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The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of…

The grid firing patterns are thought to provide an efficient intrinsic metric capable of supporting universal spatial metric for mammalian spatial navigation in all environments. However, whether spatial representations of grid cells in the…

Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference:…

We have investigated the interrelation between the spin glasses and the structural glasses. Spin glasses in this case are random magnets without reflection symmetry (e.g. $p$ - spin interaction spin glasses and Potts glasses) which contain…

In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the…

The brain achieves stability and plasticity in a topologically complex, shifting world through Metric-Topology Factorization (MTF), separating discrete topological indexing for context selection from continuous metric condensation for local…

We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…

Large-scale functional networks have been extensively studied using resting state functional magnetic resonance imaging. However, the pattern, organization, and function of fine-scale network activity remain largely unknown. Here we…

From the sandpoint of neural network dynamics we consider dynamical system of special type pesesses gradient (symmetric) and Hamiltonian (antisymmetric) flows. The conditions when Hamiltonian flow properties are dominant in the system are…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

Spin-orbit coupling in organic crystals is responsible for many spin-relaxation phenomena, going from spin diffusion to intersystem crossing. With the goal of constructing effective spin-orbit Hamiltonians to be used in multiscale…

Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related…

The nature of dynamics of opinion formation modeled as a decision-by-majority process in complex networks is investigated using eigenmode analysis. Hamiltonian of the system is defined, and estimated by eigenvectors of the adjacency matrix…

We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation…

Structured internal representations (cognitive maps) shape cognition, from imagining the future and counterfactual past, to transferring knowledge to new settings. Our understanding of how such representations are formed and maintained in…

Toroidal vortex is a kind of novel and exotic structured light with potential applications in photonic topology and quantum information. Here, we present the study on high harmonic generation (HHG) from the interaction of the intense…

Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…

In systems where one coordinate undergoes periodic oscillation, the net displacement in any other coordinate over a single period is shown to be given by differentiation of the action integral associated with the oscillating coordinate.…

We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…

We consider ultracold matter of spin-2 atoms in optical lattices. We derive an effective Hamiltonian for the studies of spin ordering in Mott states and investigate hyperfine spin correlations. Particularly, we diagonalize the Hamiltonian…