The Chikungunya virus (CHIKV) poses a significant global public health concern, especially in Africa. Since its first isolation in Tanzania in 1953, CHIKV has caused recurrent outbreaks, challenging healthcare systems in low-resource settings. Recent outbreaks in Africa highlight the dynamic nature of CHIKV transmission and the challenges of underreporting and underdiagnosis. Here, we review literature and analyze publicly available cases, outbreaks, and genomic data providing insights into the epidemiology, genetic diversity, and transmission dynamics of CHIKV in Africa. Our analyses reveal the circulation of geographically distinct CHIKV genotypes, with certain regions experiencing a disproportionate burden of disease. Phylogenetic analysis of sporadic outbreaks in West Africa suggests repeated emergence of the virus through enzootic spillover, which is markedly different from inferred transmission dynamics in East Africa, where the virus is often introduced from Asian outbreaks, including the recent reintroduction of the Indian Ocean lineage from the Indian subcontinent to east Africa. Furthermore, there is limited evidence of viral movement between these two regions. Understanding the history and transmission dynamics of outbreaks is crucial for public health planning. Despite advances in surveillance and research, diagnostic and surveillance challenges persist. This review and secondary analysis highlight the importance of ongoing surveillance, research, and collaboration to mitigate the burden of CHIKV in Africa and improve public health outcomes.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

The lithium-ion batteries are widely used as a power source for portable devices, including cell phones. The useful life is about 2 years or 500 cycles, contributing to the generation of waste from electrical and electronic equipment (WEEE). Mining of lithium and cobalt damages the environment and is onerous; therefore, sustainable alternatives, such as obtaining these elements from secondary sources as recycling of lithium-ion batteries, are essential to provide the inputs used in the sector. However, the metallurgical route which will used to recovering them must be considered, due to this work aims for a more environmentally favorable process using DL-malic acid 1.5 M and instead of compared with sulfuric acid 2 M, heat pretreatment of 1 h and 3 h, and for all conditions, experiments were carried out with and without adding the oxidizing agent hydrogen peroxide. The best yields occurred in presence of H2O2 10 % v/v, and heat pretreatment of 1 h: 33.49 % Co and 4.63 % Li, and 29.78 % Co e 3.44 % Li were recovered by sulfuric acid and DL-malic acid, respectively.

Visual object tracking is an important technology in camera based sensor networks, which has a wide range of practicability in auto drive system. A transformer is a deep learning model that adopts the mechanism of self-attention, and it differentially weights the significance of each part of the input data. It has been widely applied in the field of visual tracking. Unfortunately, the security of the transformer model is unclear. It makes such transformer-based applications be exposed to security threats. In this work, the security of the transformer model is investigated with the important component of autonomous driving, visual tracking. Such deep-learning-based visual tracking is vulnerable to adversarial attacks, so adversarial attacks are implemented as the security threats to conduct the investigation. First, adversarial examples are generated on top of video sequences to degrade tracking performance, and the frame-by-frame temporal motion is taken into consideration when generating perturbations over the predicted tracking results. Then, the influence of perturbations on performance is sequentially investigated and analyzed. Finally, numerous experiments on OTB100, VOT2018, and GOT-10k data sets demonstrate that the executed adversarial examples are effective on the performance drops of the transformer-based visual tracking.

Epithelial–mesenchymal transition (EMT) is defined as a cellular process during which epithelial cells acquire mesenchymal phenotypes and behavior following the downregulation of epithelial features. EMT and its reversed process, the mesenchymal-epithelial transition (MET), and the special form of EMT, the endothelial-mesenchymal transition (EndMT), have been thought as a universal dogma controlling developmental and pathological processes. More than half a century of EMT study has made it a large research field and a mainstream concept. However, discrepancies and disputes over EMT and EMT research have also grown over time. Particularly, neither the epithelial and mesenchymal states/properties nor their regulatory networks nor specific markers have been defined, rendering the EMT, MET and EndMT concepts groundless. Moreover, EMT and MET effects should not be a cause, but rather a consequence of or an accompanying effect during developmental and pathological processes. EMT and MET represented by the change in cell shapes or adhesiveness or symbolized by EMT factors are biased interpretation of the overall change in cellular property and regulatory networks during development and cancer progression. The true meaning of EMT effects in some developmental and pathological processes, such as fibrosis, needs re-evaluation. But the core EMT factors are actually a few components of the regulatory networks of neural stemness, which determines tumorigenicity and pluripotency. The EMT effects in cancer progression and neural crest formation are wrong attribution of the role of neural stemness during cancer progression and the cell-intrinsic property of neural crest cells to the unknown mesenchymal state. It is time to reassess the significance of EMT and its related concepts in scientific research.

In the promptness of the COVID-19 outbreak, it would be very important to observe and estimate the pattern of diseases to reduce the contagious infection. To study this effect, we developed a COVID-19 analytical epidemic framework that combines with isolation and lockdown effect by incorporating five various groups of individuals. Then we analyze the model by evaluating the equilibrium points and analyzing their stability as well as determining the basic reproduction number. The extensive numerical simulations show the dynamics of a different group of the population over time. Thus, our findings based on the sensitivity analysis and the reproduction number highlight the role of outbreak of the virus that can be useful to avoid a massive collapse in Bangladesh and rest of the world. The outcome of this study concludes that outbreak will be in control which ensures the social and economic stability.

Flavonoids are secondary plant metabolites involved in biological activity that are present in plentiful proportions in many plant origin foods and beverages. Owing to their chemical difference and qualities that make them beneficial for human health, they have received a lot of focus in research. This review therefore presents an account on the chemical structure of flavonoids, food sources and their metabolism with emphasis on bioavailability. And they also examine their antioxidant, anti-inflammatory, anticancer, cardiovascular protective, neuroprotective, and antimicrobial properties and reveal related molecular processes. In addition, it overviews the clinical data concerning their possible use in the prevention and treatment of chronic diseases. Some of the problems that attend current flavonoid research are also dealt with; such issues as variation in the bioactivity of flavonoids and scarcity of clinical studies. This review is designed to present current state of knowledge and to provoke further research concerning the further potential of flavonoids in enhancing human health.

Solanum indicum Linn, is commonly known as Indian Nightshade or Poison Berry belongs to the family Solanaceae. This review studied the botanical description, traditional uses of its seeds, its chemical composition, pharmacological properties and modern applications in medicinal system. The plant is rich in alkaloids, steroidal saponins, flavonoids and phenolic acids having diverse pharmacological activities and phytochemical profile. It is used in treatment of various respiratory disorders, inflammation, skin problems and gastrointestinal disease since ancient times. Scientific research in modern times also tested many of the traditional uses revealing anti-inflammatory, antioxidant, antimicrobial activities as well as some cytotoxic and even antidiabetic effects. These pharmacological activities show potential future as uses for organic drugs, natural health products, skincare formulations and agricultural advancements.

Susceptible, infective, recovered, and hospitalized/isolated individuals are placed on the cells of a nxn square lattice, where each cell is occupied by a single individual or is vacant. At discrete time units (typically one day each) all susceptibles and infectives execute a random movement and when a coincidence of the two types occurs the susceptible is converted to infective status according to some probability. Infectives are labelled by the number of days since originally infected. At each time increment the age label of the infectives is increased by one unit. When the label reaches a number like 15 or 20 days the susceptibles recover with some probability or become isolated/hospitalized. Upon reaching some age the latter types either recover or die. Probabilities for the movements and conversions from one status to another are implemented by random numbergeneration. Simulations were carried out to investigate the effect of several probability and age parameters, the size of population (proportional to nxn) and density (related to fraction of occupied cells), and the size of the movements. Mid-term gradual conversion of susceptibles to isolated was explored as intervention policy.

While there are many models of epidemic evolution perhaps the basis for such models finds itself in the lumped behavior expressed through the so-called SIR model (Susceptible, Infectious, Recovered) from which spring many related models. This paper discusses multiple analytic solutions to that equation including those that are available in closed analytic form and those for which at least one final integral has to be done numerically, so-called quasi-analytic solutions. The solutions are intrinsically time-dependent of course. The hope is that such an investigation will lead to a better understanding of when and how models can be of use in studying the dynamical evolution of diseases including, perhaps, the great influenza pandemic of 1918 together with later pandemics and epidemics not excluding the Covid-19 pandemic of the present day.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

The ongoing COVID-19 pandemic has raised numerous questions concerning the shape and range of state interventions whose goals are to reduce the number of infections and deaths. The lockdowns, which have become the most popular response worldwide, are assessed as being an outdated and economically inefficient way to fight the disease. However, in the absence of efficient cures and vaccines, there is a lack of viable alternatives. In this paper we assess the economic consequences of the epidemic prevention and control schemes that were introduced in order to respond to the COVID-19 pandemic. The analyses report the results of epidemic simulations that were obtained using the agent-based modelling methods under the different response schemes and their use in order to provide conditional forecasts of the standard economic variables. The forecasts were obtained using the DSGE model with the labour market component.

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

The original purpose of this article was to modify the original SIR equations to allow for a direct source of infection (without which the original equations would have no solutions unless one starts with an already infected population) and also to see to what extent one could obtain multiple outbreaks of an infectious disease. In the course of developing the basic ideas several other factors arose to take prominent roles.Perhaps one of the more salient factors is the point that choosing an arbitrary time to change conditions from say a lock-down for the population to a less stringent social behavior, such as allowing partial or complete opening of businesses and schools, etc. should be based on knowledge of the disease and its evolution. Such decisions are usually made by politicians who have less than full information concerning the consequences of their actions. Several examples are given to illustrate these points.

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

The celebrated geodesic congruence equation of Raychaudhuri, together with the resulting singularity theorems of Penrose and Hawking that it enabled, yield a highly general set of conditions under which a spacetime (or, more generically, a pseudo-Riemannian manifold) is expected to become geodesically incomplete. However, the proofs of these theorems traditionally depend upon a collection of assumptions about the continuum spacetime (and, in the physical case, the stress-energy distribution defined over it), including its global structure, its energy conditions, the existence of trapped null surfaces and the various volume/intersection properties of geodesic congruences, that are inherently difficult to translate to the case of discrete spacetime formalisms, such as causal set theory or the Wolfram model. Some, such as the discrete analog of Raychaudhuri's equation for the volumes of geodesic congruences, are subtle to formulate due to intrinsic differences in the behavior of discrete vs. continuous geodesics; for others, such as the definition of a trapped null surface, no appropriate translation is known for the general discrete case due to a lack of a priori coordinate information. It is therefore a non-trivial question to ask whether (and to what extent) there exist equivalently general conditions under which one expects discrete spacetimes to become geodesically incomplete, and how these conditions might differ from those in the continuum. This article builds upon previous work, in which the conformal and covariant Z4 (CCZ4) formulation of the Cauchy problem for the Einstein field equations, with constraint-violation damping, was defined in terms of Wolfram model evolution over discrete (spatial) hypergraphs for the case of vacuum spacetimes, and proceeds to consider a minimal extension to the non-vacuum case by introducing a massive scalar field distribution, defined in either spherical or axial symmetry. Under appropriate assumptions, this scalar field distribution admits a physical interpretation as a collapsing (and, in the axially-symmetric case, uniformly rotating) dust, and we are able to show, through a combination of rigorous mathematical analysis and explicit numerical simulation, that the resulting discrete spacetimes converge asymptotically to either non-rotating Schwarzschild black hole solutions or maximally-rotating (extremal) Kerr black hole solutions, respectively. Although the assumptions used in obtaining these preliminary results are very strong, they nevertheless offer hope that a more general, perhaps ultimately ``Penrose-like'', singularity theorem may be provable in the discrete spacetime case too.

To investigate the variation patterns of spectral characteristics of main branches in fruit trees due to uneven distribution of growth, pruning, and fruit quality, as well as to determine the optimal fruit vi-bration harvesting, a vibration differential model of tree branches was constructed using the concen-trated mass method. A three-dimensional model of the fruit tree was built using finite element software. The spectral characteristics of each branch were obtained using the linear sweep frequency method. The method of changing the mass of each branch was employed to simulate the variation in branch mass. The frequency of occurrence, mean acceleration, and coefficient of variation of the inherent frequencies were used as evaluation indicators. The results revealed that when the vibration frequency of the fruit tree was at the peak frequency in the tree trunk spectrum, the frequency of occurrence and mean accel-eration were optimal. And the coefficient of variation of branch acceleration was less than 1, indicating a moderate dispersion. Additionally, reducing the branch mass resulted in an increase in the peak fre-quency of the tree trunk spectrum. Therefore, the growth, pruning, and uneven distribution of the branches in fruit trees can alter the spectral characteristics. When harvesting fruit by vibration, selecting the peak frequency in the trunk vibration spectrum as the excitation force frequency yields the best fruit detachment.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barabási-Albert (BA), Erdös-Rényi (ER) and Watts-Strogatz (WS) types. Both, walkers and nodes can be either susceptible (S) or infected and infectious (I) representing their states of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with transmission of the disease via vectors (mosquitos). Infected walkers may die during the time span of their infection introducing an additional compartment D of dead walkers. Infected nodes never die and always recover from their infection after a random finite time. This assumption is based on the observation that infectious vectors (mosquitos) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers R M , R 0 with and without mortality, respectively, and prove that R M < R 0 . For R M , R 0 > 1 the healthy state is unstable whereas for zero mortality a stable endemic equilibrium exists (independent of the initial conditions) which we obtained explicitly. We observe that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, among many others.

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual, where the association between susceptible and recovered individual is disturbed by white noise. This model is based on demographic changes and is used for long term behavior. We study the stability of equilibria of the deterministic model and prove the conditions for the extinction of diseases. Then, we investigate and obtain the critical condition of the stochastic epidemic model for the extinction and the permanence in mean of the disease with the white noise. To verify our results, we present some numerical simulations for real data related to disease.

The term Air Quality (AQ) pertains to the standard of air, which has a direct impact on the health and well-being of individuals. It is crucial to maintain high Air Quality (AQ), for better health and productivity. Though most of people spend more time indoors nowadays, it is not to be overlooked that the pollutant concentration in indoor air is directly linked to the outdoor air quality. Due to the changes in occupancy patterns, outdated maintenance of ventilation systems, and structural flaws in buildings, the indoor air is significantly polluted; pollutants emitted outdoors enter indoor air through open windows, ventilation systems and infiltration. In this paper, we have proposed a new technique, DTMCPM (discrete-time Markov chain (DTMC) model for the analysis and forecasting of AQ, using the power method). Specialized sensors and equipment to measure different pollutants, such as particulate matter, ozone, nitrogen dioxide, sulfur dioxide, benzene and toluene, are used to collect data by the Institute of Pakistan Air Quality Monitor in various cities; the data is converted to US EPA standard for all pollutant species. This data is used to calculate the transition matrix, steady-state values and mean return rate for the analysis of IAQ. The calculated and actual return rates have been compared and the proposed model is found to have a low average prediction error of 2.356%.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Medical image segmentation is a critical step in various healthcare applications, aiding in diagnosis, treatment planning, and disease monitoring. In this study, we investigate the efficacy of a segmentation approach based on the 2D wavelet transform. Leveraging a dataset comprising 10 diverse medical images, we evaluate the performance of our segmentation method using three key metrics: accuracy, precision, and recall. Our findings demonstrate that the proposed approach enhances segmentation accuracy, offering promising results compared to existing methods. By harnessing the multi-resolution feature extraction capabilities of the 2D wavelet transform, our method achieves improved delineation of medical image structures, paving the way for more accurate and efficient healthcare interventions.

To assure the opacity, an optimal problem is to retain the occurring events sequences as many as possible. Contrary to such problem, the other optimal problem is to preserve the minimal occurring events sequences. In the paper, based on the choosing cost, an optimal opacity-enforcing model is presented to minimize the sum of discount choosing cost, which is not only to preserve the opacity, but also to retain the secret to the maximum. To solve the model, two scenarios on opacity are considered. For the two scenarios, some algorithms are presented to achieve the optimal solution for the model by using the method of dynamic programming. And then, the solutions produced by the algorithms are proved correctly by theoretical proof. Finally, some illustrations for the algorithms are given.

Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.

The fluid flow field at the upper airways is highly complex due to the complex structure of the airway. The inhaled particle flow, the air streamline and the interaction of the continuum and discrete phase could significantly affect the transport behaviour of the inhaled particles. A range of analytical, mathematical and computational fluid dynamics (CFD) models analyzed the airflow and particle transport in different idealized and asymmetric airway models. A precise understanding of the continuum and discrete phase interaction in realistic human airways is missing, and this study aims to develop a CFD-DEM model for particle transport in realistic airways. This study uses the CFD model for the continuum phase and the discrete element method (DEM) for the discrete phase. A soft sphere approach is used for the interaction of the discrete phase. Proper validation is performed for particle transport efficiency. The CFD-DEM model analyzed the particle transport in an idealized and realistic airway model, and different methods are used to analyze the transport behaviour. During the particle-particle interaction, a stagnation point and a high-pressure zone are observed at the airway model's carinal angle. The numerical results report higher deposition efficiency (DE) for particle-particle interaction than without interaction. The flow field becomes highly complex with the spring constant values, and higher DE is found for high spring constant values. The spring dashpot friction-dshf method shows higher deposition at the upper part of the airways than other interaction methods. The findings of this study and more case-specific analysis would improve the knowledge of aerosol transport in airways and the health risk assessment of the patient.

The stability and optimal control for an SIS epidemic model with demographics and heterogeneous control strategies (immunization and quarantine) on complex networks are investigated. The epidemic threshold, disease-free and endemic equilibria are derived. Then, global asymptotical stability about the two equilibria are studied based on different methods. Furthermore, the optimal control issue about the system is also considered. We obtain the existence and uniqueness of the optimal control and optimal control tactics. Some numerical simulations were conducted to illustrate and supplement the theoretical results. Meanwhile, the effects of the combination of various immunization and quarantine schemes are studied and also compared with the optimal control strategies.

Monitored infection and vaccination rates during past past Corona waves are used to infer a posteriori two key parameter of the SIRV-epidemic model, namely the real time variation of the (i) ratio of recovery to infection rate and (ii) ratio of vaccination to infection rate. We demonstrate that using the classical SIR model the ratio between recovery and infection rates tends to overestimate the true ratio, that is of relevance in predicting the dynamics of an epidemics in the presence of vaccinations.

The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modelling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega function. The present manuscript reports new analytical results and numerical routines suitable for parametric estimation of the SIR model. The manuscript introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The numerical approach is exemplified with data from the European Centre for Disease Prevention and Control (ECDC) for several European countries in the period Jan 2020 -- Jun 2020.

The accompanying mechanical behavior during the flow of ore-rock dispersion is an important factor leading to the instability and failure of the orepass in the ore storage section. It is of great significance to accurately understand the instability characteristics of the well wall in the ore section, during the ore drawing process by understanding the flow characteristics and internal mechanical transfer mechanism of ore-rock dispersion. Using the discrete element method to analyze the flow characteristics, contact compactness, stress distribution characteristics and contact force probability distribution of the ore-rock dispersion, it realizes the quantitative characterization of the damage degree of ore-rock flow, and reveals the damage mechanism of mine storage wall. The results show that: (1) The friction between ore-rock particles, between ore-rock and well wall is an important reason for the change of the macroscopic flow form of ore-rock from “one” to “V” type. (2) The compactness and stress concentration of ores are increasing with the increase of storage depth, which is shown that with the increase of storage depth, the greater the probability of well wall instability. (3) The probability distribution of contact force strength between particles decreases exponentially in the whole process of ore drawing, in which the strong chain plays a major role in the stability of the dispersion system. (4) The number of overpressure and the overpressure coefficient can be used to quantitatively characterize the wall damage degree under the action of ore-rock flow. The dynamic side pressure decreases periodically in the form of exponential fluctuations, and the dynamic load formed by the ore-rock flow mainly played a role in the lower area of the ore storage section.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

In this paper we present two algorithms for computing discrete logarithms. We present some properties and show how we break the Diffie-Hellman protocol, which is considered to be very secure.

Diabetic retinopathy (DR) is the primary factor leading to vision impairment and blindness in diabetic people. Uncontrolled diabetes can damage the retinal blood vessels. Initial detection and prompt medical intervention are vital in preventing progressive vision impairment. Today's growing medical field poses more significant workload and diagnostic demands on medical professionals. In the proposed study, a convolutional neural network (CNN) is employed to detect the stages of DR. This research is crucial for studying DR because of its innovative methodology incorporating two different public datasets. This strategy enhances the model's capacity to generalize unseen DR images, as each dataset encompasses unique demographics and clinical circumstances. The network can learn and capture complicated hierarchical image features with asymmetric weights. Each image undergoes preprocessing using contrast-limited adaptive histogram equalization (CLAHE) and the discrete wavelet transform (DWT). The model is trained and validated using the combined datasets of Dataset for Diabetic Retinopathy (DDR) and the Asia Pacific Tele-Ophthalmology Society (APTOS). The CNN model is tuned with different learning rates and optimizers. The CNN model with Adam optimizer achieved 70% accuracy and an area under curve (AUC) score of 0.82. The recommended study results may reduce diabetes-related vision impairment by early DR severity identification.

Today, maritime transport is responsible for moving approximately 80 percent of the volume of world trade, which has favored Colombia, which, due to its geographical position, has managed to become one of the most competitive and dynamic economies in the world. South America. For this reason, this investigation is carried out in a port of their country, with the aim of identifying and analyzing restrictions or critical points that may cause delays in the unloading of goods, these would also cause delays in the loading of vehicles. To do this, it began with a diagnosis of the current situation through interviews with the operational personnel of the port, then a simulated model was designed in the ARENA software, in which it was observed that the weighing activities are where the queues were formed, this will cause a delay in the download. As possible solutions, it is recommended to senior management that a proper verification of the operation of the weighing equipment be carried out in order to unload goods more quickly. In addition, a replacement weighing equipment must be purchased. With this change, it would be possible to reduce inefficiencies or cost overruns caused by download delays, which are reducing the fluidity of the goods and the competitiveness of the organization

This paper presents a discrete compartmental Susceptible-Exposed-Infected-Recovered/Dead (SEIR/D) model to address the expansion of Covid-19 pandemic. When time passes, the status of the cells is determined by binary rules that update following both a neighbourhood and a delay pattern. The model assumes the environmental parameters have a crucial impact on the expansion of the disease so a grid is assigned to each parameter to model the single effect caused by this parameter. The expansion is then the weighted sum of all the grids. This proposal shows how the grid architecture, along with an update rule and a neighbourhood pattern is a valuable tool to model the pandemic expansion. This model has already been analyzed in previous works and compared with the corresponding continuous models solved by ordinary differential equations (ODE), coming to find the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the illness. The delays (between Susceptible and Asymptomatic, Asymptomatic and Infected, Infected and Recovered/Dead) may have a crucial impact on both the peak of Infected and the Recovery/Death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and in the case of plant pests.

In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.

Aiming at the problems of high cost of manual pulling, low reliability of existing pulling devices, high breaking rate and high leakage rate in the process of cotton stalk reuse after leaving the field in Xinjiang cotton area, a loosening soil and root-cutting cotton stalk pulling the setting machine has been researched and designed, established the root-cutting force model, calculated and optimized the key parameters of the V-shaped root-cutting knife, and determined the range of slide cutting angle, cutting edge angle and soil entry angle. The shoveling process simulation of V-shaped root-cutting knife and root-soil complex was constructed, and the working mechanism of V-shaped root-cutting knife was clarified. In order to verify the reliability and operation performance of the V-shaped root-cutting knife, the slide cutting angle, cutting edge angle and soil entry angle were used as the test factors, the response surface test of three-factors and three-levels was carried out with root-breaking force and mean value of the cutting resistance as the test index. The test results were analyzed by variance analysis, the significant of influencing factors on the root-breaking force are in a descending order as: slide cutting angle, cutting edge angle, soil entry angle; the degree of influence on the mean value of the cutting resistance are as follows: slide cutting angle, soil entry angle, cutting edge angle. In order to make the V-shaped root-cutting knife achieve the optimal working state, the parameters of the test index were optimized, and the optimal design parameters of the V-shaped root-cutting knife were set as follows: the slide cutting angle was 48.3°, cutting edge angle was 43.4°, and soil entry angle was 26.2°. The field uprooting test showed that the average pass rate of root breakage was 94.8% and the average pull-out rate of the cotton stalk was 93.2%. This study provides theoretical guidance for the development of root breaking mechanism of cotton straw harvester.

Background: The electroretinogram is a clinical test used to assess the function of the photoreceptors and retinal circuits of various cells in the eye, with the recorded waveform being the result of the summated response of neural generators across the retina. Methods: The present investigation involved an analysis of the electroretinogram waveform in both the time and time-frequency domain through the utilization of the discrete wavelet transform and continuous wavelet transform techniques. The primary aim of this study was to monitor and evaluate the effects of treatment in a New Zealand rabbit model of endophthalmitis via electroretinogram waveform analysis and to compare these with normal human electroretinograms Results: The wavelet scalograms were analyzed using various mother wavelets, including the Daubechies, Ricker, Wavelet Biorthogonal 3.1 (bior3.1), Morlet, Haar, and Gaussian wavelets. Distinctive variances were identified in the wavelet scalograms between rabbit and human electroretinograms. The wavelet scalograms in the rabbit model of endophthalmitis showed recovery with treatment in parallel with the time -domain features. Conclusions: The study compared Adult, Child, and Rabbit electroretinogram responses using DWT and CWT, finding that Adult signals had higher power than Child signals, and Rabbit signals showed differences in a-wave and b-wave depending on the type of response tested, while Haar Wavelet was found to be superior in visualizing frequency components in electrophysiological signals in following the treatment of endophthalmitis and may give additional outcome measures for the management of retinal disease.

From ancient times to the present, mankind has struggled with infectious diseases that pose a serious threat to people's lives, COVID-19 pandemic has given a huge impact to the human society, which has triggered a lot of thinking. In the future, humans may encounter various unexpected disasters or awful events, therefore, should learn from COVID-19 pandemic incident that need to pay special attention to the emergency supply of manpower and materials, whether a major disaster or not. That is emergency medical management is very important in the event of a sudden outbreak. What’s more, the preparation and scheduling of emergency medical supplies well safeguards people’s lives, health, and safety. However, owing to the sudden onset of an epidemic and given the population trends, the scale of infections and the demand for supplies in the epidemic area are uncertain. The main influencing factors and mechanisms of emergency material demand under the development trend of emergencies can be studied, and materials can be allocated efficiently and effectively, so as to minimize damage. In this study, it improves upon the dynamics model of infectious diseases firstly, by establishing a demand forecasting model for a certain area, taking the Hubei province as an example. Furthermore, this dynamics model is used to predict demand for emergency supplies, such as masks, respirators, and food in the area where the disaster will occur. Experimental results demonstrate the effectiveness and reliability of this prediction model, which supports for the development of emergency material management systems, ulterior, this study provides a framework for the distribution of emergency supplies and a guideline for relief efforts.

The ongoing outbreak of the novel coronavirus pneumonia (also known as COVID-19) has triggered a series of stringent control measures in China, such as city closure, traffic restrictions, contact tracing and household quarantine. These containment efforts often lead to changes in the contact pattern among individuals of the population. Many existing compartmental epidemic models fail to account for the effects of contact structure. In this paper, we devised a pairwise epidemic model to analyze the COVID-19 outbreak in China based on confirmed cases reported during the period February 3rd--17th, 2020. By explicitly incorporating the effects of family clusters and contact tracing followed by household quarantine and isolation, our model provides a good fit to the trajectory of COVID-19 infections and is useful to predict the epidemic trend. We obtained the average of the reproduction number $R=1.494$ ($95\%$ CI: $1.483-1.507$) for Hubei province and $R=1.178$ ($95\%$ CI: $1.145-1.158$) for China (except Hubei), suggesting that some existing studies may have overestimated the reproduction number by neglecting the dynamical correlations and clustering effects. We forecasted that the COVID-19 epidemic would peak on February 13th ($95\%$ CI: February $9-17$th) in Hubei and 6 days eariler in the regions outside Hubei. Moreover the epidemic was expected to last until the middle of March in China (except Hubei) and late April in Hubei. The sensitivity analysis shows that ongoing exposure for the susceptible and population clustering play an important role in the disease propagation. With the enforcement of household quarantine measures, the reproduction number $R$ effectively reduces and epidemic quantities decrease accordingly. Furthermore, we gave an answer to the public concern on how long the stringent containment strategies should maintain. Through numerical analysis, we suggested that the time for the resumption of work and production in China (except Hubei) and Hubei would be the middle of March and the end of April, 2020, respectively. These constructive suggestions may bring some immeasurable social-economic benefits in the long run.

The normal and Poisson distribution assumptions in the normal-Poisson mixed effects regression model are often too restrictive for many real count data. Several works have independently relaxed the Poisson conditional distribution assumption for counts or the normal distribution assumption for random effects. This work couples some recent advances in these two regards to develop a skew t–discrete gamma regression model in which the count outcomes have full dispersion flexibility and random effets can be skewed and heavy tailed. Inference in the model is achieved by maximum likelihood using pseudo-adaptive Gaussian quadature. The use of the proposal is demonstrated on a popular owl sibling negotiation data. It appears that, for this example, the proposed approach outperforms models based on normal random effects and the Poisson or negative binomial count distribution.

Nonlinear single unit activity (SUA) characteristics are the useful measures to reveal the information processing and transfer features associated with Parkinson’s disease (PD) in the basal ganglia. Most of the state-of-the-art approaches to compute such parameters in continuous and discrete forms are strongly dependent on SUA recording length, noise level and input parameters. Due to the specificity of SUA data collection (mainly short recordings with relatively low signal-to-noise ratio) new techniques to evaluate neuronal nonlinear properties are needed. We have developed an encoding technique based on a mean interspike interval (ISI) value to calculate spike train discrete nonlinear features. The approach to compute mutual information (MI) of isolated neurons with its unstructured activity was also proposed. The proposed technique of SUA nonlinear features evaluation slightly depends on spike train length, has low correlations with other SUA characteristics (firing rate, coefficient of ISI variance and asymmetry index). The derived entropy measure in the subthalamic nucleus has significant positive correlation with PD severity. The proposed approach provides nonlinear features that are slightly dependent on investigated sample size and independent on input parameters. Also, the developed mean ISI based measures reflect the more complex nature of oscillatory activity in the basal ganglia, than it was thought previously. Moreover, MI, unlike entropy, takes into account the position of the spike train elements, which allows us to investigate the amount of information retained after the occurrence of temporary failures. The developed approach may be useful in describing nonlinear features of basal ganglia activity contributing to PD pathophysiology probably associated with impaired information transfer in movement disorders.

We present a modification of the logistic model of epidemics that takes into account the possibility that an epidemic can develop from multiple physically-distinct hot spots with a range of starting times. This produces an improved understanding of the time evolution of the COVID-19 epidemic taking place in the United States in the spring of 2020.

Porcine epidemic diarrhea (PED) is a swine wasting disease caused by coronavirus infection. It causes great economic damage to the swine industry worldwide. Despite the continued use of vaccines, PED outbreaks continue, highlighting the need to review the effectiveness of current vaccines and develop additional vaccines based on new platforms. Here, we review existing vaccine technologies for preventing PED and highlight promising technologies that may help control PED virus in the future.

Aiming at the APF algorithm in the collision-free path planning and LQR algorithm tracking process, there are problems such as unreachable target points, local optimization, low safety coefficient of autonomous lane change collision avoidance tracking control and poor stability, this paper proposes an optimized APF method, which solves the defects of the traditional artificial potential field method by adding the distance adjustment factor, the safety distance protection model and the sub-target virtual potential field, and at the same time generates the autonomous driving car collision-free path. The path tracking control system is designed based on feed-forward control and DLQR controller, in which the vehicle dynamics state space model is used as the basis, the model is linearized and discretized, and the corresponding constraint variables are set to minimize the control command objective cost function under the constraints, and the objective of the DLQR controller.The objective is to accurately determine the steering angle in order to achieve path tracking and eliminate the lateral error between the reference path and the actual path caused by external interference.Finally, the simulink model and CarSim parameter configuration joint simulation platform are built, and different obstacle scenarios and different speeds are selected for collision-free path planning and tracking motion simulation research and analysis, which verifies the accuracy and practicability of the algorithm, and shows more obvious advantages in obstacle avoidance ability, path smoothing degree, and collision avoidance safety stability. The ideas proposed in this paper are expected to be further extended and popularized to actual path planning problems, which has important practical significance and engineering value.

Different variants of thinning for discrete random variables are studied. The thinning procedure allows to introduce an analog of scale parameter for positive integer-valued random variables. Sufficient and necessary conditions for the existence of such a scale are given.

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. On the contrary to ongoing outbreak in China, however, there are limited secondary outbreaks caused by exported case outside the country. We here conducted simulations to estimate the impact of potential secondary outbreaks at a community outside China. Simulations using stochastic SEIR model was conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in total number of persons recovered or removed to be 997 (95% CrI 990-1,000) at day 100 and maximum number of symptomatic infectious patients per day of 335 (95% CrI 232-478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6-7.2). However, with good case scenarios with different parameter led to no secondary case. Altering parameters, especially time to hospital visit could change the impact of secondary outbreak. With this multiple scenarios with different parameters, healthcare professionals might be able to prepare for this viral infection better.

In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple model for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average immunological response. The obvious initial exponential increase is readily hindered by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the ratio C/D of contamination vs decay factors. Decreasing this ratio below a critical value leads to a tipping point beyond which the epidemic is over. By contrast, significant values of C/D may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.

This paper studies the duration patterns of unemployment spells for immigrants and the determinants of unemployment’s completion into one of a number of studied labour market states in Finland. We estimate a duration model for unemployment with competing risks of its terminating into employment, labour market training or economic inactivity. Taking into account the wide period of observation and opportunities to analyse processes of labour market integration during various periods of economic development in Finland, in combination with the individualistic character of the labour careers of immigrants, this research is beneficial owing to the many various findings concerning labour market integration of immigrants. The approach undertaken in this research has a dualistic “descriptive-dynamic” character under which integration is understood as a never-ending process, which is conditioned by a time period of long-term existence and a context of solitary action. We find that transitions out of unemployment spells have a cyclical character; after every new “cycle” in unemployment, the probability of terminating unemployment decreases further. We also find that ascriptive factors make sense in the process of job-placement of immigrants from unemployment. Therefore, the gender, education and age of immigrants, as well as the effect of the period in which first unemployment occurred, potentially predict transitions out of unemployment and further labour market integration of immigrants.

Most studies modelling population mobility and the spread of infectious diseases, particularly using meta-population-multi-patched models, tend to focus on theoretical properties and numerical simulations of such models. There is relatively scanty literature published on fit, inference and uncertainty quantification on epidemic models with population mobility. In this research, we have used three estimation techniques to solve an inverse problem and quantify its uncertainty on a human mobility-based multi-patched epidemic model, using mobile phone sensing data and COVID-19 confirmed positive cases in Hermosillo, Mexico. First, we have utilized a Brownian bridge model using mobile phone GPS data to estimate residence and mobility parameters of the epidemic model. In the second step, we have estimated the optimal model epidemiological parameters by deterministically inverting the model using a Darwinian inspired evolutionary algorithm (EA) known as the genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification on the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results show that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from HMC result into large credible intervals, improving their coverage for the observed and predicted daily incidences. We also observe improved predictions when using multi-patch model with mobility against the single-patch model.

This article presents a new methodology for modeling and analyzing discrete dynamic systems through the construction of inverse algebraic models, giving rise to the Theory of Inverse Discrete Dynamical Systems. Key concepts such as inverse modeling, structural analysis in inverse algebraic trees, and the establishment of topological equivalences for the analytical transfer of properties between the canonical system and its inverted counterpart are introduced. Central theorems on homeomorphic invariance and topological transport are demonstrated, consolidating the validity of transferring cardinal attributes between both equivalent dynamic representations. As a concrete application, an alternative proof of the historic Collatz Conjecture is presented through the rigorous construction of the associated inverse model and the analytical transfer of properties exhibited in the inverted tree structure. Furthermore, evidence has been presented on Conway's Conjecture in the Game of Life through meticulous inverse modeling in bounded cases, overcoming initial limitations of the theory in combinatorial explosions. Although a complete proof of the conjecture is not achieved, this positively expands the modeling and analysis capacity of the methodology. The impact of properly applying this novel theory to expand understanding and solve open problems in discrete dynamical systems seems vast and profound.

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

A major challenge for the dissemination, replication, and reuse of epidemiological forecasting studies during COVID-19 pandemics is the lack of clear guidelines and platforms to exchange models in a Findable, Accessible, Interoperable, and Reusable (FAIR) manner, facilitating reproducibility of research outcomes. During the beginning of pandemics, models were developed in diverse tools that were not interoperable, opaque without traceability and semantics, and scattered across various platforms - making them hard to locate, infer and reuse. In this work, we demonstrate that implementing the standards developed by the systems biology community to encode and share COVID-19 epidemiological models can serve as a roadmap to implement models as a tool in medical informatics, in general. As a proof-of-concept, we encoded and shared 24 epidemiological models using the standard format for model exchange in systems biology, annotated them with cross-references to data resources, packed up all associated files in COMBINE archives for easy sharing, and finally, disseminated the models through BioModels repository to significantly enhance their reproducibility and repurposing potential. We recommend the use of systems biology standards to encode and share models of epidemic and pandemic forecasts to improve their findability, accessibility, interoperability, reusability, and reproducibility.

Less aligned emphasis has been given to the COVID-19 infodemic coordinating with the COVID-19 outbreak. Global profusion of tangled monikers and hashtags has found their ways in daily communication and contributed to backlash against Chinese. Official naming efforts against infodemic should be meet with a fair share of identification. Based on brief critical reviews on previous multifarious naming practices, we punctuate heuristic introspection in scientific conventions and sociocultural paradigms. Infodemiological analysis promises to articulate that people around the globe are divided in their favor stigmatized monikers in the public and scientific communities because of perceptual bias. There is no positive correlation between the degree of infection in their territories and collective perceptual bias to COVID-19. The official portfolio “COVID-19” and “SARS-CoV-2” has not become de facto standard usages, but full-fledged official names are excepted to duly contribute to the resilience of negative perceptual bias and collective behavioral propensities.

This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.

With the rapid development of intelligent logistics and network environment, it has become an urgent problem to efficiently and accurately handle and analyse the huge amount of uncertain decision information. Traditional decision making methods often fail to make the best use of complex and incomplete information, especially in the field of cyber defence. To address these problems, this paper introduces a new mathematical tool, discrete multidimensional Z-numbers (MZs), for expressing and dealing with uncertainty and reliability in network defence decisions. In this paper, we first introduce the synthesis method of discrete multidimensional Z-numbers, which allows us to consider the uncertainty and reliability of multi-source information in network defence strategy. Then, the hidden probability of MZs is calculated by using the hidden probability model, and the multidimensional Z+−number is proposed, which improves the expressiveness of the model in dealing with information uncertainty. Based on MZs, we define a variety of utility functions and build a multi-attribute group decision framework for network defence around these functions. The MZs provides a novel perspective for analysing and designing response strategies, especially against highly adaptive and covert attacks. The method in this paper is verified by a case of network security assessment of an intelligent logistics company. The results show that this method can significantly improve the accuracy and efficiency of decision making, demonstrating its unique advantages and wide application potential in network defence. This integrated discrete multidimensional Z-number group decision method is not only suitable for intelligent logistics decision making, but also provides an efficient decision support tool for network defence, which helps to improve the intelligence and adaptability of network security defence.

In this study, we investigate different control scenarios through theoretical analysis and numerical simulations. To account for two important types of control for an early ascending stage of an outbreak, social distancing and treatment with antiviral medications, a compartmental model is considered with one control, $u_1(t)$, aimed to lower the disease transmission rate and the other control, $u_2(t)$, aimed to lower the period of infectiousness. In all experiments, the implementation of control strategies reduces the daily cumulative number of cases and successfully "flattens the curve". The reduction in the cumulative cases is achieved by eliminating or delaying new cases. This delay is incredibly valuable as it provides public health organizations with more time to advance antiviral treatments and devise alternative preventive measures. The main theoretical result of the paper, Theorem 3.1, concludes that the optimal control functions, $u_i(t)$, $i=1,2,$ may be increasing until some moment $\tau \in [0, T)$. However, for all $t \in [\tau, T]$, both controls, $u_i(t)$, decline as $t$ approaches $T$ (possibly causing the number of newly infected people to grow). Numerical simulations presented in Section 4 confirm theoretical findings, which indicates that, ideally, around the time $t=\tau$, the control strategy has to be upgraded and a vaccination campaign needs to start to ensure the epidemic wave does not rebound.

This study mainly explores the effect of policy formalism, equipment insufficiency, covid-19 fear and job insecurity on construction workers’ insomnia during the epidemic. The main contribution of this article is to introduce policy formalism into the exploration of the causes of insomnia among construction site workers during the epidemic. This study collected 733 valid samples of construction site workers. We tested the established hypotheses using confirmatory factor analysis and structural equation modeling. The research results found that equipment insufficiency positively affects Covid-19 fear. Policy formalism and Covid-19 fear positively affect job burnout. Social support negatively affects job burnout. Job burnout and job insecurity positively affect insomnia.

Poland suffered an epidemic of louse-borne typhus from 1916-1923, with 400,000 cases and more than 130,000 deaths. The causative factors were depressed economic conditions and a refugee crisis that engulfed Poland after World War I. The recognition of the epidemic in 1919 stimulated the creation of the League of Red Cross Societies (LRCS). However, the LCRS had limited resources and the Poles requested help from other governments and the League of Nations (LoN). The United States sent the American-Polish Relief Expedition to conduct delousing. However, the Polish-Soviet War of 1920 disrupted typhus control and exacerbated the refugee situation. The LoN belatedly organized an underfunded Epidemic Commission. The LCRS sent a research team that did ground-breaking work on the pathology of typhus. Into 1921, the epidemic continued, driven by refugees from typhus-stricken Russia. By 1924, typhus cases were finally approaching pre-World War I levels. Multiple factors lead to the amelioration of the epidemic. The repatriation of prisoners of war and displaced civilians had concluded by 1923. Also, there had been a steady influx of sanitary, food, economic, and medical aid from various organizations into Poland since 1919. Administratively, within Poland, the anti-typhus campaign was also conducted more effectively by the Extraordinary Epidemic Commissariat.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

The basis of the discrete-impulse energy supply (DIES) concept is the efficient use of supplied energy. The references describe in detail the general principles of DIES, examine the energy and thermodynamic aspects and the main mechanisms of intensification that can be initiated on the basis of this principle. DIES mechanisms conveniently can be divided into hard and soft ones. The former should be used to stimulate hydromechanical processes, and the latter to accelerate the processes of phase heat and mass transfer, or for the purpose of intensive mixing of multicomponent media. The authors have studied the possibility of using DIES to intensify the hydromechanical processes, in particular emulsification of milk fat (homogenization of milk, preparation of spreads), processing of cream cheese masses. Objects of research were whole non-homogenized milk, fat emulsions, cream cheese mass. In order to evaluate the efficiency of milk homogenization the homogenization coefficient change was studied, which was determined by centrifugation method as the most affordable and accurate one. Emulsions were evaluated according to the degree of destabilization, resistance and dispersion of the fat phase. The rheological characteristics of cheese masses were evaluated by the effective viscosity change.

In this paper we show how to efficiently implement parallel discrete simulations on Multi-Core and GPU architectures through a real example of application: a cellular automata model of laser dynamics. We describe the techniques employed to build and optimize the implementations using OpenMP and CUDA frameworks. We have evaluated the performance on two different hardware platforms that represent different target market segments: high-end platforms for scientific computing, using an Intel Xeon Platinum 8259CL server with48cores and also an NVIDIA Tesla6V100 GPU, both running on Amazon Web Server (AWS) Cloud, and on a consumer-oriented platform, using an Intel Core i9 9900k CPU and an NVIDIA GeForce GTX 1050 TI GPU. Performance results are compared and analysed in detail. We show that excellent performance and scalability can be obtained in both platforms, and we extract some important issues that imply a performance degradation for them. We also found that current Multi-Core CPUs with large core numbers can bring a performance very near to that of GPUs, even similar in some cases.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

In this paper, we introduce two discrete degenerate random variables, namely the degenerate binomial and degenerate Poisson random variables. We deduce the expectations of the degenerate binomial random variables. We compute the generating function of the moments of the degenerate Poisson random variables, which leads us to define the new type degenerate Bell polynomials, and hence obtain explicit expressions for the moments of those random variables in terms of such polynomials. We also get the variances of the degenerate Poisson random variables. Finally, we illustrate two examples of the degenerate Poisson random variables.

Let be a power function $f_{r,M}(s)$ defined for every $s$ within the finite set $M$ as follows $$f_{r,M}(s)= \begin{cases} s^r, \ &s\in M,\\ 0, \ &\mathrm{otherwise}. \end{cases} $$ Let a discrete convolution of $f_{r,M}(s)$ be denoted as follows $\mathrm{Conv}_{r,M}[n]=(f_{r,M}*f_{r,M})[n]$. Let a real coefficients $A_{m,j}$ be given by the following recurrence $$ A_{m,j} = \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \end{cases} $$ In this paper we show that for every $n>0$ the following odd-power identities involving coefficients $A_{m,j}$ and convolution transform $\mathrm{Conv}_{r,M}[n]$ hold $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals.

Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under the action of a symmetry group G, parameter space A becomes a (locally) trivial principal bundle, A ~ A/G x G, then the normalized dynamics only depends on the quotient A/G. In this way, the dynamics of fractional variables in homogeneous epidemic SI(R)S models, with standard incidence, absence of R-susceptibility and compartment independent birth and death rates, turns out to be isomorphic to (a marginally extended version of) Hethcote's classic endemic model, first presented in 1973. The paper studies a 10-parameter master model with constant and I -linear vaccination rates, vertical transmission and a vaccination rate for susceptible newborns. As recently shown by the author, all demographic parameters are redundant. After adjusting time scale, the remaining 5-parameter model admits a 3-dimensional abelian scaling symmetry. By normalization we end up with Hethcote's extended 2-parameter model. Thus, in view of symmetry concepts, reproving theorems on endemic bifurcation and stability in such models becomes needless.

This paper studies pandemic viruses that spread during the period (1759–2020) according to solar activity cycles. Our findings and results include the following: (1) The severity of a pandemic correlates negatively with the strength of solar activity; (2) Pandemic viruses are classified into three types based on their compatibility with solar activity associations. Most of them spread through the quiet Sun, where viruses survive better in cold and rainy weather, and in stable geomagnetic fields without strong disturbances; (3) The emergence of new strains of influenza viruses was manifested in two ways. First, the annual epidemics due to antigenic drift. Second, pandemics recur every 1–12 solar cycles (about 11–120 years) due to viral reassortment of new subtypes, which results in antigenic shifts; (4) Pandemic viruses have two groups according to their recurring period: first, recurring in nine solar cycles; second, recurring in twelve solar cycles. Furthermore, we reassort pandemic viruses from their previous spread in the same periodic classification. Moreover, we derive a periodicity formula for each subtype of the pandemic virus as a spread date.

In India the first case of coronavirus disease 2019 (COVID-19) reported on 30 January 2020, and thereafter cases were increasing daily after the last week of Feb. 2020. COVID-19 identified as family member of coronaviridae where previously Middle East Respiratory Syndrome MERS and Severe Acute Respiratory Syndrome SARS belongs to same family. The COVID-19 attacks on respiratory system signing fever, cough and breath shortness, in severe cases may cause pneumonia, SARS or some time death. The aim of this study work is to develop model which predicts the epidemic peak for COVID-19 in India by using the real-time data from 30 Jan to 10 May 2020. There are uncertainties while identifying the population information due to the incomplete and inaccurate data, we initiate the most popular model for epidemic prediction i.e Susceptible, Exposed, Infectious, & Recovered SEIR initially the compartmental model for the prediction. Based on the solution of the state estimation problem for polynomial system with Poisson noise, we estimate that the epidemic peak may reach the early-middle July 2020, initializing recovered R0 to 0 and Infected I0 to 1. The outcomes of the model will help epidemiologist to isolate the source of the disease geospatially and analyze the death. Also government authorities will be able to target their interventions for rapidly checking the spread of the epidemic.

Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes provide accurate approximations to the mutual information but this approach is restricted to continuous variables because the calculation of Fisher information requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations of the mutual information based on Kullback--Leibler divergence and Rényi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding. While our asymptotic formulas all work for discrete variables, one of them has consistent performance and high accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating the mutual information between the stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.

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

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

Abstract Using the Pauli algebra version of the Dirac equation six symmetric but non-equivalent copies of the QED Lagrangian are constructed. The group of symmetries is the group of outer automorphisms of the finite quaternion group, isomorphic to the group of permutations on three letters. Solutions to corresponding Dirac equations form six sectors of fermion fields. The intersections between different sectors can only contain massless fields, implying that the sectors are distinct. If the symmetry could be extended to the full Standard Model Lagrangian it would predict the ratio of dark matter to ordinary matter of 5 : 1 which is close to the ratio of 5.2 : 1 according to current observations.

Discrete distribution estimation is a fundamental statistical tool, which is widely used to perform data analysis tasks in various applications involving sensitive personal information. Due to privacy concerns, individuals may not always provide their raw information, which leads to unpredictable biases in the final results of estimated distribution. Local Differential Privacy (LDP) is an advanced technique for privacy protection of discrete distribution estimation. Currently, typical LDP mechanisms provide same protection for all items in the domain, which imposes unnecessary perturbation on less sensitive items and thus degrades the utility of final results. Although, several recent works try to alleviate this problem, the utility can be further improved. In this paper, we propose a novel notion called Item-Oriented Personalized LDP (IPLDP), which independently perturbs different items with different privacy budgets to achieve personalized privacy protection. Furthermore, to satisfy IPLDP, we propose the Item-Oriented Personalized Randomized Response (IPRR) based on the observation that the sensitivity of data shows an inverse relationship with the population size of respective individuals. Theoretical analysis and experimental results demonstrate that our method can provide fine-grained privacy protection and improve data utility simultaneously.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions.

3D printing facilitates the straightforward construction of microchannels with complex three-dimensional architectures. Here, we demonstrate 3D-printed modular mixing components that operate on the basis of splitting and recombining fluid streams to decrease interstream diffusion length. These are compared to helical mixers that operate on the principle of chaotic advection.

In this paper we introduce a computational model for the simulation of hypervelocity impact (HVI) phenomena which is based on the Discrete Element Method (DEM). Our paper constitutes the first application of DEM to the modeling and simulating of impact events for velocities beyond 5 kms⁻¹. We present here the results of a systematic numerical study on HVI of solids. For modeling the solids, we use discrete spherical particles that interact with each other via potentials. In our numerical investigations we are particularly interested in the dynamics of material fragmentation upon impact. We model a typical HVI experiment configuration where a sphere strikes a thin plate and investigate the properties of the resulting debris cloud. We provide a quantitative computational analysis of the resulting debris cloud caused by impact and a comprehensive parameter study by varying key parameters of our model. We compare our findings from the simulations with recent HVI experiments performed at our institute. Our findings are that the DEM method leads to very stable, energy–conserving simulations of HVI scenarios that map the experimental setup where a sphere strikes a thin plate at hypervelocity speed. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

This study presents a dynamic modeling approach to investigate the impact of saturation dynamics on HIV/AIDS transmission in the presence of vertical transmission and treatment strategies. The proposed model incorporates disease-free and endemic equilibria, with a focus on analyzing the basic reproduction number and conducting stability analysis. Results indicate that the disease-free equilibrium is locally asymptotically stable under certain conditions. The findings suggest that a combination of treatment interventions and awareness campaigns, along with other control measures, may play a crucial role in curbing the spread of the HIV/AIDS virus. This research contributes to understanding the complex dynamics of HIV/AIDS epidemics and highlights the importance of considering saturation effects in epidemic modeling.

Monitored differential infection rates of past Corona waves are used to infer, a posteriori, the real time variation of the ratio of recovery to infection rate as key parameter of the SIR-epidemic model. From monitored Corona waves in five different countries it is found that this ratio exhibits a linear increase at early times below the first maximum of the differential infection rate before the ratios approach a nearly constant value close to unity at the time of the first maximum with small amplitude oscillations at later times. The observed time dependencies at early times and at times near the first maximum agree favorably well with the behavior of the calculated ratio for the Gaussian temporal evolution of the rate of new infections, although the predicted linear increase of the Gauss ratio at late times is not observed.

The Dark Web is known as a place triggering a variety of criminal activities. Anonymization techniques enable illegal operations, leading to the loss of confidential information and its further use as bait, a trade product or even a crime tool. Despite technical progress, there is still not enough awareness of the Dark Web and its secret activity. In this study, we introduced the Dark Web Enhanced Analysis (DWEA), in order to analyze and gather information about the content accessed on the Dark Net based on data characteristics. The research was performed to identify how the Dark Web has been influenced by recent global events, such as the COVID-19 epidemic. The research included the usage of a crawler, which scans the network and collects data for further analysis with machine learning. The result of this work determines the influence of the COVID-19 epidemic on the Dark Net.

Our study essentially concerns the dynamic behavior of an SIRS epidemic model in discrete time. Two equilibrium points are obtained; one is disease-free while the other is endemic. We are interested in the endemic fixed point as well as its asymptotic stability. Depending on the parameters which are estimated using the data from US Department of health and SIRS modelling with optimization, two Flip and Transcritical bifurcations appear. We illustrate their diagrams, as well as their bifurcation curves using the method of Carcasses \cite{carcasses1993determination,carcasses1995singularities} for the Flip bifurcation and by an implicit function deduced from such an equation for the Transcritical bifurcation. We use the scanning of the parametric plane to have a global view of the behavior of the model and to highlight the zones of stability of the existing singularities. A superposition of the bifurcation curves with the parametric plane can show the overlap of the curves with the boundaries of the stability domains, which confirms the smooth running of the simulation and its correspondence with the theory, we finish this article with constrained optimal control applied to infection rate and recruitment rate for an SIRS discrete epidemic model. Pontryagin's maximum principle is used to determine these optimal controls. Finally using COVID-19 data in the USA, we obtain results that demonstrate the effectiveness of the proposed control strategy to mitigate the spread of the pandemic.

The first attempt to control and mitigate an epidemic outbreak caused by a previously unknown virus occurs primarily via non-pharmaceutical interventions (NPIs). In case of the SARS-CoV-2 virus, which since the early days of 2020 caused the COVID-19 pandemic, NPIs aimed at reducing transmission enabling contacts between individuals. The effectiveness of contact reduction measures directly correlates with the number of individuals adhering to such measures. Here, we illustrate by means of a very simple compartmental model how partial noncompliance with NPIs can prevent these from stopping the spread of an epidemic.

This study advances the field of solar irradiance nowcasting by introducing a discrete-level classification approach, diverging from traditional continuous measurement methods. Grounded in a need for cost-effective and modular solutions, the research employs high-resolution computer vision coupled with a deep learning framework to predict Direct Normal Irradiance (DNI). By harnessing the capabilities of a Logitech C900 1080p HD camera and an NVIDIA Jetson module, the study achieves real-time data processing, pivotal for CSP systems' operational efficiency. The core of the methodology is the ResNet-50 convolutional neural network, refined via transfer learning on a bespoke dataset, culminating in a predictive accuracy of 85.78%. This discrete classification model contrasts with conventional, costly instruments like the MS-57, offering a novel and accessible alternative for DNI estimation. Such innovation not only demonstrates high predictive accuracy but also signifies a shift towards less resource-intensive and more adaptable solar energy forecasting tools, contributing a significant leap towards optimizing renewable energy systems.

By applying a running average (with a window-size= d), we could transform Discrete data to broad-range, Continuous values. When we have more than 2 columns and one of them is containing data about the tags of classification (Class Column), we could compare and sort the features (Non-class Columns) based on the R2 coefficient of the regression for running averages. The parameters tuning could help us to select the best features (the non-class columns which have the best correlation with the Class Column). “Window size” and “Ordering” could be tuned to achieve the goal. this optimization problem is hard and we need an Algorithm (or Heuristics) for simplifying this tuning. We demonstrate a novel heuristics, Called Simulated Distillation (SimulaD), which could help us to gain a somehow good results with this optimization problem.

Pit craters, and pit crater chains, are now recognised as being an important part of the surface morphology and structure of many planetary bodies, and are particularly remarkable on Mars. Pit craters do not possess the elevated rims, ejecta deposits, or other features that are typically associated with impact craters. They are thought to arise from the drainage/collapse of a relatively weak surficial material into an open (or widening) void in a much stronger material below. The creation of such voids has been suggested to be due to extensional fracturing/dilational faulting, shallow dike intrusion, lava tube collapse amongst other hypotheses. These craters have a very distinctive expression, often presenting funnel, cone, or bowl-shaped geometries. Analogue models of pit crater formation provide a map-view picture of their initiation and evolution but give little insight into their internal structure or geometry, but produce pits that typically have steep, nearly conical cross sections. Numerical modelling studies of their formation have been limited and have produced some quite interesting, but nonetheless puzzling, results whereby the simulated pit craters had generally convex (steepening downward) slope profiles with no distinct rim; quite unlike many of those observed on Earth or on Mars. To address these issues, I present here a high-resolution, 2D discrete element model of weak cover (regolith) collapse into either a static or a widening underlying void. I use frictional and frictional-cohesive discrete elements to represent a range of probable cover rheologies. Under Martian gravitational conditions, frictional-cohesive and frictional materials produce cone, bowl and scoop-shaped pit craters. For a given cover thickness, the specific crater shape depends on the amount of underlying void space created for drainage. When void space is small relative to cover thickness, craters have bowl or scoop-shaped geometries. In contrast, when void space is large relative to cover thickness, craters have cone-shaped geometries with essentially planar (nearing angle of repose) slope profiles. Frictional-cohesive materials exhibit more distinct rims than simple frictional materials and thus may reveal some stratigraphic layering on the pit crater walls. In the limit, when drainage from the overlying cover is insufficient to fill the underlying void, ´skylights´ into the deeper structure are created. Implications of these results for the interpretation of pit craters on Earth, Mars, other planets and moons are discussed.

In this study, we consider delta fractional Sturm--Liouville (DFSL) initial value problems in the sense of delta Caputo and delta Riemann-Liouville (R--L) operators. One of the properties of delta fractional difference operators which makes it different from nabla counterpart is to shift its domain. This feature makes it more complex than the nabla fractional operator. We obtain sum representation of solutions for DFSL initial value problems with the help of $\mathcal{Z}-$ transformation. Moreover, we get analytical solutions of homogeneous DFSL problem within Riemann-Liouville (R--L) and Caputo sense, discrete Sturm--Liouville (DSL) problem, continuous fractional Sturm--Liouville (FSL) problem in the sense of R--L and Caputo operators, and continuous Sturm--Liouville (SL) differential problem. From this point of view, we compare all the solutions with each other. Consequently, we show that all results for these four eigenvalue problems are compatible with each other and approach to each other while the orders tends to one, i.e. $\Delta^{\mu }\left( \Delta x\left( t-\mu \right) \right)\cong D_{0^{+}}^{\mu }\left( x^{\prime }\left( t\right) \right)\cong \Delta^2x(n-1) \cong x^{\prime \prime }\left( t\right) =\lambda x\left( t\right),\ \mu\rightarrow1 $ . We support our results comparatively by tables and simulations in detail.

High Efficiency Video Coding (HEVC) uses an 8-point filter and a 7-point filter, which are based on the discrete cosine transform (DCT), for the 1/2-pixel and 1/4-pixel interpolations, respectively. In this paper, discrete sine transform (DST)-based interpolation filters (IF) are proposed. The first proposed DST-based IFs (DST-IFs) use 8-point and 7-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. The final proposed DST-IFs use 12-point and 11-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. These DST-IF methods are proposed to improve the motion-compensated prediction in HEVC. The 8-point and 7-point DST-IF methods showed average BD-rate reductions of 0.7% and 0.3% in the random access (RA) and low delay B (LDB) configurations, respectively. The 12-point and 11-point DST-IF methods showed average BD-rate reductions of 1.4% and 1.2% in the RA and LDB configurations for the Luma component, respectively.

We applied a generalized SEIR epidemiological model to the recent SARS-CoV-2 outbreak in the world, with a focus on Italy and its Lombardia, Piemonte, and Veneto regions. We focus on the application of a stochastic approach in fitting the model numerous parameters using a Particle Swarm Optimization (PSO) solver, to improve the reliability of predictions in the medium term (30 days). We analyze the official data and the predicted evolution of the epidemic in the Italian regions, and we compare the results with data and predictions of Spain and South Korea. We link the model equations to the changes in people’s mobility, with reference to Google’s COVID-19 Community Mobility Reports. We discuss the effectiveness of policies taken by different regions and countries and how they have an impact on past and future infection scenarios.

This paper is concerned with the optimal linear quadratic Gaussian (LQG) control problem for discrete time-varying system with multiple input delays and multiplicative noises. The main contributions are two-fold. Firstly, when the state variables can be observed exactly, we obtain a necessary and suffcient condition for the multiple-delays system in terms of the non-homogeneous relationship between the state and costate, which is the solution to the coupled forward and backward stochastic difference equations. Secondly, when the state variables are partially observed, we derive a suboptimal linear output feedback controller for the discrete-time system based on the obtained results of the optimal LQG control. Numerical examples are shown to illustrate the proposed algorithm.

This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems.

High levels of meat consumption are increasingly being criticised for ethical, environmental, and social reasons. Plant-based meat substitutes have been identified as healthy sources of protein that, in comparison to meat, offer a number of social, environmental and health benefits and may play a role in reducing meat consumption. However, there has been a lack of research on the role they can play in the policy agenda and how specific meat substitute attributes can influence consumers to replace partially replace meat in their diets.

Background: Metabolic flux analysis (MFA) is an indispensable tool in metabolic engineering. The simplest variant of MFA relies on an overdetermined stoichiometric model of the cell’s metabolism under the pseudo-steady state assumption, to evaluate the intracellular flux distribution. Despite its long history, the issue of model error in the overdetermined MFA, particularly misspecifications of the stoichiometric matrix, has not received much attention. Method: We evaluated the performance of statistical tests from linear least square regressions, namely Ramsey RESET test, F-test and Lagrange multiplier test, in detecting model misspecifications in the overdetermined MFA, particularly missing reactions. We further proposed an iterative procedure using the F-test to correct such an issue. Result: Using Chinese hamster ovary and random metabolic networks, we demonstrated that: (1) a statistically significant regression does not guarantee high accuracy of the flux estimates, (2) the removal of a reaction with a low flux magnitude can cause disproportionately large biases in the flux estimates, (3) the F-test could efficiently detect missing reactions, and (4) the proposed iterative procedure could robustly resolve the omission of reactions. Conclusion: Our work demonstrated that statistical analysis and tests could be used to systematically assess, detect and resolve model misspecifications in the overdetermined MFA.

Our aim is to provide an insight of the procedures and the dynamics that lead the spread of contagious diseases through populations. Our simulation tool can increase our understanding on the spatial parameters which affect the diffusion of a virus. SIR models are based on the hypothesis that populations are “well mixed”. Our model constitutes an attempt to focus on the effects of the specific distribution of the initially infected individuals through the population and provide insights, considering the stochasticity of the transmission process. For this purpose, we represent the population using a square lattice of nodes. Each node represents an individual that may or may not carry the virus. Nodes that carry the virus can only transfer it to susceptible neighboring nodes. This important revision of the common SIR model provides a very realistic property: the same number of initially infected individuals can lead to multiple paths, depending on their initial distribution in the lattice. This property creates better predictions and probable scenarios to construct a probability function and appropriate confidence intervals. Finally, this structure permits realistic visualizations of the results to understand the procedure of contagion and spread of a disease and the effects of any measures applied.

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.

Non-pharmacological interventions in the fight against COVID 19 include: a) suppression, which facilitates its extinction; and b) mitigation, which reduces its speed of spread. Left unmitigated, the intensive care unit bed capacity (ICU) is exceeded over its maximum supply, resulting in increased deaths. Suppression has shown in simulation models the potential for decreasing ICU occupation below its surge limit, effectively decreasing mortality. However, for avoiding a rebound in transmission, suppression must be maintained intermittently until a vaccine is available (which may take up to 2 years). The objective of this paper was to describe the mortality patterns observed in Spain, Italy and South Korea for discussing a hypothetical combined public health policy and socioeconomic model that could potentially reduce mortality while reducing the economic impact of this pandemic in Spain. The plan is based on a progressive-voluntary reinstatement to work of the population exposed to the lowest risks (healthy non-immune family units <50 y/o and immune population) and it depends on having sufficiently available ICU beds for providing adequate support. This model, if proven correct for Spain, could eventually be followed by other countries facing a similar impact of the present pandemic.

This paper deals with the formulation of a Cobot kinematic model by developing both the direct and inverse kinematics and choosing the noa transformation matrix for defining the end-effector position and orientation with respect to the base frame. These algorithms have been validated via software in Matlab environment and by means of suitable experimental tests, which have been carried out by using a UR5e Cobot. Moreover, a specific industrial application regarding the robotized assembling of a multi-cylinder IC engine, has been designed in terms of layout and corresponding automatic cycle that is intended as a sequence of the robot elementary actions. In particular, the proposed robotized cell is composed by the UR5e Cobot along with its controller and a suitable electropneumatic circuit that includes a PLC with its user interface, which are both governed by means of a specific electronic board and a switch control box. The IC engine in scale of 1:5 and specific parts of the end-effector, which takes the role of vacuum gripper and torque limiting screwdriver, have been designed and manufactured by using a 3D printer.

Amidst the escalating demands for efficient Intelligent Transportation Systems (ITS) management, the significance of accurate Origin-Destination (OD) data prediction has emerged as a paramount concern, given its indispensable role in the ITS domain. This paper introduces a groundbreaking integrated model, creatively fusing the unique strengths of Graph Convolutional Network (GCN), Residual Neural Network (ResNet), and Long Short-Term Memory Network (LSTM) into a single architecture, which we name GraphResLSTM, to exploit road segment average speed data for OD prediction. Compared with conventional road segment traffic volume data, average speed data is more readily available, significantly reducing the data accessibility barrier for OD prediction. We underscore the critical role of selection of key road segments and employs a combination of Entropy Weight Method and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to identify 41 representative road segments from the experimental road network. In the experimental phase, we simulate 86400000 seconds of traffic conditions, generating a total of 1440000 data records. Utilizing these simulated data, we design and conduct comparative experiments between models as well as data types. The results demonstrate that both the GraphResLSTM model and road segment average speed data outperform other models and data types notably in OD prediction tasks.

Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.