arXiv research

Study on identifying AMP chain graph models under known and unknown component decompositions.

The paper studies the geometry of Nakajima quiver varieties and their decompositions.

New method decomposes Markov chain rewards into persistent and transient components.

The Temperley-Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley-Lieb algebra. Our results apply to the framework which determines Khovanov homology. Consequences of our work include semi-orthogonal deco…

The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switch…

Polynomial mixing times for simulated tempering in mixture sampling problems.

The paper provides concentration inequalities for Markov chain variance estimators.

Study the JSJ-decomposition of a specific 3-manifold.

Method estimates shared and study-specific factors for multi-study data.

The data of a "2D field theory with a closed string compactification" is an equivariant chain level action of a cell decomposition of the union of all moduli spaces of punctured Riemann surfaces with each component compactified as a pseudomanifold with boundary. The axioms on the data are contained in the following ass…

The paper develops new inequalities for Markov chain sums, linking them to mixing time.

Given an open book decomposition (S,h) adapted to a closed, oriented 3-manifold M, we define a chain map from a certain Heegaard Floer chain complex associated to (S,h) to a certain embedded contact homology chain complex associated to (S,h), as defined in arXiv:1008.2734, and prove that it induces an isomorphism on th…

New proof for minimizing tunnel systems in satellite chain links.

We give a formula of the connected component decomposition of the Alexander quandle: $\mathbb{Z}[t^{\pm1}]/(f_1(t),\ldots, f_k(t))=\bigsqcup^{a-1}_{i=0}\mathrm{Orb}(i)$, where $a=\gcd (f_1(1),\ldots, f_k(1))$. We show that the connected component $\mathrm{Orb}(i)$ is isomorphic to $\mathbb{Z}[t^{\pm1}]/J$ with an expli…

This paper concerns the topology of isospectral real manifolds of certain Jacobi elements associated with real split semisimple Lie algebras. The manifolds are related to the compactified level sets of the generalized (nonperiodic) Toda lattice equations defined on the semisimple Lie algebras. We then give a cellular d…

We classify all the exceptional Dehn surgeries on the minimally twisted chain links with six and seven components.

New algorithms solve tensor problems with random components using SDP.

The paper improves SMC algorithm for multi-modal distributions by proving variance bounds.

This paper models time-series data with a mixture of Markov chains, automatically determining the number of components.

The classification of high-dimensional mu-component boundary links motivates decomposition theorems for the algebraic K-groups of the group ring A[F_mu] and the noncommutative Cohn localization Sigma^{-1}A[F_mu], for any mu>0 and an arbitrary ring A, with F_mu the free group on mu generators and Sigma the set of matric…

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…

A low-rank tensor model simplifies multi-dimensional Markov chains.

ForecastGAN improves multi-horizon time series forecasting by integrating numerical and categorical features.

P3LS preserves privacy while integrating data across companies.

In this paper, in following of the first part (which ADF tests using ACI evaluation) has conducted, Time Series (TSs) are analyzed using decomposition analysis. In fact, TSs are composed of four components including trend (long term behavior or progression of series), cyclic component (non-periodic fluctuation behavior…

New varifold example shows decomposition failure.

The study uses Markov chains to forecast cryptocurrency market dynamics.

DCDC calculates convergence rates for Markov chains using neural networks.

A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few works have provided "beyond worst-case" guarantees for such settings. For log-c…

The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.

DDD reformulated for sparse matrices, integrating trajectory and snapshot time series data.

New matrix approximation method using RBF components for better memory efficiency.

Fix an integer N>1. To each diagram of a link colored by 1,...,N, we associate a chain complex of graded matrix factorizations. We prove that the homotopy type of this chain complex is invariant under Reidemeister moves. When every component of the link is colored by 1, this chain complex is isomorphic to the chain com…

This paper derives a portfolio decomposition formula when the agent maximizes utility of her wealth at some finite planning horizon. The financial market is complete and consists of multiple risky assets (stocks) plus a risk free asset. The stocks are modelled as exponential Brownian motions with drift and volatility b…

New method uses conformal prediction for time series forecasting, accounting for temporal correlation.

Researchers propose a new SSL risk decomposition method to evaluate and improve self-supervised learning models.

Bayesian calibration speeds up ABM for pandemic modeling.

This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of subdivision invariants which we show do not all vanish for non-trivial subdivisions…

Given a closed oriented 3-manifold M, we establish an isomorphism between the Heegaard Floer homology group HF^+(-M) and the embedded contact homology group ECH(M). Starting from an open book decomposition (S,h) of M, we construct a chain map Φ^+ from a Heegaard Floer chain complex associated to (S,h) to an embedded co…

CSD learns a common component for domain generalization, outperforming existing methods.

We consider a decomposition method for compressive streaming data in the context of online compressive Robust Principle Component Analysis (RPCA). The proposed decomposition solves an $n$-$\ell_1$ cluster-weighted minimization to decompose a sequence of frames (or vectors), into sparse and low-rank components, from com…

Langevin Dynamics fails to sample from mixture distributions efficiently.

We define the twisted Blanchfield pairing of a symmetric triad of chain complexes over a group ring Z[G], together with a unitary representation of G over an Ore domain with involution. We prove that the pairing is sesquilinear, and we prove that it is hermitian and nonsingular under certain extra conditions. A twisted…

CDFD analyzes circularity and directionality in weighted directed networks.

Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC)…

Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.

We compute for all orientable irreducible geometric 3-manifolds certain complexity functions that approximate from above Matveev's natural complexity, known to be equal to the minimal number of tetrahedra in a triangulation. We can show that the upper bounds on Matveev's complexity implied by our computations are sharp…

Given a sequence of oriented links L^1,L^2,L^3,... each of which has a distinguished, unknotted component, there is a decomposition of the 3-sphere naturally associated to it, which is constructed as the components of the intersection of an infinite sequence of nested solid tori. The Bing and Whitehead continua are sim…