arXiv research

New algorithm tackles unknown utility network resource allocation.

Let F be a non-abelian finite rank free group, and let H_g be the fundamental group of a surface of genus g with one boundary component represented by D_g in H_g. So, H_g is the free group <a_1,b_1,...,a_g,b_g> and D_g is the product of commutators [a_1,b_1]...[a_g,b_g]. Given x in F, we are interested in the number nu…

In this paper we study the linearizability problem for 3-webs on a 2-dimensional manifold. With an explicit computation based on the theory developed in the paper "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp. 2643-2654), we examine a 3-web whose linearizability was claimed in the same paper. We …

In the article "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp.2643-2654), published in 2001, we studied the linearizability problem for 3-webs on a 2-dimensional manifold. Four years after the publication of our article, V.V.Goldberg and V.V.Lychagin in the paper "On linearization of planar three-…

Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness…

Large size models are implemented in recently ASR system to deal with complex speech recognition problems. The num- ber of parameters in these models makes them hard to deploy, especially on some resource-short devices such as car tablet. Besides this, at most of time, ASR system is used to deal with real-time problem …

New method for fair resource allocation in AI-aware networks with unknown utility functions.

Paper proves Pareto efficient insurance for multiple entities.

Study of multiplicative connections in Lie groupoids.

Study rectifying curves in 3D multiplicative Euclidean space.

The paper classifies symmetric triads with multiplicities and their applications.

New method identifies proxies for causal effects on multiple outcomes.

We define a concept which we call multiplicity. First, multiplicity of a morphism is defined. Then the multiplicity of an object over another object is defined to be the minimum of the multiplicities of all morphisms from one to another. Based on this multiplicity, we define a pseudo distance on the class of objects. W…

We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle. We extend the notion of $n$-parallel biquandle operations for any integer $n$, an…

Study finds methods to learn multiple solutions from single task in offline RL.

Let $(M,ω)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $μ:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to decide a multiplicity freenes of the action. As an application we give the complete cl…

MKLpy simplifies Multiple Kernel Learning in Python.

Recently neural networks and multiple instance learning are both attractive topics in Artificial Intelligence related research fields. Deep neural networks have achieved great success in supervised learning problems, and multiple instance learning as a typical weakly-supervised learning method is effective for many app…

X-SHAP assesses multiplicative variable contributions in machine learning models.

New infinite-dimensional representations with bounded multiplicity found for Lie groups.

Classifies compact multiplicity free quasi-Hamiltonian manifolds.

Paper describes how to extend multiple conjugation quandles using maps.

New method constructs multiple group racks, differing from known constructions.

Framework for generating multiple clusterings from multi-view data.

Adapts manifold structure for better clustering performance.

The paper introduces new measures to quantify variability in decision tree models due to observational multiplicity.

M3E2 neural network estimates multiple treatment effects.

Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.

In this paper we prove that the generic singularities of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modeled by closed self-shrinkers with multiplicity has multiplicity one. Together with the previous result by Colding-Minicozzi in [CM12], we conclude that the only generic singularity of mean curva…

Describes curves on surfaces with punctures and boundaries.

Introduces Rashomon Capacity to measure predictive multiplicity in probabilistic classifiers.

Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately multiplicative into a genuinely multiplicative connection. The proof of this fa…

Study ruled surfaces with finite multiplicity, focusing on their curves and singularities.

New example of surface flow converging to a plane with multiplicity 2.

A (quasi-)Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify multiplicity free Hamiltonian actions for (twisted) loop groups or, equivalently, multiplicity free (twisted) quasi-Hamiltonian manifolds for simply connected compact Lie groups. …

Multi-view clustering aims at integrating complementary information from multiple heterogeneous views to improve clustering results. Existing multi-view clustering solutions can only output a single clustering of the data. Due to their multiplicity, multi-view data, can have different groupings that are reasonable and …

Three counterexamples show higher eigenvalue multiplicities than conjectured.

We introduce the notion of a conjugation-free geometric presentation for a fundamental group of a line arrangement's complement, and we show that the fundamental groups of the following family of arrangements have a conjugation-free geometric presentation: A real arrangement L, whose graph of multiple points is a union…

Polynomial algorithm for multiplication on one-hole torus skein algebra.

Proves $C^{1,1}$ regularity for multiple membrane solutions.

Framework improves gradient estimation for faster training convergence.

On a Riemannian compact manifold, we give existence and multiplicity results for solutions of elliptic PDE by introducing isometry invariances. When the groups we used have finite orbits, we get multiplicity results for equations with the classical critical Sobolev exponent, for instance the Yamabe equation. When there…

Develops theory of weightings for Lie groupoids and algebroids.

Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. Th…

Motivated by our attempt to recast Cartan's work on Lie pseudogroups in a more global and modern language, we are brought back to the question of understanding the linearization of multiplicative forms on groupoids and the corresponding integrability problem. From this point of view, the novelty of this paper is that w…

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower …

Develops a method for solving optimal stopping problems with multiple exercise rights.

Researchers create initial data for multiple collapsing boson stars.