相关论文: A note on the Screaming Toes game
A derangement is a permutation with no fixed point, and a nonderangement is a permutation with at least one fixed point. There is a one-term recurrence for the number of derangements of $n$ elements, and we describe a bijective proof of…
Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such…
We explore the cycle types of a class of biased random derangements, described as a random game played by some children labeled $1,\cdots,n$. Children join the game one by one, in a random order, and randomly form some circles of size at…
Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting…
Parrondo's paradox refers to the counter-intuitive situation where a winning strategy results from a suitable combination of losing ones. Simple stochastic games exhibiting this paradox have been introduced around the turn of the…
The Minority Game (MG) behaves as a stochastically perturbed deterministic system due to the coin-toss invoked to resolve tied strategies. Averaging over this stochasticity yields a description of the MG's deterministic dynamics via mapping…
The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…
We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online video-game (http://arora.ccs.neu.edu) where players are…
Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…
A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the…
We compare complex networks built from the game of go and obtained from databases of human-played games with those obtained from computer-played games. Our investigations show that statistical features of the human-based networks and the…
The study of environmentally induced superselection and of the process of decoherence was originally motivated by the search for the emergence of classical behavior out of the quantum substrate, in the macroscopic limit. This limit, and…
We consider a class of simple one parameter families of interval maps, and we study how metric (resp. topological) entropy changes as the parameter varies. We show that in many cases the entropy displays a semi-regular behaviour, i.e. it is…
A piecewise continuous map for modeling bursting and spiking behaviour of isolated neuron is proposed. The map was created from phenomenological viewpoint. The map demonstrates oscillations, which are qualitatively similar to oscillations…
We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…
We present a quantum implementation of Parrondo's game with randomly switched strategies using 1) a quantum walk as a source of ``randomness'' and 2) a completely positive (CP) map as a randomized evolution. The game exhibits the same…
A derangement of a graph $G=(V,E)$ is an injective function $f:V\to V$ such that for all $v\in V$, $f(v)\neq v$ and $(v,f(v))\in E$. Not all graphs admit a derangement and previous results have characterized graphs with derangements using…
The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…
Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial…
Quantitative measures of randomness in games are useful for game design and have implications for gambling law. We treat the outcome of a game as a random variable and derive a closed-form expression and estimator for the variance in the…