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).
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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Telecommunication is a critical driver of economic and social development. 5G technologies are state-of-the-art in telecommunication, setting strong and open-ended requirements for implementing systems. Current system...
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Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research ***,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a sy...
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Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research ***,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical *** propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier *** this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical ***,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical *** to computational complexity,calculations are not performed for higher dimensional ***,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be ***,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.
Non-destructive testing of composites is an important issue in the modern aircraft *** are susceptible to the barely visible impact damage which can affect the residual strength of the material and occurs both during ...
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Non-destructive testing of composites is an important issue in the modern aircraft *** are susceptible to the barely visible impact damage which can affect the residual strength of the material and occurs both during production and *** continuum model for describing the damaged zone is *** slip theory relations used for a continuous distribution of slip planes are *** the initial stage,the isotropic background model is *** model allows the material slippage along the fractures based on the Coulomb friction law with the small viscous *** this regime,the govern system of equations becomes *** overcome this difficulty,the explicit-implicit grid-characteristic scheme is *** standard ultrasound diagnostic procedure of damaged composite materials is successfully *** with the trivial free-surface fracture model,different reactions on the compression and stretch waves are *** approach provided an effective way for the simulation of complex dynamic behavior of damage zones.
The computer vision field has wide applications in various areas, including sports. Almost all sports events have been exploiting the best features. Sports videos are structure-based, and due to this characteristic, t...
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We give a complete structure theorem for 1-complex s, t Hamiltonian paths in rectangular grid graphs. We use the structure theorem to design an algorithm to reconfigure one such path into any other in linear time, mak...
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The reliability of BiCGStab and IDR solvers for the exponential scheme discretization of the advection-diffusion-reaction equation is *** resulting discretization matrices have real *** consider BiCGStab,IDR(S),BiCGSt...
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The reliability of BiCGStab and IDR solvers for the exponential scheme discretization of the advection-diffusion-reaction equation is *** resulting discretization matrices have real *** consider BiCGStab,IDR(S),BiCGStab(L)and various modifications of BiCGStab,where S denotes the dimension of the shadow space and L the degree of the polynomial used in the polynomial *** implementations of BiCGStab exist which are equivalent in exact arithmetic,however,not in finite precision *** modifications of BiCGStab we consider are;choosing a random shadow vector,a reliable updating scheme,and storing the best intermediate *** is shown that the Local Minimal Residual algorithm,a method similar to the“minimize residual”step of BiCGStab,can be interpreted in terms of a time-dependent advection-diffusion-reaction equation with homogeneous Dirichlet boundary conditions for the residual,which plays a key role in the convergence *** to the real eigenvalues,the benefit of BiCGStab(L)compared to BiCGStab is shown to be modest in numerical ***-sparse(*** random)shadow residual turns out to be essential for the reliability of *** reliable updating scheme ensures the required tolerance is truly *** the best intermediate solution has no significant *** is to modify BiCGStab with a random shadow residual and the reliable updating scheme,especially in the regime of large P´eclet and small Damk¨ohler *** alternative option is IDR(S),which outperforms BiCGStab for problems with strong advection in terms of the number of matrix-vector *** MATLAB code used in the numerical experiments is available on GitLab:https://***/ChrisSchoutrop/krylov-adr,a C++implementation of IDR(S)is available in the Eigen linear algebra library:http://***.
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