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The classical question whether nonholonomic dynamics is realized as limit of friction forces was first posed by Carath\'eodory. It is known that, indeed, when friction forces are scaled to infinity, then nonholonomic dynamics is obtained as…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…
Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…
Dynamical systems are abstract models of interaction between space and time. They are often used in fields such as physics and engineering to understand complex processes, but due to their general nature, they have found applications for…
In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and…
This paper derives an optimal control strategy for a simple stochastic dynamical system with constant drift and an additive control input. Motivated by the example of a physical system with an unexpected change in its dynamics, we take the…
Rhythmic fluctuations in acoustic energy and accompanying neuronal excitations in cortical oscillations are characteristic of human speech, yet whether a corresponding rhythmicity inheres in the articulatory movements that generate speech…
Much evidence seems to suggest cortex operates near a critical point, yet a single set of exponents defining its universality class has not been found. In fact, when critical exponents are estimated from data, they widely differ across…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
We study a stylized dynamic assortment planning problem during a selling season of finite length $T$. At each time period, the seller offers an arriving customer an assortment of substitutable products and the customer makes the purchase…
Recent work has identified nonlinear deterministic structure in neuronal dynamics using periodic orbit theory. Troublesome in this work were the significant periods of time where no periodic orbits were extracted - "dynamically dark"…
Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion…
Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…
The original continuous-time "goldfish" dynamical system is characterized by two neat formulas, the first of which provides the $N$ Newtonian equations of motion of this dynamical system, while the second provides the solution of the…
Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one…
In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
Dynamics and uncertainty are essential features of real-life argumentation, and many recent studies have focused on integrating both aspects into Dung's well-known abstract Argumentation Frameworks (AFs). This paper proposes a combination…
It has long been hypothesized that operating close to the critical state is beneficial for natural and artificial systems. We test this hypothesis by evolving foraging agents controlled by neural networks that can change the system's…