We show that on every Ramanujan graph G, the simple random walk exhibits cutoff: when G has n vertices and degree d, the total-variation distance of the walk from the uniform distribution at time t = d d−2 logd−1 n + s √ logn is asymptotically P(Z > c s) where Z is a standard normal variable and c = c(d) is an explicit constant. Furthermore, for all 1 ≤ p ≤ ∞, d-regular Ramanujan graphs minimiz...

Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsystem critical to the OSC scheme is the focusing optics used to image radiati...

Undulator radiation from synchrotron light sources must be transported down a beam line the source to sample. A partially coherent photon may represented in phase space using Wigner function, and its transport use some similar techniques that are familiar particle transport. We describe this process case is composed of linear focusing defocusing sections as well apertures. present compact repre...

We will define a problem regarding locating a simple random walk on a graph, and give bounds for the optimal solution on toruses of dimension 2,3. 1 Hunting a Random Walker There are several natural variants of the hunting problem, here is one. A bird performs a random walk on a graph. At each step a hunter picks a vertex and either catches the bird or gets to see if the bird visited there befo...

In the purpose to provide further information in respect of the relationship between metabolism and post partum (PP) ovarian activity resumption in dairy cows, the aim of the present study was to characterize the energy balance (EB) and leptin, NEFA and IGF-I plasma levels in Swedish Red and White (SRW) cows with and without ovarian activity re-initiation within 7 weeks PP. The study was conduc...

The Baltic Sea is a unique and sensitive brackish-water ecosystem vulnerable to damage from shipping activities. Despite high levels of maritime safety in the area, there continued risk oil spills associated harmful environmental impacts. Achieving common situational awareness between spill response decision makers other actors, such as merchant vessel Vessel Traffic Service center operators, a...

Grain futures contracts that permit physical delivery do so through an exchange of instruments. Because instruments can be held indefinitely, extant research shows assign inflexible and low storage rates relative to the market price facilitate basis nonconvergence. In response notable episode nonconvergence in mid- late-2000s, Chicago Mercantile Exchange (CME) Group introduced variable rate (VS...