arXiv research

In this paper we further investigate the geometry of monads of order-preserving functionals and of positively homogeneous functionals. We prove that for any compactum X with $w(X) = τ$ the map $μ_F X$, where $F\in\{O,OH\}$, is homeomorphic to trivial $I^τ$-fibration if and only if $X$ is openly generated $χ$-homogeneou…

Polytopes $A(P)$ for posets $P$ compactify spaces of order-preserving maps.

Algorithm confirms non-order-preserving braids, proving infinite family not order-preserving.

In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in arXiv:1305.2620, we show that order preserving representations into Lie groups of Hermit…

New method calibrates deep networks by preserving top-k predictions.

OP-GFNs sample candidates in order-preserving proportion to a learned reward function.

Method preserves order in hierarchical clustering of ordered data.

A new method estimates rare events using tensor trains.

We present a novel factor analysis method that can be applied to the discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited only after some other factors are activated. Precedence-ordering arise in appli…

Enhances image classification by integrating semantic hierarchy into CNN models.

New set class preserves Fourier series terms for planar ovals, leading to isoperimetric inequalities.

New criterion for bi-ordering free groups under automorphisms.

The thesis introduces methods to use semantic hierarchy in image classification.

MCNet improves uncertainty calibration in online advertising by modeling complex relations and balancing performance.

Efficiently learns and transports posterior densities for real-time inference.

Framework analyzes neural network dynamics for better understanding and optimization.

Paper generalizes tensor-train approximation for complex random variables.

A new index rebalancing strategy reduces large constituent weights without undesirable effects.

It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…

Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish tha…

It is well-known that there is a faithful representation of braid groups on automorphism groups of free groups, and it is also well-known that free groups are bi-orderable. We investigate which n-strand braids give rise to automorphisms which preserve some bi-ordering of the free group rank n. As a consequence of our w…

TMTF improves time series visualization by separating dynamic regimes.

The paper develops a Galois theory for cluster algebras and Riemann surfaces.

A lot of attention has been devoted to multimedia indexing over the past few years. In the literature, we often consider two kinds of fusion schemes: The early fusion and the late fusion. In this paper we focus on late classifier fusion, where one combines the scores of each modality at the decision level. To tackle th…

Introduces a differentiable approximation to the zero-one loss.

In the past few years, a lot of attention has been devoted to multimedia indexing by fusing multimodal informations. Two kinds of fusion schemes are generally considered: The early fusion and the late fusion. We focus on late classifier fusion, where one combines the scores of each modality at the decision level. To ta…

New framework detects directional influence in multivariate time series.

Paper finds formulas for mutual information and MMSE in matrix tensor product problems.

CNNs, RNNs, GCNs, and CapsNets have shown significant insights in representation learning and are widely used in various text mining tasks such as large-scale multi-label text classification. However, most existing deep models for multi-label text classification consider either the non-consecutive and long-distance sem…

A new framework separates classifier calibration and discrimination.

Improved change point detection using matched filters for non-parametric tests.

Develops a new nonparametric trace regression model for high-dimensional data.

The article explores the mapping class group using unicellular maps and provides filtrations.

Constructs a moment map flow for isotropic maps on surfaces.

Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to effectively and accurately access the required map remains a challenge today. Previo…

The paper constructs biharmonic maps between spheres using polynomial maps.

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

Research explores real algebraic realization of round fold maps of codimension -1.

The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Paper defines and studies Clairaut warped product Riemannian maps.

The paper explores unique continuation properties for polyharmonic maps between Riemannian manifolds.

The hyperelliptic mapping class group has been studied in various contexts within topology and algebraic geometry. What makes this study tractable is that there is a surjective map from the hyperelliptic mapping class group to a mapping class group of a punctured sphere. The more general family of superelliptic mapping…

This paper constructs real algebraic maps that are topologically special generic maps.

A Reeb space is defined as the space of all the connected components of inverse images of a smooth map, which is a fundamental tool in studying smooth manifolds using generic smooth maps whose codimensions are not positive such as Morse functions, their higher dimensional versions including fold maps and general stable…

The paper constructs gluing maps for harmonic maps between Riemannian manifolds.

Characterizes a general range decreasing group homomorphism.

The paper examines $HM$-tensional and $HS$-tensional maps between Riemannian manifolds.