arXiv research

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

The paper provides criteria and curvatures for singularities of curves in R^N.

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…

We consider the notion of multiple gap as a finite set of ideals that cannot be separated. We study the different types of such objects that can be found in the Boolean algebra of subsets of the natural numbers modulo finite sets.

Let G be a finite group of complex n by n unitary matrices generated by reflections acting on C^n. Let R be the ring of invariant polynomials, and χbe a multiplicative character of G. Let Ω^χbe the R-module of χ-invariant differential forms. We define a multiplication in Ω^χand show that under this multiplication Ω^χha…

Enhances anomaly detection using multiple reference datasets.

Solutions to a quadratic matrix equation are linked to strongly regular graphs and multiplicative characters.

Study on Bayesian deep linear networks with multiple outputs and convolutional layers.

For a hyperbolic surface S of finite type we consider the set A(S) of angles between closed geodesics on S. Our main result is that there are only finitely many rational multiples of πin A(S).

It is known that the volume function for hyperbolic manifolds of dimension $\geq 3$ is finite-to-one. We show that the number of nonhomeomorphic hyperbolic 4-manifolds with the same volume can be made arbitrarily large. This is done by constructing a sequence of finite-sided finite-volume polyhedra with side-pairings t…

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…

Let $G$ be a compact connected semisimple Lie group, let $K$ be a closed subgroup of $G$, let $Γ$ be a finite subgroup of $G$, and let $τ$ be a finite-dimensional representation of $K$. For $π$ in the unitary dual $\widehat G$ of $G$, denote by $n_Γ(π)$ its multiplicity in $L^2(Γ\backslash G)$. We prove a strong multip…

We learn linear models from nonlinear systems using multiple trajectories and regularization.

Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical convergence away from finitely many points. We show that the limit of a sequence …

We show that finite parallel transports of vectors in Riemannian spaces, determined by the multiplication law in the deformed groups of diffeomorphisms, and sequences of infinitesimal parallel transports of vectors along geodesics are equivalent.

Researchers create initial data for multiple collapsing boson stars.

In this paper, we study the critical case of the Allard regularity theorem. Combining with Reifenberg's topological disk theorem, we get a critical Allard-Reifenberg type regularity theorem. As a main result, we get the topological finiteness for a class of properly immersed surfaces in $\mathbb{R}^n$ with finite Willm…

We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first…

Study learns dynamics of linear systems from multiple short trajectories.

We characterize finitely generated torsion-free Kleinian groups for which the real length spectrum (without multiplicities) is discrete.

Researchers study fairness-accuracy tradeoffs in predictive models for multiple groups.

On any compact manifold of dimension greater than 4, we prescribe the volume and any finite part of the spectrum of the Witten Laplacian acting on $p$-form for $0<p<n$. In particular, we prescribe the multiplicity of the first eigenvalues. On 3-dimensional manifolds, we give examples of multiple first eigenvalue for 1-…

New data shows multiple black holes can form from modified vacuum data.

Let $G$ be a group with a finite subgroup $H$. We define the $L^2$-multiplicity of an irreducible representation of $H$ in the $L^2$-homology of a proper $G$-CW-complex. These invariants generalize the $L^2$-Betti numbers. Our main results are approximation theorems for $L^2$-multiplicities which extend the approximati…

We prove a strong multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces i.e. if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then all closed geodesics have the same length.

On any compact manifold of dimension greater than 3, we exhibit a metric whose first positive eigenvalue for the Laplacian acting on p-form is of multiplicity 2. As a corollary, we prescribe the volume and any finite part of the spectrum of the Hodge Laplacian with multiplicity 1 or 2.

In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the commensurability class. In addition, we show that any finite volume hyperbolic 3-manifold …

Proposes using Wasserstein barycenters for robust optimization with multiple data sources.

Researchers calculate the volume of Seifert representations for graph manifolds and their covers.

We give a complete proof of a propagation theorem of multiplicity-free property from fibers to spaces of global sections for holomorphic vector bundles. The propagation theorem is formalised in three ways, aiming for producing various multiplicity-free theorems in representation theory for both finite and infinite dime…

On any compact manifold of dimension $n\geq3$ with boundary, we prescibe any finite part of the Steklov spectrum whithin a given conformal class. In particular, we prescribe the multiplicity of the first eigenvalues. On a compact surface with boundary, we show that the multiplicity of the $k$-th eigenvalue is bounded i…

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent $α$ of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that …

Paper detects gradual changes in cluster structure using MC fusion.

No arbitrage in financial markets with special semimartingales.

Empirical study compares finite- and infinite-width BNNs, revealing performance differences under model mismatch.

The paper proves properties of surfaces with finite curvature in 3D space.

We study a multiplicative transient price impact model for an illiquid financial market, where trading causes price impact which is multiplicative in relation to the current price, transient over time with finite rate of resilience, and non-linear in the order size. We construct explicit solutions for the optimal contr…

New quantum invariant is asymptotically multiplicative under cyclic covers.

Paper proposes AdaDetect for FDR-controlled novelty detection.

We show that, in finite dimensions, the only monotone metrics for which the (+1) and (-1) affine connections are mutually dual are constant multiples of Bogoliubov-Kubo-Mori metric

The article discusses extensions of Harish-Chandra's admissibility theorem.

Flexible framework for optimal trading across multiple asset venues.

We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is finite dimensional, extends to tangles, and categorifies a scalar-multiple of the sl(2) Reshetikhin-Turaev invariant. We expe…

Single-timescale analysis improves convergence in multi-sequence stochastic approximation.

Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set of irreducible representations of G. Let T be a maximal torus of G with Lie algebra Lie(T). We construct a finite number of piecewise polynomial …

The study examines the long-term behavior of mean curvature flows in closed 3-manifolds.

Study on geodesics proving index and intersection bounds, with examples of multiplicity.

We study Farrell Nil-groups associated to a finite order automorphism of a ring $R$. We show that any such Farrell Nil-group is either trivial, or infinitely generated (as an abelian group). Building on this first result, we then show that any finite group that occurs in such a Farrell Nil-group occurs with infinite mu…