arXiv research

Algorithm constructs triangulations for Heegaard splittings and related 3-manifolds.

New construction reduces Vietoris-Rips complex construction time.

Algorithm trisects 4D book into three chapters.

Algorithm constructs Kirby diagrams for 4D open books.

Extends Seifert algorithm to 3-manifolds via surgery.

This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such structures.

This paper presents a new algorithm "A" for constructing Seifert surfaces from n-bridge projections of links. The algorithm produces minimal complexity surfaces for large classes of braids and alternating links. In addition, we consider a family of knots for which the canonical genus is strictly greater than the genus,…

We construct the solution to the periodic Cauchy problem of the Schrödinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric algorithm of solving this periodic Cauchy problem follows. Theoretical and experimental results will be discussed.

Coherent uncertainty quantification is a key strength of Bayesian methods. But modern algorithms for approximate Bayesian posterior inference often sacrifice accurate posterior uncertainty estimation in the pursuit of scalability. This work shows that previous Bayesian coreset construction algorithms---which build a sm…

Constructs algorithms to recognize and classify 2D surfaces.

Algorithm of construction of all knots, links with given number of crosses on diagram of knot, link is offered. This algorithm is based on simple proposition, that there is a representation of knot (link) as closure of braid with n threads and length of this braid does not exceed n(4n-5)+2.

New method constructs confidence sets for GLMs via game theory.

We consider a class of finite Markov moment problems with arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the non-unique solution families. Moreover, we present a constructive algorithm to solve the moment problems numeric…

In the paper, we focus on complexity of C5.0 algorithm for constructing decision tree classifier that is the models for the classification problem from machine learning. In classical case the decision tree is constructed in $O(hd(NM+N \log N))$ running time, where $M$ is a number of classes, $N$ is the size of a traini…

We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined ad…

Statistical learning is the process of estimating an unknown probabilistic input-output relationship of a system using a limited number of observations. A statistical learning machine (SLM) is the algorithm, function, model, or rule, that learns such a process; and machine learning (ML) is the conventional name of this…

Algorithm constructs prediction sets with PAC guarantees in label shift settings.

We show through case studies that it is easier to estimate the fundamental limits of data processing than to construct explicit algorithms to achieve those limits. Focusing on binary classification, data compression, and prediction under logarithmic loss, we show that in the finite space setting, when it is possible to…

We construct a Kirby diagram of the rational homology ball used in "generalized rational blow-down" developed by Jongil Park. The diagram consists of a dotted circle and a torus knot. The link is simpler, but the parameters are a little complicate. Euclidean Algorithm is used three times in the construction and the pro…

Quantum algorithm improves portfolio construction accuracy.

Let $\CV$ be a vector field distribution on manifold $M$. We give an efficient algorithm for the construction of local coordinates on $M$ such that $\CV$ may be locally expressed as some partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from $\Bbb R$ to $\Bbb R^q$,…

Fast and efficient homology algorithms are in demand in the applied sciences for analyzing solid materials and proteins, processing digital imaging data, or pattern classification among others. Recent advances employ discrete Morse theory as a preprocessor. Research in this area has lead to the need to find complicated…

The paper verifies stable handleslide triviality of some R-links and shows many are stably equivalent.

Algorithm constructs surfaces with specific Veech groups in lattice strata.

Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional compact submanifold $M$ in $\mathbb{R}^D$, we establish the spectral convergence rate…

Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners. However, existing construction algorithms are mostly based on heuristics and do not exp…

Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.

Algorithm constructs and classifies weaving diagrams using combinatorial methods.

In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data approximately lie. In particular, the basis construction algorithms developed in ma…

Ensemble methods have been shown to be an effective tool for solving multi-label classification tasks. In the RAndom k-labELsets (RAKEL) algorithm, each member of the ensemble is associated with a small randomly-selected subset of k labels. Then, a single label classifier is trained according to each combination of ele…

New method for constructing truncated vine copulas.

Sphere-bases for simplicial and cubical complexes are constructed and analyzed.

Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and classification problems. The algorithm does not apply Markov Chain Monte Carlo and does…

Spin networks boost quantum algorithms solving SU(2) symmetric problems.

Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Alg…

It is a survey on recent results in constructive sparse approximation. Three directions are discussed here: (1) Lebesgue-type inequalities for greedy algorithms with respect to a special class of dictionaries, (2) constructive sparse approximation with respect to the trigonometric system, (3) sparse approximation with …

Optimizes portfolio construction using Bayesian methods and variational techniques.

In their precedent work, the authors constructed closed oriented hyperbolic surfaces with pseudo-Anosov homeomorphisms from certain class of integral matrices. In this paper, we present a very simple algorithm to compute the Teichmueller polynomial corresponding to those surface homeomorphisms by first constructing an …

Optimal algorithm converts weak to strong learner with less data.

New method calibrates local volatility models to marginal distributions.

Review of MLMC in financial engineering, focusing on option pricing and risk management.

What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which the distinctions in previous papers can be made formal. In addition to characte…

Transformers can adaptively select and perform various machine learning tasks in context.

Constructs manifolds from quantum codes with novel geometric properties.

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…

This work optimizes induced correlation in joint graph embeddings.

We have defined weight of the pair $(\langle S \mid R \rangle, R)$ for a given presentation $\langle S \mid R \rangle$ of a group, where the number of generators is equal to the number of relations. We present an algorithm to construct crystallizations of 3-manifolds whose fundamental group has a presentation with two …

Transforms offline algorithms to online with low regret in random order model.