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.
Investigates stochastic networks on disordered lattices, converging to Brownian web in 2D.
The objective of this paper is to present some geometric aspects of surfaces associated with theta function solutions of the periodic 2D-Toda lattice. For this purpose we identify the -dimensional Euclidean space with the algebra which allows us to construct the generalized Weierstrass formula …
Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable ``ultra-local'' Poisson bracket algebra defined on di…
Formula for 2-bridge link Alexander polynomials via integer walks.
The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financia…
Following the previous authors works (joint with I.A.Dynnikov) we develop a theory of the discrete analogs of the differential-geometrical (DG) connections in the triangulated manifolds. We study a nonstandard discretization based on the interpretation of DG Connection as linear first order (''triangle'') difference eq…
Periodic surfaces have a limited number of bending modes, equal to their membrane modes.
Explains a 2D color exchange invariant correspondence to 3D linking numbers.
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…
The standard Feynman diagrammatic approach to quantum field theories assumes that perturbation theory approximates the full quantum theory at small coupling even when a mathematically rigorous construction of the latter is absent. On the other hand, two-dimensional Yang-Mills theory is a rare (if not the only) example …
TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice model on a thin torus (2D), and implement the algorithm using TensorNetwork. We…
Tensor networks and RNNs are equivalent, improving wave function encoding.
Quantum phase diagrams for Chern topological insulators show jumps at critical loci.
We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and t…
In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the 2D Voter Model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. I…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and …
Hybrid subgroups found in non-arithmetic PU(2,1) lattices.
2D CNNs approximate Korobov functions with near-optimal rates.
New property identifies arithmetic lattices from nonuniform lattices.
Research finds bounds for knots in hexagonal lattice and classifies 11-stick knots.
This work compares lattice-free and lattice-based training criteria for LVCSR.
We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology o…
Proposes a model to generate 3D-aware images from 2D images.
Course on arithmetic lattices at EPFL.
We give a simple example showing that a knot or link diagram that lies in the lattice is not necessarily the projection of a lattice stick knot or link in the lattice, and we give a necessary and sufficient condition for when a knot or link diagram that lies in the lat…
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
Enhances 2D face recognition with 3D features using active illumination.
New rigidity theorem for product of lattices.
A novel method compresses point cloud attributes by folding them onto a 2D grid.
This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to conj…
The paper finds incommensurable lattices in complex models of Baumslag-Solitar groups.
Proves a lattice version of the Atiyah-Singer index theorem.
Vertex distortion measures how far lattice knots deviate from straight lines.
Regular integer lattices are characterized by k unit vectors that build up their generator matrices. These have rank k for D-lattices, and are rank-deficient for A-lattices, for E_6 and E_7. We count lattice points inside hypercubes centered at the origin for all three types, as if classified by maximum infinity norm i…
In this paper we use techniques from convex projective geometry to produce many new examples of thin subgroups of lattices in special linear groups that are isomorphic to the fundamental groups of finite volume hyperbolic manifolds. More specifically, we show that for a large class of arithmetic lattices in SO(n,1) it …
For many automated driving functions, a highly accurate perception of the vehicle environment is a crucial prerequisite. Modern high-resolution radar sensors generate multiple radar targets per object, which makes these sensors particularly suitable for the 2D object detection task. This work presents an approach to de…
We show that the set of even positive definite lattices that arise from smooth, simply-connected 4-manifolds bounded by a fixed homology 3-sphere can depend on more than the ranks of the lattices. We provide two homology 3-spheres with distinct sets of such lattices, each containing a distinct nonempty subset of the ra…
The paper proves residual finiteness of certain lattices and constructs surfaces with specific fundamental groups.
A celebrated theorem of Hadwiger states that the Euler-Poincaré characteristic is the the unique invariant and continuous valuation on the distributive lattice of compact polyhedra in R^n that assigns value one to each convex non-empty such polyhedron. This paper provides an analogue of Hadwiger's result for finitely p…
New method reconstructs 3D shapes from 2D images using Kendall's shape space.
Geometric interpretation of 2d-4d wall-crossing formulas.
The cubic lattice stick index of a knot type is the least number of sticks necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p,p+1)-torus knots, and show how composing and taking satellites can be used to obtain t…
New method finds lattice polygons that can be dissected into triangles with integer areas.
The paper establishes T-duality for 2D σ-models with H-flux.
New theorem shows embedding restrictions for manifold skeletons.
L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.
The paper refines transformations of lattice diagrams and introduces dotted diagrams.