Hardness of approximation results for the problem of finding the stopping distance in Tanner graphs

Tanner Graph representation of linear block codes is widely used by iterative decoding algorithms for recovering data transmitted across a noisy communication channel from errors and erasures introduced by the channel. The stopping distance of a Tanner graph T for a binary linear block code C determines the number of erasures correctable using iterative decoding on the Tanner graph T when data is transmitted across a binary erasure channel using the code C. We show that the problem of finding the stopping distance of a Tanner graph is hard to approximate within any positive constant approximation ratio in polynomial time unless P = NP. It is also shown as a consequence that there can be no approximation algorithm for the problem achieving an approximation ratio of 2(log n)(1-epsilon) for any epsilon > 0 unless NP subset of DTIME(n(poly(log n))).

Predictive testing for familial adenomatous polyposis in a rural South Indian community

During the course of genome studies in a rural community in the South Indian state of Karnataka, DNA-based investigations and counselling for familial adenomatous polyposis (FAP) were requested via the community physician. The proposita died in 1940 and FAP had been clinically diagnosed in 2 of her 5 children, both deceased. DNA samples from 2 affected individuals in the third generation were screened for mutations in the APC gene, and a frame-shift mutation was identified in exon 15 with a common deletion at codon 1061. Predictive testing for the mutation was then organized on a voluntary basis. There were 11 positive tests, including confirmatory positives on 2 persons diagnosed by colonoscopy, and to date surgery has been successfully undertaken on 3 previously undiagnosed adults. The ongoing success of the study indicates that, with appropriate access to the facilities offered by collaborating centres, predictive testing is feasible for diseases such as FAP and could be of significant benefit to communities in economically less developed countries.

A New Approach to 2-Asummability Testing

A relationship between 2-monotonicity and 2-asummability has been established and thereby a fast method for testing 2-asummability of switching functions derived. The approach is based on the fact that only a particular type of 2-sums need be examined for 2-asummability testing of 2-monotonic switching functions. These 2-sums are those which contain more than five 1's. 2-asummability testing for these 2-sums can be easily done by using the authors' technique.

On the hardness and elastic modulus of bulk metallic glass matrix composites

The influences of the amorphous matrix and crystalline dendrite phases on the hardness and elastic moduli of Zr/Ti-based bulk metallic glass matrix composites have been assessed. While the moduli of the composites correspond to those predicted by the rule of mixtures, the hardness of the composites is similar to that of the matrix, suggesting that the plastic flow in the composites under constrained conditions such as indentation is controlled by the flow resistance of the contiguous matrix. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The hardness of approximating the boxicity, cubicity and threshold dimension of a graph

A k-dimensional box is the Cartesian product R-1 X R-2 X ... X R-k where each R-i is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. A unit cube in k-dimensional space or a k-cube is defined as the Cartesian product R-1 X R-2 X ... X R-k where each R-i is a closed interval oil the real line of the form a(i), a(i) + 1]. The cubicity of G, denoted as cub(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-cubes. The threshold dimension of a graph G(V, E) is the smallest integer k such that E can be covered by k threshold spanning subgraphs of G. In this paper we will show that there exists no polynomial-time algorithm for approximating the threshold dimension of a graph on n vertices with a factor of O(n(0.5-epsilon)) for any epsilon > 0 unless NP = ZPP. From this result we will show that there exists no polynomial-time algorithm for approximating the boxicity and the cubicity of a graph on n vertices with factor O(n(0.5-epsilon)) for any epsilon > 0 unless NP = ZPP. In fact all these hardness results hold even for a highly structured class of graphs, namely the split graphs. We will also show that it is NP-complete to determine whether a given split graph has boxicity at most 3. (C) 2010 Elsevier B.V. All rights reserved.

The influence of chemical additives on surface charge and hardness of hematite

The zeta potential of high-purity hematite at pH 6 and in a 10−3N NaCl solution has been determined at different concentrations of acetone using the streaming potential technique and the results correlated with the microhardness of the mineral. The zeta potential has been found to decrease as the hardness increases reaching a minimum at 10 cc per litre concentration of acetone when the hardness reaches a maximum. The results have been explained on the basis of competitive adsorption of chloride ions and acetone molecules at low concentrations of acetone and coadsorption of both species above 10 cc per litre concentration. Acetone in distilled water and 10−3N NaCl in distilled water decrease the microhardness of hematite individually between pH 5 to 7 and in combination increase the microhardness reaching a maximum at pH 6.

Use of adult male bonnet monkeys (Macaca radiata) for testing the biological activity of gonadotropin releasing hormone and its analogues

The effect of injecting agonistic and antagonistic analogues of gonadotropin releasing hormone analogues on serum testosterone levels was checked in adult and immature male bonnet monkeys. Of the agonistic analogues Buserelin, Ovurelin and D-Phe6 Gln8 GnRH were found to be most potent in increasing serum testosterone levels in the adult male bonnet monkeys. While 27-month-old monkeys responded well to des Gly10 GnRH, only marginal response was observed in the case of 15-month-old monkeys. Studies carried out with Ovurelin indicated that it was not effective in causing desensitization in adult monkeys. The antagonistic analogue was effective in blocking nocturnal surge of serum testosterone. Based on these studies it is suggested the adult male bonnet monkeys can be effectively used for testing the activity of GnRH analogues.

Testing the efficacy of a chilli-tobacco rope fence as a deterrent against crop-raiding elephants

Chilli-based repellents have shown promise as deterrents against crop-raiding elephants in Africa. We experimented with ropes coated with chilli-based repellent as a cheap alternative to existing elephant cropraid deterrent methods in India. Three locations (Buxa Tiger Reserve, Wyanad Wildlife Sanctuary and Hosur Forest Division) representing varying rainfall regimes from high to low, and with histories of intense elephant-agriculture conflict, were selected for the experiments that were conducted over 2-3 months during the pre-harvest period of the kharif season in late 2006. Chilli and tobacco powder mixed with waste oil was applied to ropes strung around agricultural fields of 1.4-5.5 km perimeter and elephant approaches were monitored. Elephants breached the rope fences a few times at all three study sites. Female-led herds were far more deterred (practically 100% reduction) than were solitary males (c. 50%) by the chilli-tobacco rope. Efficacy of this method as a deterrent was significantly better in the low-rainfall regime relative to medium and high-rainfall regimes. The initial promising results present a case for more rigorous experimentation; these would help determine if the elephants avoiding the rope are responding physiologically to the chilli-tobacco smell or merely reacting cautiously to a novel substance in their environment.

Effect of microstructure and hardness on the grinding abrasive wear resistance of a ball bearing steel

Grinding media wear appears to be non-linear with the time of grinding in a laboratory-scale ball mill. The kinetics of wear can be expressed as a power law of the type w=atb, where the numerical constant a represents wear of a particular microstructure at time t = 1 min and b is the wear exponent which is independent of the particle size prevailing inside a ball mill at any instant of time of grinding. The wear exponent appears to be an indicator of the cutting wear mechanism in dry grinding: a plot of the inverse of the normalised wear exponent (Image ) versusHs (where Hs is the worn surface hardness of the media) yields a curve similar to that of a wear resistance plot obtained in the case of two-body sliding abrasive wear. This method of evaluating the cutting wear resistance of media is demonstrated by employing 15 different microstructures of AISI-SAE 52100 steel balls in dry grinding of quartz in a laboratory-scale ball mill.

Role of Surface Texture, Roughness, and Hardness on Friction During Unidirectional Sliding

In the present investigation, experiments were conducted by unidirectional sliding of pins made of FCC metals (Pb, Al, and Cu) with significantly different hardness values against the steel plates of various surface textures and roughness using an inclined pin-on-plate sliding apparatus in ambient conditions under both the dry and lubricated conditions. For a given material pair, it was observed that transfer layer formation and the coefficient of friction along with its two components, namely adhesion and plowing, are controlled by the surface texture of the harder mating surfaces and are less dependent of surface roughness (R (a)) of the harder mating surfaces. The effect of surface texture on the friction was attributed to the variation of the plowing component of friction for different surfaces. It was also observed that the variation of plowing friction as a function of hardness depends on surface textures. More specifically, the plowing friction varies with hardness of the soft materials for a given type of surface texture and it is independent of hardness of soft materials for other type of surface texture. These variations could be attributed to the extent of plane strain conditions taking place at the asperity level during sliding. It was also observed that among the surface roughness parameters, the mean slope of the profile, Delta (a), correlated best with the friction. Furthermore, dimensionless quantifiable roughness parameters were formulated to describe the degree of plowing taking place at the asperity level.

The scratch hardness and friction of a soft rigid-plastic solid

The paper describes an experimental and analytical study of the normal and scratch hardnesses of a model soft rigid-plastic solid. The material known as ‘Plasticine’, a mixture of dry particles and a mineral oil, has been deformed with a range of rigid conical indentors with included angles of between 30° and 170°. The sliding velocity dependence of the computed scratch hardness and friction has been examined in the velocity range 0.19 mm/s to 7.3 m/s. Data are also described for the time dependence of the normal hardness and also the estimated rate dependence of the intrinsic flow stress. The latter values were estimated from data obtained during the upsetting of right cylinders. Three major conclusions are drawn from these data and the associated analysis. (1) A first-order account of the scratching force may be provided by adopting a model which sums the computed plastic deformation and interfacial sliding contributions to the total sliding work. This is tantamount to the adoption of the two-term non-interacting model of friction. (2) For this system during sliding, at high sliding velocities at least, the interface shear stress which defines the boundary condition is not directly related to the bulk shear stress. The interface rheological characteristics indicate an appreciable dependence on the imposed strain or strain rate. In particular, the relative contributions of the slip and stick boundary conditions appear to be a function of the imposed sliding velocity. (3) The computed normal and scratch hardness values are not simply interrelated primarily because of the evolving boundary conditions which appear to exist in the scratching experiments.

Microtensile testing of a free-standing Pt-aluminide bond coat

A finite element method (FEM)-based study has been carried out for the design of flat microtensile samples to evaluate tensile properties of Pt-aluminide (PtAl) bond coats. The critical dimensions of the sample have been determined using a two-dimensional elastic stress analysis. In the present testing scheme, the ratio of the dimensions of the holding length to the fillet radius of the sample was found important to achieve failure within the gage length. The effect of gage length and grip head length also has been examined. The simulation predictions have been experimentally verified by conducting microtensile test of an actual PtAl bond coat at room temperature. The sample design and testing scheme suggested in this study have also been found suitable for evaluation of tensile properties at high temperature. (C) 2010 Elsevier Ltd. All rights reserved.