Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl

Modelling Drosophila motion vision pathways for decoding the direction of translating objects against cluttered moving backgrounds

Decoding the direction of translating objects in front of cluttered moving backgrounds, accurately and efficiently, is still a challenging problem. In nature, lightweight and low-powered flying insects apply motion vision to detect a moving target in highly variable environments during flight, which are excellent paradigms to learn motion perception strategies. This paper investigates the fruit fly Drosophila motion vision pathways and presents computational modelling based on cuttingedge physiological researches. The proposed visual system model features bio-plausible ON and OFF pathways, wide-field horizontal-sensitive (HS) and vertical-sensitive (VS) systems. The main contributions of this research are on two aspects: (1) the proposed model articulates the forming of both direction-selective and direction-opponent responses, revealed as principalfeaturesofmotionperceptionneuralcircuits,inafeed-forwardmanner;(2)italsoshowsrobustdirectionselectivity to translating objects in front of cluttered moving backgrounds, via the modelling of spatiotemporal dynamics including combination of motion pre-filtering mechanisms and ensembles of local correlators inside both the ON and OFF pathways, which works effectively to suppress irrelevant background motion or distractors, and to improve the dynamic response. Accordingly, the direction of translating objects is decoded as global responses of both the HS and VS systems with positive ornegativeoutputindicatingpreferred-direction or null-direction translation.The experiments have verified the effectiveness of the proposed neural system model, and demonstrated its responsive preference to faster-moving, higher-contrast and larger-size targets embedded in cluttered moving backgrounds

Orientation cues for high-flying nocturnal insect migrants: do turbulence-induced temperature and velocity fluctuations indicate the mean wind flow?

Migratory insects flying at high altitude at night often show a degree of common alignment, sometimes with quite small angular dispersions around the mean. The observed orientation directions are often close to the downwind direction and this would seemingly be adaptive in that large insects could add their self-propelled speed to the wind speed, thus maximising their displacement in a given time. There are increasing indications that high-altitude orientation may be maintained by some intrinsic property of the wind rather than by visual perception of relative ground movement. Therefore, we first examined whether migrating insects could deduce the mean wind direction from the turbulent fluctuations in temperature. Within the atmospheric boundary-layer, temperature records show characteristic ramp-cliff structures, and insects flying downwind would move through these ramps whilst those flying crosswind would not. However, analysis of vertical-looking radar data on the common orientations of nocturnally migrating insects in the UK produced no evidence that the migrants actually use temperature ramps as orientation cues. This suggests that insects rely on turbulent velocity and acceleration cues, and refocuses attention on how these can be detected, especially as small-scale turbulence is usually held to be directionally invariant (isotropic). In the second part of the paper we present a theoretical analysis and simulations showing that velocity fluctuations and accelerations felt by an insect are predicted to be anisotropic even when the small-scale turbulence (measured at a fixed point or along the trajectory of a fluid-particle) is isotropic. Our results thus provide further evidence that insects do indeed use turbulent velocity and acceleration cues as indicators of the mean wind direction

Hands-On Parameter Search for Neural Simulations by a MIDI-Controller

Computational neuroscientists frequently encounter the challenge of parameter fitting – exploring a usually high dimensional variable space to find a parameter set that reproduces an experimental data set. One common approach is using automated search algorithms such as gradient descent or genetic algorithms. However, these approaches suffer several shortcomings related to their lack of understanding the underlying question, such as defining a suitable error function or getting stuck in local minima. Another widespread approach is manual parameter fitting using a keyboard or a mouse, evaluating different parameter sets following the users intuition. However, this process is often cumbersome and time-intensive. Here, we present a new method for manual parameter fitting. A MIDI controller provides input to the simulation software, where model parameters are then tuned according to the knob and slider positions on the device. The model is immediately updated on every parameter change, continuously plotting the latest results. Given reasonably short simulation times of less than one second, we find this method to be highly efficient in quickly determining good parameter sets. Our approach bears a close resemblance to tuning the sound of an analog synthesizer, giving the user a very good intuition of the problem at hand, such as immediate feedback if and how results are affected by specific parameter changes. In addition to be used in research, our approach should be an ideal teaching tool, allowing students to interactively explore complex models such as Hodgkin-Huxley or dynamical systems

Modeling Slope Instability as Shear Rupture Propagation in a Saturated Porous Medium

When a region of intense shear in a slope is much thinner than other relevant geometric lengths, this shear failure may be approximated as localized slip, as in faulting, with strength determined by frictional properties of the sediment and effective stress normal to the failure surface. Peak and residual frictional strengths of submarine sediments indicate critical slope angles well above those of most submarine slopes—in contradiction to abundant failures. Because deformation of sediments is governed by effective stress, processes affecting pore pressures are a means of strength reduction. However, common methods of exami ning slope stability neglect dynamically variable pore pressure during failure. We examine elastic-plastic models of the capped Drucker-Prager type and derive approximate equations governing pore pressure about a slip surface when the adjacent material may deform plastically. In the process we identify an elastic-plastic hydraulic diffusivity with an evolving permeability and plastic storage term analogous to the elastic term of traditional poroelasticity. We also examine their application to a dynamically propagating subsurface rupture and find indications of downslope directivity.Earth and Planetary SciencesEngineering and Applied Science

An Automated Paradigm for Drosophila Visual Psychophysics

Background: Mutations that cause learning and memory defects in Drosophila melanogaster have been found to also compromise visual responsiveness and attention. A better understanding of attention-like defects in such Drosophila mutants therefore requires a more detailed characterization of visual responsiveness across a range of visual parameters. Methodology/Principal Findings: We designed an automated behavioral paradigm for efficiently dissecting visual responsiveness in Drosophila. Populations of flies walk through multiplexed serial choice mazes while being exposed to moving visuals displayed on computer monitors, and infra-red fly counters at the end of each maze automatically score the responsiveness of a strain. To test our new design, we performed a detailed comparison between wild-type flies and a learning and memory mutant, dunce. We first confirmed that the learning mutant dunce displays increased responsiveness to a black/green moving grating compared to wild type in this new design. We then extended this result to explore responses to a wide range of psychophysical parameters for moving gratings (e.g., luminosity, contrast, spatial frequency, velocity) as well as to a different stimulus, moving dots. Finally, we combined these visuals (gratings versus dots) in competition to investigate how dunce and wild-type flies respond to more complex and conflicting motion effects. Conclusions/Significance: We found that dunce responds more strongly than wild type to high contrast and highly structured motion. This effect was found for simple gratings, dots, and combinations of both stimuli presented in competition

Asymptotic Expansions for the Sojourn Time Distribution in the M/G/1M/G/1-PS Queue

We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. Our results demonstrate the possible tail behaviors of the unconditional distribution, which was previously known in the cases $G=M$ and $G=D$ (where it is purely exponential). We assume that the service density decays at least exponentially fast. We use various methods for the asymptotic expansion of integrals, such as the Laplace and saddle point methods.Comment: 45 page

Inhibiting ERK Activation with CI-1040 Leads to Compensatory Upregulation of Alternate MAPKs and Plasminogen Activator Inhibitor-1 following Subtotal Nephrectomy with No Impact on Kidney Fibrosis

Extracellular-signal regulated kinase (ERK) activation by MEK plays a key role in many of the cellular processes that underlie progressive kidney fibrosis including cell proliferation, apoptosis and transforming growth factor β1-mediated epithelial to mesenchymal transition. We therefore assessed the therapeutic impact of ERK1/2 inhibition using a MEK inhibitor in the rat 5/6 subtotal nephrectomy (SNx) model of kidney fibrosis. There was a twentyfold upregulation in phospho-ERK1/2 expression in the kidney after SNx in Male Wistar rats. Rats undergoing SNx became hypertensive, proteinuric and developed progressive kidney failure with reduced creatinine clearance. Treatment with the MEK inhibitor, CI-1040 abolished phospho- ERK1/2 expression in kidney tissue and prevented phospho-ERK1/2 expression in peripheral lymphocytes during the entire course of therapy. CI-1040 had no impact on creatinine clearance, proteinuria, glomerular and tubular fibrosis, and α-smooth muscle actin expression. However, inhibition of ERK1/2 activation led to significant compensatory upregulation of the MAP kinases, p38 and JNK in kidney tissue. CI-1040 also increased the expression of plasminogen activator inhibitor-1 (PAI-1), a key inhibitor of plasmin-dependent matrix metalloproteinases. Thus inhibition of ERK1/2 activation has no therapeutic effect on kidney fibrosis in SNx possibly due to increased compensatory activation of the p38 and JNK signalling pathways with subsequent upregulation of PAI-1

Interfacial Tension of the Lipid Membrane Formed from Phosphatidylcholine–Decanoic Acid and Phosphatidylcholine–Decylamine Systems

Interfacial tension has been determined for phosphatidylcholine (PC)–decanoic acid (DA) and PC–decylamine (DE) membranes. PC (lecithin), DA and DE were used in the experiments; the interfacial tension values of the pure components are 1.62 × 10−3, −2.38 × 10−2 and −3.88 × 10−2 N/m (hypothetical values for DA and DE), respectively. The 1:1 complexes were formed during formation of PC–DA and PC–DE membranes. The following parameters describing the complexes were determined: the surface concentrations of the lipid membranes formed from these complexes, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_{3}^{ - 1}$$\end{document}; the interfacial tensions of such membranes, γ3; and the stability constants of these complexes, K

The effects of symmetry on the dynamics of antigenic variation

In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, we show how many of the observed dynamical regimes can be explained in terms of the symmetry of interactions between different antigenic variants. The results of this analysis are quite generic, and have wider implications for understanding the dynamics of immune escape of other parasites, as well as for the dynamics of multi-strain diseases.Comment: 21 pages, 4 figures; J. Math. Biol. (2012), Online Firs