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.
Defines continuous versions of combinatorial objects from lattice paths.
Study restrictions on digitally continuous functions and their effects.
A discrete analog of the Tzitzeica equation is found in the form of quad-equation. Its continuous symmetry is an inhomogeneous Narita--Bogoyavlensky type lattice equation which defines a discretization of the Sawada--Kotera equation. The integrability of these discretizations is proven by construction of the Lax repres…
Analog method solves portfolio optimization problems faster and more efficiently.
Analyses cohomology relations for moving frames and coframes.
Proves monotonicity of parabolic frequency on all manifolds without curvature assumptions.
We prove that the partial -estimate holds for metrics along Aubin's continuity method for finding Kähler-Einstein metrics, confirming a special case of a conjecture due to Tian. We use the method developed in recent work of Chen-Donaldson-Sun on the analogous problem for conical Kähler-Einstein metrics.
Continuity of earthquake flow map transfers Teichmüller dynamics results.
Proves real analyticity on surfaces based on restrictions.
This paper applies reactor theory to supply chain management.
Graph neural networks are explained through heat diffusion analogy.
Characterizes billiard and quasigeodesic flows in polyhedral convex bodies.
Shy maps preserve path-connectedness in continuous functions.
We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the investor's orders and trade among themselves to attain Pareto optimal allocatio…
Paper tackles noisy neural networks and proposes a method to enhance their robustness.
New Riesz distributions for differential forms on Euclidean space.
ADAC uses analogous policies to improve RL exploration without sacrificing stability.
In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some (partially known) assertions on the asymptotic of the mean value points for various class…
Paper studies continuous prediction with experts' advice using differential equations.
New proof shows path-connectedness of actions on intervals and circles.
Continuous metrics on manifolds with singularities are shown to be Einstein.
Bidirectional attention is shown to be equivalent to a continuous bag of words model with mixture-of-experts.
Generalization bounds derived for neural ODEs and deep residual networks.
Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trad…
New urn problem considers unknown sampling method.
Author finds the solutions of the Christoffel problem for open and closed surfaces in Riemannian space. The Christoffel problem is reduced to the problem of construction the continuous G-deformations preserving the sum of principal radii of curvature for every point of surface in Riemannian space. G-deformation transfe…
Financial markets investors are involved in many games -- they must interact with other agents to achieve their goals. Among them are those directly connected with their activity on markets but one cannot neglect other aspects that influence human decisions and their performance as investors. Distinguishing all subgame…
In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge and the option pricing partial differential equation. Approximately reversible tr…
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Ri…
This expository article discusses some connections between the geometry of a hyperbolic 3-manifold homotopy-equivalent to a surface, and the combinatorial properties of its end invariants. In particular a necessary and sufficient condition is stated for the manifold to have arbitrarily short geodesics, in terms of a se…
A graph's winding numbers around two non-adjacent vertices differ by ±1.
We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process. Optimal portfolios and maximum expected log--linear utilities from terminal wealth f…
In this paper, we study continuous Kakeya line and needle configurations, of both the oriented and unoriented varieties, in connected Lie groups and some associated homogenous spaces. These are the analogs of Kakeya line (needle) sets (subsets of where it is possible to turn a line (respectively an inter…
Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups and rectangular bands. The ideal properties of higher order rect…
A new method for CT-DCEGs simplifies inference for asymmetric processes.
We show that if a Fano manifold is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then admits a Kähler-Einstein metric. This is a strengthening of the solution of the Yau-Tian-Donaldson conjecture for Fano manifolds by Chen-Donaldson-Sun, and can be used to ob…
Continuous-time Kyle model shows privacy subsidy from noise-perturbed order flow.
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically eval…
Defines half-volume spectrum for manifolds and proves Weyl law holds.
A number of modern learning tasks involve estimation from heterogeneous information sources. This includes classification with labeled and unlabeled data as well as other problems with analogous structure such as competitive (game theoretic) problems. The associated estimation problems can be typically reduced to solvi…
Negative results for neural network approximations on multi-dimensional spaces.
Study of evolutes of polygons and curves in higher dimensions.
This primer explains diffusion models in general state spaces.
Defines a geometric dimension for Lorentzian spaces, distinguishing spacelike and null subspaces.
Proposes HypCSE for enhanced hierarchical clustering.
Proves a conjecture about knotted spheres using plane Floer homology.
Model resolves asset pricing puzzles with price-impact.
For free boundary problems on Euclidean spaces, the monotonicity formulas of Alt-Caffarelli-Friedman and Caffarelli-Jerison-Kenig are cornerstones for the regularity theory as well as the existence theory. In this article we establish the analogs of these results for the Laplace-Beltrami operator on Riemannian manifold…