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.
Sharp conditions found for solving heat equation on Riemannian manifolds.
We prove local in time Strichartz estimates without loss for the restriction of the solution of the Schroedinger equation, outside a large compact set, on a class of asymptotically hyperbolic manifolds.
We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in and the velocity fields in . These estimates are obtained using geometric considerations which show th…
We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index…
In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the Klein-Gordon equation on asymptotically de Sitter spaces and provide a heuristic argument for the non-existence of a global dispersive estimate on these spaces. The weights in the estimates depend on the ma…
Proves well-posedness for Einstein equations with specific boundary conditions.
New boundary conditions solve Cauchy problem for Dirac operators on spacetimes.
EP learns like BPTT but with local weight updates.
Proves well-posedness for Einstein equations with specific boundary data.
In this paper, we study the problem of locating a predefined sequence of patterns in a time series. In particular, the studied scenario assumes a theoretical model is available that contains the expected locations of the patterns. This problem is found in several contexts, and it is commonly solved by first synthesizin…
We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuat…
Study on well-posedness of vacuum Einstein equations with specific boundary conditions.
In this article we will show that the Macro-Economy and its growth can be modelled and explained exactly in principle by commonly known Field Theory from theoretical physics. We will show the main concepts and calculations needed and show that calculation and prediction of economic growth then gets indeed possible in D…
Study local expansions of continuous-time processes using Ito signature properties.
We propose a particularly structured Boltzmann machine, which we refer to as a dynamic Boltzmann machine (DyBM), as a stochastic model of a multi-dimensional time-series. The DyBM can have infinitely many layers of units but allows exact and efficient inference and learning when its parameters have a proposed structure…
We introduce certain spherically symmetric singular Ricci solitons and study their stability under the Ricci flow from a dynamical PDE point of view. The solitons in question exist for all dimensions , and all have a point singularity where the curvature blows up; their evolution under the Ricci flow is in sh…
This paper presents the Poisson-randomized gamma dynamical system (PRGDS), a model for sequentially observed count tensors that encodes a strong inductive bias toward sparsity and burstiness. The PRGDS is based on a new motif in Bayesian latent variable modeling, an alternating chain of discrete Poisson and continuous …
CoLoRA models predict PDE solutions quickly and accurately with minimal data.
What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made, it remains challenging. Physicists usually apply the concepts and methods in stat…
In frictionless financial markets, no-arbitrage is a local property in time. This means that a discrete time model is arbitrage-free if and only if there does not exist a one-period-arbitrage. With capital gains taxes, this equivalence fails. For a model with a linear tax and one non-shortable risky stock, we introduce…
New method uses randomized sparse neural networks to solve time-dependent PDEs more accurately and efficiently.
Alternative wavelet analysis method for financial signals.
Neural IVP solves IVPs with neural networks, overcoming scaling and conditioning issues.
Local Neural Operators enable efficient system-level analysis of complex PDEs.
In sequence learning tasks such as language modelling, Recurrent Neural Networks must learn relationships between input features separated by time. State of the art models such as LSTM and Transformer are trained by backpropagation of losses into prior hidden states and inputs held in memory. This allows gradients to f…
EP algorithm improved for CNNs and real-time learning.
We prove the local-in-time well-posedness for the solution of the compressible Euler equations in -D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, \fw) \in H^s\times H^s\times H^{s'}$, . The classical local well-posedness result for the compressible Euler equations in -D holds f…