arXiv research

In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic mar…

New model recognizes emotions with missing modalities, improving accuracy.

TGNN4I model forecasts irregularly observed graph data using ODEs.

GoTube verifies neural networks over time, scaling to large horizons.

In this introductory paper, we discuss how quantitative finance problems under some common risk factor dynamics for some common instruments and approaches can be formulated as time-continuous or time-discrete forward-backward stochastic differential equations (FBSDE) final-value or control problems, how these final val…

We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point i…

This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.

Let $M$ be a closed manifold and let $N$ be a connected manifold without boundary. For each $k\in\mathbb{N}$ the set of $k$ times continuously differentiable maps between $M$ and $N$ has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open $C^k$ topology. We provide a det…

Study evolutes of curves with varying smoothness.

Training deep neural networks at the edge on light computational devices, embedded systems and robotic platforms is nowadays very challenging. Continual learning techniques, where complex models are incrementally trained on small batches of new data, can make the learning problem tractable even for CPU-only embedded de…

Estimates curvature for long-time continuity method solutions.

Time-continuous emotion prediction has become an increasingly compelling task in machine learning. Considerable efforts have been made to advance the performance of these systems. Nonetheless, the main focus has been the development of more sophisticated models and the incorporation of different expressive modalities (…

As we enter into the big data age and an avalanche of images have become readily available, recognition systems face the need to move from close, lab settings where the number of classes and training data are fixed, to dynamic scenarios where the number of categories to be recognized grows continuously over time, as we…

Let M be a bounded open plane domain. Let f be a continuous function on the closure of M, 3-times continuously differentiable in M, which vanish on the boundary. Polterovich and Sodin proved that the values of f cannot exceed the norm of the hessian of f, averaged over the entire domain M. In this paper we study the eq…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data eff…

The so called Jenkins-Serrin problem is a kind of Dirichlet problem for graphs with prescribed mean curvature that combines, at the same time, continuous boundary data with regions of the boundary where the boundary values explodes either to $+\infty$ or to $-\infty.$ We give a survey on the development of Jenkins-Serr…

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we calculate an evolution process p(t, \cdot) which transports p0 to p1 by using th…

Treatment effects can be estimated from observational data as the difference in potential outcomes. In this paper, we address the challenge of estimating the potential outcome when treatment-dose levels can vary continuously over time. Further, the outcome variable may not be measured at a regular frequency. Our propos…

The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the numérai…

A mesh-free method solves continuum-marginal optimal transport problems.

The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete and continuous stochastic processes (random exchange models) as well as related…

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these method…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated state space can correspond to numerical solutions to certain mathematical optimiza…

New deep learning method solves stochastic control problems.

Extends GCN-SIR model for US COVID-19 spread analysis.

The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that…

Flexible Hawkes model with Gaussian process self-effects for time-dependent data.

New neural networks with variable time constants for better time-series prediction.

NDMs enable non-linear transformations in diffusion models for better generative tasks.

This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.

Study bounds for European basket call options in a discrete-time market model with price jumps.

Time-continuous dimensional descriptions of emotions (e.g., arousal, valence) allow researchers to characterize short-time changes and to capture long-term trends in emotion expression. However, continuous emotion labels are generally not synchronized with the input speech signal due to delays caused by reaction-time, …

Continuous control imitation learning fails if expert actions are smooth.

Flow on weighted graphs sharpens Bakry-Émery curvature.

New RNN model handles long-term dependencies in irregularly-sampled time series.

Automates PDE model reduction with time-scale separation.

Despite increasing attention paid to the need for fast, scalable methods to analyze next-generation neuroscience data, comparatively little attention has been paid to the development of similar methods for behavioral analysis. Just as the volume and complexity of brain data have grown, behavioral paradigms in systems n…

This work is a short, self-contained introduction to subriemannian geometry with special emphasis on Chow's Theorem. As an application, a regularity result for the Poincaré Lemma is presented. At the beginning, the definitions of a subriemannian geometry, horizontal vector fields and horizontal curves are given. Then t…

The curse of dimensionality affects neural network optimization, especially with smooth functions.

Locally convex classes on manifolds linked to Ricci curvature bounds.

Method infers causal structure from system behaviors using RKHS and kernel $ε$-machines.

The recent research report of U.S. Department of Energy prompts us to re-examine the pricing theories applied in electricity market design. The theory of spot pricing is the basis of electricity market design in many countries, but it has two major drawbacks: one is that it is still based on the traditional hourly sche…

Graph convolutions can enhance high frequencies, leading to over-sharpening.

The paper studies continuous submodular functions and their optimization.

The paper studies ideal flows of closed curves, classifying critical points and proving flow behavior.

Predicting stochastic cellular dynamics as emerging from the mechanistic models of molecular interactions is a long-standing challenge in systems biology: low-level chemical reaction network (CRN) models give raise to a highly-dimensional continuous-time Markov chain (CTMC) which is computationally demanding and often …

EP algorithm improved for CNNs and real-time learning.