相关论文: Understanding visual map formation through vortex …
Simplified models are a necessary steppingstone for understanding collective neural network dynamics, in particular the transitions between different kinds of behavior, whose universality can be captured by such models, without prejudice.…
Over the last few decades, a lot of progress has been made in understanding different aspects of the brain's ability to form abstract representations, but a specific mechanism for how they are created and used remains to emerge. Here, we…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
The entanglement Hamiltonian $H_E$, defined through the reduced density matrix of a subsystem $\rho_A=\exp(-H_E)$, is an important concept in understanding the nature of quantum entanglement in many-body systems and quantum field theories.…
To interpret our surroundings, the brain uses a visual categorization process. Current theories and models suggest that this process comprises a hierarchy of different computations that transforms complex, high-dimensional inputs into…
Exploring the deep insights into localization, disorder, and wave transport in non-Hermitian systems is an emergent area of research of relevance in different areas of physics. Engineered photonic lattices, with spatial regions of optical…
The proposed analysis of the currently available experimental results concerning the neural cell activity in the brain area known as hippocampus suggests a particular mechanism of spatial information and memory processing. Below it is…
A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins),…
A compact analytic model is proposed to describe the combined orientation preference (OP) and ocular dominance (OD) features of simple cells and their layout in the primary visual cortex (V1). This model consists of three parts: (i) an…
Most computational accounts of cognitive maps assume that stability is achieved primarily through sensory anchoring, with self-motion contributing to incremental positional updates only. However, biological spatial representations often…
In this paper, we present a new leader-follower type solution to the formation maneuvering problem for multiple, nonholonomic wheeled mobile robots. The solution is based on the graph that models the coordination among the robots being a…
The effective spin Hamiltonian method is widely adopted to simulate and understand the behavior of magnetism. However, the magnetic interactions of some systems, such as itinerant magnets, are too complex to be described by any explicit…
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
We investigate global stability and dynamics of large ecological networks by classical methods of the dynamical system theory, including Hamiltonian methods, and averaging. Our analysis exploits the network topological structure, namely,…
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
We present the results of our theoretical study on the effects of geometrical frustration and the interplay between spin and orbital degrees of freedom in vanadium spinel oxides $A$V$_2$O$_4$ ($A$ = Zn, Mg or Cd). Introducing an effective…
Spatial learning across many species is impaired by lesions in the hippocampus, a subcortical brain structure whose cellular composition changes substantially over its 5 to 6 week lifetime from mainly excitatory neurons during development…