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We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is…
The study of connectivity and coordination has drawn increasing attention in recent decades due to their central role in driving markets, shaping societal dynamics, and influencing biological systems. Traditionally, observable connections,…
The properties of excited nuclear matter and the quest for a phase transition which is expected to exist in this system are the subject of intensive investigations. High energy nuclear collisions between finite nuclei which lead to matter…
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on…
We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems…
Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…
We study the onset of spontaneous dynamics in the follower force model of an active filament, wherein a slender elastic filament in a viscous liquid is clamped normal to a wall at one end and subjected to a tangential compressive force at…
The concept of temporal networks provides a framework to understand how the interaction between system components changes over time. In empirical communication data, we often detect non-Poissonian, so-called bursty behavior in the activity…
Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental cellular processes. As they move, motor proteins exert compressive forces on the filaments to which they are attached,…
After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective…
This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection…
One of the classic data mining tasks is to discover bursts, time intervals, where events occur at abnormally high rate. In this paper we revisit Kleinberg's seminal work, where bursts are discovered by using exponential distribution with a…
Bifurcation theory is a powerful tool for studying how the dynamics of a neural network model depends on its underlying neurophysiological parameters. However, bifurcation theory has been developed mostly for smooth dynamical systems and…
Exploiting the full potential of MBs for applications requires a good understanding of their complex dynamics. Improved understanding of MB oscillations can lead to further enhancement in optimizing their efficacy in many applications and…
In the absence of inhibition, excitatory neuronal networks can alternate between bursts and interburst intervals (IBI), with heterogeneous length distributions. As this dynamic remains unclear, especially the durations of each epoch, we…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
We investigate the properties of the standard perturbative expansions which describe the early stages of the dynamics of gravitational clustering. We show that for hierarchical scenarios with no small-scale cutoff perturbation theory always…
We introduce a model of fracture which includes the out-of-plane degrees of freedom necessary to describe buckling in a thin-sheet material. The model is a regular square lattice of elastic beams, rigidly connected at the nodes so as to…
The detection of phase transitions is a central task in many-body physics. To automate this process, the task can be phrased as a classification problem. Classification problems can be approached in two fundamentally distinct ways: through…