Related papers: The Chaos Within Sudoku
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
Challenges for physical solitaire puzzle games are typically designed in advance by humans and limited in number. Alternatively, some games incorporate rules for stochastic setup, where the human solver randomly sets up the game board…
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such…
Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations…
The conditions for a Runge--Kutta method to be of order $p$ with $p\ge 5$ for a scalar non-autonomous problem are a proper subset of the order conditions for a vector problem. Nevertheless, Runge--Kutta methods that were derived…
Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…
The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed…
In this paper, a new concept, i.e. ultra-chaos, is proposed for the first time. Unlike a normal-chaos, statistical properties such as the probability density functions (PDF) of an ultra-chaos are sensitive to tiny disturbances. We…
Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. We derive conditions…
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We explore the quantum chaos of the coadjoint orbit action. We study quantum fluctuation around a saddle point to evaluate the soft mode contribution to the out-of-time-ordered correlator. We show that the stability condition of the…
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we continue the study of a prequel paper on the pile shuffle and its capabilities as a sorting device. We study two sort feasibility problems of…
Partial rigidity is a quantitative notion of recurrence and provides a global obstruction which prevents the system from being strongly mixing. A dynamical system $(X, \mathcal{X}, \mu, T)$ is partially rigid if there is a constant $\delta…
In this letter, we show that coherent structures are related to folds of horseshoes which are present in chaotic systems. We develop techniques that allow us to construct coherent structures by manipulating folds in three prototypical…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…