Mark Kac gave an explicit formula for the expectation of the number, νn(Ω), of zeros of a random polynomial, Pn(z) = n ∑ j=0 ηjz j , in any measurable subset Ω of the reals. Here, η0, . . . , ηn are independent standard normal random variables. In fact, for each n > 1, he obtained an explicit intensity function gn for which Eνn(Ω) = ∫ Ω gn(x)dx. Inspired by that result, Larry Shepp and I found ...

Using ns-2 simulations, this paper evaluates an Adaptive Explicit Congestion Notification (AECN) router. By receiving round-trip time (RTT) source hints from each TCP flow, AECN divides flows into flow groups based on RTT ranges. AECN uses distinct flow group drop probabilities and a mark front scheme to provide higher goodput and better fairness than Random Early Detection (RED) and Explicit C...

Explicit Congestion Notification (ECN) for IP networks has received considerable attention in recent years, and has been shown to improve TCP goodput. Previous studies have centered on scenarios in which TCP with ECN (TCP/ECN) traffic competes with ECN-unaware traffic. This paper presents case studies in which moderately short flows are all ECN-capable, and compare them with the corresponding c...

This project evaluates performance of of TCP RENO under Random Early Detection (RED) and Explicit Congestion Notification (ECN) -based schemes of congestion avoidance. The evaluation is done in a number of Wide Area Network (WAN) scenarios, which are analyzed for throughput, droprate and fairness.

We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series representations for the characteristic function and for the density of a free stable distribution. All of these formulas bear close resemblance to the corresponding expre...

We prove a central limit theorem (CLT) for the product of class random singular matrices related to Hill’s equation studied by Adams–Bloch–Lagarias. The CLT features an explicit formula variance in terms distribution matrix entries and this allows exact calculation some examples. Our proof relies on novel connection theory [Formula: see text]-dependent sequences which also leads interesting pre...

The MCNP5 Monte Carlo code has been frequently used to model HTGRs with explicit geometric representation of fuel compacts or pebbles, including the microscopic fuel kernels within them. The random locations of fuel kernels within each fuel compact or pebble, and of pebbles within the core, however, present difficulties. A new, on-the-fly, stochastic geometry model for MCNP5 has been developed ...

We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree. We give a criterion for the existence of a giant component, which is both necessary and sufficient, and which becomes explicit when f is linear. Otherwise it all...