Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients alpha(il) and eta(iml) are derived. We prove that when the velocity field is nonhelical, the transport coefficient alpha(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X-3 and time tau; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Radler, M. Rheinhardt, and P. J. Kapyla Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor eta(ij) (tau). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

Optimal control of arrivals to queues with delayed queue length information

We consider discrete-time versions of two classical problems in the optimal control of admission to a queueing system: i) optimal routing of arrivals to two parallel queues and ii) optimal acceptance/rejection of arrivals to a single queue. We extend the formulation of these problems to permit a k step delay in the observation of the queue lengths by the controller. For geometric inter-arrival times and geometric service times the problems are formulated as controlled Markov chains with expected total discounted cost as the minimization objective. For problem i) we show that when k = 1, the optimal policy is to allocate an arrival to the queue with the smaller expected queue length (JSEQ: Join the Shortest Expected Queue). We also show that for this problem, for k greater than or equal to 2, JSEQ is not optimal. For problem ii) we show that when k = 1, the optimal policy is a threshold policy. There are, however, two thresholds m(0) greater than or equal to m(1) > 0, such that mo is used when the previous action was to reject, and mi is used when the previous action was to accept.

Lazy structure sharing for query optimization

We study lazy structure sharing as a tool for optimizing equivalence testing on complex data types, We investigate a number of strategies for implementing lazy structure sharing and provide upper and lower bounds on their performance (how quickly they effect ideal configurations of our data structure). In most cases when the strategies are applied to a restricted case of the problem, the bounds provide nontrivial improvements over the naive linear-time equivalence-testing strategy that employs no optimization. Only one strategy, however, which employs path compression, seems promising for the most general case of the problem.

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.

Lasing in active, sub-mean-free path-sized systems with dense, random, weak scatterers

We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent: with experimentally observed features. (C) 1997 Optical Society of America.

Novel correlations in two dimensions: Two-body problem

We discuss a many-body Hamiltonian with two- and three-body interactions in two dimensions introduced recently by Murthy, Bhaduri and Sen. Apart from an analysis of some exact solutions in the many-body system, we analyse in detail the two-body problem which is completely solvable. We show that the solution of the two-body problem reduces to solving a known differential equation due to Heun. We show that the two-body spectrum becomes remarkably simple for large interaction strengths and the level structure resembles that of the Landau levels. We also clarify the 'ultraviolet' regularization which is needed to define an inverse-square potential properly and discuss its implications for our model.

On the problem of spurious patterns in neural associative memory models

The problem of spurious patterns in neural associative memory models is discussed, Some suggestions to solve this problem from the literature are reviewed and their inadequacies are pointed out, A solution based on the notion of neural self-interaction with a suitably chosen magnitude is presented for the Hebb learning rule. For an optimal learning rule based on linear programming, asymmetric dilution of synaptic connections is presented as another solution to the problem of spurious patterns, With varying percentages of asymmetric dilution it is demonstrated numerically that this optimal learning rule leads to near total suppression of spurious patterns. For practical usage of neural associative memory networks a combination of the two solutions with the optimal learning rule is recommended to be the best proposition.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

An inverse problem for the Helmholtz equation involving two semi-infinite fluids

An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two fluids, and (iii) the strength of an acoustic source assumed to be situated at the interface of the two fluids. These are determined from the pressure on the interface produced by the acoustic source. The effect of the surface tension force at the interface is taken into account in this paper. The application of the proposed analytical method to solve the inverse problem is also illustrated with several examples. In particular, exact solutions of two direct problems are first derived using standard classical methods which are then used in our proposed inverse method to recover the unknowns of the corresponding inverse problems. The results are found to be in excellent agreement.

Video coding mode decision as a classification problem

In this paper, we show that it is possible to reduce the complexity of Intra MB coding in H.264/AVC based on a novel chance constrained classifier. Using the pairs of simple mean-variances values, our technique is able to reduce the complexity of Intra MB coding process with a negligible loss in PSNR. We present an alternate approach to address the classification problem which is equivalent to machine learning. Implementation results show that the proposed method reduces encoding time to about 20% of the reference implementation with average loss of 0.05 dB in PSNR.

Data rectification and detection of trend shifts in jet engine path measurements using median filters and fuzzy logic

Filtering methods are explored for removing noise from data while preserving sharp edges that many indicate a trend shift in gas turbine measurements. Linear filters are found to be have problems with removing noise while preserving features in the signal. The nonlinear hybrid median filter is found to accurately reproduce the root signal from noisy data. Simulated faulty data and fault-free gas path measurement data are passed through median filters and health residuals for the data set are created. The health residual is a scalar norm of the gas path measurement deltas and is used to partition the faulty engine from the healthy engine using fuzzy sets. The fuzzy detection system is developed and tested with noisy data and with filtered data. It is found from tests with simulated fault-free and faulty data that fuzzy trend shift detection based on filtered data is very accurate with no false alarms and negligible missed alarms.

Dynamic path profile aided recompilation in a JAVA just-in-time compiler

Just-in-Time (JIT) compilers for Java can be augmented by making use of runtime profile information to produce better quality code and hence achieve higher performance. In a JIT compilation environment, the profile information obtained can be readily exploited in the same run to aid recompilation and optimization of frequently executed (hot) methods. This paper discusses a low overhead path profiling scheme for dynamically profiling AT produced native code. The profile information is used in recompilation during a subsequent invocation of the hot method. During recompilation tree regions along the hot paths are enlarged and instruction scheduling at the superblock level is performed. We have used the open source LaTTe AT compiler framework for our implementation. Our results on a SPARC platform for SPEC JVM98 benchmarks indicate that (i) there is a significant reduction in the number of tree regions along the hot paths, and (ii) profile aided recompilation in LaTTe achieves performance comparable to that of adaptive LaTTe in spite of retranslation and profiling overheads.

Least path criterion (LPC) for unique indexing in a two-dimensional decagonal quasilattice

The least path criterion or least path length in the context of redundant basis vector systems is discussed and a mathematical proof is presented of the uniqueness of indices obtained by applying the least path criterion. Though the method has greater generality, this paper concentrates on the two-dimensional decagonal lattice. The order of redundancy is also discussed; this will help eventually to correlate with other redundant but desirable indexing sets.

The restriction mapping problem revisited

In computational molecular biology, the aim of restriction mapping is to locate the restriction sites of a given enzyme on a DNA molecule. Double digest and partial digest are two well-studied techniques for restriction mapping. While double digest is NP-complete, there is no known polynomial-time algorithm for partial digest. Another disadvantage of the above techniques is that there can be multiple solutions for reconstruction. In this paper, we study a simple technique called labeled partial digest for restriction mapping. We give a fast polynomial time (O(n(2) log n) worst-case) algorithm for finding all the n sites of a DNA molecule using this technique. An important advantage of the algorithm is the unique reconstruction of the DNA molecule from the digest. The technique is also robust in handling errors in fragment lengths which arises in the laboratory. We give a robust O(n(4)) worst-case algorithm that can provably tolerate an absolute error of O(Delta/n) (where Delta is the minimum inter-site distance), while giving a unique reconstruction. We test our theoretical results by simulating the performance of the algorithm on a real DNA molecule. Motivated by the similarity to the labeled partial digest problem, we address a related problem of interest-the de novo peptide sequencing problem (ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000, pp. 389-398), which arises in the reconstruction of the peptide sequence of a protein molecule. We give a simple and efficient algorithm for the problem without using dynamic programming. The algorithm runs in time O(k log k), where k is the number of ions and is an improvement over the algorithm in Chen et al. (C) 2002 Elsevier Science (USA). All rights reserved.