Efficient algorithms for domination and Hamilton circuit problems on permutation graphs

The domination and Hamilton circuit problems are of interest both in algorithm design and complexity theory. The domination problem has applications in facility location and the Hamilton circuit problem has applications in routing problems in communications and operations research.The problem of deciding if G has a dominating set of cardinality at most k, and the problem of determining if G has a Hamilton circuit are NP-Complete. Polynomial time algorithms are, however, available for a large number of restricted classes. A motivation for the study of these algorithms is that they not only give insight into the characterization of these classes but also require a variety of algorithmic techniques and data structures. So the search for efficient algorithms, for these problems in many classes still continues.A class of perfect graphs which is practically important and mathematically interesting is the class of permutation graphs. The domination problem is polynomial time solvable on permutation graphs. Algorithms that are already available are of time complexity O(n2) or more, and space complexity O(n2) on these graphs. The Hamilton circuit problem is open for this class.We present a simple O(n) time and O(n) space algorithm for the domination problem on permutation graphs. Unlike the existing algorithms, we use the concept of geometric representation of permutation graphs. Further, exploiting this geometric notion, we develop an O(n2) time and O(n) space algorithm for the Hamilton circuit problem.

Narrowband random excitation of a limit cycle system

The response of the Van der Pol oscillator to stationary narrowband Gaussian excitation is considered. The central frequency of excitation is taken to be in the neighborhood of the system limit cycle frequency. The solution is obtained using a non-Gaussian closure approximation on the probability density function of the response. The validity of the solution is examined with the help of a stochastic stability analysis. Solution based on Stratonovich''s quasistatic averaging technique is also obtained. The comparison of the theoretical solutions with the digital simulations shows that the theoretical estimates are reasonably good.

New Approximation Algorithms for Minimum Cycle Bases of Graphs

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over F-2 generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k >= 1, we give (2k - 1)-approximation algorithms with expected running time O(kmn(1+2/k) + mn((1+1/k)(omega-1))) and deterministic running time O(n(3+2/k) ), respectively. Here omega is the best exponent of matrix multiplication. It is presently known that omega < 2.376. Both algorithms are o(m(omega)) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Theta(m(omega) ) bound. We also present a 2-approximation algorithm with expected running time O(M-omega root n log n), a linear time 2-approximation algorithm for planar graphs and an O(n(3)) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.

High-temperature low-cycle fatigue behavior of a NIMONIC PE-16 superalloy—Correlation with deformation and fracture

Low-cycle fatigue (LCF) responses of NIMONIC PE-16 for various prior microstructures and strain amplitudes have been evaluated and the fatigue behavior has been explained in terms of the operative deformation mechanisms. Total strain-controlled LCF tests were performed at 923 K on samples possessing three different prior microstructures: alloy A in solution-annealed condition (free of γ′ and carbides), alloy B with double aging treatment (spherical γ′ of 18-nm diameter and M23C6), and alloy C with another double aging treatment (γ′ of size 35 nm, MC and M23C6). All three microstructures exhibited an intial cyclic hardening followed by a period of gradual softening at 923 K. Coffin-Manson plots describing the plastic strain amplitudevs number of reversals to failure showed that alloy A had maximum fatigue life while C showed the least. Alloy B exhibited a two-slope behavior in the Coffin-Manson plot over the strain amplitudes investigated. This has been ascribed to the change in the degree of homogeneity of deformation at high and low strain amplitudes. Transmission electron microscopic studies were carried out to characterize the various deformation mechanisms and precipitation reactions occurring during fatigue testign. Fresh precipitation of fine γ′ was confirmed by the development of “mottled contrast” in alloy C. Evidence for the shearing of the ordered γ′ precipitates was revealed by the presence of superdislocations in alloy C. Repeated shearing during cyclic loading led to the reduction in the size of the γ′ and consequent softening. Coarser γ′ precipitates were associated with Orowan loops. The observed fatigue behavior has been rationalized based on the micromechanisms stated above and on the degree of homogenization of slip assessed by slipband spacing measurements on tested samples.

Effect of strain rate on the high-temperature low-cycle fatigue properties of a nimonic PE-16 superalloy

Strain-rate effects on the low-cycle fatigue (LCF) behavior of a NIMONIC PE-16 superalloy have been evaluated in the temperature range of 523 to 923 K. Total-strain-controlled fatigue tests were per-formed at a strain amplitude of +/-0.6 pct on samples possessing two different prior microstructures: microstructure A, in the solution-annealed condition (free of gamma' and carbides); and microstructure B, in a double-aged condition with gamma' of 18-nm diameter and M23C6 carbides. The cyclic stress response behavior of the alloy was found to depend on the prior microstructure, testing temperature, and strain rate. A softening regime was found to be associated with shearing of ordered gamma' that were either formed during testing or present in the prior microstructure. Various manifestations of dynamic strain aging (DSA) included negative strain rate-stress response, serrations on the stress-strain hysteresis loops, and increased work-hardening rate. The calculated activation energy matched well with that for self-diffusion of Al and Ti in the matrix. Fatigue life increased with an increase in strain rate from 3 x 10(-5) to 3 x 10(-3) s-1, but decreased with further increases in strain rate. At 723 and 823 K and low strain rates, DSA influenced the deformation and fracture behavior of the alloy. Dynamic strain aging increased the strain localization in planar slip bands, and impingement of these bands caused internal grain-boundary cracks and reduced fatigue life. However, at 923 K and low strain rates, fatigue crack initiation and propagation were accelerated by high-temperature oxidation, and the reduced fatigue life was attributed to oxidation-fatigue interaction. Fatigue life was maximum at the intermediate strain rates, where strain localization was lower. Strain localization as a function of strain rate and temperature was quantified by optical and scanning electron microscopy and correlated with fatigue life.

Low cycle fatigue behaviour of a nitrogen modified 316L stainless steel at 823 K

Strain controlled low cycle fatigue tests on solution annealed nitrogen modified 316L stainless steel have been conducted in air at 823 K to ascertain the influence of strain rate and strain amplitude. Effect of strain rate was examined from 3x10(-5) s(-1) to 3 x 10(-2) at a fixed strain amplitude of +/- 0.6%. The influence of strain amplitude was evaluated between +/- 0.25 % and +/- 1.0% at a constant strain rate of 3x10(-3) s(-1). The cyclic stress response at all testing conditions is characterized by an initial hardening followed by saturation. Serrated flow, a characteristic feature of dynamic strain ageing (DSA) was seen at strain rates lower than 3x10(-3) s(-1). Fatigue life was found to decrease with decrease in strain rate. The reduction in fatigue resistance is attributed mainly to the detrimental effects associated with DSA.

Small Ubiquitin-related Modifier Ligase Activity of Mms21 Is Required for Maintenance of Chromosome Integrity during the Unperturbed Mitotic Cell Division Cycle in Saccharomyces cerevisiae

The SUMO ligase activity of Mms21/Nse2, a conserved member of the Smc5/6 complex, is required for resisting extrinsically induced genotoxic stress. We report that the Mms21 SUMO ligase activity is also required during the unchallenged mitotic cell cycle in Saccharomyces cerevisiae. SUMO ligase-defective cells were slow growing and spontaneously incurred DNA damage. These cells required caffeine-sensitive Mec1 kinase-dependent checkpoint signaling for survival even in the absence of extrinsically induced genotoxic stress. SUMO ligase-defective cells were sensitive to replication stress and displayed synthetic growth defects with DNA damage checkpoint-defective mutants such as mec1, rad9, and rad24. MMS21 SUMO ligase and mediator of replication checkpoint 1 gene (MRC1) were epistatic with respect to hydroxyurea-induced replication stress or methyl methanesulfonate-induced DNA damage sensitivity. Subjecting Mms21 SUMO ligase-deficient cells to transient replication stress resulted in enhancement of cell cycle progression defects such as mitotic delay and accumulation of hyperploid cells. Consistent with the spontaneous activation of the DNA damage checkpoint pathway observed in the Mms21-mediated sumoylation-deficient cells, enhanced frequency of chromosome breakage and loss was detected in these mutant cells. A mutation in the conserved cysteine 221 that is engaged in coordination of the zinc ion in Loop 2 of the Mms21 SPL-RING E3 ligase catalytic domain resulted in strong replication stress sensitivity and also conferred slow growth and Mec1 dependence to unchallenged mitotically dividing cells. Our findings establish Mms21-mediated sumoylation as a determinant of cell cycle progression and maintenance of chromosome integrity during the unperturbed mitotic cell division cycle in budding yeast.

The origin of the solar magnetic cycle

After summarizing the relevant observational data, we discuss how a study of flux tube dynamics in the solar convection zone helps us to understand the formation of sunspots. Then we introduce the flux transport dynamo model and assess its success in modelling both the solar cycle and its departures from strictly periodic behaviour.

Numerical Modelling of the Observed Diurnal Cycle of Indian Monsoon Rainfall

We have analysed the diurnal cycle of rainfall over the Indian region (10S-35N, 60E-100E) using both satellite and in-situ data, and found many interesting features associated with this fundamental, yet under-explored, mode of variability. Since there is a distinct and strong diurnal mode of variability associated with the Indian summer monsoon rainfall, we evaluate the ability of the Weather Research and Forecasting Model (WRF) to simulate the observed diurnal rainfall characteristics. The model (at 54km grid-spacing) is integrated for the month of July, 2006, since this period was particularly favourable for the study of diurnal cycle. We first evaluate the sensitivity of the model to the prescribed sea surface temperature (SST), by using two different SST datasets, namely, Final Analyses (FNL) and Real-time Global (RTG). It was found that with RTG SST the rainfall simulation over central India (CI) was significantly better than that with FNL. On the other hand, over the Bay of Bengal (BoB), rainfall simulated with FNL was marginally better than with RTG. However, the overall performance of RTG SST was found to be better than FNL, and hence it was used for further model simulations. Next, we investigated the role of the convective parameterization scheme on the simulation of diurnal cycle of rainfall. We found that the Kain-Fritsch (KF) scheme performs significantly better than Betts-Miller-Janjić (BMJ) and Grell-Devenyi schemes. We also studied the impact of other physical parameterizations, namely, microphysics, boundary layer, land surface, and the radiation parameterization, on the simulation of diurnal cycle of rainfall, and identified the “best” model configuration. We used this configuration of the “best” model to perform a sensitivity study on the role of various convective components used in the KF scheme. In particular, we studied the role of convective downdrafts, convective timescale, and feedback fraction, on the simulated diurnal cycle of rainfall. The “best” model simulations, in general, show a good agreement with observations. Specifically, (i) Over CI, the simulated diurnal rainfall peak is at 1430 IST, in comparison to the observed 1430-1730 IST peak; (ii) Over Western Ghats and Burmese mountains, the model simulates a diurnal rainfall peak at 1430 IST, as opposed to the observed peak of 1430-1730 IST; (iii) Over Sumatra, both model and observations show a diurnal peak at 1730 IST; (iv) The observed southward propagating diurnal rainfall bands over BoB are weakly simulated by WRF. Besides the diurnal cycle of rainfall, the mean spatial pattern of total rainfall and its partitioning between the convective and stratiform components, are also well simulated. The “best” model configuration was used to conduct two nested simulations with one-way, three-level nesting (54-18-6km) over CI and BoB. While, the 54km and 18km simulations were conducted for the whole of July, 2006, the 6km simulation was carried out for the period 18 - 24 July, 2006. The results of our coarse- and fine-scale numerical simulations of the diurnal cycle of monsoon rainfall will be discussed.

Exergetic analysis of carbon dioxide vapour compression refrigeration cycle using the new fundamental equation of state

The purpose of this paper is to present exergy charts for carbon dioxide (CO2) based on the new fundamental equation of state and the results of a thermodynamic analysis of conventional and trans-critical vapour compression refrigeration cycles using the data thereof. The calculation scheme is anchored on the Mathematica platform. There exist upper and lower bounds for the high cycle pressure for a given set of evaporating and pre-throttling temperatures. The maximum possible exergetic efficiency for each case was determined. Empirical correlations for exergetic efficiency and COP, valid in the range of temperatures studied here, are obtained. The exergy losses have been quantified. (C) 2003 Elsevier Ltd. All rights reserved.

Albedo enhancement of marine clouds to counteract global warming: impacts on the hydrological cycle

Recent studies have shown that changes in solar radiation affect the hydrological cycle more strongly than equivalent CO(2) changes for the same change in global mean surface temperature. Thus, solar radiation management ``geoengineering'' proposals to completely offset global mean temperature increases by reducing the amount of absorbed sunlight might be expected to slow the global water cycle and reduce runoff over land. However, proposed countering of global warming by increasing the albedo of marine clouds would reduce surface solar radiation only over the oceans. Here, for an idealized scenario, we analyze the response of temperature and the hydrological cycle to increased reflection by clouds over the ocean using an atmospheric general circulation model coupled to a mixed layer ocean model. When cloud droplets are reduced in size over all oceans uniformly to offset the temperature increase from a doubling of atmospheric CO(2), the global-mean precipitation and evaporation decreases by about 1.3% but runoff over land increases by 7.5% primarily due to increases over tropical land. In the model, more reflective marine clouds cool the atmospheric column over ocean. The result is a sinking motion over oceans and upward motion over land. We attribute the increased runoff over land to this increased upward motion over land when marine clouds are made more reflective. Our results suggest that, in contrast to other proposals to increase planetary albedo, offsetting mean global warming by reducing marine cloud droplet size does not necessarily lead to a drying, on average, of the continents. However, we note that the changes in precipitation, evaporation and P-E are dominated by small but significant areas, and given the highly idealized nature of this study, a more thorough and broader assessment would be required for proposals of altering marine cloud properties on a large scale.

Scan cell reordering to minimize peak power during test cycle: A graph theoretic approach

Scan circuit is widely practiced DFT technology. The scan testing procedure consist of state initialization, test application, response capture and observation process. During the state initialization process the scan vectors are shifted into the scan cells and simultaneously the responses captured in last cycle are shifted out. During this shift operation the transitions that arise in the scan cells are propagated to the combinational circuit, which inturn create many more toggling activities in the combinational block and hence increases the dynamic power consumption. The dynamic power consumed during scan shift operation is much more higher than that of normal mode operation.