Algorithm constructs triangulations for Heegaard splittings and related 3-manifolds.
problem Constructing triangulations for Heegaard splittings and related 3-manifolds.
method Algorithm using Regina to generate triangulations from combinatorial presentations of Heegaard diagrams.
result Triangulations with cutwidth bounded by 4g−2 for genus-g Heegaard splittings. Estimating data limits easier than building algorithms to achieve them.
problem Achieving the fundamental limits of data processing.
method Case studies on binary classification, data compression, and prediction.
result Estimators of limits can be constructed with fewer samples than explicit algorithms to achieve limits.
Quantum version of C5.0 algorithm improves decision tree construction time.
problem Improving the efficiency of decision tree construction in machine learning.
method Improved classical algorithm and applied quantum subroutines for faster decision tree construction.
result Quantum algorithm reduces decision tree construction time significantly.
New construction reduces Vietoris-Rips complex construction time.
problem Efficiently constructing Vietoris-Rips complexes.
method Inductive construction avoiding unnecessary comparisons.
result Significant reduction in computational complexity.
Gradient boosts monomial-order-free basis construction algorithms.
problem Lack of theoretical properties in monomial-order-free basis construction algorithms.
method Exploits gradient to sidestep spurious vanishing, achieve consistent output, and remove redundant bases.
result Proposes methods that equip monomial-order-free algorithms with theoretical properties.
Algorithm trisects 4D book into three chapters.
problem Trisecting 4D book into chapters.
method Algorithm for open book decompositions of 4-manifolds.
result Algorithm works for various types of manifolds.
Algorithm constructs Kirby diagrams for 4D open books.
problem Constructing Kirby diagrams for 4D open books.
method Algorithm using Heegaard diagrams of pages.
result Diffeomorphic open books constructed with different pages and monodromies.
Extends Seifert algorithm to 3-manifolds via surgery.
problem Construct Seifert surfaces in arbitrary 3-manifolds.
method Uses surgery on framed links in S^3 to extend classical algorithm.
result Explicit construction of Seifert surfaces in 3-manifolds.
Geometrically solves Schrödinger flow on sphere.
problem Solving periodic Cauchy problem for Schrödinger flow on sphere.
method Explicit geometric algorithm for construction of solutions.
result Explicit geometric algorithm for solving Schrödinger flow on sphere.
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.
Algorithm constructs polynomials with specific nodal sets.
problem Creating a polynomial with a prescribed knot or link as its zero level set.
method Algorithm constructs a polynomial f in u, v, and v such that its zero level set on the unit three-sphere matches a given braid. result Bounds on the degree of the constructed polynomial in terms of braid data.
The paper explores the complexities of algorithmic fairness and the assumptions needed for different fairness mechanisms.
problem The lack of a unified understanding of algorithmic fairness across different papers.
method Introducing a mathematical framework that includes the observed space, decision space, and construct space to analyze fairness mechanisms.
result Different fairness mechanisms require different assumptions about the relationship between unobservable variables (construct space) and observable variables (observed space).
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,…
New algorithm reduces Bayesian posterior uncertainty estimation error.
problem Bayesian methods often sacrifice accurate uncertainty estimation for scalability.
method Greedy Iterative Geodesic Ascent (GIGA) for optimal Bayesian coreset construction.
result GIGA reduces posterior approximation error by orders of magnitude.
Constructs algorithms to recognize and classify 2D surfaces.
problem Recognizing and classifying 2D surfaces in dynamic systems.
method Discrete topological structures and algorithms for simplicial and CW-complexes.
result Determines the topological type of 2-manifolds.
New algorithm improves similarity graph construction for nearest neighbor search.
problem Improving nearest neighbor search performance with more effective similarity graphs.
method Probabilistic model of a similarity graph learned through reinforcement learning.
result Higher recall rates achieved for the same number of distance computations.
New method constructs confidence sets for GLMs via game theory.
problem Developing reliable confidence intervals for GLM parameters.
method Reduction to sequential prediction games with low regret.
result Online-to-confidence-set conversions provide new types of intervals.
Survey on greedy algorithms for sparse approximation.
problem Sparse approximation using greedy algorithms.
method Greedy algorithms, Lebesgue-type inequalities, trigonometric system, tensor product structure.
result Constructive sparse approximation methods provided for various cases.
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.
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…
Paper presents efficient algorithms for constructing confidence intervals in algorithmic leveraging.
problem Efficiently constructing confidence intervals for algorithmic leveraging regression coefficients.
method Developed efficient algorithms for finite sample confidence intervals.
result Confidence intervals have the desired coverage probabilities, outperforming bootstrap methods.
Algorithm constructs trisection of 4-manifolds from simplices.
problem Decompose 4-manifolds into simpler pieces.
method Algorithm transforms manifold description into trisection using curves on a surface.
result First explicit complexity bounds for trisection genus in terms of simplices.
Algorithm constructs graphic matroid from graph's flow lattice.
problem Constructing graphic matroid from graph's flow lattice.
method Based on Amini's result linking Voronoi cell geometry to graph structure.
result Algorithmic construction of graphic matroid from lattice of integer flows.
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…
Algorithm constructs JSJ decomposition for hyperbolic groups.
problem Constructing JSJ decompositions for hyperbolic groups.
method Combinatorial and geometric analysis of immersed cycles in CAT(0) square complexes.
result First algorithm with explicit time bound for JSJ decompositions.
Machine learning improves cybersecurity by learning from data.
problem Designing effective detection algorithms for cyber threats.
method Machine learning algorithms to learn from security data.
result ML algorithms can improve threat hunting and remediation.
Algorithm constructs prediction sets with PAC guarantees in label shift settings.
problem Reliable uncertainty quantification in the face of distribution shift.
method Estimates predicted probabilities and confusion matrix, then propagates uncertainty through Gaussian elimination to compute confidence intervals and construct prediction sets.
result Satisfies PAC guarantees and produces smaller, more informative prediction sets.
Train quantum networks to implement target algorithms.
problem Designing quantum computers with minimal external control.
method Supervised quantum gate training for subset evolution.
result Quantum networks implement target algorithms efficiently.
NNK algorithm improves neighborhood and graph construction for machine learning.
problem Ad hoc selection of k and ε parameters in kNN and ε-neighborhood methods.
method NNK algorithm for better sparse signal approximation.
result NNK leads to superior performance in local neighborhood and graph-based machine learning tasks.
Quantum algorithm improves portfolio construction accuracy.
problem Efficiently constructing portfolios with real-world constraints.
method Sampling-based CVaR Variational Quantum Algorithm (VQA) combined with local-search post-processing.
result Achieved a relative solution error of 0.49% on IBM Heron processors.
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…
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 R to Rq,…
Improved SVD for shifted matrices without explicit matrix construction.
problem Efficiently estimating SVD of shifted matrices.
method Shifted Randomized SVD algorithm.
result More efficient matrix factorization and low-rank approximation.
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.
problem Stable handleslide triviality of R-links as potential counterexamples to the generalized property R conjecture.
method Implemented an algorithm to construct all R-links explicitly and verified their stable handleslide triviality.
result Many R-links are stably handleslide equivalent.
Algorithm constructs surfaces with specific Veech groups in lattice strata.
problem Finding all translation surfaces with a given lattice Veech group.
method Developed an algorithm and provided a new proof of finiteness.
result Algorithm constructs all translation surfaces with a given lattice Veech group.
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 RD, we establish the spectral convergence rate…
Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.
problem Lower complexity bounds for finite-sum optimization problems with various component functions.
method Developed novel approach to construct hard instances and analyzed PIFO algorithms.
result Established lower complexity bounds for convex-concave and nonconvex-strongly-concave objectives.
Paper studies Fenchel-Young losses for classifier construction.
problem Creating effective loss functions for classifiers.
method Analyzes Fenchel-Young losses from generalized entropies, formulates conditions for separation margins and sparse support.
result Fenchel-Young losses can induce predictive distributions with separation margins and sparse support.
Algorithm constructs and classifies weaving diagrams using combinatorial methods.
problem Classifying unique weaving diagrams with over/under information.
method Systematic algorithm based on tiling and crossing matrices.
result Classification of periodic structures based on minimum crossings.
Classifies Seifert fibrations of lens spaces.
problem Classifying Seifert fibrations of lens spaces.
method Algorithmic construction of Seifert fibrations over base orbifolds.
result All Seifert fibrations are equivalent to certain standard models.
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.
problem High-dimensional parameter space in vine copulas.
method Propose a new score and algorithm for constructing truncated vines.
result New algorithms exploit conditional independences.
Automated Bayesian inference for massive datasets with theoretical guarantees.
problem Intractable posterior inference in massive datasets.
method Hilbert coreset construction under log-likelihood space inner-product norm.
result Fully-automated, scalable Bayesian inference with theoretical guarantees.
Simplified algorithm for Teichmueller polynomial from matrix homeomorphisms.
problem Computing Teichmueller polynomial from pseudo-Anosov homeomorphisms.
method Constructing invariant track, identifying homology groups, computing Alexander polynomial.
result Simplified algorithm for Teichmueller polynomial computation.
Sphere-bases for simplicial and cubical complexes are constructed and analyzed.
problem Constructing and analyzing geometric properties of sphere-bases for simplicial and cubical complexes.
method Algorithmically-specified family of k+1-simplices or k+1-cubes are used to form the boundaries of sphere-bases.
result Geometric properties of constructed sphere-bases are investigated.
Algorithm constructs confidence sets for deep neural networks with PAC guarantees.
problem Ensuring reliable predictions for deep neural networks with high confidence.
method Combines calibrated prediction and learning theory bounds.
result Constructs PAC confidence sets for various deep models.
Spin networks boost quantum algorithms solving SU(2) symmetric problems.
problem Efficiently solving SU(2) symmetric problems on quantum hardware.
method Using SU(2) equivariant variational quantum circuits based on spin networks.
result Spin networks provide a direct implementation for SU(2) equivariant quantum circuits.