Related papers: Symmetry invariance for adapting biological system…
A symmetry is a `change without change'. As simple as it sounds, this concept is the fundamental cornerstone that unifies all branches of theoretical physics. Virtually all physical laws -- ranging from classical mechanics and…
Within the germinal center in follicles, B-cells proliferate, mutate and differentiate, while being submitted to a powerful selection~: a micro-evolutionary mechanism at the heart of adaptive immunity. A new foreign pathogen is confronted…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
Uncertainty-aware prediction is essential for safe motion planning, especially when using learned models to forecast the behavior of surrounding agents. Conformal prediction is a statistical tool often used to produce uncertainty-aware…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power-law form for power spectra of temporal fluctuations of all scales ranging…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial…
The fluctuation-dissipation (F-D) theorem is a fundamental result for systems near thermodynamic equilibrium, and justifies studies between microscopic and macroscopic properties. It states that the nonequilibrium relaxation dynamics is…
Emergent behaviors occur in a vast array of systems across many scales, and are of fundamental physical importance because of the intrinsic difficulty in linking microscopic system properties to macroscopic behaviors. Here we study the…
In previous work it was shown that if a control system $\mathcal{V}\subset TM$ on manifold $M$ has a control symmetry group $G$ then it very often has group quotients (or symmetry reductions) $\mathcal{V}/G$ which are static feedback…
This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…
The Minority Game framework was recently generalized to account for the possibility that agents adapt not only through strategy selection but also by diversifying their response according to the kind of dynamical regime, or the risk, they…
Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We…
The proteins involved in cells' mechanobiological processes have evolved specialized and surprising responses to applied forces. Biochemical transformations that show catch-to-slip switching and force-induced pathway switching serve…
Deterministic dynamical systems such as the baker maps are useful to shed light on some of the conditions verified by deterministic models in non-equilibrium statistical physics. We investigate a 2D dynamical system, enjoying a weak form of…
In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…
It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate…
While model architectures and training strategies have become more generic and flexible with respect to different data modalities over the past years, a persistent limitation lies in the assumption of fixed quantities and arrangements of…