We define a family of functions F from a domain U to a range R to be dispersing if for every set S ⊆ U of a certain size and random h ∈ F , the expected value of |S| − |h[S]| is not much larger than the expectation if h had been chosen at random from the set of all functions from U to R. We give near-optimal upper and lower bounds on the size of dispersing families and present several applicati...

Research on the effect of implicit and explicit instruction on developing learners’ explicit knowledge by the use of measures of explicit knowledge abounds in the literature. However, measuring learners’ implicit knowledge employing fine-grained measures has rarely been the concern of researchers in the field. Therefore, the present study is an attempt to scrutinize the effectiveness of implici...

As a generalization of the classical Metric Scaling solution for a nite set of points, a countable set of uncorrelated random variables is obtained from an arbitrary continuous random variable X. The properties of these variables allow us to regard them as Principal Axes for X with respect to the distance function d(u; v) = p ju ? vj. Explicit results are obtained for uniform and negative expon...

We consider populations represented by random collections of real-valued points, and explore their statistical resilience to random perturbations-seeking populations whose statistics remain qualitatively unchanged by the action of arbitrary random perturbations of a certain type. Studying a general physical perturbation scheme, we obtain an explicit characterization of statistically resilient p...

Vertices of an affiliation network are linked to features and two vertices are declared adjacent whenever they share a common feature. We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks. We establish the asymptotic degree distribution and provide explicit asymptotic formulas for assortativity and clustering coefficients showing how these edge...

Suppose that A1, . . . , AN are independent random matrices whose atoms are iid copies of a random variable ξ of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when ξ is gaussian then N−1 log ‖AN . . . A1‖ converges to a non-random limit. We extend this result to more general matrices with explicit rate of convergence. Our method relies on a simple...

A uniform random vector over a simplex is generated. An explicit expression for the first moment of its largest spacing is derived. The result is used in a proposed diagnostic tool which examines the validity of random number generators. It is then shown that the first moment of the largest uniform spacing is related to the dependence measure of random vectors following any extreme value distri...

In particle-in-cell (PIC) simulation, errors in space charge forces are of random character. It results in an unphysical increase of effective beam emittance, even while symplectic integrator is used. To establish quantitative measure of this effect on beam dynamics, an analytical model of equilibrium beam affected by random errors in space charge field calculations is considered. An explicit e...

It is shown in this note that the one-term Edgeworth expansion for the standardized sample mean of n independent lattice random vectors when perturbed by a random variable (l/&)U is the same as in the strongly non-lattice case, where U is a bounded random variable depending only on a basis of the associated minimal lattice. An explicit form of U is given. Some applications to the student&d stat...

In this paper, we derive explicit formulas for the surface averaged first-exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a nontrivial potential landscape. We also compute quantities of interest for modeling surface reactions and other dynamic processes, such as the residence time in a subvolume, the joint...