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We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Neural circuits are able to perform computations under very diverse conditions and requirements. The required computations impose clear constraints on their fine-tuning: a rapid and maximally informative response to stimuli in general…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
This paper introduces the \textit{truncator} map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify…
Binary Neural Networks (BNNs) significantly reduce computational complexity and memory usage in machine and deep learning by representing weights and activations with just one bit. However, most existing training algorithms for BNNs rely on…
The effect of dipolar and exchange interactions within pairs of paramagnetic electronic states on Pauli-blockade-controlled spin-dependent transport and recombination rates during magnetic resonant spin excitation is studied numerically…
Current artificial neural networks are trained with parameters encoded as floating point numbers that occupy lots of memory space at inference time. Due to the increase in the size of deep learning models, it is becoming very difficult to…
Binding energy is a fundamental thermodynamic property that governs molecular interactions, playing a crucial role in fields such as healthcare and the natural sciences. It is particularly relevant in drug development, vaccine design, and…
Binary neural networks have attracted tremendous attention due to the efficiency for deploying them on mobile devices. Since the weak expression ability of binary weights and features, their accuracy is usually much lower than that of…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
This paper proposes a neuronal circuitry layout and synaptic plasticity principles that allow the (pyramidal) neuron to act as a "combinatorial switch". Namely, the neuron learns to be more prone to generate spikes given those combinations…
Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task related neural dynamics we study trained Recurrent Neural Networks. We develop a Mean Field Theory for Reservoir Computing…
We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…
Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed…
A natural orbital functional for electronic systems with any value of the spin is proposed. This energy functional is based on a new reconstruction for the two-particle reduced density matrix (2RDM) of the multiplet, that is, of the mixed…
Maintaining stable internal representations of continuous variables is fundamental for effective robotic control. Continuous attractor networks provide a biologically inspired mechanism for encoding such variables, yet neuromorphic…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non- canonical transformations in general also change the statistics of the operators involved. In…
This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep…
Convolutional neural networks have recently achieved significant breakthroughs in various image classification tasks. However, they are computationally expensive,which can make their feasible mplementation on embedded and low-power devices…