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arXiv Preprints
Universality in s-wave and higher partial wave Feshbach resonances: an illustration with a single atom near two scattering centers
It is well-known that cold atoms near s-wave Feshbach resonances have universal properties that are insensitive to the short-range details of the interaction. What is less known is that atoms near higher partial wave Feshbach resonances also have rem...
physics:cond-mat:stat-mech
arXiv Preprints
Graph cobordisms and Heegaard Floer homology
We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsváth and Szabó's TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we give an ex...
math:math:GT
arXiv Preprints
Deep Learning Estimation of Absorbed Dose for Nuclear Medicine Diagnostics
The distribution of absorbed dose in radionuclide therapy with Lu$^{177}$ can be approximated by convolving an image of the time-integrated activity distribution with a dose voxel kernel representing different tissue types. This fast but inaccurate a...
stat:stat:MLcs:cs:LGphysics:physics:med-phstat:stat:CO
arXiv Preprints
Cross ratios and cubulations of hyperbolic groups
Many geometric structures associated to surface groups can be encoded in terms of invariant cross ratios on their circle at infinity; examples include points of Teichmüller space, Hitchin representations and geodesic currents. We add to this picture...
math:math:GTmath:math:DGmath:math:GR
arXiv Preprints
Quillen metric for singular families of Riemann surfaces with cusps and compact perturbation theorem
We study the behavior of the Quillen metric for the family of Riemann surfaces with cusps when the additional cusps are created by degeneration.
More precisely, in our previous paper, we've seen that the renormalization of the Quillen metric a...
math:math:DGmath:math:AG
arXiv Preprints
The Compression method and applications
In this paper, we introduce and develop the method of compression of points in space. We introduce the notion of the mass, the rank, the entropy, the cover and the energy of compression. We leverage this method to prove some class of inequalities rel...
math:math:NT
arXiv Preprints
Deforming cubulations of hyperbolic groups
We describe a procedure to deform cubulations of hyperbolic groups by "bending hyperplanes". Our construction is inspired by related constructions like Thurston's Mickey Mouse example, walls in fibred hyperbolic $3$-manifolds and free-...
math:math:GTmath:math:GR
arXiv Preprints
Finite difference method on flat surfaces with a flat unitary vector bundle
We establish an asymptotic relation between the spectrum of the discrete Laplacian associated to discretizations of a half-translation surface with a flat unitary vector bundle and the spectrum of the Friedrichs extension of the Laplacian with von Ne...
math:math:DGmath:math:FAmath:math:SP
arXiv Preprints
Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion
We study the asymptotic expansion of the determinant of the graph Laplacian associated to discretizations of a half-translation surface endowed with a flat unitary vector bundle. By doing so, over the discretizations, we relate the asymptotic expansi...
math:math:PRphysics:math-phmath:math:MPmath:math:COmath:math:DGmath:math:FA
arXiv Preprints
Automorphisms of contact graphs of ${\rm CAT(0)}$ cube complexes
We show that, under weak assumptions, the automorphism group of a ${\rm CAT(0)}$ cube complex $X$ coincides with the automorphism group of Hagen's contact graph $\mathcal{C}(X)$. The result holds, in particular, for universal covers of Salvetti ...
math:math:GTmath:math:GR
arXiv Preprints
Summarizing the performances of a background subtraction algorithm measured on several videos
There exist many background subtraction algorithms to detect motion in videos. To help comparing them, datasets with ground-truth data such as CDNET or LASIESTA have been proposed. These datasets organize videos in categories that represent typical c...
cs:cs:CV
arXiv Preprints
On the Road with 16 Neurons: Mental Imagery with Bio-inspired Deep Neural Networks
This paper proposes a strategy for visual prediction in the context of autonomous driving. Humans, when not distracted or drunk, are still the best drivers you can currently find. For this reason we take inspiration from two theoretical ideas about t...
cs:cs:CVcs:cs:LGstat:stat:ML
arXiv Preprints
Analysis of the QCD Kondo phase using random matrices
We propose a novel random matrix model that describes the QCD Kondo phase. The model correctly implements both the chiral symmetry of light quarks and the SU(2) spin symmetry of heavy quarks. We analytically take the large-N limit with N the matrix s...
physics:hep-thphysics:hep-latphysics:hep-phphysics:nucl-th
arXiv Preprints
Etale and crystalline companions, II
Let $X$ be a smooth scheme over a finite field of characteristic $p$. In answer to a conjecture of Deligne, we establish that for any prime $\ell \neq p$, an $\ell$-adic Weil sheaf on $X$ which is algebraic (or irreducible with finite determinant) ad...
math:math:NTmath:math:AG
arXiv Preprints
Uniform K-stability of polarized spherical varieties
We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying the correspo...
math:math:AGmath:math:CVmath:math:DG
arXiv Preprints
On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities
We prove that Schur polynomials in Chern forms of Nakano and dual Nakano positive vector bundles are positive as differential forms. Moreover, modulo a statement about the positivity of a "double mixed discriminant" of linear operators on m...
math:math:AGmath:math:DG
arXiv Preprints
On Monge-Ampère volumes of direct images
This paper is devoted to the study of the asymptotics of Monge-Ampère volumes of direct images associated with high tensor powers of an ample line bundle. We study the leading term of this asymptotics and provide a classification of bundles saturati...
math:math:DGmath:math:SP
arXiv Preprints
The 2020s Political Economy of Machine Translation
This paper explores the hypothesis that the diversity of human languages, right now a barrier to interoperability in communication and trade, will become significantly less of a barrier as machine translation technologies are deployed over the next s...
cs:cs:CYcs:cs:CL
arXiv Preprints
Stably semiorthogonally indecomposable varieties
A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of a noncommutatively stably semiorthogonally indecomposable (NSSI) variety. This propery implies, among other th...
math:math:AG
arXiv Preprints
Trivalent vertices and bordered knot Floer homology in the standard basis
We define new algebras, local bimodules, and bimodule maps in the spirit of Ozsvath-Szabo's bordered knot Floer homology. We equip them with the structure of 2-representations of the categorified negative half U^- of U_q(gl(1|1)), 1-morphisms of...
math:math:GTmath:math:QAmath:math:RT