arXiv research

Paper proposes an alternative to MLE for GLMs with non-canonical link functions.

New Hamiltonian Monte Carlo method for non-canonical dynamics.

Hamiltonian Monte Carlo (HMC) exploits Hamiltonian dynamics to construct efficient proposals for Markov chain Monte Carlo (MCMC). In this paper, we present a generalization of HMC which exploits \textit{non-canonical} Hamiltonian dynamics. We refer to this algorithm as magnetic HMC, since in 3 dimensions a subset of th…

This paper introduces $\infty$- and $n$-fold vector bundles as special functors from the $\infty$- and $n$-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of $n$-fold vector bundles and we prove that any $n$-fold vector bundle admits a non-canonical isomorphism to a decomposed …

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order $2r$ where $r>1$ is odd or congruent to $2$ modulo $4$. In this paper we consider…

New non-canonical flows found via parabolic Allen-Cahn equations.

We study parameter inference in large-scale latent variable models. We first propose an unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several previously proposed frequentist or Bayesian methods. We then propose a novel inference…

The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of a principal bundle. As a consequence of the Lagrangian approach, a Kelvin-Noeth…

We prove that for any complete three-manifold with a lower Ricci curvature bound and a lower bound on the volume of balls of radius one, a solution to the Ricci flow exists for short time. Actually our proof also yields a (non-canonical) way to flow and regularize some interior region of a non-complete initial data sat…

We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, …

We provide a coordinate-free version of the local classification, due to A. G. Walker [Quart. J. Math. Oxford (2) 1, 69 (1950)], of null parallel distributions on pseudo-Riemannian manifolds. The underlying manifold is realized, locally, as the total space of a fibre bundle, each fibre of which is an affine principal b…

This article studies hypoellipticity on general filtered manifolds. We extend the Rockland criterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix and describe its precise analytic structure. We use this result to study Rockland sequences, a notion generalizing elliptic sequences to fil…

Develops a new non-abelian framework for Riemann surfaces and differential equations.

This paper generalizes Batchelor's theorem in $C^\infty$-superschemes.

The Milnor fibre of a $\mathbb{Q}$-Gorenstein smoothing of a Wahl singularity is a rational homology ball $B_{p,q}$. For a canonically polarised surface of general type $X$, it is known that there are bounds on the number $p$ for which $B_{p,q}$ admits a symplectic embedding into $X$. In this paper, we give a recipe to…

Derives stochastic and dissipative dynamics preserving Gibbs measure.

For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint surfaces in $B^{4}$. In this paper, we describe the set of genera of such surfaces in terms of the $h$-function, which is a link invariant from Heegaard Floer homology. In particular, we use the $h$-function to give lower bou…

ZSPO optimizes RL from unknown link functions using human feedback.

New link invariants from diagram colorings match link widths.

Formula for arborescent link tails using theta functions.

We study Heegaard Floer homology and various related invariants (such as the $h$-function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the $h$-function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Fl…

Paper computes link determinants using Fourier-Hadamard transforms.

The paper explores fibered and quasi-positive links, introducing new families and invariants.

We give a necessary condition for a meromorphic function in several variables to give rise to a Milnor fibration of the local link (respectively of the link at infinity). In the case of two variables we give some necessary and sufficient conditions for the local link (respectively the link at infinity) to be fibred.

Study variations of Riemannian submersions to maintain geodesic fibers and positive curvatures.

Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.

New tests for VaR and ES forecast encompassing using flexible link functions.

It is shown that, in the 1-jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian isotopic to the 1-jet of the 0-function, and thus cannot be distinguished by the cla…

We give a closed formula for the multivariable Conway potential function of any graph link in a homology sphere. As corollaries, we answer three questions by Walter Neumann about graph links.

The elliptic Hall algebra governs torus link homology.

Characterizes Lie groups with specific structures and finds a correspondence between carrollian and galilean Lie algebras.

Study on colored Jones polynomial and link complements.

This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.

Proposes a new model for high-dimensional data analysis with unknown link function.

An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth four-dimensional cobordism between surgeries on links. By applying $d$-invariant inequalities for this cobordism we obtain inequalities between the $H$-functions of links, whi…

Geometrically describes the linear and quadratic forms for rational links.

New method optimizes policies without assuming known link functions between preferences and rewards.

Study on multiple linking numbers, extending Gauss diagram formulas.

We show that the head and tail functions of the colored Jones polynomial of adequate links are the product of head and tail functions of the colored Jones polynomial of alternating links that can be read-off an adequate diagram of the link. We apply this to strengthen a theorem of Kalfagianni, Futer and Purcell on the …

Link signature limit depends on linking matrix under specific polynomial condition.

New polynomial invariants for virtual links are stronger than F-polynomials.

Derives FPDE for equity-linked insurance pricing.

Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.

Study links in 3-manifolds, linking volume to polynomial coefficients.

This paper provides a theoretical and computational justification of the long held claim that of the similarity of the probit and logit link functions often used in binary classification. Despite this widespread recognition of the strong similarities between these two link functions, very few (if any) researchers have …

Symmetric function $L_{M,N}$ lifts torus link homology.

The slope invariant is shown to be unchanged by concordance of colored links.

Study on singularities of specific polynomial functions.