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A representative investor generates realistic and complex security price paths by following this trading strategy: if, a few ticks ago, the market asset had two consecutive upticks or two consecutive downticks, then sell, and otherwise buy.…
Individual traffic significantly contributes to climate change and environmental degradation. Therefore, innovation in sustainable mobility is gaining importance as it helps to reduce environmental pollution. However, effects of new ideas…
Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying…
Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of…
Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
The existence of stylized facts in financial data has been documented in many studies. In the past decade the modeling of financial markets by agent-based computational economic market models has become a frequently used modeling approach.…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We propose a discrete traffic flow model with discrete time. Continuum limit of this model is equivalent to the optimal velocity model. It has also an ultradiscrete limit and a piecewise-linear type of traffic flow model is obtained. Both…
We develop a modeling technique based on interpreted systems in order to verify temporal-epistemic properties over access control policies. This approach enables us to detect information flow vulnerabilities in dynamic policies by verifying…
In this paper, we present a novel fraud-proof mechanism that achieves fast finality and, when combined with optimistic execution, enables real-time transaction processing. State-of-the-art optimistic rollups typically adopt a 7-day…
Our goal is to solve both problems of adverse selection and moral hazard for multi-agent projects. In our model, each selected agent can work according to his private "capability tree". This means a process involving hidden actions, hidden…
Understanding and quantifying the dynamics of disordered out-of-equilibrium models is an important problem in many branches of science. Using the dynamic cavity method on time trajectories, we construct a general procedure for deriving the…
What networks can form and persist when agents are self-interested? Can such networks be efficient? A substantial theoretical literature predicts that the only networks that can form and persist must have very special shapes and that such…
We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…
Modeling Internet growth is important both for understanding the current network and to predict and improve its future. To date, Internet models have typically attempted to explain a subset of the following characteristics: network…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…
Recently, in order to explore the mechanism behind wealth or income distribution, several models have been proposed by applying principles of statistical mechanics. These models share some characteristics, such as consisting of a group of…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
We present a new efficient computational approach for time-dependent first-order Hamilton-Jacobi-Bellman PDEs. Since our method is based on a time-implicit Eulerian discretization, the numerical scheme is unconditionally stable, but…