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Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, the self-organized behavioral development provides more questions than answers. Are there special functional units for…
Recently, deep feedforward neural networks have achieved considerable success in modeling biological sensory processing, in terms of reproducing the input-output map of sensory neurons. However, such models raise profound questions about…
The structure and performance of neural networks are intimately connected, and by use of evolutionary algorithms, neural network structures optimally adapted to a given task can be explored. Guiding such neuroevolution with additional…
Neural network (NN) interatomic potentials provide fast prediction of potential energy surfaces, closely matching the accuracy of the electronic structure methods used to produce the training data. However, NN predictions are only reliable…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
Recent experimental results based on multi-electrode and imaging techniques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the…
We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…
Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in…
The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…
A case study of arithmetic dynamics over the rationals on the Markoff surface is presented, in particular the local-global dynamical property of strong residual periodicity. The dynamical system induced by the composition of any two of the…
For non-uniform cellular automata (NUCA) with finite memory over an arbitrary universe with multiple local transition rules, we show that pointwise nilpotency, pointwise periodicity, and pointwise eventual periodicity properties are…
In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to…
Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on…