相关论文: How long is the Chaos Game?

A continuous-state branching process in varying environments is constructed by the pathwise unique solution to a stochastic integral equation driven by time-space noises. The process arises naturally in the limit theorem of Galton--Watson…

We give an algorithm for solving stochastic parity games with almost-sure winning conditions on {\it lossy channel systems}, under the constraint that both players are restricted to finite-memory strategies. First, we describe a general…

Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this…

In 1964 Shapley devised a family of games for which fictitious play fails to converge to Nash equilibrium. The games are two-player non-zero-sum with 3 pure strategies per player. Shapley assumed that each player played a specific pure…

The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…

We present the control of the high-dimensional chaos, with possibly a large number of positive Lyapunov-exponents, of unknown time-delay systems to an arbitrary goal dynamics. We give an existence-and-uniqueness theorem for the control…

For systems that involve particle production through branching processes the concept of chaos is explored. The measures that can describe their behaviors are investigated. Monte Carlo simulation is used to generate events according to…

Procedural generation is used across game design to achieve a wide variety of ends, and has led to the creation of several game subgenres by injecting variance, surprise or unpredictability into otherwise static designs. Information games…

The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…

In this paper, we propose a new efficient algorithm to compute the value function for zero-sum stopping games featuring two players with opposing interests. This can be seen as a game version of the ''forward algorithm'' for (one-player)…

Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…

The presence of a period-doubling cascade in dynamical systems that depend on a parameter is one of the basic routes to chaos. It is rarely mentioned that there are virtually always infinitely many cascades whenever there is one. We report…

Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…

Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of…

Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by blocks of $N_{k}$ symbols also within the alphabet (with…

Dynamical systems in nature such as fluid flows, heart beat patterns, rainfall variability, stock market price fluctuations, etc. exhibit selfsimilar fractal fluctuations on all scales in space and time. Power spectral analyses of fractal…

We present a general prediction scheme of failure times based on updating continuously with time the probability for failure of the global system, conditioned on the information revealed on the pre-existing idiosyncratic realization of the…

The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…

This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for…

This paper focuses on a class of continuous-time controlled Markov chains with time-inconsistent and distribution-dependent cost functional (in some appropriate sense). A new definition of time-inconsistent distribution-dependent…