A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves log-concavity of cluster algebra coefficients for type .
Bracelets and theta bases match in various cluster algebras.
Optimizes basis for density-based atomic representations to enhance compactness and accuracy.
Unified theory linking atom-centered and message-passing models for molecular properties.
Deep neural network predicts molecular wave functions in minimal basis.
In many signal processing applications, the aim is to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as "atoms" allow us to define "atomic norms" that can be used to formulate convex regularizations for the reconstruction problem. …
In this thesis we study asymptotic behavior of projective embeddings of abelian varieties and their amoebas. The projective embeddings are given by theta functions. It is known that a Lagrangian fibration of the abelian variety determines a basis of theta functions. After reviewing the relation from the viewpoint of ge…
New features for quantum calculations learn N-center Hamiltonian matrix elements.
Geometric GNNs model 3D atomic systems with rotations and translations.
Study on planar graph braid groups' second homology.
Gradient-based training and pruning for radial basis function networks in materials physics.
A new method predicts electron density accurately from atom-centered models.
We present a new procedure to determine the growth function of a homogeneous Garside monoid, with respect to the finite generating set formed by the atoms. In particular, we present a formula for the growth function of each Artin--Tits monoid of spherical type (hence of each braid monoid) with respect to the standard g…
A novel method computes Wigner kernels for atomic environments, achieving state-of-the-art accuracy.
Sparse coding, which is the decomposition of a vector using only a few basis elements, is widely used in machine learning and image processing. The basis set, also called dictionary, is learned to adapt to specific data. This approach has proven to be very effective in many image processing tasks. Traditionally, the di…
A new graph model HMG and neural network HMGNN improve molecule property predictions.
Study theta-curves on torus in 3-sphere, classifying them.
We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the theta functions and monopole data of the genus 4 curve to be given in terms of g…
Determinants of theta curves and symmetric graphs are studied.
Proves prime theta-curves for knots on minimal genus surfaces.
Formula for arborescent link tails using theta functions.
We prove a folklore theorem of W. Thurston which provides necessary and sufficient conditions for primality of a certain class of theta-curves. Namely, a theta-curve in the 3-sphere with an unknotted constituent knot U is prime if and only if lifting the third arc of the theta-curve to the double branched cover over U …
DimeNet uses directional message passing to improve molecular predictions.
The Kinoshita graph is the most famous example of a Brunnian theta graph, a nontrivial spatial theta graph with the property that removing any edge yields an unknot. We produce a new family of diagrams of spatial theta graphs with the property that removing any edge results in the unknot. The family is parameterized by…
The paper analyzes spectral properties of connection Laplacian on tori, proving convergence to real torus.
In this article we give necessary and sufficient conditions for two triples of integers to be realized as the Thurston-Bennequin number and the rotation number of a Legendrian theta-graph with all cycles unknotted. We show that these invariants are not enough to determine the Legendrian class of a topologically planar …
The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a reparameterization of the Riemann-Theta Boltzmann machine modelling the original probability…
Proves existence of flat connection on theta functions for G-bundles.
The normalized Yamada polynomial is a polynomial invariant in variable A for theta-curves. In this work, we show that the coefficients of the power series obtained from this polynomial by the substitution A=e^x=1+x+x^2/2+x^3/6+... are finite-type invariants for theta-curves although the coefficients of original polynom…
We prove an optimal systolic inequality for nonpositively curved Dyck's surfaces. The extremal surface is flat with eight conical singularities, six of angle theta and two of angle 9pi - theta, for a suitable theta with cos(theta) in Q(sqrt{19}). Relying on some delicate capacity estimates, we also show that the extrem…
Study theta functions and adiabatic curvature on Abelian varieties.
We determine the abelianization of the symmetric mapping class group of a double unbranched cover using the Riemann theta constant, Schottky theta constant, and the theta multiplier. We also give lower bounds of the abelianizations of some finite index subgroups of the mapping class group.
The paper proves rigidity of certain Dirac operators using theta functions.
New indefinite false theta functions match homological blocks for a specific 3-manifold.
KineticSim accelerates financial market simulations 3406x over CPU.
The paper constructs a canonical connection on bundles over Riemann surfaces and relates it to the theta divisor.
We establish an existence and uniqueness theorem for prime decompositions of theta-curves in -manifolds.
KineticSim: A lightweight, high-performance execution engine for real-time market simulators
Improved Kriging model reduces prediction errors.
Quantum modularity proven for specific theta series.
We construct an analogue of the classical theta-function on an Abelian variety for closed 4-dimensional symplectic manifolds which are T^2-bundles over T^2 with the zero Euler class. We use our theta-functions for a canonical symplectic embedding of these manifolds into complex projective spaces (an analogue of the Lef…
The Kodaira--Thurston M manifold is a compact, 4-dimensional nilmanifold which is symplectic and complex but not Kaehler. We describe a construction of theta-functions associated to M which parallels the classical theory of theta-functions associated to the torus (from the point of view of representation theory and geo…
New findings on prime theta-curves with simple tangles.
We study the Selberg zeta and the theta function associated to bundles over even-dimensional locally symmetric spaces of rank one.
Proves resurgence properties for Habiro elements from radial limits of theta series.
New techniques prove quantum modularity for various functions.
This paper is a continuation of our work on theta and zeta functions In the previous papers we considered the case of even dimensional rank one symmetric spaces of non-compact type. The present is concerned with the odd-dimensional case, i.e. with odd-dimensional real hyperbolic manifolds. It is the natural appearence …
For a Riemann surface with cusps we define a theta function using the eigenvalues of the Laplacian and the singularities of the scattering determinant. We provide its meromorphic continuation and discuss its singularities.