For fixed $r\geq 3$ and $n$ divisible by $r$, let ${\mathcal H}={\mathcal H}^r_{n,M}$ be the random $M$-edge $r$-graph on $V=\{1,\ldots ,n\}$; that is, H}$ is chosen uniformly from $M$-subsets of K}:={V \choose r}$ ($:= \{\mbox{$r$-subsets $V$}\}$). Shamir's Problem (circa 1980) asks, roughly, for what $M=M(n)$ likely to contain a perfect matching (that $n/r$ disjoint $r$-sets)? In 2008 Johan...

Experiments in which monkeys have to select or estimate the location of a target are revealing more about the role of the dorsal premotor cortex in decision making.

We discuss Peter Buneman’s suggestion that a fibre connection to the internet — a hub — should be available within every circle enclosing a population of at least 2,000 people (a b-circle). This poses the problem of finding a small set, H, of hubs, such that every b-circle contains a hub. We show that a greedy algorithm does not lead to an optimal set of hubs. Instead it models market forces, w...

Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparis...

It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling be...

The issue of when to intervene in the evolution of a production system is the focus of this study. The interventions take the form of changes to production depending on the current value of the products. Each change incurs a charge representing costs such as physical expansion, overtime or new hiring when production increases and costs such as severance or shut down when production decreases. T...

This paper proposes a target damage calculation method based on the profit-loss value of warhead fragment group. The group is discretized into fan-shaped column dispersion arrangement model, and angle its intersection with combined to establish dynamic density model In addition, function calculate number fragments hitting target’s surface devised. capability matrix constructed according quality...