This paper analyzes the robust dissipativity of uncertain stochastic generalized neural networks (USGNNs) with Markovian jumping parameters and time-varying delays. In practical applications most of the systems refer to uncertainties, hence, the norm-bounded parameter uncertainties and stochastic disturbance are considered. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and by employing integral inequalities LMI-based sufficient conditions of the considered systems are established. Numerical simulations are given to show the merit of the presented results.

This article presents a method of segmenting images with gray levels that uses Onicescu's information energy calculated in the context of the neutrosophic theory. Starting from the information energy calculation for complete neutrosophic information, it is shown how to extend its calculation for incomplete and inconsistent neutrosophic information. The segmentation method is based on calculation of thresholds for separating the gray levels using the local maximum points of the Onicescu information energy.

The purpose of this paper is threefold: (i) to introduce and study the Euler-Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemannian manifolds; (ii) to analyze some decomposable multivariate dynamics represented by Euler-Lagrange PDEs of least squares Lagrangians generated by flatness PDEs and Riemannian metrics; (iii) to give examples of explicit flat extremals and non-flat approximations.

In this paper we provide an ``expository overview" of classic epidemic projection models. Starting with the simple case of an epidemic that grows exponentially we then investigate ``compartmental" models. These assume that the growth of an infected population is limited endogenously by the size of the underlying pool of susceptibles. We then describe a new family of so-called "Exo-r" statistical models, which hinge on an exogenously driven growth rate of the infected population. This family, which can be used to model both infections and deaths, captures parsimoniously both the depletion of susceptibles and the effect of interventions such as lockdowns and ``social distancing". The model is used to fit numbers of Covid-19 infections in China. It is also used to model and project deaths in the United States. Results are used to inform a discussion on i) the challenges at hand and ii) the extent to which epidemic projection models may be useful despite being wrong.

Targeted radionuclide therapy (TRT) has recently seen a surge in popularity, with the use of radionuclides conjugated to small molecules and antibodies. Similarly, immunotherapy also has shown promising results – an example being chimeric antigen receptor (CAR) T-cells therapy in hematologic malignancies. Moreover, TRT and CAR T therapies possess unique features that require special consideration when determining how to dose, time, and sequence combination treatments, including the distribution of TRT dose in the body, the decay rate of the radionuclide, and the proliferation and persistence of the CAR-T cells. These characteristics complicate additive or synergistic effects of combination therapies and warrant a mathematical treatment which includes these dynamics in relation to the proliferation and clearance rates of the target tumor cells. Here we combine two previously published mathematical models in a multiple myeloma setting to explore the effects of dose, timing, and sequencing of TRT and CAR-T cell based therapies. We find that for a fixed TRT and CAR-T cell dose, the tumor proliferation rate is the most important parameter in determining the best timing of TRT and CAR T therapies.

3D Zernike moments based on 3D Zernike polynomials have been successfully applied to the field of voxelized 3D shape retrieval and have attracted more attention in biomedical image processing. As the order of 3D Zernike moments increases, both computational efficiency and numerical accuracy decrease. Due to this phenomenon, a more efficient and stable method for computing high-order 3D Zernike moments was proposed in this study. The proposed recursive formula for computing 3D Zernike radial polynomials combines the recursive calculation of spherical harmonics to develop a voxel-based algorithm for the calculation of 3D Zernike moments. The algorithm was applied to the 3D shape Michelangelo's David with a size of 150×150×150 voxels. As compared to the method without additional acceleration, the proposed method uses a group action of order sixteen orthogonal group and saving unnecessary iterations, the factor of speed-up is 56.783±3.999 when the order of Zernike moments is between 10 and 450. The proposed method also obtained an accurate reconstructed shape with the error rate (normalized mean square error) of 0.00 (4.17×10^-3) when the reconstruction was computed for all moments up to order 450.

In this paper, we study the existence of the random -pullback attractor of a non-autonomous local modified stochastic Swift-Hohenberg equation with multiplicative noise in stratonovich sense. It is shown that a random -pullback attractor exists in when its external force has exponential growth. Due to the stochastic term, the estimate are delicate, we overcome this difficulty by using the Ornstein-Uhlenbeck(O-U) transformation and its properties.

In this paper we provide a highly selected review and synthesis on some of the recent and notable contribution to research in portfolio analysis. A unique perspective on this development in the literature is offered in this paper by judiciously identifying a few sample eigenvalues adjustment patterns in a portfolio that leads to an improvement in the out-of-sample portfolio Sharpe ratio when the population covariance matrix admits a high-dimensional factor model. These patterns unveil a key insight into a portfolio performance improvement and shed an important light on the effectiveness of a few recently introduced ”robust to estimation errors” covariance matrix estimation approaches, which were not originally designed with the goal to improve the out-of-sample portfolio performance.

In this paper, by extending some results of informational genomics, we present a new randomness test based on the empirical entropy of strings and some properties of repeatability and unrepeatability of substrings of certain lengths. We give the theoretical motivations of our method and some experimental results of its application to a wide class of strings: decimal representations of real numbers, roulette outcomes, logistic maps, linear congruential generators, quantum measurements, natural language texts, and genomes. It will be evident that the evaluation of randomness resulting from our tests does not distinguish among the different sources of randomness (natural, or pseudo-casual).

In real financial market, the delayed market feedback and the delayed effect of government macro-control are inevitable. And both the delay of market feedback and the delay of macro-control effect bring about the mathematical difficulties in studying stabilization and synchronization of the hyper-chaotic financial system. However, employing Lyapunov function method, differential mean value theorem, suitable bounded hypotheses and pulse control technology results in the globally asymptotical stabilization and synchronization criteria. It is the first paper to drive the stabilization and synchronization criteria under the assumptions of the double delays. Finally, numerical examples illuminate the effectiveness of the proposed methods.

There is no method of predicting the price of an option other than hedging strategies such as the binomial hedging strategy, the Black-Scholes hedging strategy and others. The price of an option is defined to be equal to the amount the seller needs to implement a hedging strategy. We will study these two basic hedging strategies in terms of their feasibility and we will see that the Black-Scholes hedging strategy is not feasible because this strategy demands instantaneously rebuilding the replicating portfolio. Consequently, the real world prices of the options are not relevant at all with the Black-Scholes hedging strategy! We will suitably redefine the binomial hedging strategy so that it will be practically useful and present other feasible and generally more effective hedging strategies with some of them are practically useful for options with no tradable underlying assets. Finally, we will mention some open questions related to the above.

Information-related measures are useful tools for multi-variable data analysis, as measures of dependence among variables, and as descriptions of order and disorder in biological and physical systems. Measures, like marginal entropies, mutual / interaction / multi -information, have long been used in a number of fields including descriptions of systems complexity and biological data analysis. The mathematical relationships among these measures are therefore of significant inherent interest. Relations between common information measures include the duality relations based on Möbius inversion on lattices. These are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). While these relationships are of significant interest there has been, to our knowledge, no systematic examination of the full range of relationships of this diverse range of functions into a unifying formalism as we do here. In this paper we define operators on functions on these lattices based on the Möbius inversions that map functions into one another (Möbius operators). We show that these operators form a simple group isomorphic to the symmetric group S₃. Relations among the set of functions on the lattice are transparently expressed in terms of the operator algebra, and, applied to the information measures, can be used to derive a wide range of relationships among diverse information measures. The Möbius operator algebra is naturally generalized which yields extensive new relationships. This formalism now provides a fundamental unification of information-related measures, and the isomorphism of all distributive lattices with the subset lattice implies an even broader application of these results.

Energy efficiency of Data Center (DC) operations heavily relies on IT and cooling systems performance. A reliable and efficient cooling system is necessary to produce a persistent flow of cold air to cool servers that are subjected to constantly increasing computational load due to the advent of IoT- enabled smart systems. Consequently, increased demand for computing power will bring about increased waste heat dissipation in data centers. In order to bring about a DC energy efficiency, it is imperative to explore the thermal characteristics analysis of an IT room (due to waste heat). This work encompasses the employment of an unsupervised machine learning modelling technique for uncovering weaknesses of the DC cooling system based on real DC monitoring thermal data. The findings of the analysis result in the identification of areas for energy efficiency improvement that will feed into DC recommendations. The methodology employed for this research includes statistical analysis of IT room thermal characteristics, and the identification of individual servers that frequently occur in the hotspot zones. A critical analysis has been conducted on available big dataset of ambient air temperature in the hot aisle of ENEA Portici CRESCO6 computing cluster. Clustering techniques have been used for hotspots localization as well as categorization of nodes based on surrounding air temperature ranges. The principles and approaches covered in this work are replicable for energy efficiency evaluation of any DC and thus, foster transferability. This work showcases applicability of best practices and guidelines in the context of a real commercial DC that transcends the set of existing metrics for DC energy efficiency assessment.

Critical infrastructures are those that are essential. For this type of infrastructure, it is necessary to implement analytical methodologies that will allow us to quickly obtain the susceptibility or resilience and possible damage generated in extreme precipitation episodes, through a holistic perspective in which the factors linked to hydrological risk intervene. In particular, urban hydraulic infrastructures are analyzed considering the degree of criticality, defined as the number of interactions on the different activities of the population. For this purpose, a hydrological risk analysis methodology is required. This methodology is focused on an integral approach of the system indicators to be analyzed and linked to the hydrological threat. This work proposes to delimit and analyze those factors that involve risk using an analytical expression. This model will estimate the damage to these infrastructures breaking down the factors involved in the risk equation and analyzing their variability according to the intrinsic characteristics linked to them as well as the interaction with external factors.

We introduce a new, and quite general variational model for opinion dynamics based on pairwise interaction potentials and a range of opinion evolution protocols ranging from random interactions to global synchronous flows in the opinion state space. The model supports the concept of topic “coupling”, allowing opinions held by individuals to be changed via indirect interaction with others on different subjects. Interaction topology is governed by a graph that determines interactions. Our model, which is really a family of variational models, has, as special cases, many of the previously established models for the opinion dynamics. After introducing the model, we study the dynamics of the special case in which the potential is either a tent function or a constructed bell-like curve. We find that even in these relatively simple potential function examples there emerges interesting behavior. We also present results of preliminary numerical explorations of the behavior of the model to motivate questions that can be explored analytically

This paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}²)),y_{n+1}=A+B((x_{n})/(x_{n-m}²)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

In this paper we investigate the global asymptotic stability of following system ofhigher order difference equations with quadratic terms:xn+1=A+Byn/yn−m^2, yn+1=A+Bxn/xn−m^2, where A and B are positive numbers and the initial values are positive numbers.We also study the boundedness, rate of convergence and oscillation behaviour of thesolutions of related system.

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.

Malaria is a critical fevered illness caused by Plasmodium parasites transmitted among people through the bites of infected female Anopheles mosquitoes. Public awareness about the disease is important for the control of disease. This article proposes a mathematical model to study the dynamics of malaria disease transmission with the influence of awareness-based control interventions. We found two equilibria of the model, namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable globally if basic reproduction number (R0) is less than unity (R0<1). Some basic mathematical properties of the proposed model, such as nonnegativity and boundedness of solutions, the feasibility of the equilibrium points and their stability properties, have been studied. Finally, we adopted optimal control to minimize the cost of disease control and solve the problem by formulating Hamiltonian functional. The optimal use of insecticides for controlling the mosquito population is determined. Numerical simulations have been provided for the confirmation of the analytical results. We conclude that media awareness with optimal control approach is best for cost-effective malaria disease management.

In this age of Facebook, Instagram, and Twitter, there is rapidly growing interest in understanding network-enabled opinion dynamics in large groups of autonomous agents. The phenomena of opinion polarization, the spread of propaganda and fake news, and the manipulation of sentiment is of interest to large numbers of organizations and people. Whether it is the more nefarious players such as foreign governments that are attempting to sway elections or it is more open and above board, such as researchers who want to make large groups of people aware of helpful innovations, what is at stake is often significant. In this paper, we review opinion dynamics including the extensions of many classical models as well as some new models that deepen understanding. For example, we look at models that track the evolution of an individual’s power, that include noise, and that feature sequentially dependent topics, to name a few. While the first papers studying opinion dynamics appeared over 60 years ago, there is still a great deal of room for innovation and exploration. We believe that the political climate and the extraordinary (even unprecedented) events in the sphere of politics in the last few years will inspire new interest and new ideas. It is our aim to help those interested researchers understand what has already been explored in a significant portion of the field of opinion dynamics. We believe that in doing this, it will become clear that there is still much to be done.

By partly generalizing the Lipschitz condition of existing results to the generalized Lipschitz one, the author utilizes a fixed point theorem, variational method and Lyapunov function method to derive the unique existence of globally asymptotical input-to-state stability of positive stationary solution for Gilpin-Ayala competition model with diffusion and delayed feedback under Dirichlet zero boundary value. Remarkably, it is the first paper to derive the unique existence of the stationary solution of reaction-diffusion Gilpin-Ayala competition model, which is globally asymptotical input-to-state stability. And numerical examples illuminate the effectiveness and feasibility of the proposed methods.

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.

In this study, by using Least Square Method, the dataset for the Gross Domestic Product per capita is modeled as a function satisfying the fractional differential equation. The function itself is assumed to be the finite summation of its previous values and the derivatives with unknown coefficients. Then, the prediction for the upcoming years is done by having an approach dividing the dataset into 4 regions corresponding to four different tasks. The mathematical model of the Gross Domestic Product (GDP) per capita of the countries (and union) which are Brazil, China, European Union (EU), India, Italy, Japan, UK, the USA, Spain, and Turkey is constructed with a new methodology called as the deep assessment method which comes from the expressing an arbitrary function modeling the dataset as the finite summation of its previous values and the derivatives with unknown coefficient. The method uses the fractional calculus properties combining with Least Square Method and is compared to Long short-term memory (LSTM) algorithm which is a special type of neural network used for time sequences in general.

Present study offers mathematical calculations of the roll-coating procedure lubricated with upper Convected Maxwell Fluid. An incompressible isothermal viscoelastic fluid is considered with roll and the porous web having uniform velocities. By employing Lubrication Approximation Theory, the desired equations of motion for the fluid concerned over porous web are modelled and analyzed. The suction rate on the web and injection rate at the roll surface are anticipated proportionate. Results for velocity profile and pressure gradient are obtained analytically. Fluid parameters of industrial significance i.e. detachment point, pressure, sheet /roll separating force, power contribution and coating thickness are also calculated numerically. Substantial and monotonic increase is witnessed in these quantities with the increase of flow parameters.

This research investigates a model for the COVID-19 outbreak in Indonesia by analyzing comorbid diseases, self-quarantine, government-provided quarantine, and immunization regimens. Some model parameters are derived from academic journals, others are extrapolated from data collected by the Indonesian Ministry of Health in 2020, and others are assumed. Evaluation of the model reveals non-endemic equilibrium points, endemic equilibrium points, and the basic reproduction number (BRN). The contact rate and infected probability factors impact the increase in the number of COVID-19-infected individuals with comorbid disease within a group. According to the sensitivity analysis of the BRN, the key parameters impacting the spread of COVID-19 are the rate of susceptible recruitment, the rate of contact, the COVID-19 infection death rate, and the likelihood of infection. In addition, sensitivity analyses are provided to examine the effect of parameter changes on subpopulations. We discovered that the natural death rate is the most sensitive parameter based on the sensitivity index after reaching equilibrium. Symmetry aspects appear in some of the visualization of the model’s solution and the BRN and parameters’ sensitivity.

Diabetes is a serious health problem throughout the world, including in Indonesia. The International Diabetes Federation (IDF) reports that the number of adults with diabetes is increasing every year. The Behavioral Risk Factor Surveillance System (BRFSS) is a survey conducted by the Centers for Disease Control and Prevention (CDC) in the United States. Classification methods in data mining techniques are used to classify diabetics and non-diabetics. The data mining process is carried out by preprocessing, feature selection, and dataset classification stages. In the preprocessing stage, data cleaning, data formatting, and data oversampling are carried out using the Synthetic Minority Over-sampling Technique (SMOTE). Next, the feature selection stage is carried out using the Particle Swarm Optimization (PSO) algorithm to find the best attributes. The dataset classification stage is carried out using the CART Model Decision Tree algorithm. The results of the performance evaluation of the CART algorithm are calculated using the confusion matrix and the MAE value, the results obtained for the CART algorithm without SMOTE and PSO obtained the best accuracy of 75.34% and the MAE value of 0.2466, while the CART algorithm using SMOTE and PSO can increase accuracy by 10 .94% to 86.28% and an MAE value of 0.1372.

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

We review a modern differential geometric description of the fluid isotropic motion and featuring it the diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. There is analyzed the adiabatic liquid dynamics, within which, following the general approach, there is explained in detail, the nature of the related Poissonian structure on the fluid motion phase space, as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product. We also present a modification of the Hamiltonian analysis in case of the isotermal liquid dynamics. We study the differential-geometric structure of the adiabatic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and invariant theory. In particular, we construct an infinite hierarchies of different kinds of integral magneto-hydrodynamic invariants, generalizing those before constructed in the literature, and analyze their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, some generalization of the canonical Lie-Poisson type bracket is obtained.

We use a system biology approach to translate the interaction of Bacillus Calmette-Gurin (BCG) + interleukin 2 (IL-2) for the treatment of bladder cancer into a mathematical model. The model is presented as a system of differential equations with the following variables: number of tumor cells, bacterial cells, immune cells, and cytokines involved in the tumor-immune response. This work investigates the delay effect induced by the proliferation of tumor antigen-specific effector cells after the immune system destroys BCG-infected urothelium cells following BCG and IL-2 immunotherapy in the treatment of bladder cancer. For the proposed model, three equilibrium states are found analytically. The stability of all equilibria is analyzed using the method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs).

In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in two-price financial models (where there is a bid-ask price spread), the set of attainable gains is not a subspace anymore. We use convex optimization, and the conic property of this region to characterize the “No-Arbitrage” principle in financial models with the bid-ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.

In this article, the connections amid matroid and other notions have been studied. The structure of matroid could be a reflection of some other structure in lattice theory, group theory, other algebraic structure, graph theory, combinatorics and enumeration theory.

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.

A correct system design can be systematically obtained from a specification model of a real-time system that integrates hybrid measurements in a realistic industrial environment, this has been carried out through complete Matlab / Simulink / Stateflow models. However, there is a widespread interest in carrying out that modeling by resorting to Machine Learning models, which can be understood as Automated Machine Learning for Real-time systems that present some degree of hybridization. An induction motor controller which must be able to maintain a constant air flow through a filter is one of these systems and it is discussed in the paper as a study case of closed-loop control system. The article discusses a practical application of ML methods that demonstrates how to replace such closed loop in industrial control systems with a Simulink block generated from neural networks to show how the proposed procedure can be applied to derive complete hybrid system designs with artificial neural networks (ANN). In the proposed ANN-based method to design a real-time hybrid system with continuous and discrete components, we use a typical design of a neural network, in which we define the usual phases: training, validation, and testing. The generated output of the model is made up of reference variables values of the cyber-physical system, which represent the functional and dynamic aspects of model. They are used to feed Simulink/Stateflow blocks in the real target system.

The efficient generation of high-quality random numbers is essential in the operation of cryptographic modules. The quality of a random number generator is evaluated by the min-entropy of its entropy source. Typical method used to achieve high min-entropy of the output sequence is an entropy accumulation based on a hash function. This is grounded in the famous Leftover Hash Lemma which guarantees a lower bound on the min-entropy of the output sequence. However, the hash function based entropy accumulation has slow speed in general. For a practical perspective we need a new efficient entropy accumulation with the theoretical background for the min-entropy of the output sequence. In this work, we obtain the theoretical bound for the min-entropy of the output random sequence through the very efficient entropy accumulation using only bitwise XOR operations, where the input sequences from the entropy source are independent. Moreover we examine our theoretical results by applying to the quantum random number generator that uses dark noise arising from image sensor pixels as its entropy source.

This article presents a new method of segmenting images with gray levels. The method is based on determining several thresholds for separation of gray levels. The determination of these thresholds is done using the certainty of the neutrosophic information. The concept of this method can be stated simply: to choose the local maximums for the neutrosophic certainty.

The widely used logistic model for epidemic case reporting data may be either restrictive or unrealistic in presence of containment measures when implemented after an epidemic outbreak. For flexibility in epidemic case reporting data modelling, we combined an exponential growth curve for the early epidemic phase with a flexible growth curve to account for the potential change in growth pattern after implementation of containment measures. We also fitted logistic regression models to recoveries and deaths from the confirmed positive cases. In addition, the growth curves were integrated into a SIQR (Susceptible, Infective, Quarantined, Recovered) model framework to provide an overview on the modelled epidemic wave. We focused on the estimation of: (1) the delay between the appearance of the first infectious case in the population and the outbreak (“epidemic latency period"); (2) the duration of the exponential growth phase; (3) the basic and the time-varying reproduction numbers; and (4) the peaks (time and size) in confirmed positive cases, active cases and new infections. The application of this approach to COVID-19 data from West Africa allowed to discuss the effectiveness of some containment measures implemented across the region.

We investigate, whereas the SU(4)/SU(2) model, is viable for describing strong interactions. The existing problems of confinement and asymptotic freedom, two phenomena that can not be described by the SU(3) model, might indicate that we need something "larger" than the SU(3) model. The considered coset SU(4)/SU(2) or the Stiefel manifold V^2(C_4) contains an su(3) algebra, plus additional degrees of freedom that resembes the Feddev-Poppov concept. The richer structure of this coset, give us enough room, to seek for new phenomena, as its dimensionality is 12. The consideration of the SU(4)/SU(2) model flavors firstly the unification of nuclear fields (strong and weak) in an SU(4) model.

We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

In the present study we introduce a deterministic mathematical model in order to study the interaction between the human immune system and a virus, like COVID 19. The mathematical analysis is based on the tools of dynamical systems theory, by modeling the interactions between the immune system and the virus, using a predator-prey method and following the ideas of G. Moza, from \cite{TGV}. It will be obtained some conclusions with medical relevance and the main three of them are the followings: 1) A deficiency of a single type of immunity in the early stages of virus proliferation, may lead to a large virus multiplication and the human body can loses the fight against this virus; 2) If the level of all components of the immunity system are at the normal threshold from the first moment of the infection and the immune system kill the virus at higher rate than the rate of virus reproduction, then the human body has the ability to stop the multiplication of the virus and liquidate it, that means the virus will be destroyed; 3) If the level of at least one type of immunity can be increased beyond the normal threshold, by medical interventions (like vaccination) in the early stages of virus infection, then the immune system has a better chance to win the fight with the virus.

The capacitated team orienteering problem with time windows (CTOPTW) is a NP-hard combinatorial optimization problem. In the CTOPTW, a set of customers is given each with a profit, a demand, a service time and a time window. A homogeneous fleet of vehicles is available for serving customers and collecting their associated profits. Each vehicle is constrained by a maximum tour duration and a limited capacity. The CTOPTW is concerned with the determination of a preset number of vehicle tours that begin and end at a depot, visit each customer no more than once while satisfying the time duration, time window and vehicle capacity constraints on each tour. The objective is to maximize the total profit collected. In this study we propose an iterated local search (ILS) algorithm to deal with the CTOPTW. ILS is a single solution based meta-heuristic that successively invokes a local search procedure to explore the solution space. A perturbation operator is used to modify the current local optimum solution in order to provide a starting solution for the local search procedure. As different problems and instances have different characteristics, the success of the ILS is highly dependent on the local search procedure, the perturbation operator(s) and the perturbation strength. The basic ILS uses a single perturbation operator and the perturbation strength remains the same during the optimization process. To address these issues, we use three different perturbation operators and a varying perturbation strength which changes as the algorithm progresses. The idea is to assign a larger perturbation strength in the early stages of the search in order to focus on exploring the search space. The perturbation strength is gradually decreased so that we focus more on exploitation. The computational results show that the proposed ILS algorithm is able to generate high quality solutions on the CTOPTW benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both the solution quality and computational time. Moreover, the proposed ILS produces 21 best known results and 5 new best solutions.

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Rapid climate change requires more powerful and precise modeling methods to forecast future climate variability. The GSTARIMA Model is efficient, combining space-time analysis with the Autoregressive Moving Average (ARIMA) Model. The integration of heteroscedasticity error and the Kriging method can strengthen the Model's ability to handle the problem of non-constant error variance in the GSTARIMA Model and forecast at unobserved locations of climate observations. This paper's Systematics Literature Review (SLR) is presented comprehensively with the principal aim of developing a thorough understanding of applying the GSTARIMA Model with heteroskedasticity error and the Kriging Method in climate forecasting following the Data Analytics Lifecycle methodology. The Systematic Literature Review (SLR) process consists of three main stages. We sourced the articles from databases such as Scopus, Dimensions, and EBSCO-Host The subsequent stage involved conducting a comprehensive literature review using the PRISMA method to ensure rigor and depth. Additionally, we performed bibliometric analysis to enhance rigor. Lastly, we conducted a gap analysis session to scrutinize existing research on the GSTARIMA Model and identify new opportunities. This literature review reveals that integrating GSTARIMA Model with heteroscedasticity errors and the Kriging method is suitable for climate forecasting. This research inspires researchers to contribute to the improvement and refinement of the Model, making it a more potent and valuable tool in climate forecasting.

The aim of this work is to explain the behaviour of the multiresistance percentage of Pseudomona aeruginosa in some countries of Europe through a multivariate statistical analysis and machine learning validation, using data from the European Antimicrobial Resistance Surveillance System, the World Health Organization and the World Bank. First, we will use a descriptive analysis and a principal components analysis. Then, we use a k-means clustering to determine the countries and regions that are most affected by the antibiotic resistance. Second, we expand the database by adding some socioeconomic, governance and antibiotic-consumption variables. We then run a data panel regression analysis to determine some functions that relates the multiresistance percentage with those new variables. Finally, we use machine learning techniques to validate a pooling panel data case, using XGBoost and random forest algorithms. The results of the data panel analysis indicate that the most important variables for the multiresistance percentage are corruption control and the rule of law. Similar results are found with the machine learning validation analysis, where the human development index is an additional important variable for the multiresistance percentage.

Nowadays the practice of developing algorithms to maintain the confidentiality of data shows that there is a lack of some features, such as velocity, predictability, etc. Generating pseudorandom numbers is one such problem that lies in the basement of many algorithms, even in hardware microprograms. An unreliable generator can cause cyberattacks on it, despite the security in the upper layers. At the same time, the algorithm should be fast enough to provide uninterrupted circuit work for the entire system. The paper presents a new algorithm generating pseudorandom numbers on cellular automata, which is not only fast and easy-repeating, but unpredictable enough and can be used in cryptographic systems. Using the NIST statistical test suite for random and pseudorandom number generators (PRNG), it is shown that the presented algorithm is more than three times superior to the state-of-the-art methods and algorithms in terms of ? − ?????. A high level of the presented algorithm’s parallelization allows for implementation it effectively on calculators with parallel structure. CPU-based architecture, FPGA-based architecture, CUDA- based architecture of PRNG and different PRNG implementations are presented to confirm high performance of the proposed solution.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Instead of the conventional 0 and 1 values, bipolar reasoning uses -1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., “uncertain” lies between “impossible” and “totally sure”). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e., William of Ockham and Nicholas of Autrecourt, who embodied a bipolar mode of thought that is eminently modern. Starting from the trivial observation that “once a wheat sheaf is sealed and tied up, the packed down straws display the same orientation”, we work up a new theory of the bipolar nature of networks, suggesting that orthodromic (i.e., feedforward, bottom-up) projections might be functionally coupled with antidromic (i.e., feedback, top-down) projections via the mathematical apparatus of presheaves/globular sets. When an entrained oscillation such as a neuronal spike propagates from A to B, changes in B might lead to changes in A, providing unexpected antidromic effects. Our account points towards the methodological feasibility of novel neural networks in which message feedback is guaranteed by backpropagation mechanisms endowed in the same feedforward circuits. Bottom-up/top-down transmission at various coarse-grained network levels provides fresh insights in far-flung scientific fields such as object persistence, memory reinforcement, visual recognition, Bayesian inferential circuits and multidimensional activity of the brain. Implying that axonal stimulation by external sources might backpropagate and modify neuronal electric oscillations, our theory also suggests testable previsions concerning the optimal location of transcranial magnetic stimulation’s coils in patients affected by drug-resistant epilepsy.

A calibrated mathematical model of antiviral immune response to SARS-CoV-2 infection is developed. The model considers the innate and antigen-specific responses to SARS-CoV-2 infection. Recently published data sets from human challenge studies with SARS-CoV-2 were used for parameter estimation. Understanding the regulation of multiple intertwined reaction components of the immune system is necessary for linking the clinical phenotypes of COVID-19 with the kinetics of immune responses. Consideration of multiple immune reaction components in a single calibrated mathematical model allowed us to address some fundamental issues related to pathogenesis of COVID-19, i.e. sensitivity of the peak viral load to parameters characterizing the specific response components, the kinetic coordination of the individual responses, and the factors favoring a prolonged viral persistence. The model provides a tool for predicting the infectivity of patients, i.e. the amount of virus which is transmitted via droplets from the person infected with SARS-CoV-2, depending on the time of infection. The thresholds in the relative unbalance between innate and adaptive response parameters which lead to a prolonged persistence of SARS-CoV-2 due to the loss of a kinetic response synchrony/coordination were identified.

We consider a control problem for a diffusive PDE model of heterogeneous population of thermostatically controlled loads (TCLs) aiming to balance the aggregate power consumption within a given amount of time. Using the Green’s function approach, the problem is formulated as an approximate controllability problem for a residue depending on control parameters nonlinearly. A sufficient condition for approximate controllability is derived in terms of initial temperature distribution, operation time of TCLs and threshold value of the aggregate power consumption. Case studies allow to reveal the advantages of the proposed solution from numerical calculations point of view.

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

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.

The negative binomial regression model (NBRM) is a generalized linear model which relaxes the restrictive assumption by the Poisson regression model when the variance is equal to the mean. The estimation of the parameters of the NBRM is obtained using the maximum likelihood (ML) method. Maximum likelihood estimator becomes unstable when the explanatory variables are linearly dependent, a situation known as multicollinearity. Based on this, we developed a new estimator called modified jackknifed Negative Binomial Kibria-Lukman (MJNBKL) estimator for the radiation of multicollinearity in NBRM using four different biasing (shrinkage) parameters. We establish superiority condition for MJNBKL estimator over the ones. The performance MJNBKL estimator was ascertained by comparing it with the existing ones through a Monte Carlo simulation study and two real life application datasets. The results of the simulation and real life application show that MJNBKL estimator outperformed the other estimators compared with by having the smallest MSE across all sample sizes and for different levels of correlation for the four biasing parameters used and the third biasing parameter is the optimal shrinkage parameter with the lowest MSE.

Often, when solving forward, inverse or data assimilation problems, only a part of the solution is needed. As a model, we consider the stationary diffusion problem. We demonstrate an algorithm that can compute only a part or a functional of the solution, without calculating the full inversion operator and the complete solution. It is a well-known fact about partial differential equations that the solution at each discretisation point depends on the solutions at all other discretisation points. Therefore, it is impossible to compute the solution only at one point, without calculating the solution at all other points. The standard numerical methods like a conjugate gradient or Gauss elimination compute the whole solution and/or the complete inverse operator. We suggest a method which can compute the solution of the given partial differential equation 1) at a point; 2) at few points; 3) on an interface; or a functional of the solution, without computing the solution at all points. The required storage cost and computational resources will be lower as in the standard approach. With this new method, we can speed up, for instance, computation of the innovation in filtering or the likelihood distribution, which measures the data misfit (mismatch). Further, we can speed up the solution of the regression, Bayesian inversion, data assimilation, and Kalman filter update problems. Applying additionally the hierarchical matrix approximation, we reduce the cubic computational cost to almost linear $\mathcal{O}(k^2n \log^2 n)$, where $k\ll n$ and $n$ is the number of degrees of freedom. Up to the hierarchical matrix approximation error, the computed solution is exact. One of the disadvantages of this method is the need to modify the existing deterministic solver.

Symbolic pole/zero analysis is an important step when designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. In this study, we present a mathematical model combined with a heuristic-metaheuristic solution method for the symbolic pole/zero simplification in operational transconductance amplifiers (OTA). At first, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is performed for the simplification of the derived symbolic pole/zero expressions. The developed method has been tested on three analog OTAs. The obtained results show the effectiveness of the proposed method to achieve accurate simplified symbolic pole/zero expressions with the least complexity.

Radiation Fireballs are singular phenomena which involve severe thermal radiation and consequently, they need to be duly assessed and prevented. Although the radiative heat transfer produced by a sphere is relatively well known, the shadowing measures implemented to control the fireball’s devastating effects have frequently posed a difficult analytical instance, mainly due to its specific configuration. In this article, since the usual solving equations for the said cases are impractical, the authors propose a novel graphic-algorithm method that sorts the problem efficiently for different kinds of obstructions and relative positions of the fireball and the defenses. Adequate application of this method may improve the safety of a significant number of facilities exposed to such risks.

Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells and CAR T cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T cells and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load and tumor burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model.

Digital twins are the foundation of autonomous off-road vehicles. Dynamic reduction methods are one of several ways to develop digital twins for off-road vehicles. The article commences with a comprehensive overview of the most widely used dynamic reduction methods and then introduces performance metrics for assessing their efficacies in the context of digital twins. The paper additionally includes a detailed mathematical derivation of the state-space representation for reduced-order finite element models. The state-space representation of the reduced finite element models facilitates their export to problem-solving environments for dynamic analysis. The state-space models are eventually solved utilizing the built-in libraries of numerical solvers in textual and graphical programming platforms. In addition, the article identifies the set of solvers that best suit the simulation of virtual models for off-road vehicles. This article also includes an evaluation of the simulation results of digital models with modes ranging from 0 to 30 Hz. In addition, the article demonstrates the lower bound of the frequency range necessary and sufficient to be retained in off-road vehicle virtual models. Finally, the paper presents the simulation outcomes for digital models of commercial off-road vehicles with custom-built control, electrical, and control systems.

We present a differentially private extension of the block coordinate descent based on objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, the algorithm also offers a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from an analysis without differential privacy. The algorithm’s performance is compared with the standard block coordinate descent algorithm and the trade-off between utility and privacy is studied. The performance is studied using both artificial test data and the forest fires data set. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.

The kind of set which is based on edges, is introduced. The analysis on this set is done in the matter of operation which are the classes of graphs. The general notion which is related to this concept, is up. The set of edges is seen in the matter of common vertex, entitled neighbor edges and the set of edges which has specific condition on the vertices of graphs, entitled ghost set. The kind of viewpoint when the edges are up so the kind of efforts to assign some notions which get the sensible result of edges which make sense about these two types of notions. Notions of having some attributes about vertices concerning edges and edges' attributes to get result about edges in the matter of vertices.

This article develops duality principles and numerical results for a large class of non-convex variational models. The main results are based on fundamental tools of convex analysis, duality theory and calculus of variations. More specifically the approach is established for a class of non-convex functionals similar as those found in some models in phase transition. Finally, in the last section we present a concerning numerical example and the respective software.

In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number n after several iterations. This formula is used in one case that we analyze using the mathematical complete induction method in the process of demonstrating the conjecture.

This paper presents an algorithm for the fully automatic mesh generation for the finite element analysis of ships and offshore structures. The quality requirements on the mesh generator are imposed by the acceptance criteria of the classification societies as well as the need to avoid shear locking when using low degree shell elements. The meshing algorithm will be generating quadrilateral dominated meshes (consisting of quads and triangles) and the mesh quality requirements mandate that quadrilaterals with internal angles close to $90\degree$ are to be preferred. The geometry is described by a dictionary containing points, rods, surfaces and openings. The first part of the proposed method consist of an algorithm to automatically clean the geometry. The corrected geometry is then meshed by the frontal Delaunay mesh generator as implemented in the gmsh package. We present a heuristic method to precondition the cross field of the frontal quadrilateral mesher. Also the influence of the order in which the plates are meshed will be explored as a preconditioning step.

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

A method for noise reduction of spectra based on fitting a multi-window model is presented. The spectrum is modeled as the sum of the polynomial background and Lorentzian peaks. This model applies to all points in the spectrum and to all window sizes. An iterative algorithm is used for fitting. Based on the initial data, the background calculated by the direct least squares method is subtracted. Positive data values ​​are inverted using the 1/x function and the same procedure is used to fit the Lorentzian peaks. The weighted sum of all windows fit containing the point to be processed is used as the result. The weighting factors are calculated by evaluating the quality of the fit. The performance of the presented method is compared with the Savitsky-Golay method and the wavelet noise reduction method. The proposed approach provides good noise reduction performance without using user-entered parameters.

We compute explicitly trace of one-dimensional diffusion process which can be regarded as a Dirichlet form on graphs and we study its conservativeness property. Finally, we give an example of a discretization of one dimensional diffusion of Bessel's process with order $\nu$.

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.

Unlike the volume, the expression for the lateral area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. As this form is relatively used in engineering, the inability to determine its surface, represents a serious hindrance for several problems which arise in radiative transfer, lighting and construction, to cite just a few. Since this particular shape can be conceived as a set of linearly dwindling ellipses which remain parallel to a circular directrix, a typical problem appears when looking for the length of such ellipses. We conceived a new procedure which, in principle, consists in dividing the surface into infinitesimal elliptic strips to which we have subsequently applied Ramanujan’s second approximation. In this fashion, we can obtain the perimeter of any ellipse pertaining to the said form as a function of the radius of the directrix and the position of the ellipse’s center on the X-axis. Integrating the so-found perimeters of the differential strips for the whole span of the conoid, an unexpected solution emerges through the newly found number psi (ψ). As the strips are slanted in the symmetry axis, their width is not uniform and we need to perform some adjustments in order to complete the problem with sufficient precision. Relevant implications for technology, building science, radiation and structure are derived in the ensuing discussion.

Magnetic Nanoparticles (MNPs) is a promising technique to cure brain diseases. On the one hand, by serving as drug carriers, they can bypass the blood-brain barrier and deliver drug molecules to the brain parenchyma; on the other hand, their transport trajectory can be manipulated by applying an external magnetic field. However, due to the complex microstructure of brain tissues, e.g. the anisotropy of white matter (WM), how to achieve desired drug distribution patterns, e.g. uniform distribution, by tuning the drug delivery system is largely unknown. Here, in this study, by adopting a mathematical model capable of capturing the diffusion trajectories of MNPs in the microstructures, we systematically investigated the effects of key parameters in the MNPs delivery system on the equivalent diffusion coefficient of MNPs in the microenvironment of brain WM. The results show that uniform distribution of MNPs in anisotropic tissues can be achieved by adjusting the particle size and magnetic field. We have not only obtained a deeper understanding on how to optimise the MNPs delivery system, it can also be anticipated that an improved mathematical model could even help to achieve complex drug distribution patterns in the complicated brain environment by designing an appropriate combination of the key parameters.

Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave, had subsequent waves of the COVID-19 infections and it remains to be seen whether there will be more waves. In this paper, we formulate a deterministic model for COVID-19 incorporating dynamic non-pharmaceutical interventions, dubbed social dynamics. The model steady states are determined and their stability analysed. Numerical simulations are carried out to determine the pack of various parameters that influence the social dynamics. In South Africa, the first wave was the only wave in which the only interventions rested solely on human behavior. The model is thus fitted to COVID-19 data on the first wave in South Africa. The results presented in this paper have implications on the trajectory of the pandemic in the presence of changing social processes.

Pancreatic cancer represents one of the difficult problems of contemporary medicine. The development illness evolves very slowly, takes place in special sake (stroma) and manifests clinically close to a final stage. Another feature of this pathology is a coexistence (symbiotic) effect between cancer cells and normal cells inside stroma. All these aspects make it difficult to understand the pathogenesis of pancreatic cancer and develop a proper therapy. The emergence of pancreatic pre-cancer and cancer cells represents a branching stochastic process engaging populations of 64 cells differing in the number of acquired mutations. In this study we formulate and calibrate the mathematical model of pancreatic cancer using the quasispecies framework. The mathematical model incorporates the mutation matrix, fineness landscape matrix and the death rates. Each element of the mutation matrix presents the probability of appearing a specific mutation in the branching sequence of cells representing the accumulation of mutations. The model incorporates the cancer cell elimination by effect CD8 T cells (CTL). The down-regulation of the effector function of CTLs and exhaustion are parameterized. The symbiotic effect of coexistence of normal and cancer cells is considered. The computational predictions obtained with the model are consistent with empirical data. The modelling approach can be used to investigate other types of cancers and examine various treatment procedures.

This paper presents a cooperative parallel tabu search meta-heuristic for the vehicle routing problem with time windows. It is based on the scheme in which several search threads cooperate by asynchronously exchanging information on the best solutions identified. The exchanges are performed through a mechanism called adaptive memory which holds and manages a pool of solutions. This enforces the asynchronous strategy of information exchanges and ensures the independence of the individual search threads. Each of these independent threads implements a tabu search meta-heuristic. Comprehensive computational experiments and comparisons to best known solutions show that the proposed cooperative parallel tabu search algorithm is able to achieve 48 new best solutions on VRPTW benchmark instances.

In recent years, there has been a growing interest in the preoperative modeling of fluid-structure interaction in the treatment of cerebral aneurysms. In this study, we investigate two cases involving laminar incompressible fluid flow interacting with hyperelastic materials (a vertical flap and aneurysm walls) under the effect of fluid flow. We present a finite element method (FEM) for these prototypical two-dimensional ($2D$) configurations, taking into account the complex flows and deformation of the variant's structure models. We use an Arbitrary Lagrangian-Eulerian (ALE) formulation in a continuum, fully monolithic coupled way, and discretize the fluid and solid domains using the quadratic LBB stable $P_2P_1$ finite element pair to approximate the displacement, velocity, and pressure spaces independently. The resulting discretized form of the nonlinear algebraic system is linearized using a variant of Newton's procedure, and the Jacobian matrices are approximated via the divided difference method. The resulting linear systems are solved using a direct solver MUMPS. We evaluate hydrodynamic forces such as drag and lift coefficients for nonlinear elastic material models, including Saint-Venant Kirchoff, Neo-Hookean, and Mooney-Rivlin (2 parameters) separately. To gain more physical insight into the problem, we verify the computed results by comparing the velocity, viscosity, and pressure fields. Our aim is to qualitatively analyze the changes in the mechanics of the wall behavior of the elasticity of the flap vs. the complexity of deformation, interface, details for prototypical flow situations, corresponding displacement, and deformation. We also provide a physical interpretation of blood flow magnitude and basic hemodynamic phenomena of wall shear stresses (WSS) in aneurysma and the range of deformation. Overall, this study presents a comprehensive approach to modeling fluid-structure interaction in cerebral aneurysms, which could help in the development of more effective treatment strategies.

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.

In this paper, the existence of two nontrivial stationary solutions for the nonlinear Gilpin Ayala two species competition model is given by using the mountain pass lemma, and the local stability criterion of the trivial solution is given by using Lyapunov function method. Based on the local stability criterion, we give some suggestions on how to avoid the population extinction. This is, when the population is on the verge of extinction, we should try our best to avoid the diffusion behavior and reduce the diffusion coefficient, otherwise the species are easy to go extinct. Numerical example shows the effectiveness of the proposed method.

The process of revitalising quiescent cells in order for them to proliferate plays a pivotal role in the repair of warn out tissues as well as for tissue homeostasis. This process is also crucial in the growth, development and well-being of higher multi-cellular organisms such as mammals. Deregulation of quiescent-proliferation transition is related to many diseases, in particular cancer. Recent studies have revealed that this process is regulated tightly by the Rb−E2F bistable switch mechanism. Based on experimental observations, in this study, we formulate a mathematical model to examine the effect of the growth factor concentration on the proliferation-quiescence transition in human cells. Working with a non-dimensionalised model, we prove positivity, boundedness and uniqueness of solutions. To understand model solution behaviour close to bifurcation points, we carry out bifurcation analysis, which is further verified by use of numerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcation and numerical analysis of the model predicted a transition between stable, bistable and stable states, which are dependent on the growth factor concentration parameter (GF). The derived predictions confirm experimental observations.

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in reduced dimensional space. In practical applications, snapshots are in high dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is infeasible, so our main computational goal is estimating the eigenvalue and eigenvectors of the DMD operator in a projected domain. We will generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage cost. While clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, generally the results can be excellent nonetheless, and quality understood through a well-developed theory of random projections. We will demonstrate that modes can be calculated for a low cost by the projected data with sufficient dimension.

A regularization approach to model selection, within a generalized HJM framework, is introduced which learns the closest arbitrage-free model to a prespecified factor model. This optimization problem is represented as the limit of a one-parameter family of computationally tractable penalized model selection tasks. General theoretical results are derived and then specialized to affine term-structure models where new types of arbitrage-free machine learning models for the forward-rate curve are estimated numerically and compared to classical short-rate and the dynamic Nelson-Siegel factor models.

Remanufacturing is a way for product recovery initiative and maintaining sufficient production flow to satisfy customer demand through circular economy. Recently, manufacturers have been progressively incorporating remanufacturing processes, making their supply chain vulnerable to disruptions. Among the disruptions that usually occur is the shortage in spare parts supply, which causes unexpected delay in production and possible loss of sales. In the face of potential disruption, it is essential for remanufacturing facilities to manage their supply chains in an optimum manner as to decrease the adverse impact of disruptions to their business. In this study, a two-stage production-inventory system is analysed by developing a cost-minimisation model focusing on the recovery schedule after a disruption occurrence in sourcing spare parts for a remanufacturer’s production cycle. The developed model was solved using the branch and bound algorithm. Through numerical experiments, the results indicate that the optimal recovery schedule and the number of recovery cycles are significantly dependant on disruption time, lost sales and backorder costs. Moreover, a sensitivity analysis shows that the lost sales option seems to be more effective than the backorder option in optimising the system’s overall cost. The proposed model could assist managers in deciding the optimal production strategy while providing interesting managerial insights into vital spare parts recovery issues when disruption strikes.

The aim of this work is to introduce a mathematical model representing the evolution of the temperature in a vegetation cover and the ground underneath it. Vegetation, and its interaction with soil, plays a very important role in the protection of soil surface from the action of sun and precipitations. A reduction in the vegetated mass increase the risk of desertification, soil erosion or surface runoffs which which can give rise to soil loss and sediment retention. These processes can favour climate change and global warming, which are major concerns nowadays. The mathematical model presented takes into account the main processes involved in vegetation cover and the interaction with the soil, among which, we can mention the Leaf Area Index, which is a dimensionless quantity defined as the one-sided green leaf area per unit ground surface area, or albedo and co-albedo which are clearly influenced by the vegetation. It is also considered a nonlinear heat capacity in the soil which incorporates the latent heat of fusion, when the phase change takes place. The numerical technique used to solve the mathematical model is based on a finite volume scheme with Weighted Essentially Non Oscillatory technique for spatial reconstruction and the third order Runge-Kutta Total Variation Diminishing numerical scheme is used for time integration. Some numerical examples are solved to obtain the distribution of temperature both in the vegetation cover and the soil.

The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

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

In this work we develop a new algorithm for efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where number of the grid-points is dependent on the input parameter $y$. The error analysis we performed shows that the MATLAB implementation meets the requirements for radiative transfer applications involving the HITRAN spectroscopic database. The run-time test shows that this MATLAB implementation provides rapid computation especially at smaller range of the parameter x.

In this paper study, we develop a Bayesian Network model selection principle that address addresses the incommensurability of network features obtained from incongruous datasets and overcomes performance irregularities of the Minimum Description Length model selection principle. This is achieved (i) by approaching model evaluation as a classification problem, (ii) by estimating the effect that sampling error has on the satisfiability of conditional independence criterion, as reflected by Mutual Information, and (iii) by utilizing this error estimate to penalize uncertainty in the Minimum Uncertainty (MU) model selection principle. We validate our findings numerically and demonstrate the performance advantages of the MU criterion. Finally, we illustrate the advantages of the new model evaluation framework on a tRNA structural biology example.

Working memory refers to the capability of the nervous system to selectively retain short-term memories in an active state. The long-standing viewpoint is that neurons play an indispensable role and working memory is encoded by synaptic plasticity. Furthermore, some recent studies have shown that calcium signaling assists the memory processes and the working memory might be affected by the astrocyte density. Over the last few decades, growing evidence has also revealed that astrocytes exhibit diverse coverage of synapses which are considered to participate in neuronal activities. However, very little effort has yet been made to attempt to shed light on the potential correlations between these observations. Hence, in this article we will leverage a computational neuron-astrocyte model to study the short-term memory performance subject to various astrocytic coverage and we will demonstrate that the short-term memory is susceptible to this factor. Our model may also provide plausible hypotheses for the various sizes of calcium events as they are reckoned to be correlated with the astrocytic coverage.

In this work, the problem is considered for eliminating a non-uniform rectilinear smearing of an image by mathematical and computer-based way, for example, a picture of several cars taken with a fixed camera and moving with different speeds. The problem is described by a set of 1-dimensional Fredholm integral equations (IEs) of the first kind of convolution type with a 1-dimensional point spread function (PSF) at uniform smearing and by a set of new 1-dimensional IEs of a general type (not convolution type) with a 2-dimensional PSF at non-uniform smearing. The problem is also described by one 2-dimensional IE of convolution type with a 2-dimensional PSF at uniform smearing and by a new 2-dimensional IE of a general type with a 4-dimensional PSF at non-uniform smearing. The problem for solving Fredholm IE of the first kind is ill-posed (unstable). Therefore, IEs of convolution type are solved by the Fourier transform (FT) method and Tikhonov's regularization (TR), and IEs of general type are solved by the quadrature/cubature and TR methods. Moreover, the magnitude of the image smear Δ is determined by the original “spectral method”, which increases the accuracy of image restoration. It is shown that the use of a set of 1-dimensional IEs is preferable to one 2-dimensional IE in the case of non-uniform smearing. In the inverse problem (image restoration), the Gibbs effect (the effect of false waves) in the image may occur. It can be edge or inner. The edge effect is well suppressed by the proposed technique “diffusing the edges". In the case of an inner effect, it is eliminated with difficulty, but the image smearing itself plays the role of diffusing and suppresses the inner Gibbs effect to a large extent. It is shown (in the presence of impulse noise in an image) that the well-known Tukey median filter can distort the image itself, and the Gonzalez adaptive filter also distorts the image (but to a lesser extent). We propose a modified adaptive filter. A software package was developed in MatLab and illustrative calculations are performed.

Increasing rate of seepage velocity from several formation characteristics, such as permeability and porosity, in water aquifer environment greatly prompt pollution of water reservoirs within a short period of time. Considerably, migration rate of dissolved heavy metals from Solid Waste Dumpsites (SWD), such as municipal dumpsites and landfills, through heterogeneous aquifer environment, and finally into nearby water reservoirs are mainly influenced by variation of seepage velocity within the soil and water environment. This presents a dynamic system for water pollution that was studied using a formulated mathematical model to describe the transport process of dissolved heavy metals, mainly characterized by seepage velocities, within the water aquiferous environment. Permeability, porosity, fluid pressure and concentration of heavy metals in aquiferous environment were used as principal parameters that influence seepage velocity of the metals, in dissolved state, through the structural formation of water aquifers. The derived mathematical equations that constitute the model of this study were generated through Darcy’s law and the equation of continuity. The model was validated on structural river aquifer sediments, and it was solved using graphical method through matlab open-source software. The initial and boundary conditions were obtained by discretizing the geological setting of flow region so as to transform the gradient of the head, into the time domain.

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.

Background: Articles published in scholarly journals form part of the scientific evidence base. It is the responsibility of the scientific community to maintain its integrity. In 2011 the BMJ commissioned a feature article to draw attention to an article that had appeared in another journal- The Lancet 13 years previously. The Lancet had already retracted the article. These actions exemplify the best traditions of scientific record-keeping. Objective: This submission examines whether the main claims summary made in the BMJ were factual. Method: We examine what was published in the Lancet against what was published in the BMJ and verify against the findings in the GMC hearings transcripts and verdict of the UK High Court. Results: The 6 points highlighted in BMJ had errors and need to be corrected. Conclusions: There are significant differences between what was reported in the Lancet paper and what was alleged to be there by the BMJ. This article aims only to point to errors in the BMJ article, to set the record straight. It does not show there was a causal association between MMR vaccination and autism.

In this paper, an analytical form of the Unit Step Function (or Heaviside Step function) is presented. This important function constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics. In particular, Heaviside Step Function is performed in a very simple manner by the use of a finite number of standard operations, as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical expressions, is that the proposed exact formula contains two arbitrary single - valued continuous functions which satisfy only one restriction. In addition, the proposed representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Beta function, Logistic function. Besides, it is neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

In this paper, our goal is to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate $\eta$-convexity conditions for locally Lipschitzian functions

Starting from a very simple economic scenario, we build on it a game and then we introduce a general strategy able to reduce a regression problem to an equivalent binary classification problem. This reduction scheme (that we call adaptive reduction or also dynamic reduction) can be also used to derive a new boosting algorithm for regression problems named bOOst^d. The bOOst^d algorithm is very simple to implement, and it can use any learning algorithm with no priori assumptions. We present a conjecture for bOOst^d performances, which ensures a little error on training set. More important we can also provide a very good theoretical upper bound for the generalization error. We give a set of preliminary experimental results that seems to confirm our conjecture for bOOst^d performances on training set and the theoretical assumptions for the generalization error. We also provide a possible justification of why boosting often does not overfit. Finally, we leave some open problems and argue that in the future an adaptive single boosting (with an unique code) algorithm for binary, multi class and regression problems can be derived.

The main objective of this study is to find out the influence of cooperation and intra-specific competition in escaping predation through refuge of the prey population and the effect of the two intra-specific interactions on the dynamics of prey-predator systems. For this purposes, two mathematical models with Holling type-II functional response function have been proposed and analyzed. The first model includes cooperation among prey populations whereas the second one incorporates intra-specific competition. Existence conditions and stability of different equilibrium points of both models have been carried out for the qualitative behaviour of the systems. Refuge through intra-specific competition has a stabilizing role, whereas cooperation has a destabilizing role on the system dynamics. Periodic oscillations are observed in both the systems through Hopf bifurcation. From the analytical and numerical findings, we conclude that intra-specific competition affects the prey population and continuously checks the refuge class under a critical value, and thus it never becomes too large to cause predator extinction due to food scarcity. Conversely, cooperation leads maximum individuals to escape predation through the refuge so that predators will suffer from low predation success.

The known three-component reaction-diffusion system modeling competition and co-existence of different language speakers is under study. A modification of this system is proposed, which is examined by Lie symmetry method; furthermore exact solutions in the form of traveling fronts are constructed and their properties are identified. Plots of the traveling fronts are presented and the relevant interpretation describing the language shift occurred in Ukraine during the Soviet times is suggested

In this paper we study a conjecture proposed by P.Duxbury , C.laror , L.Leduino de Salles Neto in 2021\cite{conjecture} on the Golumb Ruler Problem which is a classical optimization model in discrete case . In \cite{conjecture} the authors constucted a continuous model for the Golumb Ruler Problem associated to the discrete case and conjectured that the optimal value of both cases are equal . We deal with this conjecture via algebraic geometrical methods .

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

The present paper is concerned with the study of the quality of life index. Such an index has become an important index for measuring the well-being of individuals. However, the quality of life index is always a subjective, intangible, and often hard to quantify with precision due to the lack of quantitative models dealing with. The main goal of the present paper is thus to propose a mathematical, quantitative model for the measurement of a quality of life index. The main novelty is firstly the construction of a wavelet dynamic multiscale model to quantify and investigate the effect of time scale on the quality of life index measuring. The proposed procedure is acted empirically on a sample corresponding to Saudi Arabia as a case of study during the period from 2003 to 2020 as part of the 2030-vision plan. Saudi Arabia has implemented the so-called 2030-vision plan where the quality of life improvement is one of the main goals to be attempted. The findings show that wavelets are capable to localize the time-wise behavior of the index contrarily to classical studies which estimate a global view of the index. Moreover, the study shows the link between the quality of life behavior and many other indices.

This short paper demonstrates that the galactic spiral equations developed from ROTASE model can be used to morphologically simulate the phyllotactic spiral-ring patterns of plants. It is also noticed during this project that although the numbers in the Fibonacci sequence dominate the phyllotactic numbers, there are still significant phyllotactic numbers are not in the Fibonacci sequence, however, most of those numbers are well fit into a Fibonacci sibling sequence starting with numbers 0 and 2. Many plants show the phyllotactic number pairs of 10-16, 16-26 and 26-42 from the Fibonacci sibling sequence, which is the second dominated sequence in the phyllotaxis.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

In this paper, the authors employ Mountain Pass Lemma, the method of weak solution regularization and Lyapunov function method to derive the unique existence of globally exponential stable positive stationary solution of a single-species model with diffusion and delayed feedback. The obtained stability criterion illuminates that under some suitable conditions, a certain internal competition is conducive to the overall stability of the population, and a certain amount of family planning is conducive to the overall stability of the population. A numerical example and three tables show the effectiveness of the proposed methods.

In this lecture notes, we will introduce Asymptotics, then we will give a short glimpse on Perturbation theory (regular versus singular), which plays a crucial role especially in theoretical physics. Our goal is to find Asymptotic series that approximates the values of integrals depending on some parameter or the solutions of differential equations. These methods that lead to obtain more effective algorithms of numerical evaluation are called: Asymptotic Methods.

The Fractal Analysis of Medical Images is an investigation field in those that numerous results of important value have been obtained. This work describes the basic foundations of the Fractal Analysis and its application has more than enough medical images, leaning on in five scientific investigations.