Although deep learning-based approximation algorithms have been applied very successfully to numerous problems,at the moment the reasons for their performance are not entirely understood from a mathematical point of *...
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Although deep learning-based approximation algorithms have been applied very successfully to numerous problems,at the moment the reasons for their performance are not entirely understood from a mathematical point of ***,estimates for the convergence of the overall error have been obtained in the situation of deep supervised learning,but with an extremely slow rate of *** this note,we partially improve on these *** specifically,we show that the depth of the neural network only needs to increase much slower in order to obtain the same rate of *** results hold in the case of an arbitrary stochastic optimization algorithm with *** initializations.
Poverty is still a global problem that must be immediately eradicated by Sustainable Development Goals (SDGs) 1, namely ending poverty anywhere and in any form. In 2021, West Papua province will have the 2nd most sign...
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The growing number of COVID-19 cases puts pressure on healthcare services and public institutions *** pandemic has brought much uncertainty to the global economy and the situation in *** methods and modeling technique...
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The growing number of COVID-19 cases puts pressure on healthcare services and public institutions *** pandemic has brought much uncertainty to the global economy and the situation in *** methods and modeling techniques are important tools for governments to manage critical situations caused by pandemics,which have negative impact on public *** main purpose of this study is to obtain short-term forecasts of disease epidemiology that could be useful for policymakers and public institutions to make necessary short-term *** evaluate the effectiveness of the proposed attention-based method combining certain data mining algorithms and the classical ARIMA model for short-term forecasts,data on the spread of the COVID-19 virus in Lithuania is used,the forecasts of epidemic dynamics were examined,and the results were presented in the ***,the approach presented might be applied to any country and other pandemic *** COVID-19 outbreak started at different times in different countries,hence some countries have a longer history of the disease with more historical data than *** paper proposes a novel approach to data registration and machine learning-based analysis using data from attention-based countries for forecast validation to predict trends of the spread of COVID-19 and assess risks.
In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem...
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In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.
We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations ...
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We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution *** to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux *** a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant *** addition,local bounds may be imposed on scalar quantities of *** contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy *** demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.
Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka–Volterra model which defined the interaction bet...
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We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in *** a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R)[...
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We study the structure of rings which satisfy the von Neumann regularity of commutators,and call a ring R C-regularif ab-ba ∈(ab-ba)R(ab-ba)for all a,b in *** a C-regular ring R,we prove J(R[X])=N^(*)(R[X])=N^(*)(R)[X]=W(R)[X]■Z(R[X]),where J(A),N^(*)(A),W(A),Z(A)are the Jacobson radical,upper nilradical,Wedderburn radical,and center of a given ring A,respectively,and A[X]denotes the polynomial ring with a set X of commuting indeterminates over A;we also prove that R is semiprime if and only if the right(left)singular ideal of R is *** provide methods to construct C-regular rings which are neither commutative nor von Neumann regular,from any given ***,for a C-regular ring R,the following are proved to be equivalent:(i)R is Abelian;(ii)every prime factor ring of R is a duo domain;(ii)R is quasi-duo;and(iv)R/W(R)is reduced.
Recently, the modeling of fuzzy fractional differential equations (FFDEs) has been a very significant issue in many new applications in appliedsciences and engineering, while a natural tool for modeling such dynamica...
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Graph representation learning aims to represent graphs as vectors that can be utilized in downstream tasks such as graph classification. In this work, we focus on learning diverse representations that can capture the ...
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Graph representation learning aims to represent graphs as vectors that can be utilized in downstream tasks such as graph classification. In this work, we focus on learning diverse representations that can capture the graph information as much as possible. We propose quantifying graph information using graph entropy, where we define a probability distribution of a graph based on its nodes’ representations and global-graph representation. However, the computation of graph entropy is NP-hard due to the complex vertex-packing polytope involved in its definition. To address this challenge, we provide an approximation method leveraging orthonormal representations for graph entropy maximization. The proposed method is implemented via graph neural networks, resulting in informative node-level and graph-level representations. Experimental results demonstrate the effectiveness of our method in comparison to many baselines in unsupervised learning and semi-supervised learning tasks. The code of our method is available at https://***/MathAdventurer/GeMax. Copyright 2024 by the author(s)
In this article, the interval type-3 fuzzy-based state feedback control is proposed for the stabilization problem of interval type-3 fuzzy systems (IT3FSs) subject to time-varying delay. Specifically, to improve the m...
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