arXiv research

Solves regularity problem for infinite-dimensional Lie groups.

Study on diffeologies on locally convex spaces and smooth multiplication of distributions.

Functor connects Lie groupoid algebras to bornological structures.

The paper proves differentiability of evolution maps in Lie groups.

New map constructed from equivariant spectra for manifold study.

Solves regularity problem for Lie groups with asymptotic estimate Lie algebras.

Counterexample disproves completeness of model space forcing regularity in infinite-dimensional Lie groups.

RPNN-EOFs model improves time series forecasting accuracy.

A hermitian algebra is a unital associative ${\mathbb C}$-algebra endowed with an involution such that the spectra of self-adjoint elements are contained in ${\mathbb R}$. In the case of an algebra ${\mathcal A}$ endowed with a Mackey-complete, locally convex topology such that the set of invertible elements is open an…

Mackey showed that for a compact Lie group $K$, the pair $(K,C^{0}(K))$ has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of $K\times K$ invariant polarizations on $T^{\ast}K$. The …

Generalizes CNNs on homogeneous spaces like Euclidean and spherical surfaces.

We define and study the Burnside quotient Green ring of a Mackey functor. Some refinements of Dress induction theory are presented, together with applications to computation results for $K$-theory and $L$-theory of finite and infinite groups.

Convex functions in dual Orlicz spaces are studied under specific topologies.

We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients of the equivariant cohomology theory possess a Mackey structure. Such a structur…

We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.

Spatio-temporal RBF neural networks improve chaotic time series prediction.

Deep learning model simulates noisy dynamical systems without distributional assumptions.

Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie algebras, which in turn is phrased in terms of an integration proce…

This paper establishes a mathematical framework for G-CNNs on homogeneous spaces.

Combines Fourier methods and RNNs for efficient time series prediction.

This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein and Xu. Secondly, it is shown how this procedure is quantized by Rieffel induction…

ICA accurately estimates treatment effects even with confounders.

For the cotangent bundle $T^{*}K$ of a compact Lie group $K$, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space $L^{2}(K)$ under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state tra…

ForGAN uses GANs for probabilistic forecasting of sensory data.

Enhances supervised learning speed with KT algorithm.

Extends particle classification to curved space-times using groupoids.

Characterizes continuity of monotone functionals in mixed topology.

Improves probability distribution compression with KT algorithm.

Compress++ speeds up distribution compression to near-linear time.

Improved convergence rates for Stein Variational Gradient Descent in finite-particle settings.

Global models outperform univariate benchmarks in complex time series forecasting.

Enhanced fuzzy system predicts chaotic time series with improved accuracy.

The study examines conditions for completeness and simplicity in hom-Lie superalgebras.

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h=1} defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler m…

We give several applications of a lemma on completeness used by Osserman to show the meromorphicity of Weierstrass data for complete minimal surfaces with finite total curvature. Completeness and weak completeness are defined for several classes of surfaces which admit singular points. The completeness lemma is a usefu…

Study of knot group completions links Alexander polynomials.

Completing segments of a real tree doesn't yield a complete space.

The paper classifies 2D complete $λ$-surfaces in 3D space.

Study on geodesic completeness for Type A surfaces.

Study geodesic and affine Killing completeness in homogeneous affine surfaces.

Study directed completion of spacetimes, focusing on Schwarzschild spacetime.

Completeness of surface metrics established for Sobolev spaces.

Geodesic completeness proven for all compact locally symmetric Lorentz manifolds.

The study classifies complete Lagrangian self-shrinkers in 4D space.

The paper classifies 3D complete gradient Yamabe solitons.

Turing complete flow on 4-sphere preserves volume.

Study disproves conjecture about metric completion of curve spaces.

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete $d \times N$ matrix is finitely rank-$r$ completable if there are at …