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Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…
It has been consistently reported that many machine learning models are susceptible to adversarial attacks i.e., small additive adversarial perturbations applied to data points can cause misclassification. Adversarial training using…
Motivated by recent experiments on biomimetic membranes exposed to several aqueous phases, we theoretically study the morphology of a membrane in contact with a liquid droplet formed via aqueous phase separation. We concentrate on membranes…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
When is it safe to approximate a complicated random Boolean network (RBN) as a simplified, easier to model RBN? When can static measures of network structure be reliably used to infer the network's dynamics? This simple experiment tests the…
We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with low-dimensional unstable manifolds. Surprisingly, despite network's…
Destructive interference between signal and background processes poses a fundamental challenge in searches for top-philic scalar resonances, significantly reducing experimental sensitivity to well-motivated extensions of the Higgs sector.…
We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…
In the sequential learning problem, agents in a network attempt to predict a binary ground truth, informed by both a noisy private signal and the predictions of neighboring agents before them. It is well known that social learning in this…
In Radhakrishnan et al. [2020], the authors empirically show that autoencoders trained with usual SGD methods shape out basins of attraction around their training data. We consider network functions of width not exceeding the input…
We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently…
The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…
A neural network works as an associative memory device if it has large storage capacity and the quality of the retrieval is good enough. The learning and attractor abilities of the network both can be measured by the mutual information…
We investigate associative-memory behavior in a reconfigurable particle packing programmed by purely local cyclic driving. The system is a two-dimensional bidisperse Lennard--Jones particle assembly with periodic boundaries evolved under…
We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of…
Behavioral changes in animals and humans, as a consequence of an error or a verbal instruction, can be extremely rapid. Improvement in behavioral performances are usually associated in machine learning and reinforcement learning to synaptic…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based models have been successfully implemented as…