and ALS and we do not find correlation among CHI3L1 levels and clinical scores, spirometry parameters, PR, and neuropsychological features. Of note, red blood cells count and haemoglobin correlated with CHI3L1 levels (respectively, p&lt;0.001, r=0.63; p= 0.022, r=0.52); (4) Conclusions: CHI3L1 plasma levels resulted to be increased in the MND mimics cohort when compared to MNDs. The increase of CHI3L1 in neuroinflammatory processes could explain our findings. We confirmed that CHI3L1 plasma levels did not differentiate between ALS and HCs and nor correlate with neuropsychological impairment.

A patient in her early 20s presented with constant and progressive lower abdominal and back pain, mainly on the right side of the abdomen, purulent vaginal discharge and pyrexia. Radio-logical assessment revealed a possible tuboovarian abscess and incidental diagnosis of ipsilateral renal agenesis. The patient was treated for pelvic inflammatory disease (PID), however after antibiotic administration and since the symptoms were not resolving, an abdominal MRI was requested which revealed a uterus didelphys with two cervices, an obstructed haemivagina and evidence of haematocolpos. The diagnosis of OHVIRA syndrome was confirmed and the patient underwent an excision of the vaginal septum, drainage of the haematopyocolpos and laparoscopic drainage of the tuboovarian abscess. She achieved a good recovery.

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

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

A systematic and comprehensive review of critical applications of Blockchain Technol-ogy with Differential Privacy integration lies within the privacy and security enhancement. This paper aims to highlight the research issues in the e-health domain (e.g., Electronic Medical Rec-ords) and to review the current research directions in Differential Privacy integration with Blockchain Technology.(1) Background: The current state of the art in the e-health domain is identified as follows: (a) healthcare information poses a high level of security and privacy concerns due to its sensitivity; (b) due to vulnerabilities surrounding the healthcare system, a data breach is common and presents a risk for attacks by an adversary; and (c) the current privacy and security apparatus needs further fortification. (2) Methods: The methodology uses a systematic literature review (SLR) to identify and select relevant research papers and academic journals in DP and BT. (3) Results: The results are categorized into: e-Health Record Privacy, Real-Time Health Data, and Health Survey Data Protection to identify inherent issues with Differential Privacy integra-tion with Blockchain and technical challenges.(4) Conclusion: This review thoroughly surveyed and summarized Differential Privacy mechanisms in EMR privacy, real-time health data, and health survey data protection while highlighting challenges.