arXiv research

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

Solves regularity problem for infinite-dimensional Lie groups.

The paper proves differentiability of evolution maps in Lie groups.

New map constructed from equivariant spectra for manifold study.

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…

Characterizes continuity of monotone functionals in mixed topology.

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.

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

Functor connects Lie groupoid algebras to bornological structures.

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…

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

Deep learning model simulates noisy dynamical systems without distributional assumptions.

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

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…

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

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…

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

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.

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.

New interdisciplinary branch in math physics tackles topological interactions of polymer-like objects.

The paper develops algorithms and topological invariants for distinguishing dynamic systems.

A new approach uses circuit topology to study complex polymer interactions.

The paper explores conditions for topological rigidity in quotients of the Davis complex.

Study of digital topology concepts like hyperspaces and function graphs.

Novel theory combines combinatorial and topological elements.

This review explores TDA and TDL beyond persistent homology.

New proof for some knots being topologically slice.

Constructs algorithms to recognize and classify 2D surfaces.

Paper constructs continuous families of topological Morse functions.

Novel M-theory approach classifies topological phases of matter.

A new topological biquandle for links defined.

GANs can analyze graph topology, ranking edge sets by their importance.

New smoothing techniques for topological surfaces in 4-manifolds.

Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural topology called the $D$-topology. However, the $D$-topology has not yet been studied seriously in the existing literature. In this paper, we…

Critiques incorrect fixed point assertions in digital topology.