arXiv research

Identifies Lorentzian locally symmetric spaces where Calabi operator suffices to determine Killing operator range.

Characterizes the range of a tensor field transform in Schwartz space.

This paper extends homological stability results for configuration spaces of manifolds.

A new learning method for complex functions using kernel and range space.

Same cohomology for curves with levels, proving stable range.

The paper establishes a new pseudoisotopy result for embedding spaces, leading to computations of homotopy groups of long knots.

Study Clairaut maps on Kähler manifolds with Ricci solitons, finding curvature and scalar relations.

This paper describes results characterizing the range of the time-t heat operator on various manifolds, including Euclidean spaces, spheres, and hyperbolic spaces. The guiding principle behind these results is this: The functions in the range of the heat operator should be, roughly, those functions having an analytic c…

Study shows configuration spaces' homological dimension increases monotonically.

Gradient-free learning uses kernel and range space for solving linear equations.

Characterizes a new curvature bound with convexity of entropies.

Characterizes a general range decreasing group homomorphism.

Computes homotopy groups of diffeomorphism spaces for high-dimensional manifolds.

New conditions for weighted composition operators in group homomorphisms.

This work predicts and interpolates long-range videos using unsupervised landmarks.

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and give explicit stability ranges in many new cases. In each of these cases the stable…

Developing a range-aware Bayesian optimization framework for discovering diverse designs within target property windows.

D-LinOSS models learn to dissipate energy, improving performance on long-range tasks.

Study homotopy groups of spaces of long links and knots, finding new generators.

We describe the range of a restricted spherical mean transform, which sends a function supported inside a closed ball in a hyperbolic space to its mean values on the geodesics spheres centered at the boundary of the ball. The description resembles that of the same transform on the Euclidean spaces obtained by Mark Agra…

Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections on a principal G-bundle on a closed Riemann surface, and equivalently, the universal moduli space of semistable holomorphic G^c-bundles. Th…

Improved Mamba model for long-range sequence tasks.

We study the isoperimetric, functional and concentration properties of $n$-dimensional weighted Riemannian manifolds satisfying the Curvature-Dimension condition, when the generalized dimension $N$ is negative, and more generally, is in the range $N \in (-\infty,1)$, extending the scope from the traditional range $N \i…

SSMs have a built-in bias towards low-frequency components, which can be adjusted.

We show the existence of the full compound asymptotics of solutions to the scalar wave equation on long-range non-trapping Lorentzian manifolds modeled on the radial compactification of Minkowski space. In particular, we show that there is a joint asymptotic expansion at null and timelike infinity for forward solutions…

Financial frequency combs emerge from macroeconomic long-range memory.

Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.

Proves energy expression on Poincaré-Einstein spaces.

MambaLRP enhances Mamba models' explainability and performance.

Extends Perelman's theorem to positive intermediate curvature conditions.

SWD approximates GP for faster regression.

Study measures volume of foliations on surfaces, finding integrability range.

Study on Frechet distance properties for paths and graphs.

Constructs operations on stable moduli spaces to compare manifold cohomology.

We give a complete obstruction to turning an immersion of an m-dimensional manifold M in Euclidean n-space into an embedding when 3n>4m+4. It is a secondary obstruction, and exists only when the primary obstruction, due to Haefliger, vanishes. The obstruction lives in a twisted cobordism group, and its vanishing implie…

Researchers compute curvatures of Stiefel manifolds with new metrics.

Heat kernels are used in this paper to express the analytic index of projectively invariant Dirac type operators on G-covering spaces of compact manifolds, as elements in the K-theory of certain unconditional completions of the twisted group algebra of G. This is combined with V. Lafforgue's results in the untwisted ca…

Researchers analyze and improve latent space in NAR models.

The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in terms of tangential cohomology and in terms of group cohomology which generalize…

New neural model processes 2D data with long-range dependencies efficiently.

This paper studies the homotopy type of the moduli space of compact n-manifold thickenings of a finite complex. The main result computes the homotopy fibers of the stabilization map from n-thickenings to (n+1)-thickenings in a wide range. In particular, we obtain an EHP-type sequence for thickenings extending work of C…

Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning parameter algorithms are suggested foreground EM, Gibbs sampling and RBE algori…

New models reduce regional inequality by adjusting exchange range and asset distribution bias.

New methods avoid spectral pollution in transfer operators for accurate analysis.

The large-N limit of Segal-Bargmann transform on spheres is studied.

Curvature estimates prove existence of smooth hypersurfaces in hyperbolic space.

FEAST improves FNN's range accuracy in ocean waveguides.

In this paper, we introduce a deformation analysis of index theory over non compact manifolds, by use of new functional spaces which are the reduced version of Sobolev spaces. It allows to construct Fredholm theory for elliptic differential operators over non compact spaces which possibly do not have closed range with …