arXiv research

Characterizes causal structure dominance for latent variables.

We show that the existence of a nontrivial Massey product in the cohomology ring H^*(X) imposes global constraints upon the Riemannian geometry of a manifold X. Namely, we exhibit a suitable systolic inequality, associated to such a product. This generalizes an inequality proved in collaboration with Y. Rudyak, in the …

Develops a first-order interior-point method for solving constrained variational inequalities.

This work restricts hidden cardinality in causal models to infer causal relations.

Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that mod…

Extends Gromov's optimal systolic inequality to manifolds with specific cohomology properties.

Dunfield-Garoufalidis and Boyer-Zhang proved that the A-polynomial of a nontrivial knot in $S^{3}$ is nontrivial. In this paper, we use holonomy perturbations to prove the non-triviality of the A-polynomial for a nontrivial, null-homotopic knot in an irreducible 3-manifold. Also, we give a strong constraint on the A-po…

Detects causal scenarios with inequality constraints among classical correlations.

Sharp inequalities in unit ball with constraints on moments.

Unified framework certifies predictor performance under distribution shift.

A carpet is a metric space homeomorphic to the Sierpinski carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poinca…

DiffSlack learns neural networks with nonlinear constraints via learnable slack variables.

Paper derives inequalities for eigenvalues of Witten-Laplacian under fixed volume constraint.

The paper studies bi-slant Riemannian maps to Kenmotsu manifolds and derives inequalities.

Proves existence of solutions to Einstein constraints with specific boundary conditions and verifies Penrose inequality.

New proof of Sobolev inequality with constraints on sphere.

New method uses logical relations to derive bounds and inequality constraints from causal models.

We construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3-manifold which does not have the convergence properties needed in order to prove a Penrose--type inequality. This contrasts sharply with the asymptotically flat case. The main idea consists in combining inverse mean curvature flow …

New inequality criterion for a mean field equation on spheres.

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type i…

OLLA framework efficiently samples from constrained distributions with nonconvex constraints.

Proves strict inequality for minimizers of Willmore energy under isoperimetric constraints.

Recent work has shown that a country's productive structure constrains its level of economic growth and income inequality. Here, we compare the productive structure of countries in Latin America and the Caribbean (LAC) with that of China and other High-Performing Asian Economies (HPAE) to expose the increasing gap in t…

The paper proves a spin manifold's 4D quasi-Einstein satisfies Hitchin-Thorpe inequality.

Proves Hölder-type inequality for Lagrangians' distance.

Paper finds inequalities for eigenvalues of buckling problems on special metric spaces.

We prove that if the unit codisc bundle of a closed Riemannian manifold embeds symplectically into a symplectic cylinder of radius one then the length of the shortest nontrivial closed geodesic is at most half the area of the unit disc.

A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.

Generalizes Cheeger inequality to Carnot-Carathéodory spaces.

Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.

Paper presents a method to solve variational inequalities with general constraints without requiring analytic solutions.

Optimization with inequality constraints using embedded gradient vector field method

Sharp inequalities on curved spaces with bounded curvature.

Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MC…

The paper classifies energy-minimizing sets in specific domains.

We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a $U(1)^2$ symmetry. A novel feature is the fact that such surfaces can have the nontrivial topologies $S^1 \times S^2$ and $L(p,q)$. In addition to t…

Study preserves planar and graphical properties of curves under elastic flow.

In dimension $4$, we show that a nontrivial flat cone cannot be approximated by smooth Ricci shrinkers with bounded scalar curvature and Harnack inequality, under the pointed-Gromov-Hausdorff topology. As applications, we obtain uniform positive lower bounds of scalar curvature and potential functions on Ricci shrinker…

Study optimal consumption with drawdown limits over a fixed time frame.

Research shows finiteness in triangulations with girth constraints.

We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of linearizability of characteristic webs on all solutions imposes simple second-order con…

Given a diagram $D$ of a knot $K$, we consider the number $c(D)$ of crossings and the number $b(D)$ of overpasses of $D$. We show that, if $D$ is a diagram of a nontrivial knot $K$ whose number $c(D)$ of crossings is minimal, then $1+\sqrt{1+c(D)} \leq b(D)\leq c(D)$. These inequalities are shape in the sense that the …

Data processing inequalities link Fisher information to local differential privacy constraints.

We derive general Novikov-Morse type inequalities in a Conley type framework for flows carrying cocycles, therefore generalizing our results in [FJ2] derived for integral cocycle. The condition of carrying a cocycle expresses the nontriviality of integrals of that cocycle on flow lines. Gradient-like flows are distingu…

New algorithm tackles stochastic optimization with inequality constraints.

A new GP method enforces physical constraints in probabilistic terms.

The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce the $\textit{inflation technique}$ for tackling this problem. An inflation of a…