Related papers: Inverse problems in spin models
We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
With the completion of human genome mapping, the focus of scientists seeking to explain the biological complexity of living systems is shifting from analyzing the individual components (such as a particular gene or biochemical reaction) to…
A new lattice model of interacting electrons is presented. It can be viewed as a classical Hubbard model in which the energy associated to electron itinerance is proportional to the total number of possible electron jumps. Symmetry…
Discussions of the hippocampus often focus on place cells, but many neurons are not place cells in any given environment. Here we describe the collective activity in such mixed populations, treating place and non-place cells on the same…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
Spin states of two-dimensional Wigner clusters are considered at low temperatures, when all electrons are in ground coordinate states. The spin subsystem behavior is determined by antiferromagnetic exchange integrals. The spin states in…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments…
Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the…
Humans and animals exhibit a range of interesting behaviors in dynamic environments, and it is unclear how our brains actively reformat this dense sensory information to enable these behaviors. Experimental neuroscience is undergoing a…
Collective electronic fluctuations in correlated materials give rise to various important phenomena, such as existence of the charge ordering, superconductivity, Mott insulating and magnetic phases, plasmon and magnon modes, and other…
An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…
Network psychometrics conceptualises psychological constructs as emergent properties of systems of interacting variables. Energy-based probabilistic models have gained popularity as models of these interactions, but their psychometric…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
In a statistical physics context, inverse problems consist in determining microscopic interactions such that a system reaches a predefined collective state. A complex collective state may be prescribed by specifying the overlap distribution…
The Ising model, originally developed for understanding magnetic phase transitions, has become a cornerstone in the study of collective phenomena across diverse disciplines. In this review, we explore how Ising and Ising-like models have…
In this paper we study the macroscopic behavior of the inertial spin (IS) model. This model has been recently proposed to describe the collective dynamics of flocks of birds, and its main feature is the presence of an auxiliary dynamical…
Network models are used to study interconnected systems across many physical, biological, and social disciplines. Such models often assume a particular network-generating mechanism, which when fit to data produces estimates of…
For any system, whether physical or non-physical, knowledge of the form and strength of inter-individual interactions is a key-information. In an approach based on statistical physics one needs to know the interaction Hamiltonian. For…