Related papers: Loop interactions and their representations in Foc…
We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of…
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific…
A general description of elastic matter and the long-range elastic interaction is propose. The type of the far-field interaction is determined by the way of breaking in the continuum distribution of the elastic field produced by topological…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
We prove many new results about interacting Fock spaces. We pose many open problems; for most of them we prove that their solutions have no choice but being nontrivial. We ask the kind reader to consult the extended abstract in the paper.
Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more…
Interactions play a key role in understanding objects and scenes, for both virtual and real world agents. We introduce a new general representation for proximal interactions among physical objects that is agnostic to the type of objects or…
Interactions in complex systems are widely observed across various fields, drawing increased attention from researchers. In mathematics, efforts are made to develop various theories and methods for studying the interactions between spaces.…
We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
We consider recurrence versus transience for models of random walks on domains of $\mathbb{Z}^d$, in which monotone interaction enforces domain growth as a result of visits by the walk (or probes it sent), to the neighborhood of domain…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
The total homology of the loop space of the configuration space of ordered distinct n points in R^m has a structure of a Hopf algebra defined by the 4-term relations if m>2. We describe a relation of between the cohomology of this loop…
We study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly…
Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the…
Evolutionary relationships between species are usually represented in phylogenies, i.e. evolutionary trees, which are a type of networks. The terminal nodes of these trees represent species, which are made of individuals and populations…
The approaches to quantum field theories based in the so called loop representation deserved much attention recently. In it, closed curves and holonomies around them play a central role. In this framework the group of loops and the group of…
Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer…
In the context of the coarse-graining of loop quantum gravity, we introduce loopy and tagged spin networks, which generalize the standard spin network states to account explicitly for non-trivial curvature and torsion. Both structures relax…
We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…