25 papers · ranked by Valyu relevance
Jing He, Qi-wei Kong, Ho-Chung Lui, Haitao Liu + 1 more
The definition of factor space and a unified optimization based classification model were developed for linear programming and supervised learning. Intelligent behaviour appeared in a decision process can be treated as a moving point y, the dynamic state observed and controlled by the agent, moving in a factor space…
Jason Rader, Terry Lyons, Patrick Kidger
We introduce Lineax, a library bringing linear solves and linear least-squares to the JAX+Equinox scientific computing ecosystem. Lineax uses general linear operators, and unifies linear solves and least-squares into a single, autodifferentiable API. Solvers and operators are user-extensible, without requiring the user…
Sebastian Schmidt, Jarno N. Alanko
A fundamental operation in computational genomics is to reduce the input sequences to their constituent k-mers. For maximum performance of downstream applications it is important to store the k-mers in small space, while keeping the representation easy and efficient to use (i.e. without k-mer repetitions and in plain…
Theodoros Anagnostopoulos, Evanthia Zervoudi, Christos Anagnostopoulos, Apostolos Christopoulos + 1 more
Linear regression analysis focuses on predicting a numeric regressand value based on certain regressor values. In this context, k-Nearest Neighbors (k-NN) is a common non-parametric regression algorithm, which achieves efficient performance when compared with other algorithms in literature. In this research effort an…
Yu Huo, Hongpei Li, Xiao Wang, Xiaochen Du + 1 more
When analysing two-dimensional data sets, scientists are often interested in regions where one variable depends linearly on the other. Typically they use an ad hoc method to do so. Here we develop a statistically rigorous, Bayesian approach to infer the optimal partitioning of a data set into contiguous piece-wise…
Authors not listed
We present a fast, asymptotically linear-scaling implementation of the perturbative quadruples energy correction in coupled-cluster theory using local natural orbitals. Our work follows the domain-based local pair natural orbital (DLPNO) approach previously applied to lower levels of excitations in coupled-cluster…
Alexander Dobler, Martin Nöllenburg
Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their contained elements. The efficacy of linear diagrams heavily depends on having few…
Yaru Fu, Xiaoyu Jiang, Yanpeng Zheng, Zhaolin Jiang
We present two fast algorithms for finding the solution of the nonsingular lower Hessenberg quasi-Toeplitz linear system stem from Markov chain. And we confirm the complexity of these two algorithms is both O $n\log n$ based on the fact that a lower Hessenberg quasi-Toeplitz matrix can be written as the sum of a…
Jan Schröder, Yair Censor, Philipp Süss, Karl-Heinz Küfer
Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the…
Md. Hasin Abrar, Paul Medvedev
Understanding structural properties of k-mer multisets is crucial to designing space-efficient indices to query them. A potentially novel source of structure can be found in the rank function of a k-mer multiset. In particular, the rank function of a k-mer multiset can be approximated by a piece-wise linear function…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Jiahong Wu, Nan Liu, Wei Kang, Jun Chen + 1 more
In this paper, we study a three-layer wiretap network including the source node in the top layer, N nodes in the middle layer and L sink nodes in the bottom layer. Each sink node recovers the message generated from the source node correctly via the middle layer nodes that it has access to. Furthermore, it is required…
Amir Hossein Salehi Shayegan
In this work, we present a solution to the critical limitation of qubit capacity in near-term quantum hardware by giving a hybrid framework that integrates the spectral element method (SEM) with distributed quantum computing. Using domain decomposition techniques, the additive and multiplicative Schwarz methods, the…
Arya Chakraborty
— While time complexity and space complexity of an algorithm helps to determine its efficiency when time or space needs to be optimized respectively, they fail to determine the more efficient algorithm when time and space both need to be optimized simultaneously. This resulted in the development of the A1-Score Factor…
Pier Paolo Poier, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Andrea Brilli, Morteza Kimiaei, Giampaolo Liuzzi, Stefano Lucidi
This paper is devoted to the analysis of worst case complexity bounds for linesearchtype derivative-free algorithms for the minimization of general non-convex smooth functions. We prove that two linesearch-type algorithms enjoy the same complexity properties which have been proved for pattern and direct search…
Stefan Hougardy, Meike Neuwohner, Ulrike Schorr
In Placement Legalization, it is often assumed that (almost) all standard cells possess the same height and can therefore be aligned in cell rows, which can then be treated independently. However, this is no longer true for recent technologies, where a substantial number of cells of double- or even arbitrary…
Pier Paolo Poir, Louis Lagardère, Jean-Philip Piquemal
We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate…
Sepideh Aghamolaei, Kevin Buchin, Timothy M. Chan, Jacobus Conradi + 4 more
Computing the convex hull of a planar $n$-point set $P$ is one of the most fundamental problems in computational geometry. It has an $Ω(n \log n)$ lower bound in the algebraic computation tree model, and many convex hull algorithms match this bound. Classical results show that, under special input assumptions, sub-$O(n…
Patrick Kunzmann
Alignment searches are fast heuristic methods to identify similar regions between two sequences. This group of algorithms is ubiquitously used in a myriad of software to find homologous sequences or to map sequence reads to genomes. Often the first step in alignment searches is k-mer decomposition: listing all…
Andrew McCluskey
The use of mathematical transformations to reduce non-linear functions to linear problems, which can be tackled with analytical linear regression, is commonplace in the chemistry curriculum. The linearization procedure, however, assumes an incorrect statistical model for real experimental data; leading to biased…
Yuyong Tan, Jianfeng Wang, Bin Wang, Yongquan Zhou
The intelligent optimization algorithm has become a key tool in complex and intertwined engineering and science fields. However, with the increasing complexity of the problem and the rapid expansion of the data scale, the performance of the algorithm has been challenged unprecedentedly. The artificial lemming algorithm…
Yi Sun
We demonstrate how the combination of a shifted clustering algorithm and a fast-marching- based algorithm is able to generate good approximations of the Minimum Free Energy Path (MFEP) if a Free Energy Landscape (FEL) is given. Then, we show that using this kind of approximation as the MFEP's first guess and the string…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
AKHIL SHAJAN, Madushanka Manathunga, Andreas Goetz, Kenneth Merz
Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and…