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.
AI stocks hedge against AI singularity's economic impact.
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.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
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.
Minimal displacement set in weakly systolic complexes is systolic and embeds isometrically.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
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…
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 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.
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.
This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of loc…
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.
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 …
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…
Study optimal retirement time and consumption with habitual persistence.
Proposes a new consumption strategy based on martingale principles.
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 paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional averag…
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.
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…
Study optimal consumption for loss-averse agents considering past spending peaks.
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 …
Study many-player investment-consumption games with power FPPs, finding market-risk preference affects consumption.
Solves pair trading problem using consumption-investment theory.
Investor optimizes investment and consumption under uncertain market conditions with constraints.
The paper examines smoothness of value function in consumption-investment models with borrowing constraints.
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…
Paper uses CVAE to simulate tariff impacts on electricity consumption.
Paper examines power consumption in neural networks using various activation functions.
A continuous-time consumption-investment model with constraint is considered for a small investor whose decisions are the consumption rate and the allocation of wealth to a risk-free and a risky asset with logarithmic Brownian motion fluctuations. The consumption rate is subject to an upper bound constraint which linea…
Study metrics on quandles, a knot theory algebraic system.
The paper analyzes optimal consumption with past spending maximum as a reference.
For a wide range of clinical applications, such as adaptive treatment planning or intraoperative image update, feature-based deformable registration (FDR) approaches are widely employed because of their simplicity and low computational complexity. FDR algorithms estimate a dense displacement field by interpolating a sp…
New algorithm detects anomalies by forcing samples to displace mass in low-density regions.
The paper solves a consumption-investment problem with state-dependent lower bounds.