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GraphFlow is a visual workflow system designed to improve the reliability of agentic AI automation in multi-step, mission-critical processes. In these workflows, small errors compound rapidly: under an idealized model of independent steps,…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
We construct a data-driven model of flows in graphs that captures the essential elements of the movement of workers between jobs in the companies (firms) of entire economic systems such as countries. The model is based on the observation…
We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of…
Interacting random matrix systems are fundamental to modern theoretical physics and data science, yet a unified framework for their analysis has been lacking. This work introduces such a universal framework, built upon two novel concepts:…
We propose in this paper to consider the stock market as a physical system assimilate to a fluid evolving in a macroscopic space subject to a Force that influences its movement over time where this last is arising from the collision between…
Recent theoretical work has highlighted that quantizing a superconducting circuit in the presence of time-dependent flux $\Phi(t)$ generally produces Hamiltonian terms proportional to $d\Phi/dt$ unless a special allocation of the flux…
Advances in Reinforcement Learning (RL) span a wide variety of applications which motivate development in this area. While application tasks serve as suitable benchmarks for real world problems, RL is seldomly used in practical scenarios…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…
We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal…
The purpose of this article is to introduce a new L\'evy process, termed Variance Gamma++ process, to model the dynamic of assets in illiquid markets. Such a process has the mathematical tractability of the Variance Gamma process and is…
Data-Driven Response Regime Exploration and Identification (DR$^2$EI) is a novel and fully data-driven method for identifying and classifying response regimes of a dynamical system without requiring human intervention. This approach is a…
Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from…
The Value Iteration (VI) algorithm is an iterative procedure to compute the value function of a Markov decision process, and is the basis of many reinforcement learning (RL) algorithms as well. As the error convergence rate of VI as a…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to…
Information Field Dynamics (IFD) by Torsten En{\ss}lin provides a tool to construct simulation schemes for data vectors $d(T)$ from measurements $d(0)$ which describe certain features of a physical process (signal), without any concrete…
With the rise of renewable energy sources and their high variability in generation, the management of power grids becomes increasingly complex and computationally demanding. Conventional AC-power-flow simulations, which use the…
For decades, researchers and practitioners typically measure macroscopic traffic flow variables, i.e., density, flow, and speed, using time or space cuts, and then construct the fundamental diagrams of traffic flow. With the advent of…
We attempt to explain stock market dynamics in terms of the interaction among three variables: market price, investor opinion and information flow. We propose a framework for such interaction and apply it to build a model of stock market…