Results 21 to 30 of about 2,473,621 (173)
Algorithmic market making in dealer markets with hedging and market impact
Mathematical Finance, Volume 33, Issue 1, Page 41-79, January 2023., 2023 Abstract In dealer markets, dealers provide prices at which they agree to buy and sell the assets and securities they have in their scope. With ever increasing trading volume, this quoting task has to be done algorithmically in most markets such as foreign exchange (FX) markets or corporate bond markets. Over the last 10 years, many mathematical models
Alexander Barzykin +2 more
wiley +1 more source
Faster Gröbner bases for Lie derivatives of ODE systems via monomial orderings [PDF]
, 2022 Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze these models is to compute and then symbolically process the polynomial system obtained by sufficiently many Lie ...
arxiv +1 more source
On the almost‐circular symplectic induced Ginibre ensemble
Studies in Applied Mathematics, Volume 150, Issue 1, Page 184-217, January 2023., 2023 Abstract We consider the symplectic‐induced Ginibre process, which is a Pfaffian point process on the plane. Let N be the number of points. We focus on the almost‐circular regime where most of the points lie in a thin annulus SN$\mathcal {S}_{N}$ of width O1N$O\left(\frac{1}{N}\right)$ as N→∞$N \rightarrow \infty$. Our main results are the bulk scaling
Sung‐Soo Byun, Christophe Charlier
wiley +1 more source
Multiscale Modeling & simulation, 2005 For the numerical simulation of the circulatory system, geometrical multiscale models based on the coupling of systems of differential equations with different spatial dimensions are becoming common practice [L. Formaggia et al., Comput. Vis. Sci., 2 (1999)
M. Fernández +2 more
semanticscholar +1 more source
Geometric integration on spheres and some interesting applications [PDF]
J. Computational and Applied Mathematics, v.151(2003) n.1,
pp.141-170, 2011 Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility of these algorithms, we present representative calculations for reduced free rigid body motion (a conservative ...
arxiv +1 more source
Correcting auto-differentiation in neural-ODE training [PDF]
arXiv, 2023 Does the use of auto-differentiation yield reasonable updates to deep neural networks that represent neural ODEs? Through mathematical analysis and numerical evidence, we find that when the neural network employs high-order forms to approximate the underlying ODE flows (such as the Linear Multistep Method (LMM)), brute-force computation using auto ...
arxiv
Embedding Capabilities of Neural ODEs [PDF]
arXiv, 2023 A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results about the exact embedding of maps in different neural ODE architectures in low and high dimension.
arxiv
Neural Ordinary Differential Equation based Recurrent Neural Network Model [PDF]
arXiv, 2020 Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE) is explored with a new extension.
arxiv
Edge of Chaos Theory Unveils the First and Simplest Ever Reported Hodgkin–Huxley Neuristor
Advanced Electronic Materials, EarlyView.This manuscript presents the first and simplest ever‐reported electrical cell, which leverages one memristor on Edge of Chaos to reproduce the three‐bifurcation cascade, marking the entire life cycle from birth to extinction via All‐to‐None effect of an electrical spike, also referred to as Action Potential, across axon membranes under monotonic ...
Alon Ascoli +12 more
wiley +1 more source
Variational formulations of ODE-Net as a mean-field optimal control problem and existence results [PDF]
arXiv, 2023 This paper presents a mathematical analysis of ODE-Net, a continuum model of deep neural networks (DNNs). In recent years, Machine Learning researchers have introduced ideas of replacing the deep structure of DNNs with ODEs as a continuum limit. These studies regard the "learning" of ODE-Net as the minimization of a "loss" constrained by a parametric ...
arxiv