Nearest Neighbor (NN) searching is a challenging problem in data management and has been widely studied in data mining, pattern recognition and computational geometry. The goal of NN searching is efficiently reporting the nearest data to a given object as a query. In most of the studies both the data and query are assumed to be precise, however, due to the real applications of NN searching, suc...

consider search designs for searching one nonzero 2- or 3-factor interaction under the search linear model. in the noisy case, search probability is given by shirakura et al. (ann. statist. 24(6) (1996) 2560). in this paper some new properties of the searching probability are presented. new properties of the search probability enable us to compare designs, which depend on an unknown parameter ?...

Consider search designs for searching one nonzero 2- or 3-factor interaction under the search linear model. In the noisy case, search probability is given by Shirakura et al. (Ann. Statist. 24(6) (1996) 2560). In this paper some new properties of the searching probability are presented. New properties of the search probability enable us to compare designs, which depend on an unknown parameter ?...

Consider a C vector field together with an ergodic invariant probability that has l nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of l differential equations which is a reduced form of Liao’s “standard system”. We show that the Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given ...

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for n × n win-lose-draw games (i.e. (−1, 0, 1) matrix games) nonzero probabilities smaller than n are never needed. We also construct an explicit n × n win-lose game such that the unique optimal strategy uses a nonzero probability as small as n. This is done by constructing an explicit (−1, ...

It is shown that determining whether a quantum computation has a nonzero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation.

We compute exactly the statistics of number records in a discrete-time random walk model on line where walker stays at given position with nonzero probability $0\leq p \leq 1$, while complementary $1-p$, it jumps to new jump length drawn from continuous and symmetric distribution $f_0(\eta)$. have shown that, for arbitrary $p$, up step $N$ is completely universal, i.e., independent $f_0(\eta)$ ...

Consider a two-person general-sum game on n × n payoff random matrices A and B with iid continuous entries, for large n. It is shown that the probability that there exists a pure strategy Nash equilibrium that is not pure Pareto optimal remains bounded away from 0 and 1 as n increases. We also consider the number of mixed strategy Nash equilibria: It is shown that for a mixed strategy Nash equi...

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum channel. Error correction and unambiguous error correction with nonzero probability are discussed in terms of unambiguous unitary quantum channels. We not o...