Related papers: Braidlab: A Software Package for Braids and Loops

This work presents an extension of graph-based SLAM methods to exploit the potential of 3D laser scans for loop detection. Every high-dimensional point cloud is replaced by a compact global descriptor, whereby a trained detector decides…

We present Matrix Distributed Processing, a C++ library for fast development of efficient parallel algorithms. MDP is based on MPI and consists of a collection of C++ classes and functions such as lattice, site and field. Once an algorithm…

We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems $\partial_i \boldsymbol j = M_i \boldsymbol j$ for one or several…

Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…

Machine Learning (ML) techniques are indispensable in a wide range of fields. Unfortunately, the exponential increase of dataset sizes are rapidly extending the runtime of sequential algorithms and threatening to slow future progress in ML.…

The Libra Toolkit is a collection of algorithms for learning and inference with discrete probabilistic models, including Bayesian networks, Markov networks, dependency networks, and sum-product networks. Compared to other toolkits, Libra…

Path planning for multiple tethered robots is a challenging problem due to the complex interactions among the cables and the possibility of severe entanglements. Previous works on this problem either consider idealistic cable models or…

When writing high-performance code for numerical computation in a scripting language like MATLAB, it is crucial to have the operations in a large for-loop vectorized. If not, the code becomes too slow to use, even for a moderately large…

Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on…

We begin with a review of the notion of a braid group. We then discuss some known solutions to decision problems in braid groups. We then move on to proving new results in braid group algorithmics. We offer a quick solution to the…

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular,…

We develop an optimization framework for identifying ideal Mixed Binary Linear Programs (MBLP) which is linear when using known input data and nonconvex quadratic over parametric input data. These techniques are applied to various…

This paper is an overview of Image Processing and Analysis using Scilab, a free prototyping environment for numerical calculations similar to Matlab. We demonstrate the capabilities of SIP -- the Scilab Image Processing Toolbox -- which…

Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years effective statistical methods for fitting power laws have been developed, but appropriate use of…

Randomized numerical linear algebra - RandNLA, for short - concerns the use of randomization as a resource to develop improved algorithms for large-scale linear algebra computations. The origins of contemporary RandNLA lay in theoretical…

In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…

The prevalence of software systems has become an integral part of modern-day living. Software usage has increased significantly, leading to its growth in both size and complexity. Consequently, software development is becoming a more…

Deep learning holds immense promise for spectroscopy, yet research and evaluation in this emerging field often lack standardized formulations. To address this issue, we introduce SpectrumLab, a pioneering unified platform designed to…

Real-world data for classification is often labeled by multiple annotators. For analyzing such data, we introduce CROWDLAB, a straightforward approach to utilize any trained classifier to estimate: (1) A consensus label for each example…

Microscopy and particle-based simulations are both powerful techniques to study aggregated particulate matter such as colloidal gels. The data provided by these techniques often contains information on a wide array of length scales, but…