We give a simple and new randomized primality testing algorithm by reducing primality testing for number n to testing if a specific univariate identity over Z n holds.We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works over Z n for any n. The running time of the algorithms is polynomial in the size of arithmetic circuit representing the input polynomial and the error parameter. These algorithms use fewer random bits and work for a larger class of polynomials than all the previously known methods, for example, the Schwartz-Zippel test [Schwartz 1980;Zippel 1979], Chen-Kao and Lewin-Vadhan tests [Chen and Kao 1997;Lewin and Vadhan 1998].

We give a simple and new primality testing algorithm by reducing primality testing for number n to testing if a specific univariate identity over Z n holds.We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works over Z n for any n. The running time of the algorithms is polynomial in the size of arithmetic circuit representing the input polynomial and the error parameter. These algorithms use fewer random bits and work for a larger class of polynomials than all the previously known methods, e.g., the Schwartz-Zippel test [18,21], 10].Our algorithms first transform the input polynomial to a univariate polynomial and then use Chinese remaindering over univariate polynomials to efficiently test if it is zero.

Prediction of fold from amino acid sequence of a protein has been an active area of research in the past few years, but the limited accuracy of existing techniques emphasizes the need to develop newer approaches to tackle this task. In this study, we use contact map prediction as an intermediate step in fold prediction from sequence. Contact map is a reduced graph-theoretic representation of proteins that models the local and global inter-residue contacts in the structure. We start with a population of random contact maps for the protein sequence and "evolve" the population to a "high-feasibility" configuration using a genetic algorithm. A neural network is employed to assess the feasibility of contact maps based on their 4 physically relevant properties. We also introduce 5 parameters, based on algebraic graph theory and physical considerations, that can be used to judge the structural similarity between proteins through contact maps. To predict the fold of a given amino acid sequence, we predict a contact map that will sufficiently approximate the structure of the corresponding protein. Then we assess the similarity of this contact map with the representative contact map of each fold; the fold that corresponds to the closest match is our predicted fold for the input sequence. We have found that our feasibility measure is able to differentiate between feasible and infeasible contact maps. Further, this novel approach is able to predict the folds from sequences significantly better than a random predictor.

Runtime analysis of evolutionary algorithms has become an important part in the theoretical analysis of randomized search heuristics. The first combinatorial problem where rigorous runtime results have been achieved is the well-known single source shortest path (SSSP) problem. Scharnow, Tinnefeld and Wegener [PPSN 2002, J. Math. Model. Alg. 2004 proposed a multi-objective approach which solves the problem in expected polynomial time. They also suggest a related single-objective fitness function. However, it was left open whether this does solve the problem efficiently, and, in a broader context, whether multi-objective fitness functions for problems like the SSSP yield more efficient evolutionary algorithms. In this paper, we show that the single objective approach yields an efficient (1+1) EA with runtime bounds very close to those of the multi-objective approach.

This paper represents the prospect of mustard oil as a renewable and alternative fuel. To cope up with present load-shedding situation and to reduce the dependency on imported fuel, Bangladesh government is encour- aging the use of renewable energy sources. Since diesel engines have versatile uses including small irrigation pumping systems, and standby small electricity generators, use of diesel fuel is much higher than any other gasoline fuels. In Bangladesh mustard oil has been in use as edible oil throughout the country. Mustard is a widely growing plant in Bangladesh and every year the production of mustard seed exceeds the demand. So the endeavor was to use the surplus mustard oil as an alternative to diesel fuel. Fuel properties are determined in the fuel testing laboratory with standard procedure. An experimental set-up is then made to study the performance of a small diesel engine in the heat engine laboratory using different blends of bio-diesel converted from mustard oil. It is found that bio-diesel has slightly different properties than diesel fuel. It is also observed that with bio-diesel, the engine is capable of running without difficulty but with a deviation from its optimum performance. Initially different blends of bio-diesel (i.e. B20, B30, B50 etc,) have been used to avoid complicated modification of the engine or the fuel supply system. Finally, a comparison of engine performance for different blends of bio-diesel has been carried out to determine the optimum blend for different operating conditions