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In this paper, we study the bead model: beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two consecutive beads on a wire; there must be exactly one bead on each…

We investigate sensitivity to cumulative perturbations for a few dynamical system classes of practical interest. A system is said to have bounded sensitivity to cumulative perturbations (bounded sensitivity, for short) if an additive…

The aim of this paper is to investigate the well-posedness of a class of boundary control and observation systems on a one dimensional spatial domain. We derive a necessary and sufficient condition characterizing the well-posedness of these…

The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…

Pearl and Dechter (1996) claimed that the d-separation criterion for conditional independence in acyclic causal networks also applies to networks of discrete variables that have feedback cycles, provided that the variables of the system are…

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…

We look for signals of critical behavior in the Yukawa sector. By reviewing a set of models for the fermion masses, we select those where a symmetry-breaking order parameter sits at a transition point between a disordered phase and an…

Continuous phase transitions in spin systems can be formulated as percolation of suitably defined clusters. We review this equivalence and then discuss how in a similar way, the color deconfinement transition in SU(2) gauge theory can be…

Conformal fields with boundaries give rise to rich critical phenomena that can reveal information about the underlying conformality. While most existing studies focus on Hermitian systems, here we explore boundary critical phenomena in a…

In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit…

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise…

We develop theory to understand an intriguing property of diffusion models for image generation that we term critical windows. Empirically, it has been observed that there are narrow time intervals in sampling during which particular…

Quantum criticality in the presence of strong quenched randomness remains a challenging topic in modern condensed matter theory. We show that the topology and anomaly associated with average symmetry can be used to predict certain…

We study a classical spin model (more precisely a class of models) with O(N) symmetry that can be viewed as a simplified $D$ dimensional lattice model. It is equivalent to a non-translationinvariant one dimensional model and contains the…

We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second order…

This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and…

We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor…

Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…

In this paper we prove a combinatorial theorem for finite labellings of trees, and show that it is equivalent to a theorem for finite covers of metric trees and a fixed point theorem on metric trees. We trace how these connections mimic the…

We perform a dynamical system analysis of a cosmological model with linear dependence between the vacuum density and the Hubble parameter, with constant-rate creation of dark matter. We show that the de Sitter spacetime is an asymptotically…