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.
Derives EoM for DNNs to describe GD dynamics precisely.
The paper studies bifurcations in discrete dynamical systems on manifolds.
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the continuous bicycle transformation, recently studied by Foote, Levi, and Tabachnikov. We prove that the respective monodromy is a Moebius transform…
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the reduction process is a discrete dynamical system that we call the discrete reduce…
Gradient-based methods for games suffer from discrete update steps that cause drift, affecting performance.
The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.
Study on 2-valued dynamics on complex plane, showing some dynamics can't be group actions.
The paper develops algorithms and topological invariants for distinguishing dynamic systems.
Paper analyzes symbolic-dynamics inspired Markov modeling for time-series data.
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold encodes the dynamics up to conjugation and inversion. We also prove a generaliz…
The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they generally suffer from this problem of lacking prior knowledge to …
Paper introduces dynamic strategies for multi-period investment models.
DICE learns population dynamics from discrete samples.
New methods use transport maps to improve Langevin dynamics for sampling.
Floer constructs homology from flow lines in generalized dynamical systems and combinatorial vector fields.
Discrete-time systems can be characterized by simple flat coordinates and their shifts.
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point of view. In mathematical t…
We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from discretizing an ordinary differential equation with a semi-implicit Euler integrat…
Develop contact Tulczyjew formalism for dissipative dynamics on skew algebroids.
The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamic…
This paper considers the computational power of constant size, dynamic Bayesian networks. Although discrete dynamic Bayesian networks are no more powerful than hidden Markov models, dynamic Bayesian networks with continuous random variables and discrete children of continuous parents are capable of performing Turing-co…
NCDSSM models irregularly sampled time series with improved imputation and forecasting.
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie groupoid may be described in terms of Lagrangian implicit difference equations …
We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a financial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and sufficient condition for a Dyn…
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout are the notion of the LM-measure and the notion of the update rule that, we believe, are the key tools for stud…
This work extends reduction processes for nonholonomic discrete mechanical systems.
For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For sy…
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss i…
A new method reduces high-dimensional state space for dynamic choice models.
Algorithm tackles adaptive discretization in adversarial Lipschitz bandits for dynamic pricing and auctions.
In this paper, we develop the continuous time dynamic topic model (cDTM). The cDTM is a dynamic topic model that uses Brownian motion to model the latent topics through a sequential collection of documents, where a "topic" is a pattern of word use that we expect to evolve over the course of the collection. We derive an…
New Y-systems for Miquel dynamics are Möbius invariant.
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of …
Accelerates convergence in global non-convex optimization with reversible diffusion.
A new method reduces complexity in estimating dynamic choice models.
We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.
GDM models time series with smoother transitions and interpretable states.
Extends option pricing model to incorporate market factor dynamics.
Study dynamics of automorphisms on cubic surfaces and their connection to Painlevé 6.
Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex , from which topological and geometrical informations of can be efficiently computed, in particular its homology or Morse-Smale d…
Novel discretization of Euler equations for incompressible fluids.
A new diffusion model uses efficient conditional estimators for discrete data.
First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an -valued best bid price process and an -valued volume process. …
The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schrödinger equation. In this paper, we present its discrete analogue, namely, a model of defor…
Poisson Midpoint Method improves Langevin Dynamics for diffusion models.
New method reduces discrete flow transitions, improving perplexity estimation.
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations, especially into the geometric structure of those dynamical systems and their structur…