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.
Paper studies second order tail probabilities in risk models.
In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in The classification gives some interesting phenomena and consequences including: the family of curves conv…
The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.
In this paper we derive a refined asymptotic expansion, near an isolated singularity, for conformally flat metrics with constant positive Q-curvature and positive scalar curvature. The condition that the metric has constant Q-curvature forces the conformal factor to satisfy a fourth order nonlinear partial differential…
In classical surface theory there are but few known examples of surfaces admitting nontrivial isometric deformations and fewer still non-simply-connected ones. We consider the isometric deformability question for an immersion x: M \to R^3 of an oriented non-simply-connected surface with constant mean curvature H. We pr…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form of flows of a given geodesic curvature is proposed. For illustration, the proble…
In recent years, there has been a growing interest in geometric evolution in heterogeneous media. Here we consider curvature driven fows of planar curves, with an additional space-dependent forcing term. Motivated by a homogenization problem, we look for estimates which depend only on the uniform norm of the forcing te…
Study no-arbitrage conditions in 1D diffusion markets with interest rates.
Proposes a Coulomb-like model for international trade flows, fitting real-world data.
Up to symmetries, the orbits of three equal masses under an inverse cube force with zero angular momentum and constant moment of inertia can be reparametrized as the geodesics of a complete, negatively curved metric on a pair of pants. The ends of the pants represent binary collisions. Here we will examine the visibili…
CAMEL embeds data into a manifold using curvature-augmented forces.
ITF improves DSR but inflates curvature, while marginal likelihood reduces it, affecting QoIs.
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
Reinforcement Learning (RL) methods have been proven successful in solving manipulation tasks autonomously. However, RL is still not widely adopted on real robotic systems because working with real hardware entails additional challenges, especially when using rigid position-controlled manipulators. These challenges inc…
The paper presents a method to infer unknown forcing functions in differential equations using Gaussian processes and adjoints.
In this paper, we would like to give an answer to \textbf{Problem 1} below issued firstly in [J. Mao, Eigenvalue estimation and some results on finite topological type, Ph.D. thesis, IST-UTL, 2013]. In fact, by imposing some conditions on the mean curvature of the initial hypersurface and the coefficient function of th…
We develop SHOPPER, a sequential probabilistic model of shopping data. SHOPPER uses interpretable components to model the forces that drive how a customer chooses products; in particular, we designed SHOPPER to capture how items interact with other items. We develop an efficient posterior inference algorithm to estimat…
We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our methodology applies to the case when the dynamics of the aggregate claims process …
Revisits elastic string model to explain interest rate correlations.
Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …
Study rigidifies non-compact manifolds with specific curvature conditions.
Identifies conjugate points in spherical harmonics solutions of quasi-geostrophic equations.
Unified framework for photon and massive particle hypersurfaces in stationary spacetimes.
Bishop's volume comparison theorem states that a compact -manifold with Ricci curvature larger than the standard -sphere has less volume. While the traditional proof uses geodesic balls, we present another proof using isoperimetric hypersurfaces, also known as "soap bubbles," which minimize area for a given volum…
We study the effects of approximate inference on the performance of Thompson sampling in the -armed bandit problems. Thompson sampling is a successful algorithm for online decision-making but requires posterior inference, which often must be approximated in practice. We show that even small constant inference error …
Theoretical models of the strong nuclear interaction contain unknown coupling constants (parameters) that must be determined using a pool of calibration data. In cases where the models are complex, leading to time consuming calculations, it is particularly challenging to systematically search the corresponding paramete…
Geometric integrator preserves coadjoint orbits in dissipative systems.
Analyzes harmonic and biharmonic maps from gradient Ricci solitons.
The possibility of the global Lagrangian reduction of a mechanical system with symmetry is shown to be connected with the characteristic class of a principal fiber bundle of the configuration space over the factor manifold. It is proved that the reduced system is globally Lagrangian if and only if the product of the mo…
Many domains of science have developed complex simulations to describe phenomena of interest. While these simulations provide high-fidelity models, they are poorly suited for inference and lead to challenging inverse problems. We review the rapidly developing field of simulation-based inference and identify the forces …
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
Unified field theory from higher-order Riemannian geometry.
New algorithm efficiently trains machine learning models to atomic forces data.
The paper integrates dissipative and curl forces using geometric methods.
A robust machine learning approach forecasts U.S. Treasury yields, reducing risk for investors.
Improved CG force-field learning from all-atom data.
We extend the lifecycle model (LCM) of consumption over a random horizon (a.k.a. the Yaari model) to a world in which (i.) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii.) a consumer can adapt their consumption strategy to new information about their mortality rate (a.k.a. h…
A network of independently trained Gaussian processes (StackedGP) is introduced to obtain predictions of quantities of interest with quantified uncertainties. The main applications of the StackedGP framework are to integrate different datasets through model composition, enhance predictions of quantities of interest thr…
The classification of Finsler spaces of constant curvature is an interesting and important topic of research in differential geometry. In this paper we obtain necessary and sufficient conditions for generalized Kropina space to be of constant flag curvature.
In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with constant Gaussian cur…
This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. In physical, this surface can be considered as an electrically charged membrane with a constant charge per area in a radially symmetric potential. The evolution of such surface has been investigated by …
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph matching methods can be applied directly to recover the missing correspondences,…
Paper introduces a PDE-free method for decomposing forces in any dimension.
Proposes linking energy and force uncertainty in deep learning potentials.
We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equ…
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study symmetries in the systems with gyroscopic forces to find out when these systems admi…
We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits an…
The paper studies how test particles' mass and charge vary in Kaluza-Klein models.