arXiv research

Characterizes Anosov representations and strongly convex cocompact groups with eigenvalue gaps.

Machine learning predicts band gaps for large organic crystals.

We construct finite-gap solutions to the modified Novikov-Veselov equations, describe their spectral properties and the reduction to the modified Korteweg--de Vries equation and explain its relation to soliton deformations of tori and the Willmore conjecture.

Price gap, defined as the logarithmic price difference between the first two occupied price levels on the same side of a limit order book (LOB), is a key determinant of market depth, which is one of the dimensions of liquidity. However, the properties of price gaps have not been thoroughly studied due to the less avail…

The paper proves gap properties for critical metrics under specific conditions.

Study equilibrium measures on manifolds without conjugate points with visibility covering.

We present a separation property for the gaps in the length spectrum of a compact Riemannian manifold with negative curvature. In arbitrary small neighborhoods of the metric for some suitable topology, we show that there are negatively curved metrics with a length spectrum exponentially separated from below. This prope…

New method for conformal prediction under Markovian data reduces coverage gap.

New Dynkin condition for manifolds with boundary yields bi-Lipschitz equivalence and spectral properties.

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct new complexes from existing ones and an extensive library of triangulations of …

Resolves gap problem for quaternion-Hermitian structures.

Study spectral properties on manifolds with conical singularities, proving new inequalities.

Improved gap-dependent bounds for reinforcement learning with linear approximations.

In this paper, we study the properties of the first global term in the polyhomogeneous expansions for Liouville's equation. We obtain rigidity and gap results for the boundary integral of the global coefficient. We prove that such a boundary integral is always nonpositive, and is zero if and only if the underlying doma…

CR method improves convergence for nonconvex optimization under KL property.

Develops correlation number for specific potentials and Hitchin representations.

The paper proposes a method to test properties of the optimal assortment in multinomial logit models.

Isobenefit Lines can offer a certain range of applicability in Location Theory and Gravitational Models for Urban and Geography Economics, in positional decision processes made by citizens, and, last but not least, in land value and property market theories and analysis. The value of a land, or a property, in a generic…

Study estimates gaps in semigroup products, proving embedding properties.

The study examines hyperbolic 3-manifolds with uniform spectral gaps for coclosed 1-forms.

Discover gaps in q-series exponents for 3d N=2 theories.

Study on geodesics on high genus expander surfaces, proving filling and non-simple properties.

Jones polynomial gaps removed for quasi-alternating links.

Solves the Wiegold problem by showing free products of left-orderable groups have normal rank > 1.

New study on neural network calibration, linking it to generalization gap.

Reply to Tetlock et al. on tail risk and probability gap.

The paper extends sequences while preserving statistical properties using a mixture model.

This paper connects ultrametric overlap gap properties to parametric RDT for symmetric binary perceptrons.

The paper examines properties of generalized τ-quasi Ricci-harmonic metrics and proves rigidity results.

Uniform counting formulas for orthogeodesics in Kleinian groups converge.

The trace set of a Fuchsian group $Γ$ ist the set of length of closed geodesics in the surface $Γ\backslash \mathbb{H}$. Luo and Sarnak showed that the trace set of a cofinite arithmetic Fuchsian group satisfies the bounded clustering property. Sarnak then conjectured that the B-C property actually characterizes arithm…

Generative model for 3D molecules respects symmetry for targeted properties.

New bounds close the score matching gap for diffusion models.

New empirical PAC-Bayes bound for Markov chains with finite state space.

We study the spectral gap of the Erdős--Rényi random graph through the connectivity threshold. In particular, we show that for any fixed $δ> 0$ if $p \ge \frac{(1/2 + δ) \log n}{n},$ then the normalized graph Laplacian of an Erdős--Rényi graph has all of its nonzero eigenvalues tightly concentrated around $1$. We est…

New complexity measure explains neural network generalization gap.

Study spectral properties of sub-Laplacians in Carnot groups.

Convex clustering can only learn convex clusters, with significant gaps between clusters.

Study develops a new method for creating fair models.

Study ergodic properties of geodesic flows on specific manifolds without conjugate points.

The paper improves tensor completion bounds using spectral gap.

We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented.

We show that there exists a universal positive constant $\varepsilon_0 > 0$ with the following property: Let $g$ be a positive Einstein metric on $S^4$. If the Yamabe constant of the conformal class $[g]$ satisfies $Y(S^4, [g]) >\frac{1}{\sqrt{3}} Y(S^4, [g_{\mathbb S}]) - \varepsilon_0$ where $g_{\mathbb S}$ denot…

The paper analyzes sparse PCA for incomplete data and proves support recovery conditions.

Random feature model shows slow self-correction of generalization gap.

We prove a Liouville theorem for the plurisubharmonic functions on complete Kaelher manifolds. As the applications, we prove a splitting theorem for complete Kaehler manifolds with nonnegative biscetional curvature in terms of the linear growth harmonic functions and a optomal gap theorem for such manifolds.

Free adversarial training reduces the generalization gap compared to vanilla method.