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Linear - Astrophysics Data System

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Last Updated: 22 September 2022

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Linear Network Coding Based Fast Data Synchronization for Wireless Ad Hoc Networks with Controlled Topology

Rapid data synchronization in wireless ad hoc networks is a difficult and critical issue. We introduce two linear network coding and all-to-all broadcast synchronization algorithms for wireless ad hoc networks under operator's custody in this article. For profiting the benefits of NC, we recommend both data block selection and transmitting node selection. Simulation results show that our algorithms significantly reduce the times slots used for data synchronization in comparison to the baseline that does not use NC.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220908255H/abstract


EcoFormer: Energy-Saving Attention with Linear Complexity

However, current binarization technologies are limited to minimizing the exposure loss for the input distribution's statistically, while leaving out the attention mechanism's pairwise similarity modeling at the heart of the attention mechanism. We recommend a new binarization paradigm tailored to high-dimensional softmax attention by kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. In a self-supervised manner, the kernelized hash functions were found to be able to replicate the ground-truth similarity relationships derived from the attention map. We can approximate linear complexity by expressing it as a dot-product of binary codes based on the equivalence between the internal product of binary codes and the Hamming distance, as well as the associative property of matrix multiplication. EcoFormer consistently achieves comparable results with standard attentions, despite using less funds, according to extensive studies.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220909004L/abstract


A Causality-DeepONet for Causal Responses of Linear Dynamical Systems

We propose a DeepONet structure with causality to represent the causal linear operators in Banach spaces of time-dependent signals. In citationtianpingchen1995, the universal approximations to nonlinear operators is extended to operators with causalities, and the proposed Causality-DeepONet maintains the physical causality in its framework.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220908397L/abstract


The Marchenko method to solve the general system of derivative nonlinear Schrödinger equations

To solve the inverse scattering problem for the linear system associated with the derivative NLS equations, a system of integral equations is presented, which is the equivalent of Marchenko integral equations. The corresponding reduced Marchenko integral equation is found in the reduced case, where the two potentials in the linear system are related to each other through complicated conjugation.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220908426A/abstract


A Decoupled and Linear Framework for Global Outlier Rejection over Planar Pose Graph

Loop closure outliers corrupted planar pose graph optimization, resulting in a robust framework for the planar pose graph optimization. Our framework first decoupling the massive PGO problem wrapped by a Truncated Least Squares kernel into two subproblems. To rewrite the first subproblem that was originally devised with rotation matrices, the framework, which framework, introduces a linear angle representation.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220908543W/abstract


Inference of nonlinear causal effects with GWAS summary data

However, conventional theories hold linear causal relationships partially for simplicity and partially for the lack of GWAS summary data. The former is estimated by a ratio-adjusted inverse regression, a nonlinear regression, and a marginal causal effect and a nonlinear transition, where the former is estimated via sliced inverse regression and a sparse instrumental variable regression, and the latter is estimated by a ratio-adjusted inverse regression. 18 causal genes associated with Alzheimer's disease have been identified with Alzheimer's disease, including APOE and TOMM40, in comparison to seven other genes that were not accessible by two-stage least squares considering only linear relationships. Our findings indicate that nonlinear gene-trait associations are the most effective of IV regression for determining potentially nonlinear gene-trait associations.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220908889D/abstract


Modified PSO based PID Sliding Mode Control using Improved Reaching Law for Nonlinear systems

With improved reaching legislation, a new model based nonlinear control method, called PID type sliding mode control, is introduced in this paper. For the optimized parameters, particle swarm intelligent optimization is used to enhance the consistency of the second order nonlinear differential equations with unknown parameters. This paper discusses the current slide surface engineering, the proposed power rate exponential scaling law, parameter optimization with modified particle swarm optimization, and the key characteristics of adding an integral term in the sliding mode, such as robustness and higher convergence, through extensive mathematical simulation.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220909170S/abstract


Faster Randomized Interior Point Methods for Tall/Wide Linear Programs

Interior Point Methods are one of the most commonly used techniques to solve LPs both in theory and in practice. We investigate both feasible and infeasible IPMs for the special case in which the number of variables is much larger than the number of constraints. We present a preconditioning algorithm that when combined with Conjugate Gradient or Chebyshev Iteration's iterative solvers, lead to a cost-effective, approximately optimal solution, without increasing iteration complexity.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220908722C/abstract


Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss

We look at fast collisions between pulsed optical beams in a linear medium with poor cubic loss caused by non-degenerate two-photon absorption. We introduce two small parameters and use it to obtain general formulas for the pulse-beam's shape and amplitude, which are reproduced in the collision-induced changes in the pulsed-beam's shape and amplitude. In previous experiments of fast two-pulse collisions, the values of the collision-induced changes in the pulsed-beam's shape in both configurations are higher by one to two orders of magnitude relative to those obtained in previous studies of fast two-pulse collisions. In addition, we show that for nonlocalized installations, the amplitude shift curve vs. the difference between the first-order dispersion coefficients for the two pulsed-beams has two local minima. In the case of poor nonlinear loss, this is the first report of a deviation of the graph from the intended funnel shape that was found in all previous studies of fast two-pulse collisions.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220909113P/abstract


Linear TreeShap

Decision trees are well-known due to their simplicity in interpretation. We need deep trees or groups of trees in order to improve accuracy. Shapley values have recently emerged as a common way to explain tree-based machine learning models' predictions. It gives a linear weight to features that are independent of the tree's configuration. Linear TreeShap is the same as TreeShape, and it needs the same amount of memory.

Source link: https://ui.adsabs.harvard.edu/abs/2022arXiv220908192Y/abstract

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions