Related papers: Statistical Field Theory and Neural Structures Dyn…
We present a unified field-theoretic framework for the dynamics of activity and connectivity in interacting neuronal systems. Building upon previous works, where a field approach to activity--connectivity dynamics, formation of collective…
This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the…
This paper elaborates on the effective field theory for the connectivity field previously introduced in ([7]). We demonstrate that dynamic interactions among connectivities induce modifications in the background state. These modifications…
We continue our study of a field formalism for large sets of interacting neurons, together with their connectivity functions. Expanding upon the foundation laid in ([9]), we formulate an effective formalism for the connectivity field in the…
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…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these…
A rich variety of amorphous solids are found in nature and technology, including ones formed via the vulcanization of long, flexible molecules. A special class -- those featuring a wide gap between the long timescales over which constraints…
In a previous work, we applied a field formalism to analyze capital allocation and accumulation within a network of investors and firms. In that framework, financial agents could invest in firms or in other investors, and banks-introduced…
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
Brain-computer interfaces surged extraordinary developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This…
In a series of precedent papers, we have presented a comprehensive methodology, termed Field Economics, for translating a standard economic model into a statistical field-formalism framework. This formalism requires a large number of…
Nonlinear dynamical modeling of interaction between automatic and conscious processes in the human brain is considered in terms of the quaternion fields. The interaction is due, particularly, to the nonlinear firing rate of neurons.…
Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and…
Activity in the human brain moves between diverse functional states to meet the demands of our dynamic environment, but fundamental principles guiding these transitions remain poorly understood. Here, we capitalize on recent advances in…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Field theories for complex systems traditionally focus on collective behaviors emerging from simple, reciprocal pairwise interaction rules. However, many natural and artificial systems exhibit behaviors driven by microscopic decision-making…