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.
The paper proposes a model to learn motion perception in V1 using vector and matrix representations.
Sparse elasticity reconstruction from local displacements reduces error.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
This paper explores the possibility that asset prices, especially those traded in large volume on public exchanges, might comply with specific physical laws of motion and probability. The paper first examines the basic dynamics of asset price displacement and finds one can model this dynamic as a harmonic oscillator at…
The paper shows subexponential growth and displacement bounds for random walks on graphs with bounded degrees and non-negative curvature.
We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.
In this paper we prove the Conley conjecture and the almost existence theorem in a neighborhood of a closed nowhere coisotropic submanifold under certain natural assumptions on the ambient symplectic manifold. Essential to the proofs is a displacement principle for such submanifolds. Namely, we show that a topologicall…
New displacement technique vanishes bounded cohomology in all degrees.
Nonnegative sectional curvature linked to matrix displacement convexity.
We define the symplectic displacement energy of a non-empty subset of a compact symplectic manifold as the infimum of the Hofer-like norm [5] of symplectic diffeomorphisms that displace the set. We show that this energy (like the usual displacement energy defined using Hamiltonian diffeomorphisms) is a strictly positiv…
The Homogeneity Conjecture explores if constant displacement isometries imply homogeneous spaces.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
Minimal displacement set in weakly systolic complexes is systolic and embeds isometrically.
We discuss in this article a property of action of groups by isometries called "well displacing". An action is said to be well displacing, if the displacement function is equivalent to the the displacement function for the action on the Cayley graph. We relate this property with the fact that orbit maps are quasi-isome…
The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators encoding forms of shift invariance akin to convolutions. We introduce a class of LDR ma…
Alexandrov spaces with non-negative curvature are characterized by the matrix displacement convexity of an entropy tensor.
In this article we study the Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces in the spheres as Lagrangian submanifolds embedded in complex hyperquadrics.
We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By dropping the quadratic restriction on the measurement of an infinitesimal distance, the…
New curvature measure for optimal transport with specific cost function.
Training models to prefer certain responses can unintentionally shift probability to harmful ones.
We prove that the displacement energy of a stable coisotropic submanifold is bounded away from zero if the ambient symplectic manifold is closed, rational and satisfies a mild topological condition.
The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.
We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincaré inequality and the measure contraction property follow from t…
We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations of Floer cohomology, displaceability of Lagrangian correspond…
Study automorphism groups of quandles up to order 10.
In this paper we make the first steps towards developing a theory of intersections of coisotropic submanifolds, similar to that for Lagrangian submanifolds. For coisotropic submanifolds satisfying a certain stability requirement we establish persistence of coisotropic intersections under Hamiltonian diffeomorphisms, ak…
Paper derives formulas for surface variations in shell theory.
The paper proves stability of curvature bounds in geometric analysis.
In this paper we give an explicit description of the bounded displacement isometries of a class of spaces that includes the Riemannian nilmanifolds. The class of spaces consists of metric spaces (and thus includes Finsler manifolds) on which an exponential solvable Lie group acts transitively by isometries. The bounded…
We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and generically has infinitely many leaf-wise intersection points. Moreover, any Stein …
In this study, we present a machine learning approach to infer the worker and student mobility flows on daily basis from static censuses. The rapid urbanization has made the estimation of the human mobility flows a critical task for transportation and urban planners. The primary objective of this paper is to complete i…
Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computation…
The paper studies the action of automorphisms on train tracks and finds that the set of minimally displaced points is co-compact.
We prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the Theorem for Kleinian groups due to Anderson-Canary-Culler-Shalen. As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as …
This study uses Twitter to analyze traveler behavior in Manhattan.
Hexagon grid patterns emerge from conformal isometry in grid cell neural networks.
Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates. In particular, state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra. The typical measures of fit used to …
We prove local Poincaré inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is that of weak CD(K,N) spaces as defined by Lott and Villani. The second class of spaces we study consists of spaces where we have a …
Study of rigid body displacements in a projective space over dual numbers with geometric interpretations.
Study uses satellite data to predict tailings dam collapse risk.
A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.
The paper studies how grid cell patterns emerge in neural networks.
In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is base…
One of the most well-known results in the theory of optimal transportation is the equivalence between the convexity of the entropy functional with respect to the Riemannian Wasserstein metric and the Ricci curvature lower bound of the underlying Riemannian manifold. There are also generalizations of this result to the …
In this paper, it is shown that every point in the hyperbolic 3-space is moved at a distance at least by one of the isometries of length at most in a 2-generator Klenian group which is torsion-free, not co-compact and contains no parabolic. Also some lower bounds fo…
Study metrics on quandles, a knot theory algebraic system.
New algorithm detects anomalies by forcing samples to displace mass in low-density regions.
We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new criterion called "squared asset expectation" (SAE), related to a version of the cost v…