Authors:Sirasrete Phoosree, Weerachai Thadee Abstract: The non-linear space-time fractional Estevez-Mansfield-Clarkson (EMC) equation and the non-linear space-time fractional Ablowitz-Kaup-Newell-Segur (AKNS) equation showed the motion of waves in the shallow water equation and the optical fiber equation, respectively. The process used to solve these equations is to transform the non-linear fractional partial differential equations (PDEs) into the non-linear ordinary differential equations by using the Jumarie's Riemann-Liouville derivative and setting the solution in the finite series combined with the simple equation (SE) method with the Bernoulli equation. The new traveling wave solutions were the exponential functions resulting in the physical wave effects are produced in the form of kink waves and represented by the two-dimensional graph, three-dimensional graph, and contour graph. In addition, the comparison of the solutions revealed that the new solutions have a more convenient and easier format. PubDate: 2022-05-13T00:00:00Z

Authors:Vladimir Zykov, Eberhard Bodenschatz Abstract: The stability of rigidly rotating spiral waves is a very important topic in the study of nonlinear reaction-diffusion media. Computer experiments carried out with a slightly modified Barkley model showed that, in addition to one region of instability observed earlier in the original Barkley model, there is another one exhibiting completely different properties. The wave instability in the second region is not related to the Hopf bifurcation. Moreover, hysteresis effects are observed at the boundary of the region. This means that in the vicinity of this region of instability, direct integration of the model equations leads either to a rigidly rotating or meandering spiral, depending on the initial conditions. PubDate: 2022-05-13T00:00:00Z

Authors:Jan Heiland, Peter Benner, Rezvan Bahmani Abstract: The control of general nonlinear systems is a challenging task in particular for large-scale models as they occur in the semi-discretization of partial differential equations (PDEs) of, say, fluid flow. In order to employ powerful methods from linear numerical algebra and linear control theory, one may embed the nonlinear system in the class of linear parameter varying (LPV) systems. In this work, we show how convolutional neural networks can be used to design LPV approximations of incompressible Navier-Stokes equations. In view of a possibly low-dimensional approximation of the parametrization, we discuss the use of deep neural networks (DNNs) in a semi-discrete PDE context and compare their performance to an approach based on proper orthogonal decomposition (POD). For a streamlined training of DNNs directed to the PDEs in a Finite Element (FEM) framework, we also discuss algorithmical details of implementing the proper norms in general loss functions. PubDate: 2022-04-29T00:00:00Z

Authors:Musyoka Kinyili, Justin B. Munyakazi, Abdulaziz Y. A. Mukhtar Abstract: The question of whether to drop or to continue wearing face masks especially after being vaccinated among the public is controversial. This is sourced from the efficacy levels of COVID-19 vaccines developed, approved, and in use. We develop a deterministic mathematical model that factors in a combination of the COVID-19 vaccination program and the wearing of face masks as intervention strategies to curb the spread of the COVID-19 epidemic. We use the model specifically to assess the potential impact of wearing face masks, especially by the vaccinated individuals in combating further contraction of COVID-19 infections. Validation of the model is achieved by performing its goodness of fit to the Republic of South Africa's reported COVID-19 positive cases data using the Maximum Likelihood Estimation algorithm implemented in the fitR package. We first consider a scenario where the uptake of the vaccines and wearing of the face masks, especially by the vaccinated individuals is extremely low. Second, we consider a scenario where the uptake of the vaccines and wearing of the face masks by people who are vaccinated is relatively high. Third, we consider a scenario where the uptake of the vaccines and wearing of the face masks by the vaccinated individuals is on an upward trajectory. Findings from scenario one and scenario two, respectively, indicate a highly surging number of infections and a low recorded number of infections. For scenario three, it shows that the increased extent of wearing of the face masks by the vaccinated individuals at increasing levels of vaccine and face mask average protection results in a highly accelerated decrease in COVID-19 infections. However, wearing face masks alone also results in the reduction of the peak number of infections at increasing levels of face mask efficacy though the infections delay clearing. PubDate: 2022-04-27T00:00:00Z

Authors:Laura Cifuentes-Fontanals, Elisa Tonello, Heike Siebert Abstract: Understanding control mechanisms in biological systems plays a crucial role in important applications, for instance in cell reprogramming. Boolean modeling allows the identification of possible efficient strategies, helping to reduce the usually high and time-consuming experimental efforts. Available approaches to control strategy identification usually focus either on attractor or phenotype control, and are unable to deal with more complex control problems, for instance phenotype avoidance. They also fail to capture, in many situations, all possible minimal strategies, finding instead only sub-optimal solutions. In order to fill these gaps, we present a novel approach to control strategy identification in Boolean networks based on model checking. The method is guaranteed to identify all minimal control strategies, and provides maximal flexibility in the definition of the control target. We investigate the applicability of the approach by considering a range of control problems for different biological systems, comparing the results, where possible, to those obtained by alternative control methods. PubDate: 2022-04-26T00:00:00Z

Authors:Roberto R. Rivera-Durón, Ricardo Sevilla-Escoboza, Qui-Ling Wang Abstract: The obtainment of a dynamical logic gate (DLG), which is a device capable of implementing several logic functions using the same model, has been one of the goals of the scientific community. Dynamical systems, specifically those that display chaotic behavior, have been widely used to emulate different logic gates which are the basis of general-purpose computing. In this study, we present a methodology based on unstable dissipative systems of type 1 (UDS-1), a kind of dynamical system capable of generating multi-scrolls and multi-stability. Using these two features, we codify inputs, subsequently, we get the adequate output, developing in this way a dynamical (reconfigurable) logic gate that performs any of the sixteen possible logic functions of two inputs. A highlight of the proposed methodology is that the selection of the desired logic gate is realized just by varying a couple of parameters. PubDate: 2022-04-25T00:00:00Z

Authors:Olawale O. Kehinde, Justin B. Munyakazi, Appanah R. Appadu Abstract: Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-non-existent. In this article, we study a two-dimensional semilinear singularly perturbed convection-diffusion problems. Our approach requires linearization of the continuous semilinear problem using the quasilinearization technique. We then discretize the resulting linear problems in the framework of non-standard finite difference methods. A rigorous convergence analysis is conducted showing that the proposed method is first-order parameter-uniform convergent. Finally, two test examples are used to validate the theoretical findings. PubDate: 2022-04-21T00:00:00Z

Authors:Issam Dawoud, Mohamed R. Abonazel, Fuad A. Awwad Abstract: In the linear regression model, the multicollinearity effects on the ordinary least squares (OLS) estimator performance make it inefficient. To solve this, several estimators are given. The Kibria-Lukman (KL) estimator is a recent estimator that has been proposed to solve the multicollinearity problem. In this paper, a generalized version of the KL estimator is proposed, along with the optimal biasing parameter of our proposed estimator derived by minimizing the scalar mean squared error. Theoretically, the performance of the proposed estimator is compared with the OLS, the generalized ridge, the generalized Liu, and the KL estimators by the matrix mean squared error. Furthermore, a simulation study and the numerical example were performed for comparing the performance of the proposed estimator with the OLS and the KL estimators. The results indicate that the proposed estimator is better than other estimators, especially in cases where the standard deviation of the errors was large and when the correlation between the explanatory variables is very high. PubDate: 2022-04-20T00:00:00Z

Authors:Venera Khoromskaia, Boris N. Khoromskij Abstract: Tensor numerical methods, based on the rank-structured tensor representation of d-variate functions and operators discretized on large n⊗d grids, are designed to provide O(dn) complexity of numerical calculations contrary to O(nd) scaling by conventional grid-based methods. However, multiple tensor operations may lead to enormous increase in the tensor ranks (curse of ranks) of the target data, making calculation intractable. Therefore, one of the most important steps in tensor calculations is the robust and efficient rank reduction procedure which should be performed many times in the course of various tensor transforms in multi-dimensional operator and function calculus. The rank reduction scheme based on the Reduced Higher Order SVD (RHOSVD) introduced by the authors, played a significant role in the development of tensor numerical methods. Here, we briefly survey the essentials of RHOSVD method and then focus on some new theoretical and computational aspects of the RHOSVD and demonstrate that this rank reduction technique constitutes the basic ingredient in tensor computations for real-life problems. In particular, the stability analysis of RHOSVD is presented. We introduce the multi-linear algebra of tensors represented in the range-separated (RS) tensor format. This allows to apply the RHOSVD rank-reduction techniques to non-regular functional data with many singularities, for example, to the rank-structured computation of the collective multi-particle interaction potentials in bio-molecular modeling, as well as to complicated composite radial functions. The new theoretical and numerical results on application of the RHOSVD in scattered data modeling are presented. We underline that RHOSVD proved to be the efficient rank reduction technique in numerous applications ranging from numerical treatment of multi-particle systems in material sciences up to a numerical solution of PDE constrained control problems in ℝd. PubDate: 2022-04-19T00:00:00Z

Authors:Evangelos Georganas, Dhiraj Kalamkar, Sasikanth Avancha, Menachem Adelman, Deepti Aggarwal, Cristina Anderson, Alexander Breuer, Jeremy Bruestle, Narendra Chaudhary, Abhisek Kundu, Denise Kutnick, Frank Laub, Vasimuddin Md, Sanchit Misra, Ramanarayan Mohanty, Hans Pabst, Brian Retford, Barukh Ziv, Alexander Heinecke Abstract: During the past decade, novel Deep Learning (DL) algorithms, workloads and hardware have been developed to tackle a wide range of problems. Despite the advances in workload and hardware ecosystems, the programming methodology of DL systems is stagnant. DL workloads leverage either highly-optimized, yet platform-specific and inflexible kernels from DL libraries, or in the case of novel operators, reference implementations are built via DL framework primitives with underwhelming performance. This work introduces the Tensor Processing Primitives (TPP), a programming abstraction striving for efficient, portable implementation of DL workloads with high-productivity. TPPs define a compact, yet versatile set of 2D-tensor operators [or a virtual Tensor Instruction Set Architecture (ISA)], which subsequently can be utilized as building-blocks to construct complex operators on high-dimensional tensors. The TPP specification is platform-agnostic, thus, code expressed via TPPs is portable, whereas the TPP implementation is highly-optimized and platform-specific. We demonstrate the efficacy and viability of our approach using standalone kernels and end-to-end DL & High Performance Computing (HPC) workloads expressed entirely via TPPs that outperform state-of-the-art implementations on multiple platforms. PubDate: 2022-04-18T00:00:00Z

Authors:Adriano A. Batista, Severino Horácio da Silva Abstract: In this work, we adapt the epidemiological SIR model to study the evolution of the dissemination of COVID-19 in Germany and Brazil (nationally, in the State of Paraíba, and in the City of Campina Grande). We prove the well posedness and the continuous dependence of the model dynamics on its parameters. We also propose a simple probabilistic method for the evolution of the active cases that is instrumental for the automatic estimation of parameters of the epidemiological model. We obtained statistical estimates of the active cases based on the probabilistic method and on the confirmed cases data. From this estimated time series, we obtained a time-dependent contagion rate, which reflects a lower or higher adherence to social distancing by the involved populations. By also analyzing the data on daily deaths, we obtained the daily lethality and recovery rates. We then integrate the equations of motion of the model using these time-dependent parameters. We validate our epidemiological model by fitting the official data of confirmed, recovered, death, and active cases due to the pandemic with the theoretical predictions. We obtained very good fits of the data with this method. The automated procedure developed here could be used for basically any population with a minimum of adaptation. Finally, we also propose and validate a forecasting method based on Markov chains for the evolution of the epidemiological data for up to 2 weeks. PubDate: 2022-04-13T00:00:00Z

Authors:Christos Psarras, Lars Karlsson, Rasmus Bro, Paolo Bientinesi Abstract: The Canonical Polyadic (CP) tensor decomposition is frequently used as a model in applications in a variety of different fields. Using jackknife resampling to estimate parameter uncertainties is often desirable but results in an increase of the already high computational cost. Upon observation that the resampled tensors, though different, are nearly identical, we show that it is possible to extend the recently proposed Concurrent ALS (CALS) technique to a jackknife resampling scenario. This extension gives access to the computational efficiency advantage of CALS for the price of a modest increase (typically a few percent) in the number of floating point operations. Numerical experiments on both synthetic and real-world datasets demonstrate that the new workflow based on a CALS extension can be several times faster than a straightforward workflow where the jackknife submodels are processed individually. PubDate: 2022-04-12T00:00:00Z

Authors:Fenglian Li, Tiantian Yuan, Yan Zhang, Wenpei Liu Abstract: Although face recognition has received a lot of attention and development in recent years, it is one of the research hotspots due to the low efficiency of Single Sample Per Person (SSPP) information in face recognition. In order to solve this problem, this article proposes a face recognition method based on virtual sample generation and multi-scale feature extraction. First, in order to increase the training sample information, a new NMF-MSB virtual sample generation method is proposed by combining the Non-negative Matrix Factorization (NMF) reconstruction strategy with Mirror transform(M), Sliding window(S), and Bit plane(B) sample extension methods. Second, a feature extraction method (named WPD-HOG-P) based on Wavelet Packet Decomposition, Histograms of Oriented Gradients, and image Pyramid is proposed. The proposed WPD-HOG-P method is beneficial to multi-scale facial image feature extraction. Finally, based on the extracted WPD-HOG-P features, the recognition model is established by using a grid search optimization support vector machine. Experimental results on ORL and FERET data sets show that the proposed method has higher recognition rates and lower computational complexity than the benchmark methods. PubDate: 2022-04-08T00:00:00Z

Authors:Axel Hutt Abstract: Additive noise has been known for a long time to not change a systems stability. The discovery of stochastic and coherence resonance in nature and their analytical description has started to change this view in the last decades. The detailed studies of stochastic bifurcations in the last decades have also contributed to change the original view on the role of additive noise. The present work attempts to put these pieces of work in a broader context by proposing the research direction ANISE as a perspective in the research field. ANISE may embrace all studies that demonstrates how additive noise tunes a systems evolution beyond just scaling its magnitude. The article provides two perspective directions of research. The first perspective is the generalization of previous studies on the stationary state stability of a stochastic random network model subjected to additive noise. Here the noise induces novel stationary states. A second perspective is the application of subgrid-scale modeling in stochastic random network model. It is illustrated how numerical parameter estimation complements and extends subgrid-scale modeling and render it more powerful. PubDate: 2022-04-08T00:00:00Z

Authors:Cem Savas Bassoy Abstract: Numerical tensor calculus has recently gained increasing attention in many scientific fields including quantum computing and machine learning which contain basic tensor operations such as the pointwise tensor addition and multiplication of tensors. We present a C++ design of multi-dimensional iterators and iterator-based C++ functions for basic tensor operations using mode-specific iterators only, simplifying the implementation of algorithms with recursion and multiple loops. The proposed C++ functions are designed for dense tensor and subtensor types with any linear storage format, mode and dimensions. We demonstrate our findings with Boost's latest uBlas tensor extension and discuss how other C++ frameworks can utilize our proposal without modifying their code base. Our runtime measurements show that C++ functions with iterators can compute tensor operations at least as fast as their pointer-based counterpart. PubDate: 2022-04-07T00:00:00Z

Authors:Yang Chen, Yijia Ma, Wei Wu Abstract: Temporal point process, an important area in stochastic process, has been extensively studied in both theory and applications. The classical theory on point process focuses on time-based framework, where a conditional intensity function at each given time can fully describe the process. However, such a framework cannot directly capture important overall features/patterns in the process, for example, characterizing a center-outward rank or identifying outliers in a given sample. In this article, we propose a new, data-driven model for regular point process. Our study provides a probabilistic model using two factors: (1) the number of events in the process, and (2) the conditional distribution of these events given the number. The second factor is the key challenge. Based on the equivalent inter-event representation, we propose two frameworks on the inter-event times (IETs) to capture large variability in a given process—One is to model the IETs directly by a Dirichlet mixture, and the other is to model the isometric logratio transformed IETs by a classical Gaussian mixture. Both mixture models can be properly estimated using a Dirichlet process (for the number of components) and Expectation-Maximization algorithm (for parameters in the models). In particular, we thoroughly examine the new models on the commonly used Poisson processes. We finally demonstrate the effectiveness of the new framework using two simulations and one real experimental dataset. PubDate: 2022-04-04T00:00:00Z

Authors:Farai Julius Mhlanga, Lazarus Rundora Abstract: In this article, we treat the existence and uniqueness of strong solutions to the Cauchy problem of stochastic equations of the form dXt=αXtdt+σXtγdBt,X0=x>0. The construction does not require the drift and the diffusion coefficients to be Lipschitz continuous. Sufficient and necessary conditions for the existence of a global positive solution of non-homogeneous stochastic differential equations with a non-Lipschitzian diffusion coefficient are sought using probabilistic arguments. The special case γ = 2 and the general case, that is, γ > 1 are considered. A complete description of every possible behavior of the process Xt at the boundary points of the state interval is provided. For applications, the Cox-Ingersoll-Ross model is considered. PubDate: 2022-03-30T00:00:00Z

Authors:Muzaffer Ayvaz, Lieven De Lathauwer Abstract: We introduce the Tensor-Based Multivariate Optimization (TeMPO) framework for use in nonlinear optimization problems commonly encountered in signal processing, machine learning, and artificial intelligence. Within our framework, we model nonlinear relations by a multivariate polynomial that can be represented by low-rank symmetric tensors (multi-indexed arrays), making a compromise between model generality and efficiency of computation. Put the other way around, our approach both breaks the curse of dimensionality in the system parameters and captures the nonlinear relations with a good accuracy. Moreover, by taking advantage of the symmetric CPD format, we develop an efficient second-order Gauss–Newton algorithm for multivariate polynomial optimization. The presented algorithm has a quadratic per-iteration complexity in the number of optimization variables in the worst case scenario, and a linear per-iteration complexity in practice. We demonstrate the efficiency of our algorithm with some illustrative examples, apply it to the blind deconvolution of constant modulus signals, and the classification problem in supervised learning. We show that TeMPO achieves similar or better accuracy than multilayer perceptrons (MLPs), tensor networks with tensor trains (TT) and projected entangled pair states (PEPS) architectures for the classification of the MNIST and Fashion MNIST datasets while at the same time optimizing for fewer parameters and using less memory. Last but not least, our framework can be interpreted as an advancement of higher-order factorization machines: we introduce an efficient second-order algorithm for higher-order factorization machines. PubDate: 2022-03-30T00:00:00Z

Authors:Zhanshan (Sam Ma Abstract: Power laws (PLs) have been found to describe a wide variety of natural (physical, biological, astronomic, meteorological, and geological) and man-made (social, financial, and computational) phenomena over a wide range of magnitudes, although their underlying mechanisms are not always clear. In statistics, PL distribution is often found to fit data exceptionally well when the normal (Gaussian) distribution fails. Nevertheless, predicting PL phenomena is notoriously difficult because of some of its idiosyncratic properties, such as lack of well-defined average value and potentially unbounded variance. Taylor's power law (TPL) is a PL first discovered to characterize the spatial and/or temporal distribution of biological populations. It has also been extended to describe the spatiotemporal heterogeneities (distributions) of human microbiomes and other natural and artificial systems, such as fitness distribution in computational (artificial) intelligence. The PL with exponential cutoff (PLEC) is a variant of power-law function that tapers off the exponential growth of power-law function ultimately and can be particularly useful for certain predictive problems, such as biodiversity estimation and turning-point prediction for Coronavirus Diease-2019 (COVID-19) infection/fatality. Here, we propose coupling (integration) of TPL and PLEC to offer a methodology for quantifying the uncertainty in certain estimation (prediction) problems that can be modeled with PLs. The coupling takes advantage of variance prediction using TPL and asymptote estimation using PLEC and delivers CI for the asymptote. We demonstrate the integrated approach to the estimation of potential (dark) biodiversity of the American gut microbiome (AGM) and the turning point of COVID-19 fatality. We expect this integrative approach should have wide applications given duel (contesting) relationship between PL and normal statistical distributions. Compared with the worldwide COVID-19 fatality number on January 24th, 2022 (when this paper is online), the error rate of the prediction with our coupled power laws, made in the May 2021 (based on the fatality data then alone), is approximately 7% only. It also predicted that the turning (inflection) point of the worldwide COVID-19 fatality would not occur until the July of 2022, which contrasts with a recent prediction made by Murray on January 19th of 2022, who suggested that the “end of the pandemic is near” by March 2022. PubDate: 2022-03-25T00:00:00Z