Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the "sampling interval" used in the measurement for both "steady-state" and "finite" initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A "deterministic approximation" is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

Convolutional Codes for Network-Error Correction

In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors are separated by a certain interval. We also give some bounds on the field size and the number of errors that can get corrected in a certain interval. Compared to previous network error correction schemes, using convolutional codes is seen to have advantages in field size and decoding technique. Some examples are discussed which illustrate the several possible situations that arise in this context.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Generating artificial chromosomes with probability control in genetic algorithm for machine scheduling problems

In this paper, a novel genetic algorithm is developed by generating artificial chromosomes with probability control to solve the machine scheduling problems. Generating artificial chromosomes for Genetic Algorithm (ACGA) is closely related to Evolutionary Algorithms Based on Probabilistic Models (EAPM). The artificial chromosomes are generated by a probability model that extracts the gene information from current population. ACGA is considered as a hybrid algorithm because both the conventional genetic operators and a probability model are integrated. The ACGA proposed in this paper, further employs the ``evaporation concept'' applied in Ant Colony Optimization (ACO) to solve the permutation flowshop problem. The ``evaporation concept'' is used to reduce the effect of past experience and to explore new alternative solutions. In this paper, we propose three different methods for the probability of evaporation. This probability of evaporation is applied as soon as a job is assigned to a position in the permutation flowshop problem. Experimental results show that our ACGA with the evaporation concept gives better performance than some algorithms in the literature.

Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems

An a priori error analysis of discontinuous Galerkin methods for a general elliptic problem is derived under a mild elliptic regularity assumption on the solution. This is accomplished by using some techniques from a posteriori error analysis. The model problem is assumed to satisfy a GAyenrding type inequality. Optimal order L (2) norm a priori error estimates are derived for an adjoint consistent interior penalty method.

Error-free matrix symmetrizers and equivalent symmetric matrices

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AprimeX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

Bayesian Decentralized Spectrum Sensing in Cognitive Radio Networks

This paper considers the problem of spectrum sensing, i.e., the detection of whether or not a primary user is transmitting data by a cognitive radio. The Bayesian framework is adopted, with the performance measure being the probability of detection error. A decentralized setup, where N sensors use M observations each to arrive at individual decisions that are combined at a fusion center to form the overall decision is considered. The unknown fading channel between the primary sensor and the cognitive radios makes the individual decision rule computationally complex, hence, a generalized likelihood ratio test (GLRT)-based approach is adopted. Analysis of the probabilities of false alarm and miss detection of the proposed method reveals that the error exponent with respect to M is zero. Also, the fusion of N individual decisions offers a diversity advantage, similar to diversity reception in communication systems, and a tight bound on the error exponent is presented. Through an analysis in the low power regime, the number of observations needed as a function of received power, to achieve a given probability of error is determined. Monte-Carlo simulations confirm the accuracy of the analysis.

Chance constrained uncertain classification via robust optimization

This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain data points are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as a convex second order cone program whose solution is guaranteed to satisfy the probabilistic constraint. Prior to this work, only the Chebyshev based relaxations were exploited in learning algorithms. Bernstein bounds employ richer partial information and hence can be far less conservative than Chebyshev bounds. Due to this efficient modeling of uncertainty, the resulting classifiers achieve higher classification margins and hence better generalization. Methodologies for classifying uncertain test data points and error measures for evaluating classifiers robust to uncertain data are discussed. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle data uncertainty and outperform state-of-the-art in many cases.

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 1024(3) collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number Pr-M over a large range, namely 0.01 <= Pr-M <= 10. We obtain data for a wide variety of statistical measures, such as probability distribution functions (PDFs) of the moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterize intermittency, isosurfaces of quantities, such as the moduli of the vorticity and current density, and joint PDFs, such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from a larger intermittency in the magnetic field than in the velocity field, at large Pr-M, to a smaller intermittency in the magnetic field than in the velocity field, at low Pr-M. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of Pr-M, multiscaling exponent ratios agree, at least within our error bars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.

Code design casing deterministic annealing

We address the problem of designing codes for specific applications using deterministic annealing. Designing a block code over any finite dimensional space may be thought of as forming the corresponding number of clusters over the particular dimensional space. We have shown that the total distortion incurred in encoding a training set is related to the probability of correct reception over a symmetric channel. While conventional deterministic annealing make use of the Euclidean squared error distance measure, we have developed an algorithm that can be used for clustering with Hamming distance as the distance measure, which is required in the error correcting, scenario.

Link failure detection for maintaining session continuity in packet data networks

A link failure in the path of a virtual circuit in a packet data network will lead to premature disconnection of the circuit by the end-points. A soft failure will result in degraded throughput over the virtual circuit. If these failures can be detected quickly and reliably, then appropriate rerouteing strategies can automatically reroute the virtual circuits that use the failed facility. In this paper, we develop a methodology for analysing and designing failure detection schemes for digital facilities. Based on errored second data, we develop a Markov model for the error and failure behaviour of a T1 trunk. The performance of a detection scheme is characterized by its false alarm probability and the detection delay. Using the Markov model, we analyse the performance of detection schemes that use physical layer or link layer information. The schemes basically rely upon detecting the occurrence of severely errored seconds (SESs). A failure is declared when a counter, that is driven by the occurrence of SESs, reaches a certain threshold.For hard failures, the design problem reduces to a proper choice;of the threshold at which failure is declared, and on the connection reattempt parameters of the virtual circuit end-point session recovery procedures. For soft failures, the performance of a detection scheme depends, in addition, on how long and how frequent the error bursts are in a given failure mode. We also propose and analyse a novel Level 2 detection scheme that relies only upon anomalies observable at Level 2, i.e. CRC failures and idle-fill flag errors. Our results suggest that Level 2 schemes that perform as well as Level 1 schemes are possible.

A Rotor Flux Estimation During Zero and Active Vector Periods Using Current Error Space Vector From a Hysteresis Controller for a Sensorless Vector Control of IM Drive

This paper proposes a sensorless vector control scheme for general-purpose induction motor drives using the current error space phasor-based hysteresis controller. In this paper, a new technique for sensorless operation is developed to estimate rotor voltage and hence rotor flux position using the stator current error during zero-voltage space vectors. It gives a comparable performance with the vector control drive using sensors especially at a very low speed of operation (less than 1 Hz). Since no voltage sensing is made, the dead-time effect and loss of accuracy in voltage sensing at low speed are avoided here, with the inherent advantages of the current error space phasor-based hysteresis controller. However, appropriate device on-state drops are compensated to achieve a steady-state operation up to less than 1 Hz. Moreover, using a parabolic boundary for current error, the switching frequency of the inverter can be maintained constant for the entire operating speed range. Simple sigma L-s estimation is proposed, and the parameter sensitivity of the control scheme to changes in stator resistance, R-s is also investigated in this paper. Extensive experimental results are shown at speeds less than 1 Hz to verify the proposed concept. The same control scheme is further extended from less than 1 Hz to rated 50 Hz six-step operation of the inverter. Here, the magnetic saturation is ignored in the control scheme.

A current error space vector based hysteresis controller with constant switching frequency and simple online boundary computation for VSI fed IM drive

This paper proposes a simple current error space vector based hysteresis controller for two-level inverter fed Induction Motor (IM) drives. This proposed hysteresis controller retains all advantages of conventional current error space vector based hysteresis controllers like fast dynamic response, simple to implement, adjacent voltage vector switching etc. The additional advantage of this proposed hysteresis controller is that it gives a phase voltage frequency spectrum exactly similar to that of a constant switching frequency space vector pulse width modulated (SVPWM) inverter. In this proposed hysteresis controller the boundary is computed online using estimated stator voltages along alpha and beta axes thus completely eliminating look up tables used for obtaining parabolic hysteresis boundary proposed in. The estimation of stator voltage is carried out using current errors along alpha and beta axes and steady state model of induction motor. The proposed scheme is simple and capable of taking inverter upto six step mode operation, if demanded by drive system. The proposed hysteresis controller based inverter fed drive scheme is simulated extensively using SIMULINK toolbox of MATLAB for steady state and transient performance. The experimental verification for steady state performance of the proposed scheme is carried out on a 3.7kW IM.

Network Error Correction for Unit-Delay, Memory-Free Networks Using Convolutional Codes

A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their outgoing edges. In this work, we introduce network-error correction for single source, acyclic, unit-delay, memory-free networks with coherent network coding for multicast. A convolutional code is designed at the source based on the network code in order to correct network- errors that correspond to any of a given set of error patterns, as long as consecutive errors are separated by a certain interval which depends on the convolutional code selected. Bounds on this interval and the field size required for constructing the convolutional code with the required free distance are also obtained. We illustrate the performance of convolutional network error correcting codes (CNECCs) designed for the unit-delay networks using simulations of CNECCs on an example network under a probabilistic error model.

Performance analysis of the random early detection algorithm

In this article we consider a finite queue with its arrivals controlled by the random early detection algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of transmission control protocol sources is locally considered stationary renewal or Markov modulated Poisson process with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. However, computing the performance indices for this system becomes computationally prohibitive. Thus, in the latter half of the article, we approximate the dynamics of the average queue length process asymptotically via an ordinary differential equation. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.