arXiv research

Generalizes CNNs on homogeneous spaces like Euclidean and spherical surfaces.

The paper proves differentiability of evolution maps in Lie groups.

New map constructed from equivariant spectra for manifold study.

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 …

RPNN-EOFs model improves time series forecasting accuracy.

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.

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the $C^0$-topological context, and provide necessary and sufficient regularity conditions for the (standard) $C^k$-topological setting. We prove that the evolution map is $C^0$-continuous on its domain $\textit{iff}\hspace{1pt}$ the Lie gro…

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the asymptotic estimate context. Specifically, let $G$ be a Lie group with asymptotic estimate Lie algebra $\mathfrak{g}$, and denote its evolution map by $\mathrm{evol}\colon \mathrm{D}\equiv \mathrm{dom}[\mathrm{evol}]\rightarrow G$, i.e.…

Extends particle classification to curved space-times using groupoids.

We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Shor…

Combines Fourier methods and RNNs for efficient time series prediction.

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…

In the dual $L_{Φ^*}$ of a $Δ_2$-Orlicz space $L_Φ$, that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology $τ(L_{Φ^*},L_Φ)$ if and only if on each order interval $[-ζ,ζ]=\{ξ: -ζ\leq ξ\leqζ\}$ ($ζ\in L_{Φ^*}$), it is lowe…

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

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.

Characterizes continuity of monotone functionals in mixed topology.

Improves probability distribution compression with KT algorithm.

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

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of s…

Global models outperform univariate benchmarks in complex time series forecasting.

Enhanced fuzzy system predicts chaotic time series with improved accuracy.

Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …

Generalizes uniformization to algebraic correspondences.

Study of holomorphic correspondences combining entire maps and Fuchsian groups.

Introduces non-abelian Hodge correspondence linking algebraic structures to geometry.

New geometric proof for rational tangles links-quivers correspondence.

The paper defines a category of Lagrangian correspondences in super Hilbert spaces and constructs a functorial field theory.

Proves isometric correspondence of leaves for generic rolling distributions.

Constructs correspondences on hyperelliptic surfaces combining orbifold groups and Blaschke products.

With respect to the Dolbeault complex over the flat manifold $\C^n$, an explicit description of the inverse correspondence of the twistor correspondence is given.

The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the pos…

Study Kobayashi-Hitchin correspondence for special sheaves on Kähler manifolds.

Constructs Lagrangian correspondences for Higgs bundles and holomorphic connections.

The paper extends Riemann-Hilbert correspondence to foliations.

ROBOT framework solves regression without correspondence for large data and complex models.

The main result of this paper is a discrete Lawson correspondence between discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. This is a correspondence between two discrete isothermic surfaces. We show that this correspondence is an isometry in the following sense: it preserves the metric coefficients int…

In this paper, we define the corresponding submanifolds to left-invariant Riemannian metrics on Lie groups, and study the following question: does a distinguished left-invariant Riemannian metric on a Lie group correspond to a distinguished submanifold? As a result, we prove that the solvsolitons on three-dimensional s…