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In open systems, i.e. systems operating in an environment that they cannot control and with components that may join or leave, behaviors can arise as side effects of intensive components interaction. Finding ways to understand and design…
We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizes the well-studied beta model for random graphs, which…
In this letter we derive the Cornell confining potential in a theory of interacting Abelian gauge vector and massive Kalb-Ramond tensor. The Kalb-Ramond mass is instrumental to obtain the linear confining behavior of the potential at large…
This paper studies inference in models of discrete choice with social interactions when the data consists of a single large network. We provide theoretical justification for the use of spatial and network HAC variance estimators in applied…
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary…
A general definition of the model-space effective interaction is given. The energy-independent effective hamiltonians derived in a time-independent way are classified systematically.
We perform the Monte Carlo study of the SU(3) non-Abelian Higgs model. We discuss phase structure and non-Abelian vortices by gauge invariant operators. External magnetic fields induce non-Abelian vortices in the color-flavor locked phase.…
A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…
It is shown that a gauged nonlinear $O(3)$ sigma model with anomalous magnetic moment interaction in $2+1$ dimensions is exactly integrable for static, self-dual field configurations. The matter fields are exactly equivalent to those of the…
We describe a constraint analysis for the interaction of the vector-meson octet with the baryon octet. Applying Dirac's Hamiltonian method, we verify that the standard interaction in terms of two independent SU(3) structures is consistent…
Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we propose a method to detect non-commutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects…
It is proposed that a non-Abelian adjoint two-form in BF type theories transform inhomogeneously under the gauge group. The resulting restrictions on invariant actions are discussed. The auxiliary one-form which is required for maintaining…
When modeling a social dynamics with an agent-oriented approach, researchers have to describe the structure of interactions within the population. Given the intractability of extensive network collecting, they rely on random network…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Many real-world applications of language models (LMs), such as writing assistance and code autocomplete, involve human-LM interaction. However, most benchmarks are non-interactive in that a model produces output without human involvement.…
The non-Abelian tensor gauge fields take value in extended Poincar\'e algebra. In order to define the invariant Lagrangian we introduce a vector variable in two alternative ways: through the transversal representation of the extended…
The formalism of Kohn and Sham uses a specific (model) hamiltonian which highly simplifies the many-electron problem to that of noninteracting fermions. The theorem of Hohenberg and Kohn tells us that, for a given ground state density, this…
Abelian Chern-Simons gauge theory is known to possess a `$S$-self-dual' action where its coupling constant $k$ is inverted {\it i.e.} $k \leftrightarrow {1 \over k}$. Here a vector non-abelian duality is found in the pure non-abelian…
Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not…
Large Language Models (LLMs) have demonstrated their ability to replicate human behaviors across a wide range of scenarios. However, their capability in handling complex, multi-character social interactions has yet to be fully explored,…