Related papers: Continuous transition from the extensive to the no…
Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…
This paper introduces a class of non-linear and continuous-time opinion dynamics model with additive noise and state dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power…
There are multiple explanations for stylized facts in high-frequency trading, including adaptive and informed agents, many of which have been studied through agent-based models. This paper investigates an alternative explanation by…
We present a new framework for modeling the statistical behavior of both fully developed turbulence and short-term dynamics of financial markets based on the nonextensive thermostatistics proposed by Tsallis. We also show that intermittency…
The rapidly growing field of network analytics requires data sets for use in evaluation. Real world data often lack truth and simulated data lack narrative fidelity or statistical generality. This paper presents a novel, mixed-membership,…
We study a simple model of how social behaviors, like trends and opinions, propagate in networks where individuals adopt the trend when they are informed by threshold $T$ neighbors who are adopters. Using a dynamic message-passing…
Using the minority game as a model for competition dynamics, we investigate the effects of inter-agent communications on the global evolution of the dynamics of a society characterized by competition for limited resources. The agents…
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or differential equations. We derive a system of evolution…
Queueing theory has been recently proposed as a framework to model the heavy tailed statistics of human activity patterns. The main predictions are the existence of a power-law distribution for the interevent time of human actions and two…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
We study a simple but compelling model of $n$ interacting agents via time-dependent, unidirectional communication. The model finds wide application in a variety of fields including synchronization, swarming and distributed decision making.…
We introduce an agent-based acquaintance model in which social links are created by processes in which there is no explicit homophily. In spite of the homogeneous nature of the social interactions, highly-clustered social networks can…
The question how social norms can emerge from microscopic interactions between individuals is a key problem in social sciences to explain collective behavior. In this paper we propose an agent-based model to show that randomly distributed…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
In this work, we investigate a simple nonequilibrium system with many interconnected, open subsystems, each exchanging a globally conserved resource with an external reserve. The system is represented by a random graph, where nodes…
In this paper we present a new derivation of the $H$-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we…
This paper studies deterministic consensus networks with discrete-time dynamics under persistent flows and non-reciprocal agent interactions. An arc describing the interaction strength between two agents is said to be persistent if its…
Tsallis' non-extensive entropy $S_q$ enables us to treat both a power and exponential evolutions of underlying microscopic dynamics on equal footing by adjusting the variable entropic index $q$ to proper one $q^*$. We propose an alternative…
We constructed a model that evolved from a non-equilibrium state to an equilibrium state. The model only needs two basic coefficients, including self-similar coefficients and non-equilibrium coefficients. The coefficients of the model can…