Related papers: Functional Renormalization Prediction of Rupture
Practical stabilization of input-affine systems in the presence of measurement errors and input constraints is considered in this brief note. Assuming that a Lyapunov function and a stabilizing control exist for an input-affine system, the…
In 1986 Ya.V. Tatarinov presented the foundations of the theory of weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. It is assumed that for zero value of this…
We consider the problem of mining signal temporal logical requirements from a dataset of regular (good) and anomalous (bad) trajectories of a dynamical system. We assume the training set to be labeled by human experts and that we have…
In this paper, we aim at characterizing generalized functionals of discrete-time normal martingales. Let $M=(M_n)_{n\in \mathbb{N}}$ be a discrete-time normal martingale that has the chaotic representation property. We first construct…
In the present paper we are discussing the influence of the fractal distribution of defects on the critical behavior of the system. We consider a case when the equation of motion for the order parameter contains influences of defects of…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
Many experiments record sequential trajectories where each trajectory consists of oscillations and fluctuations around zero. Such trajectories can be viewed as zero-mean functional data. When there are structural breaks (on the sequence of…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
In this paper, we further develop a recently proposed theory of time based on wavefunction collapse in general relativity. It is based on the postulations that quantum states, which violate the momentum and Hamiltonian constraints,…
Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…
Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate…
The fully nonlinear notion of resonance$-$\textit{geometrical resonance}$-$in the general context of dissipative systems subjected to spatially periodic \textit{phase-modulated} potentials is discussed. It is demonstrated that there is an…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system…
We develop methodology to detect structural breaks in the slope function of a concurrent functional linear regression model for functional time series in $C[0,1]$. Our test is based on a CUSUM process of regressor-weighted OLS residual…
We consider the problem of learning the functions computing children from parents in a Structural Causal Model once the underlying causal graph has been identified. This is in some sense the second step after causal discovery. Taking a…
This paper presents an error analysis of classical and learned Tikhonov regularization schemes for inverse problems. We first demonstrate, both theoretically and numerically, that using a fixed regularization parameter across varying noise…
Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…