Related papers: Counting Short Trajectories in Elementary Cellular…
We present numerical results on electron tunneling in a single-electron box at low temperature. The effective action of this device is equivalent to the Hamiltonian of a classical XY spin chain with long ranged interactions. Using an…
Nowadays, methodologies coming from studying physical systems are being applied to the description of a wide variety of complex systems. In particular, one can study thermodynamical methods to describe the overall behavior of many systems,…
In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed…
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of…
Deploying LLMs raises two coupled challenges: (1) monitoring--estimating where a model underperforms as traffic and domains drift--and (2) improvement--prioritizing data acquisition to close the largest performance gaps. We test whether an…
We describe a systematic method for complete enumeration of configuration classes (CCs) of the spin-1/2 Ising model in the energy-magnetization plane. This technique is applied to the antiferromagnetic Ising model in an external magnetic…
A theory of electronic transport through molecular wires is applied to analyze characteristics of a long-range electron transfer (ET) through molecular bridges in macromolecules with complex donor/acceptor subsystems. Assuming a coherent…
Transformers suffer from the computational overhead of their quadratic dependence on the length of sequences processed. We present three methods, all adding an intermediate step between training and inference/generation, which extend the…
We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy…
We present a new classification of elementary cellular automata. It is based on the structure of the network of states, connected with the transitions between them; the latter are determined by the automaton rule. Recently an algorithm has…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
Motivated by challenges arising in molecular simulation, we study reactive trajectories of the overdamped Langevin dynamics, i.e. trajectories observed as they pass from a set A corresponding to the reagents of a chemical reaction to a set…
Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the…
This paper deals with the state estimation problem in discrete-event systems modeled with nondeterministic finite automata, partially observed via a sensor measuring unit whose measurements (reported observations) may be vitiated by a…
Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited…
Large Reasoning Models (LRMs) often suffer from overthinking, generating unnecessarily long reasoning chains even for simple tasks. This leads to substantial computational overhead with limited performance gain, primarily due to redundant…
Cell migration is crucial to many physiological and pathological processes. During migration, a cell adapts its morphology, including the overall morphology and nucleus morphology, in response to various cues in complex microenvironments,…
Rule 22 elementary cellular automaton (ECA) has a 3--cell neighborhood, binary cell states, where a cell takes state `1' if there is exactly one neighbor, including the cell itself, in state `1'. In Boolean terms the cell-state transition…
We propose an approach for estimating the probability that a given small target, among many, will be the first to be reached in a molecular dynamics simulation. Reaching small targets out of a vast number of possible configurations…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…