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We introduce a natural variant of the parallel chip-firing game, called the diffusion game. Chips are initially assigned to vertices of a graph. At every step, all vertices simultaneously send one chip to each neighbour with fewer chips. As…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
When there is no independence, abnormal observations may have a tendency to appear in clusters instead of scattered along the time frame. Identifying clusters and estimating their size are important problems arising in statistics of…
Selection of the preferred classical set of states in the process of decoherence -- so important for cosmological considerations -- is discussed with an emphasis on the role of information loss and entropy. {\it Persistence of correlations}…
A rigorous proof of a theorem on the coexistence of smooth Lyapunov function and smooth planar dynamical system with one arbitrary limit cycle is given, combining with a novel decomposition of the dynamical system from the perspective of…
The HCI community commonly evaluates decision support systems based on whether they improve task performance or promote appropriate user reliance. In this work, we look beyond decision outcomes to examine the process through which users…
The replicator equation in evolutionary game theory describes the change in a population's behaviors over time given suitable incentives. It arises when individuals make decisions using a simple learning process - imitation. A recent…
A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is…
Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
In the long-time limit, an open quantum system coupled to a dissipative environment is believed to lose its coherence without driving or measurement. Counterintuitively, we provide a necessary condition on trapping the coherence of a…
This paper investigates rate-independent systems (RIS), where the dissipation functional depends not only on the rate but also on the history of the state. The latter is expressed in terms of an integral operator. We establish an existence…
Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a…
Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving…
We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
We study the cycles generated by the chip firing game associated with n-cube orientations. We show the existence of the cycles generated by parallel evolutions of even lengths from 2 to $2^n$ on $H_n$ (n >= 1), and of odd lengths different…
The erraticity in the random-cascading $\alpha$ model is revisited. It is found that in contrary to the previous expectation, even in the pure single-$\alpha$ random-cascading model without putting in any particle there exists erraticity…
This paper studies scenarios of cyclic dominance in a coevolutionary spatial model in which game strategies and links between agents adaptively evolve over time. The Optional Prisoner's Dilemma (OPD) game is employed. The OPD is an extended…
A recent experiment suggests that neural circuits may alternatively implement continuous or discrete attractors, depending on the training set up. In recurrent neural network models, continuous and discrete attractors are separately modeled…