Related papers: Sensitive dependence and transitivity of fuzzified…
Rule-based systems are a very popular form of explainable AI, particularly in the fuzzy community, where fuzzy rules are widely used for control and classification problems. However, fuzzy rule-based classifiers struggle to reach bigger…
Since their introduction, fuzzy sets and systems have become an important area of research known for its versatility in modelling, knowledge representation and reasoning, and increasingly its potential within the context explainable AI.…
In this paper, we introduce and study the notions of $\Delta$-mixing, $\Delta$-transitivity, mildly mixing, strong multi-transitivity and multi-transitivity with respect to a vector in non-autonomous discrete dynamical systems (NDS).…
In this article, we introduce a differentiability concept for fuzzy functions $\tilde{f}: F(\mathbb{R}) \to F(\mathbb{R})$, where $F(\mathbb{R})$ is the set of all fuzzy numbers. With the help of the proposed differentiability notion, we…
The dynamics of first order phase transitions are studied in the context of (3+1)-dimensional scalar field theories. Particular attention is paid to the question of quantifying the strength of the transition, and how `weak' and `strong'…
This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
In this paper, we present a proof of the consistency of the New Foundations set theory ($\mathit{NF}$). $\mathit{NF}$'s main idea is to permit very large sets (including the Universal Set) by restricting set formation to stratified…
We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical systems on compact metric spaces, and extend it to empirical measures, all continuous potentials, and all weak Gibbs states. In particular, we…
Small (but still containing many atoms) quantum systems (traditionally termed nano-systems) are dramatically different from their macroscopic or genuine microscopic (atomic) cousins. Microscopic molecular systems (with a few atoms) obey a…
We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise…
We study the ultrasensitivity of multisite binding processes where ligand molecules can bind to several binding sites, considering more particularly recent models involving complex chemical reactions in phosphorylation systems such as…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir…
We study the pairwise entanglement present in a quantum computer that simulates a dynamically localized system. We show that the concurrence is exponentially sensitive to changes in the Hamiltonian of the simulated system. Moreover,…
Let $t=t_1t_2\cdots$ be an element of the full shift with shift map $\tau$ on a finite set of characters $\mathcal{A}$ and let $ \Sigma=\text{ closure} \{\tau^i(t):\;i\in\N\cup\{0\}\}$. Let $f_t=f_{t_1,\,\infty}=\cdots\circ f_{t_2}\circ…
Non-stationarity affects the sensitivity of change detection in correlated systems described by sets of measurable variables. We study this by projecting onto different principal components. Non-stationarity is modeled as multiple normal…
Dynamical systems are often subject to forcing or changes in their governing parameters and it is of interest to study how this affects their statistical properties. A prominent real-life example of this class of problems is the…
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic…
Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a…