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Cortical circuits exhibit high levels of response diversity, even across apparently uniform neuronal populations. While emerging data-driven approaches exploit this heterogeneity to infer effective models of cortical circuit computation…

We study the entanglement spectrum (ES) of two-dimensional $C_{n}$-symmetric second-order topological insulators (TIs). We show that some characteristic higher order topological observables, e.g., the filling anomaly and its associated…

Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…

Understanding the dynamical behavior of complex systems from their underlying network architectures is a long-standing question in complexity theory. Therefore, many metrics have been devised to extract network features like motifs,…

The phenomenon of phase synchronization of oscillatory systems arising out of feedback coupling is ubiquitous across physics and biology. In noisy, complex systems, one generally observes transient epochs of synchronization followed by…

Training data is always finite, making it unclear how to generalise to unseen situations. But, animals do generalise, wielding Occam's razor to select a parsimonious explanation of their observations. How they do this is called their…

Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element…

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step…

This research report introduces ElegansNet, a neural network that mimics real-world neuronal network circuitry, with the goal of better understanding the interplay between connectome topology and deep learning systems. The proposed approach…

Emergent behavior in active systems is a complex byproduct of local, often pairwise, interactions. One such interaction is self-avoidance, which experimentally can arise as a response to self-generated environmental signals; such…

Excitable membranes are an important type of nonlinear dynamical system and their study can be used to provide a connection between physical and biological circuits. We discuss two models of excitable membranes important in cardiac and…

Some mechanisms of cardiac arrhythmias can be presented as a composition of elementary acts of block and reflection on the contacts of homogeneous areas of the conducting tissue. For study this phenomena we use an axiomatic one-dimensional…

It is well-known that biological and social interaction networks have a varying degree of redundancy, though a consensus of the precise cause of this is so far lacking. In this paper, we introduce a topological redundancy measure for…

We analyze the coherent dynamics of excitons in three dimensional topologically disordered networks with traps. If the interactions between the nodes of the network are long ranged, i.e., algebraically decaying as a function of the distance…

The electronic orders appearing in condensed matter systems are originating from the precise arrangement of atoms constituting the crystal as well as their nature. This teneous relationship can lead to highly different phases in condensed…

We study the asymptotic behavior of ``true" self-avoiding random walks on general infinite locally finite trees. In this model, the walk starts at the root and, at each step, from its current vertex chooses a neighboring edge to traverse…

Undulatory swimming is a widespread propulsion strategy adopted by many small-scale organisms including various single-cell eukaryotes and nematodes. In this work, we report a comprehensive study of undulatory locomotion of a finite…

Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…

We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits…

The underwater traps of the carnivorous plants of the Utricularia species catch their preys through the repetition of an "active slow deflation / passive fast suction" sequence. In this paper, we propose a mechanical model that describes…