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The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…
The concept of a recently proposed Forward-Forward learning algorithm for fully connected artificial neural networks is applied to a single multi output perceptron for classification. The parameters of the system are trained with respect to…
Recently, we proposed to transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model the linear dependencies instead. We…
Nonlinear optics is a rapidly growing field that has found a wide range of applications. A major limitation, however, is the demand of high power, especially for high-order nonlinearities. Here, by reconfiguring a multiple-scattering…
The book is devoted to the formation and dynamics of localized structures (vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
We employ the Q representation to study the non-classical correlations that are present from below to above-threshold in the degenerate optical parametric oscillator. Our study shows that such correlations are present just above threshold,…
Although the raison d'etre of the brain is the survival of the body, there are relatively few theoretical studies of closed-loop rhythmic motor control systems. In this paper we provide a unified framework, based on variational analysis,…
Density matrix perturbation theory [Phys. Rev. Lett. Vol. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of response properties [Phys. Rev. Lett. Vol. 92, 193002 (2004)]. In this article, we generalize…
We outline ideas on desired properties for a new generation of effective core potentials (ECPs) that will allow valence-only calculations to reach the full potential offered by recent advances in many-body wave function methods. The key…
Many deep neural network architectures loosely based on brain networks have recently been shown to replicate neural firing patterns observed in the brain. One of the most exciting and promising novel architectures, the Transformer neural…
Cooperativity arising from local interactions in equilibrium receptor systems provides gain, but does not increase sensory performance, as measured by the signal-to-noise ratio (SNR) due to a fundamental tradeoff between gain and intrinsic…
An analysis of off-diagonal long-range order in superconductors shows that the spin-spin correlation function is significantly influenced by the order if the order parameter is anisotropic on a microscopic scale. Thus, magnetic neutron…
State of the art algorithms for many pattern recognition problems rely on deep network models. Training these models requires a large labeled dataset and considerable computational resources. Also, it is difficult to understand the working…
Recent advancements in learned index structures propose replacing existing index structures, like B-Trees, with approximate learned models. In this work, we present a unified benchmark that compares well-tuned implementations of three…
Several studies have so far investigated transport properties of strongly correlated systems. Interesting features of these materials are the lack of resistivity saturation well beyond the Mott-Ioffe-Regel limit and the scaling of the…
We present nonlinear photonic circuit models for constructing programmable linear transformations and use these to realize a coherent Perceptron, i.e., an all-optical linear classifier capable of learning the classification boundary…
Neural network properties are considered in the case of the interconnection tensor rank being higher than two. This sort of interconnection tensor occurs in realization of crossbar-based neural networks. It is intrinsic for a crossbar…
Characterizing the relation between weight structure and input/output statistics is fundamental for understanding the computational capabilities of neural circuits. In this work, I study the problem of storing associations between analog…