Conditional ages and residual service times in the M/G/1 queue

In the article we study the M/G/1 queue, and collect results on the age, residual, and length of service, conditional on the number of customers present in the system. Special attention is given to the M/M/1 queue

Amplified erosion above waterfalls and oversteepened bedrock reaches

None of the conventional bedrock erosion laws can predict incision immediately upslope of a waterfall lip where the flow is accelerating toward a freefall. Considering the expected increase in flow velocity and shear stress at the lip of a waterfall, we determine erosion amplification at a waterfall lip as [equation], where [equation] is the erosion rate at the upstream end of the flow acceleration zone above a waterfall, Fr is the Froude number at this setting, and n ranges between 0.5–1.7. This amplification expression suggests that erosion at the lip could be as much as 2–5 times higher relative to erosion at a normal setting with identical hydraulic geometry. Utilizing this erosion amplification expression in numerical simulations, we demonstrate its impact on reach-scale morphology above waterfalls. Amplified erosion at the lip of a waterfall can trigger the formation of an oversteepened reach whose length is longer than the flow acceleration zone, provided incision wave velocity (Vi) at the upstream edge of the flow acceleration zone is higher than the retreat velocity of the waterfall face. Such an oversteepened reach is expected to be more pronounced when Vi increases with increasing slope. The simulations also suggest that oversteepening can eventually lead to steady state gradients adjacent to a waterfall lip provided Vi decreases with increasing slope. Flow acceleration above waterfalls can thus account, at least partially, for prevalent oversteepened bedrock reaches above waterfalls. Using the cosmogenic isotope Cl-36, we demonstrate that incision wave velocity upstream of a waterfall at the Dead Sea western escarpment is probably high enough for freefall-induced oversteepening to be feasible

A PCP Characterization of AM

We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP Theorem for NP. Similar characterizations have been given for higher levels of the Polynomial Hierarchy, and for PSPACE; however, we suggest that the result for AM might be of particular significance for attempts to derandomize this class. To test this notion, we pose some `Randomized Optimization Hypotheses' related to our stochastic CSPs that (in light of our result) would imply collapse results for AM. Unfortunately, the hypotheses appear over-strong, and we present evidence against them. In the process we show that, if some language in NP is hard-on-average against circuits of size 2^{Omega(n)}, then there exist hard-on-average optimization problems of a particularly elegant form. All our proofs use a powerful form of PCPs known as Probabilistically Checkable Proofs of Proximity, and demonstrate their versatility. We also use known results on randomness-efficient soundness- and hardness-amplification. In particular, we make essential use of the Impagliazzo-Wigderson generator; our analysis relies on a recent Chernoff-type theorem for expander walks.Comment: 18 page

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.Comment: 83 page

Field evidence for the influence of weathering on rock erodibility and channel form in bedrock rivers

Erosion processes in bedrock-floored rivers shape channel cross-sectional geometry and the broader landscape. However, the influence of weathering on channel slope and geometry is not well understood. Weathering can produce variation in rock erodibility within channel cross-sections. Recent numerical modeling results suggest that weathering may preferentially weaken rock on channel banks relative to the thalweg, strongly influencing channel form. Here, we present the first quantitative field study of differential weathering across channel cross-sections. We hypothesize that average cross-section erosion rate controls the magnitude of this contrast in weathering between the banks and the thalweg. Erosion rate, in turn, is moderated by the extent to which weathering processes increase bedrock erodibility. We test these hypotheses on tributaries to the Potomac River, Virginia, with inferred erosion rates from similar to 0.1m/kyr to \u3e0.8m/kyr, with higher rates in knickpoints spawned by the migratory Great Falls knickzone. We selected nine channel cross-sections on three tributaries spanning the full range of erosion rates, and at multiple flow heights we measured (1) rock compressive strength using a Schmidt hammer, (2) rock surface roughness using a contour gage combined with automated photograph analysis, and (3) crack density (crack length/area) at three cross-sections on one channel. All cross-sections showed significant (

Circumventing antivector immunity: potential use of nonhuman adenoviral vectors

Adenoviruses are efficient gene delivery vectors based on their ability to transduce a wide variety of cell types and drive high-level transient transgene expression. While there have been advances in modifying human adenoviral (HAdV) vectors to increase their safety profile, there are still pitfalls that need to be further addressed. Preexisting humoral and cellular immunity against common HAdV serotypes limits the efficacy of gene transfer and duration of transgene expression. As an alternative, nonhuman AdV (NHAdV) vectors can circumvent neutralizing antibodies against HAdVs in immunized mice and monkeys and in human sera, suggesting that NHAdV vectors could circumvent preexisting humoral immunity against HAdVs in a clinical setting. Consequently, there has been an increased interest in developing NHAdV vectors for gene delivery in humans. In this review, we outline the recent advances and limitations of HAdV vectors for gene therapy and describe examples of NHAdV vectors focusing on their immunogenicity, tropism, and potential as effective gene therapy vehicles

Cortical Factor Feedback Model for Cellular Locomotion and Cytofission

Eukaryotic cells can move spontaneously without being guided by external cues. For such spontaneous movements, a variety of different modes have been observed, including the amoeboid-like locomotion with protrusion of multiple pseudopods, the keratocyte-like locomotion with a widely spread lamellipodium, cell division with two daughter cells crawling in opposite directions, and fragmentations of a cell to multiple pieces. Mutagenesis studies have revealed that cells exhibit these modes depending on which genes are deficient, suggesting that seemingly different modes are the manifestation of a common mechanism to regulate cell motion. In this paper, we propose a hypothesis that the positive feedback mechanism working through the inhomogeneous distribution of regulatory proteins underlies this variety of cell locomotion and cytofission. In this hypothesis, a set of regulatory proteins, which we call cortical factors, suppress actin polymerization. These suppressing factors are diluted at the extending front and accumulated at the retracting rear of cell, which establishes a cellular polarity and enhances the cell motility, leading to the further accumulation of cortical factors at the rear. Stochastic simulation of cell movement shows that the positive feedback mechanism of cortical factors stabilizes or destabilizes modes of movement and determines the cell migration pattern. The model predicts that the pattern is selected by changing the rate of formation of the actin-filament network or the threshold to initiate the network formation