arXiv research

Quantum channels' contraction under privacy constraints studied.

The paper studies cohomology of groups with contracting elements.

Paper tackles which 3-spheres bound contractible 4-manifolds or homology 4-balls.

Study develops smart contract framework for procurement under demand variability.

New bounds for SA with arbitrary norm contractions and Markovian noise.

Based on a new coupling approach, we prove that the transition step of the Hamiltonian Monte Carlo algorithm is contractive w.r.t. a carefully designed Kantorovich (L1 Wasserstein) distance. The lower bound for the contraction rate is explicit. Global convexity of the potential is not required, and thus multimodal targ…

Recently, \citet{SuttonMW15} introduced the emphatic temporal differences (ETD) algorithm for off-policy evaluation in Markov decision processes. In this short note, we show that the projected fixed-point equation that underlies ETD involves a contraction operator, with a $\sqrtγ$-contraction modulus (where $γ$ is the …

The simplicial volume of non-R^3 contractible 3-manifolds is infinite.

In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essential coverings by contractible metric balls, and provide a uniform bound on the numbers of contractible metric balls formi…

Develops a contraction framework for MCMC mixing rates.

Proves equivalence of two types of boundaries in metric spaces.

3-manifolds with positive scalar curvature and bounded geometry are contractible.

The paper shows how heat flows and Wasserstein distances relate to space rigidity.

New examples of Kirby-Ramanujam spheres found, leading to contractible 4-manifolds.

The paper proposes modern computational methods for optimizing reinsurance contracts.

Study shows bounds on knot groups and nonembeddability of certain open manifolds.

This paper examines limits of Riemannian 2-manifolds with bounded curvature.

We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show that two monotone homotopies which have appropriate overlap can be replaced by a single monotone homotopy. The ideas used to prove this theorem…

Extends inequality for Rademacher complexities using $p$-stable variables.

We prove that if $(X,\mathsf d,\mathfrak m)$ is an essentially non-branching metric measure space with $\mathfrak m(X)=1$, having Ricci curvature bounded from below by $K$ and dimension bounded from above by $N \in (1,\infty)$, understood as a synthetic condition called Measure-Contraction property, then a sharp isoper…

We prove that any finite dimensional Alexandrov space with a lower curvature bound is locally Lipschitz contractible. As applications, we obtain a sufficient condition for solving the Plateau problem in an Alexandrov space considered by Mese and Zulkowski.

Privacy amplification improved through contraction coefficients and $E_γ$-divergence.

Characterizes Forman curvature bounds and proves curvature equivalence.

Contractible Vietoris-Rips complexes for integer n proved using discrete Morse theory.

We prove a uniform extension result for contracting maps defined on subsets of Hadamard manifolds subject to curvature bounds.

Study shows volume constraints lead to isoperimetric constant bounds in specific metric spaces.

Study contractibility of boundaries in convex sets and limit sets of subgroups.

Optimal insurance contract limits insurer's risk exposure variance.

Proposes a new generalization bound for Bayesian deep nets without strict assumptions.

Study on curvature bounds and geodesic dimension in sub-Finsler Heisenberg groups.

In principal-agent models, a principal offers a contract to an agent to perform a certain task. The agent exerts a level of effort that maximizes her utility. The principal is oblivious to the agent's chosen level of effort, and conditions her wage only on possible outcomes. In this work, we consider a model in which t…

Study analyzes smart contract adoption under bounded risk, showing stable adoption but fragile financial outcomes.

Study variance-reduced method for estimating fixed points in Banach spaces.

This paper studies convergence of horospheres in CAT(0) spaces.

The contraction inequality for Rademacher averages is extended to Lipschitz functions with vector-valued domains, and it is also shown that in the bounding expression the Rademacher variables can be replaced by arbitrary iid symmetric and sub-gaussian variables. Example applications are given for multi-category learnin…

The study provides a generalization bound for a family of implicit networks.

Measure contraction property is a synthetic Ricci curvature lower bound for metric measure spaces. We consider Sasakian manifolds with non-negative Tanaka-Webster Ricci curvature equipped with the metric measure space structure defined by the sub-Riemannian metric and the Popp measure. We show that these spaces satisfy…

Deviation inequalities and limit laws for random walks on metric spaces.

Traders and investors involved in an option contract having the underlying stock in range bound are likely to lose their initial investment. Timing in buying an option contract is of capital importance. In a recent article [1] the hypothesis of range bound market is used in conjunction to Black-Scholes equation to find…

New bounds for SGLD show error decreases with more data.

The paper finds non-isotopic exact Lagrangians in symplectic manifolds with $\mathbb{C}^*$-actions.

Proves existence and uniqueness of mean curvature flow.

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover of a naturally associated hyperplane arrangement, which is known to be simplicia…

In this paper, we prove that for every irreversible Finsler $n$-dimensional real projective space $(\mathbb{R}P^n,F)$ with reversibility $λ$ and flag curvature $K$ satisfying $\frac{16}{9}\left(\fracλ{1+λ}\right)^2<K\le 1$ with $λ<3$, there exist at least $n-1$ non-contractible closed geodesics. In addition, if the met…

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are stable, meaning that a quasi-geodesic wi…

Measure contraction properties $MCP(K,N)$ are synthetic Ricci curvature lower bounds for metric measure spaces which do not necessarily have smooth structures. It is known that if a Riemannian manifold has dimension $N$, then $MCP(K,N)$ is equivalent to Ricci curvature bounded below by $K$. On the other hand, it was ob…

The study finds non-contractible geodesics on compact Finsler space forms without intersections.

Using a new method we give elementary estimates for the capacity of non-contractible annuli on cylinders and provide examples, where these inequalities are sharp. Here the lower bound depends only on the area of the annulus. In the case of constant curvature this lower bound is obtained with the help of a symmetrizatio…