Mathematics

When simulating cohesive cracks in the XFEM framework, specific enrichment schemes are designed for the non-singular near-tip field and an iteration procedure is used to solve the nonlinearity problem. This paper focuses on convergence and accuracy analysis of XFEM enrichment schemes for cohesive cracks. Four different kinds of enrichment schemes were manufactured based on the development of XFEM. A double-cantilever beam specimen under an opening load was simulated by Matlab programming, assuming both linear and exponential constitutive models. The displacement and load factors were solved simultaneously by the Newton–Raphson iterative procedure. Finally, based on a linear or an exponential constitutive law, the influences of variations in these enrichment schemes, including (i) specialized tip branch functions and (ii) corrected approximations for blending elements, were determined and some conclusions were drawn. Full article

Multi-agent systems show great promise in the actual state of increasing interconnectedness and autonomy of computer systems. This paper presents a .NET multi-agent framework for experimenting with agents and building multi-agent simulations. Its main advantages are conceptual simplicity and ease of use, which make it suitable for teaching agent-based notions. Several algorithms, protocols and simulations using this framework are also presented. Full article

The calcium leaching effect inevitably increases the grout curtain hydraulic conductivity. It is diffucult to sample and obtain the leaching-related calculation parameters for deep-buried grout curtains. This study introduced the inversion method into the calcium leaching analysis to get proper leaching-related calculation parameters and accurate results. An inverse analysis model was proposed using the genetic algorithm (GA) and finite element analysis technology to solve the calcium leaching problems. The objective function is constructed using the hydraulic head and leakage quantity time-series measurements, which improves the uniqueness and reliability of the inverse results. The proposed method was applied to the inverse analysis of the hydraulic conductivity evolution of the grout curtain in a concrete dam foundation. The predicted water heads and leakage quantity are consistent with the monitored data, indicating the rationality of this simulation. The grout curtain hydraulic conductivity prediction in 100 years is also presented. The results illustrate the feasibility of the proposed method for determining leaching-related parameters and the hydraulic conductivity prediction in the leaching process. Full article

Under the background of new-type urbanization and rural revitalization strategy, how to promote the development of urban–rural integration has become an important issue in today’s society. This paper designed a new evaluation mechanism for the development level of urban–rural integration. Specifically, a three-level evaluation index system of urban–rural integration development level was established from four aspects: spatial integration, economic integration, social integration and living environment integration. By combining the entropy weight method with the ranking method, a combination weighting method was proposed to determine the weight of each index in the index system. Furthermore, an improved TOPSIS method based on relative entropy and grey relational degree was proposed to evaluate the development level of urban–rural integration, which considering proximity from the perspectives of distance and shape and solving the problem that some situations cannot be compared through the original model. Then, the established evaluation mechanism was applied to make an empirical analysis for evaluating the development level of urban–rural integration in Hubei Province, China. Cluster analysis and obstacle factor analysis were used to further analyze the evaluation results. Finally, according to the evaluation results, some effective countermeasures and policy implications were provided to improve the development level of urban–rural integration in Hubei Province. Full article

Many fields including clinical and manufacturing areas usually perform life-testing experiments and accelerated failure time models (AFT) play an essential role in these investigations. In these models the covariate causes an accelerant effect on the course of the event through the term named acceleration factor (AF). Despite the influence of this factor on the model, recent studies state that the form of AF is weakly or partially known in most real applications. In these cases, the classical optimal design theory may produce low efficient designs since they are highly model dependent. This work explores planning and techniques that can provide the best robust designs for AFT models with type I censoring when the form of the AF is misspecified, which is an issue little explored in the literature. Main idea is focused on considering the AF to vary over a neighbourhood of perturbation functions and assuming the mean square error matrix as the basis for measuring the design quality. A key result of this research was obtaining the asymptotic MSE matrix for type I censoring under the assumption of known variance regardless the selected failure time distribution. In order to illustrate the applicability of previous result to a study case, analytical characterizations and numerical approaches were developed to construct optimal robust designs under different contaminating scenarios for a failure time following a log-logistic distribution. Full article

In this article, we introduce a new family of symmetric-asymmetric distributions based on skew distributions and on the family of order statistics with proportional hazards. This new family of distributions is able to fit both unimodal and bimodal asymmetric data. Furthermore, it contains, as special cases, the symmetric distribution and the “skew-symmetric” family, and therefore the skew-normal distribution. Another interesting feature of the family is that the parameter controlling the distributional shape in bimodal cases takes values in the interval (0, 1); this is an advantage for computing maximum likelihood estimates of model parameters, which is performed by numerical methods. The practical utility of the proposed distribution is illustrated in two real data applications. Full article

We study algorithms for solving three problems on strings. These are sorting of n strings of length k, “the Most Frequent String Search Problem”, and “searching intersection of two sequences of strings”. We construct quantum algorithms that are faster than classical (randomized or deterministic) counterparts for each of these problems. The quantum algorithms are based on the quantum procedure for comparing two strings of length k in $O\left(\sqrt{k}\right)$ queries. The first problem is sorting n strings of length k. We show that classical complexity of the problem is $\Theta \left(nk\right)$ for constant size alphabet, but our quantum algorithm has $\tilde{O}\left(n\sqrt{k}\right)$ complexity. The second one is searching the most frequent string among n strings of length k. We show that the classical complexity of the problem is $\Theta \left(nk\right)$, but our quantum algorithm has $\tilde{O}\left(n\sqrt{k}\right)$ complexity. The third problem is searching for an intersection of two sequences of strings. All strings have the same length k. The size of the first set is n, and the size of the second set is m. We show that the classical complexity of the problem is $\Theta \left(\right(n+m\left)k\right)$, but our quantum algorithm has $\tilde{O}\left((n+m)\sqrt{k}\right)$ complexity. Full article

Bézier curves and surfaces with shape parameters have received more attention in the field of engineering and technology in recent years because of their useful geometric properties as compared to classical Bézier curves, as well as traditional Bernstein basis functions. In this study, the generalized Bézier-like curves (gBC) are constructed based on new generalized Bernstein-like basis functions (gBBF) with two shape parameters. The geometric properties of both gBBF and gBC are studied, and it is found that they are similar to the classical Bernstein basis and Bézier curve, respectively. Some free form curves can be modeled using the proposed gBC and surfaces as the applications. Full article

In this paper, we set up a stochastic model for the dynamics of active Rab5 and Rab7 proteins on the surface of endosomes and the acidification process that govern the virus–endosome fusion and endosomal escape of pH-responsive nanoparticles. We employ a well-known cut-off switch model for Rab5 to Rab7 conversion dynamics and consider two random terms: white Gaussian and Poisson noises with zero mean. We derive the governing equations for the joint probability density function for the endosomal pH, Rab5 and Rab7 proteins. We obtain numerically the marginal density describing random fluctuations of endosomal pH. We calculate the probability of having a pH level inside the endosome below a critical threshold and therefore the percentage of viruses and pH-responsive nanoparticles escaping endosomes. Our results are in good qualitative agreement with experimental data on viral escape. Full article

Selecting the most miniature possible set of genes from microarray datasets for clinical diagnosis and prediction is one of the most challenging machine learning tasks. A robust gene selection technique is required to identify the most significant subset of genes by removing spurious or non-predictive genes from the original dataset without sacrificing or reducing classification accuracy. Numerous studies have attempted to address this issue by implementing either a filter or a wrapper. Although the filter approaches are computationally efficient, they are completely independent of the induction algorithm. On the other hand, wrapper approaches outperform filter approaches but are computationally more expensive. Therefore, this study proposes an enhanced gene selection method that uses a hybrid technique that combines the Symmetrical Uncertainty (SU) filter and Reference Set Harmony Search Algorithm (RSHSA) wrapper method, known as SU-RSHSA. The framework to develop the proposed SU-RSHSA includes numerous stages: (1) investigate a novel gene selection method based on the HSA and will then determine appropriate values for the HSA’s parameters, (2) enhance the construction process of the initial harmony memory while satisfying the diversity of the solution by embedding a reference set within the HSA (RSHSA), and (3) investigates the effect of integrating Symmetrical Uncertainty (SU) as a filter and RSHSA as a wrapper (SU-RSHSA) to maximize classification accuracy by leveraging their respective advantages. The results demonstrate that the SU-RSHSA outperforms the original HSA and SU-HSA in terms of classification accuracy, a small number of selected relevant genes, and reduced computational time. More importantly, the proposed SU-RSHSA gene selection method effectively generates a small subset of salient genes with high classification accuracy. Full article

One of the main environmental problems that affects people’s health and quality of life is air pollution by particulate matter. Chile has nine of the ten most polluted cities in South America according to a report presented in 2019 by Greenpeace and AirVisual that measured the air quality index based on the levels of fine particles. Most Chilean cities are highly contaminated by particulate matter, especially during the months of April to August (the critical episode management period). The objective of this study is to predict particulate matter levels based on meteorological and climatic features, such as temperature, wind speed, wind direction, precipitation and relative air humidity in Talca, Chile, during the critical episode management periods between 2014 and 2018. Predictive models based on machine learning techniques were used, considering training datasets with meteorological and climatic data, and particulate matter levels from the three air quality monitoring stations in Talca, Chile. We carried out the training of 24 models to predict particulate matter levels considering the 24-h average and average between 05:00 to 11:00 p.m. For the model testing, data from the year 2018 during the critical episode management period were used. The obtained results indicate that our models are able to effectively predict levels of particulate matter, enabling correct management of critical episodes, especially for alert, pre-emergency and emergency conditions. We used the cross-platform and open-source programming language Python for the development and implementation of the proposed models and R-project for some visualizations. Full article

The swarms of robots are examples of artificial collective intelligence, with simple individual autonomous behavior and emerging swarm effect to accomplish even complex tasks. Modeling approaches for robotic swarm development is one of the main challenges in this field of research. Here, we present a robot-instantiated theoretical framework and a quantitative worked-out example. Aiming to build up a general model, we first sketch a diagrammatic classification of swarms relating ideal swarms to existing implementations, inspired by category theory. Then, we propose a matrix representation to relate local and global behaviors in a swarm, with diagonal sub-matrices describing individual features and off-diagonal sub-matrices as pairwise interaction terms. Thus, we attempt to shape the structure of such an interaction term, using language and tools of quantum computing for a quantitative simulation of a toy model. We choose quantum computing because of its computational efficiency. This case study can shed light on potentialities of quantum computing in the realm of swarm robotics, leaving room for progressive enrichment and refinement. Full article

Beltrami equations ${\overline{L}}_t\left(g\right)=\mu (·,t)L_t\left(g\right)$ on $S^3$ (where $L_t$, $\left|t\right|<1$, are the Rossi operators i.e., $L_t$ spans the globally nonembeddable CR structure $\mathcal{H}\left(t\right)$ on $S^3$ discovered by H. Rossi) are derived such that to describe quasiconformal mappings $f:S^3\to N\subset {\mathbb{C}}^2$ from the Rossi sphere $\left(S^3,\mathcal{H}\left(t\right)\right)$. Using the Greiner–Kohn–Stein solution to the Lewy equation and the Bargmann representations of the Heisenberg group, we solve the Beltrami equations for Sobolev-type solutions $g_t$ such that $g_t-v\in W_F^{1,2}\left(S^3,\theta \right)$ with $v\in {\mathrm{CR}}^{\infty }\left(S^3,\mathcal{H}\left(0\right)\right)$. Full article

The problem of constructing functional optimal observers (filters) for stochastic control systems with additive noises in discrete time are studied in this work. Under the assumption that there is no filter of the first order, necessary and sufficient conditions for the existence of filters of the second and third order are obtained in the canonical basis. Analytical expressions of the transfer function matrix from the input noise to the estimation error are presented. A numerical example is given to compare the performance of filters by the quadratic criterion in the steady state. Full article

Two contact models are considered, with the behavior of the materials being described by a constitutive law governed by the subdifferential of a convex map. We deliver variational formulations based on the theory of bipotentials. In this approach, the unknowns are pairs consisting of the displacement field and the Cauchy stress tensor. The two-field weak solutions are sought into product spaces involving variable convex sets. Both models lead to variational systems which can be cast in an abstract setting. After delivering some abstract results, we apply them in order to study the weak solvability of the mechanical models as well as the data dependence of the weak solutions. Full article

Cancer is a common term for many diseases that can affect anybody. A worldwide leading cause of death is cancer, according to the World Health Organization (WHO) report. In 2020, ten million people died from cancer. This model identifies the interaction of cancer cells, viral therapy, and immune response. In this model, the cell population has four parts, namely uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). This study presents the analysis of the stochastic cancer virotherapy model in the cell population dynamics. The model results have restored the properties of the biological problem, such as dynamical consistency, positivity, and boundedness, which are the considerable requirements of the models in these fields. The existing computational methods, such as the Euler Maruyama, Stochastic Euler, and Stochastic Runge Kutta, fail to restore the abovementioned properties. The proposed stochastic nonstandard finite difference method is efficient, cost-effective, and accommodates all the desired feasible properties. The existing standard stochastic methods converge conditionally or diverge in the long run. The solution by the nonstandard finite difference method is stable and convergent over all time steps. Full article

Happiness is a very important aspect in the life and well-being of all citizens; as such, it has become a key factor in personal preferences. For these reasons, it is relevant to study what factors principally affect the happiness of the population. However, the difficulties involved in measuring this concept mean that there are no clear criteria as to which aspects should be promoted in order for citizens to achieve greater happiness. This paper uses variance-based structural equation modelling (SEM)—partial least squares path modelling (PLS)—to analyse the direct and indirect effects of European citizens’ assessment of different aspects of their city related to safety, environmental quality and urban planning on their happiness. The source of information used in this study is the Flash Eurobarometer 419 prepared by Eurostat in 2015, with a total of 9799 observations. The results show how quality of life, safety, the environment and city planning have a positive and significant influence on European citizens’ happiness, especially safety. In addition, quality of life acts as a mediating variable, primarily increasing the influence of urban planning on happiness. The findings of the study point to the relevant policies that governments should undertake to ensure the happiness of their citizens. Full article

This paper investigates the spatial behavior of the solutions of thermoelastic equations of type III in a semi-infinite cylinder by using the partial differential inequalities. By setting an arbitrary positive constant in the energy expression, the fast decay rate of the solutions is obtained. Based on the results of decay, the continuous dependence and the convergence results on the boundary coefficient are established by using the differential inequality technique and the energy analysis method. The main work of this paper is to extend the study of continuous dependence to a semi-infinite cylinder, which can be used as a reference for the study of other types of partial differential equations. Full article

In practical application, facial image recognition is vulnerable to be attacked by photos, videos, etc., while some currently used artificial feature extractors in machine learning, such as activity detection, texture descriptors, and distortion detection, are insufficient due to their weak detection ability in feature extraction from unknown attack. In order to deal with the aforementioned deficiency and improve the network security, this paper proposes directional difference convolution for the deep learning in gradient image information extraction, which analyzes pixel correlation within the convolution domain and calculates pixel gradients through difference calculation. Its combination with traditional convolution can be optimized by a parameter $\theta$. Its stronger ability in gradient extraction improves the learning and predicting ability of the network, whose performance testing on CASIA-MFSD, Replay-Attack, and MSU-MFSD for face anti-spoofing task shows that our method outperforms the current related methods. Full article