The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of th...
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The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.
In this work, a novel methodological approach to multi-attribute decision-making problems is developed and the notion of Heptapartitioned Neutrosophic Set Distance Measures (HNSDM) is introduced. By averaging the Pent...
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In this paper, we propose a novel mathematical model for indirectly transmitted typhoid fever disease that incorporates the use of modern and traditional medicines as modes of treatment. Theoretically, we provide two ...
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We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in...
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We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in a two-dimensional(2D)*** focus is on the impact of different discretization methods and choices of regularization parameters on the symmetry of the numerical *** particular,we show that using the symmetric alternating direction implicit(ADI)method for time discretization helps preserve the symmetry of the solution,compared to the(non-symmetric)ADI ***,we study the effect of the regularization by the isotropic background perme-ability r>0,showing that the increased condition number of the elliptic problem due to decreasing value of r leads to loss of *** show that in this case,neither the use of the symmetric ADI method preserves the symmetry of the ***,we perform the numerical error analysis of our method making use of the Wasserstein distance.
The integration of Artificial Intelligence(AI) with Long-Term Evolution (LTE) networks offers substantial potential for improving communication infrastructure. By harnessing AI algorithms, it is possible to dynamicall...
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We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation Ei|jkα≤Ej|ikα+Ek|ijα holds for all subaddit...
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We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation Ei|jkα≤Ej|ikα+Ek|ijα holds for all subadditive bipartite entanglement measure E, all permutations under parties i,j,k, all α∈[0,1], and all pure tripartite states. Then, we rigorously prove that the nonobtuse triangle area, enclosed by side Eα with 0<α≤1/2, is a measure for genuine tripartite entanglement. Finally, it is significantly strengthened for qubits that given a set of subadditive and nonsubadditive measures, some state is always found to violate the triangle relation for any α>1, and the triangle area is not a measure for any α>1/2. Our results pave the way to study discrete and continuous multipartite entanglement within a unified framework.
In this paper, we propose a novel warm restart technique using a new logarithmic step size for the stochastic gradient descent (SGD) approach. For smooth and non-convex functions, we establish an O(1/√T) convergence ...
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In this paper, we propose a novel warm restart technique using a new logarithmic step size for the stochastic gradient descent (SGD) approach. For smooth and non-convex functions, we establish an O(1/√T) convergence rate for the SGD. We conduct a comprehensive implementation to demonstrate the efficiency of the newly proposed step size on the FashionMinst, CIFAR10, and CIFAR100 datasets. Moreover, we compare our results with nine other existing approaches and demonstrate that the new logarithmic step size improves test accuracy by 0.9% for the CIFAR100 dataset when we utilize a convolutional neural network (CNN) model.
Low Power Wide Area Networks (LPWANs) plat-forms (LoRa, NB-IoT, Sigfox) came to add a missing piece to the Internet of Things (IoT) ecosystem, namely long range communication in low power. LPWAN platforms are characte...
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Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and t...
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Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian throug...
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Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric, allowing for a standard differential geometric analysis of the latent space. Unfortunately, data manifolds are generally compact and easily disconnected or filled with holes, suggesting a topological mismatch to the Euclidean latent space. The most established solution to this mismatch is to let uncertainty be a proxy for topology, but in neural network models, this is often realized through crude heuristics that lack principle and generally do not scale to high-dimensional representations. We propose using ensembles of decoders to capture model uncertainty and show how to easily compute geodesics on the associated expected manifold. Empirically, we find this simple and reliable, thereby coming one step closer to easy-to-use latent geometries. Copyright 2024 by the author(s).
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