Optimizing Delay in Sequential Change Detection on Ad Hoc Wireless Sensor Networks

We consider the classical problem of sequential detection of change in a distribution (from hypothesis 0 to hypothesis 1), where the fusion centre receives vectors of periodic measurements, with the measurements being i.i.d. over time and across the vector components, under each of the two hypotheses. In our problem, the sensor devices ("motes") that generate the measurements constitute an ad hoc wireless network. The motes contend using a random access protocol (such as CSMA/CA) to transmit their measurement packets to the fusion centre. The fusion centre waits for vectors of measurements to accumulate before taking decisions. We formulate the optimal detection problem, taking into account the network delay experienced by the vectors of measurements, and find that, under periodic sampling, the detection delay decouples into network delay and decision delay. We obtain a lower bound on the network delay, and propose a censoring scheme, where lagging sensors drop their delayed observations in order to mitigate network delay. We show that this scheme can achieve the lower bound. This approach is explored via simulation. We also use numerical evaluation and simulation to study issues such as: the optimal sampling rate for a given number of sensors, and the optimal number of sensors for a given measurement rate

Lossy distribution source coding with side information

In a typical sensor network scenario a goal is to monitor a spatio-temporal process through a number of inexpensive sensing nodes, the key parameter being the fidelity at which the process has to be estimated at distant locations. We study such a scenario in which multiple encoders transmit their correlated data at finite rates to a distant and common decoder. In particular, we derive inner and outer bounds on the rate region for the random field to be estimated with a given mean distortion.

Distributed load adaptive scheduling for throughput and delay guarantees in fading wireless LANs

We consider a problem of providing mean delay and average throughput guarantees in random access fading wireless channels using CSMA/CA algorithm. This problem becomes much more challenging when the scheduling is distributed as is the case in a typical local area wireless network. We model the CSMA network using a novel queueing network based approach. The optimal throughput per device and throughput optimal policy in an M device network is obtained. We provide a simple contention control algorithm that adapts the attempt probability based on the network load and obtain bounds for the packet transmission delay. The information we make use of is the number of devices in the network and the queue length (delayed) at each device. The proposed algorithms stay within the requirements of the IEEE 802.11 standard.

Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Quantum Random Walks without Coin Toss

We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of classical randomised algorithms. We use this algorithm to search for a marked vertex on a hypercubic lattice in arbitrary dimensions. Our numerical and analytical results match the scaling behaviour of earlier algorithms that use a coin toss instruction.

The role of surface texture on friction and transfer layer formation during repeated sliding of Al-4Mg against steel

In the present investigation, various kinds of textures, namely, unidirectional, 8-ground, and random were attained on the die surfaces. Roughness of the textures was varied using different grits of emery papers or polishing powders. Then pins made of Al-4Mg alloys were slid against steel plates at various numbers of cycles, namely, 1, 3, 5, 10 and 20 using pin-on-plate reciprocating sliding tester. Tests were conducted at a sliding velocity of 2 minis in ambient conditions under both dry and lubricated conditions. A constant normal load of 35 N was applied in the tests. The morphologies of the worn surfaces of the pins and the formation of transfer layer on the counter surfaces were observed using a scanning electron microscope. Surface roughness parameters of the plates were measured using an optical profilometer. In the experiments, it was observed that the coefficient of friction and formation of the transfer layer depend on the die surface textures under both dry and lubricated conditions. More specifically, the coefficient of friction decreases for unidirectional and 8-ground surfaces while for random surfaces it increases with number of cycles. However, the coefficient of friction is highest for the sliding perpendicular to the unidirectional textures and least for the random textures under both dry and lubricated conditions. The difference in friction values between these two surfaces decreases with increasing number of cycles. The variation in the coefficient of friction under both dry and lubrication conditions is attributed to the change in texture of the surfaces during sliding. (C) 2011 Elsevier B.V. All rights reserved.

Low-Complexity Detection in Large-Dimension MIMO-ISI Channels Using Graphical Models

In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov random field (MRF)-based graphical model with pairwise interaction, in conjunction with message damping, and 2) use of factor graph (FG)-based graphical model with Gaussian approximation of interference (GAI). The per-symbol complexities are O(K(2)n(t)(2)) and O(Kn(t)) for the MRF and the FG with GAI approaches, respectively, where K and n(t) denote the number of channel uses per frame, and number of transmit antennas, respectively. These low-complexities are quite attractive for large dimensions, i.e., for large Kn(t). From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing Kn(t). Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance of M-QAM symbol detection.

Damping and synchronising torques contributed by a voltage regulator to a synchronous generator: a quantitative assessment

In the paper, the total damping and synchronising torques, which determine the dynamic stability of a synchronous generator in a power system, have been traced to their origin. The positive and negative components released or consumed by the voltage regulator, and by the various windings of the machine, have been isolated, with the object of making a quantitative assessment of the effects of various gains and time constants on the dynamic stability of a synchronous machine under different operating conditions. The analysis is based on the properties of quadratic invariance in tensor calculus. An alternative solution by network analysis has also been provided to establish the validity of the tensor approach.

Particle dynamics in the channel flow of a turbulent particle-gas suspension at high Stokes number. Part 1. DNS and fluctuating force model

The fluctuating force model is developed and applied to the turbulent flow of a gas-particle suspension in a channel in the limit of high Stokes number, where the particle relaxation time is large compared to the fluid correlation time, and low particle Reynolds number where the Stokes drag law can be used to describe the interaction between the particles and fluid. In contrast to the Couette flow, the fluid velocity variances in the different directions in the channel are highly non-homogeneous, and they exhibit significant variation across the channel. First, we analyse the fluctuating particle velocity and acceleration distributions at different locations across the channel. The distributions are found to be non-Gaussian near the centre of the channel, and they exhibit significant skewness and flatness. However, acceleration distributions are closer to Gaussian at locations away from the channel centre, especially in regions where the variances of the fluid velocity fluctuations are at a maximum. The time correlations for the fluid velocity fluctuations and particle acceleration fluctuations are evaluated, and it is found that the time correlation of the particle acceleration fluctuations is close to the time correlations of the fluid velocity in a `moving Eulerian' reference, moving with the mean fluid velocity. The variances of the fluctuating force distributions in the Langevin simulations are determined from the time correlations of the fluid velocity fluctuations and the results are compared with direct numerical simulations. Quantitative agreement between the two simulations are obtained provided the particle viscous relaxation time is at least five times larger than the fluid integral time.

Particle dynamics in the channel flow of a turbulent particle-gas suspension at high Stokes number. Part 2. Comparison of fluctuating force simulations and experiments

The particle and fluid velocity fluctuations in a turbulent gas-particle suspension are studied experimentally using two-dimensional particle image velocimetry with the objective of comparing the experiments with the predictions of fluctuating force simulations. Since the fluctuating force simulations employ force distributions which do not incorporate the modification of fluid turbulence due to the particles, it is of importance to quantify the turbulence modification in the experiments. For experiments carried out at a low volume fraction of 9.15 x 10(-5) (mass loading is 0.19), where the viscous relaxation time is small compared with the time between collisions, it is found that the gas-phase turbulence is not significantly modified by the presence of particles. Owing to this, quantitative agreement is obtained between the results of experiments and fluctuating force simulations for the mean velocity and the root mean square of the fluctuating velocity, provided that the polydispersity in the particle size is incorporated in the simulations. This is because the polydispersity results in a variation in the terminal velocity of the particles which could induce collisions and generate fluctuations; this mechanism is absent if all of the particles are of equal size. It is found that there is some variation in the particle mean velocity very close to the wall depending on the wall-collision model used in the simulations, and agreement with experiments is obtained only when the tangential wall-particle coefficient of restitution is 0.7. The mean particle velocity is in quantitative agreement for locations more than 10 wall units from the wall of the channel. However, there are systematic differences between the simulations and theory for the particle concentrations, possibly due to inadequate control over the particle feeding at the entrance. The particle velocity distributions are compared both at the centre of the channel and near the wall, and the shape of the distribution function near the wall obtained in experiments is accurately predicted by the simulations. At the centre, there is some discrepancy between simulations and experiment for the distribution of the fluctuating velocity in the flow direction, where the simulations predict a bi-modal distribution whereas only a single maximum is observed in the experiments, although both distributions are skewed towards negative fluctuating velocities. At a much higher particle mass loading of 1.7, where the time between collisions is smaller than the viscous relaxation time, there is a significant increase in the turbulent velocity fluctuations by similar to 1-2 orders of magnitude. Therefore, it becomes necessary to incorporate the modified fluid-phase intensity in the fluctuating force simulation; with this modification, the mean and mean-square fluctuating velocities are within 20-30% of the experimental values.

Group Actions and Elementary Number Theory

Abstract | In this article the shuffling of cards is studied by using the concept of a group action. We use some fundamental results in Elementary Number Theory to obtain formulas for the orders of some special shufflings, namely the Faro and Monge shufflings and give necessary and sufficient conditions for the Monge shuffling to be a cycle. In the final section we extend the considerations to the shuffling of multisets.

Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection.

A Refined Methodology for Durability-Based Service Life Estimation of Reinforced Concrete Structural Elements Considering Fuzzy and Random Uncertainties

A reliable method for service life estimation of the structural element is a prerequisite for service life design. A new methodology for durability-based service life estimation of reinforced concrete flexural elements with respect to chloride-induced corrosion of reinforcement is proposed. The methodology takes into consideration the fuzzy and random uncertainties associated with the variables involved in service life estimation by using a hybrid method combining the vertex method of fuzzy set theory with Monte Carlo simulation technique. It is also shown how to determine the bounds for characteristic value of failure probability from the resulting fuzzy set for failure probability with minimal computational effort. Using the methodology, the bounds for the characteristic value of failure probability for a reinforced concrete T-beam bridge girder has been determined. The service life of the structural element is determined by comparing the upper bound of characteristic value of failure probability with the target failure probability. The methodology will be useful for durability-based service life design and also for making decisions regarding in-service inspections.

Rainbow Connection Number and Connectivity

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) <= inverted right perpendicularn/2inverted left perpendicular for any 2-connected graph with at least three vertices. We conjecture that rc(G) <= n/kappa + C for a kappa-connected graph G of order n, where C is a constant, and prove the conjecture for certain classes of graphs. We also prove that rc(G) < (2 + epsilon)n/kappa + 23/epsilon(2) for any epsilon > 0.