Relation between Chandrasekhar's X-function and the eigenvalues of integral operators with difference kernels

Abstract is not available.

A Finite Variable Difference Relaxation Scheme for hyperbolic-parabolic equations

Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with an optimum spatial difference, using the Locally Exact Numerical Scheme (LENS), leading to a Finite Variable Difference Method as introduced by Sakai [Katsuhiro Sakai, A new finite variable difference method with application to locally exact numerical scheme, journal of Computational Physics, 124 (1996) pp. 301-308.], for the linear convection-diffusion equations obtained by using a relaxation system. Source terms are treated with the well-balanced scheme of Jin [Shi Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms, Mathematical Modeling Numerical Analysis, 35 (4) (2001) pp. 631-645]. Bench-mark test problems for scalar and vector conservation laws in one and two dimensions are solved using this new algorithm and the results demonstrate the efficiency of the scheme in capturing the flow features accurately.

trans gene regulation in adaptive evolution: A genetic algorithm model

This is a continuation of earlier studies on the evolution of infinite populations of haploid genotypes within a genetic algorithm framework. We had previously explored the evolutionary consequences of the existence of indeterminate—“plastic”—loci, where a plastic locus had a finite probability in each generation of functioning (being switched “on”) or not functioning (being switched “off”). The relative probabilities of the two outcomes were assigned on a stochastic basis. The present paper examines what happens when the transition probabilities are biased by the presence of regulatory genes. We find that under certain conditions regulatory genes can improve the adaptation of the population and speed up the rate of evolution (on occasion at the cost of lowering the degree of adaptation). Also, the existence of regulatory loci potentiates selection in favour of plasticity. There is a synergistic effect of regulatory genes on plastic alleles: the frequency of such alleles increases when regulatory loci are present. Thus, phenotypic selection alone can be a potentiating factor in a favour of better adaptation.

Genetic studies of the PRP17 gene of Saccharomyces cerevisiae: a domain essential for function maps to a nonconserved region of the protein

The PRP17 gene product is required for the second step of pre-mRNA splicing reactions. The C-terminal half of this protein bears four repeat units with homology to the beta transducin repeat. Missense mutations in three temperature-sensitive prp17 mutants map to a region in the N-terminal half of the protein. We have generated, in vitro, 11 missense alleles at the beta transducin repeat units and find that only one affects function in vivo. A phenotypically silent missense allele at the fourth repeat unit enhances the slow-growing phenotype conferred by an allele at the third repeat, suggesting an interaction between these domains. Although many missense mutations in highly conserved amino acids lack phenotypic effects, deletion analysis suggests an essential role for these units. Only mutations in the N-terminal nonconserved domain of PRP17 are synthetically lethal in combination with mutations in PRP16 and PRP18, two other gene products required for the second splicing reaction. A mutually allele-specific interaction between Prp17 and snr7, with mutations in U5 snRNA, was observed. We therefore suggest that the functional region of Prp17p that interacts with Prp18p, Prp16p, and U5 snRNA is the N terminal region of the protein.

An extragenic suppressor of prp24-1 defines genetic interaction between PRP24 and PRP21 gene products of Saccharomyces cerevisiae

The temperature-sensitive prp24-1 mutation defines a gene product required for the first step in pre-mRNA splicing. PRP24 is probably a component of the U6 snRNP particle. We have applied genetic reversion analysis to identify proteins that interact with PRP24. Spontaneous revertants of the temperature-sensitive (ts) prp24-1 phenotype were analyzed for those that are due to extragenic suppression. We then extended our analysis to screen for suppressors that confer a distinct conditional phenotype. We have identified a temperature-sensitive extragenic suppressor, which was shown by genetic complementation analysis to be allelic to prp21-1. This suppressor, prp21-2, accumulates pre-mRNA at the non-permissive temperature, a phenotype similar to that of prp21-1. prp21-2 completely suppresses the splicing defect and restores in vivo levels of the U6 snRNA in the prp24-1 strain. Genetic analysis of the suppressor showed that prp21-2 is not a bypass suppressor of prp24-1. The suppression of prp24-1 by prp21-2 is gene specific and also allele specific with respect to both the loci. Genetic interactions with other components of the pre-spliceosome have also been studied. Our results indicate an interaction between PRP21, a component of the U2 snRNP, and PRP24, a component of the U6 snRNP. These results substantiate other data showing U2-U6 snRNA interactions.

The Consequences of Phenotypic Plasticity in Cyclically Varying Environments: A Genetic Algorithm Study

By “phenotypic plasticity” we refer to the capacity of a genotype to exhibit different phenotypes, whether in the same or in different environments. We have previously demonstrated that phenotypic plasticity can improve the degree of adaptation achieved via natural selection (Behera & Nanjundiah, 1995). That result was obtained from a genetic algorithm model of haploid genotypes (idealized as one-dimensional strings of genes) evolving in a fixed environment. Here, the dynamics of evolution is examined under conditions of a cyclically varying environment. We find that the rate of evolution, as well as the extent of adaptation (as measured by mean population fitness) is lowered because of environmental cycling. The decrease is adaptation caused by a varying environment can, however, be partly or wholly compensated by an increase in the degree of plasticity that a genotype is capable of. Also, the reduction of population fitness caused by a variable environment can be partially offset by decreasing the total number of genetic loci. We conjecture that an increase in genome size may have been among the factors responsible for the evolution of phenotypic plasticity.

Conservative Design Optimization of Laminated Composite Structures Using Genetic Algorithms and Multiple Failure Criteria

This article analyzes the effect of devising a new failure envelope by the combination of the most commonly used failure criteria for the composite laminates, on the design of composite structures. The failure criteria considered for the study are maximum stress and Tsai-Wu criteria. In addition to these popular phenomenological-based failure criteria, a micromechanics-based failure criterion called failure mechanism-based failure criterion is also considered. The failure envelopes obtained by these failure criteria are superimposed over one another and a new failure envelope is constructed based on the lowest absolute values of the strengths predicted by these failure criteria. Thus, the new failure envelope so obtained is named as most conservative failure envelope. A minimum weight design of composite laminates is performed using genetic algorithms. In addition to this, the effect of stacking sequence on the minimum weight of the laminate is also studied. Results are compared for the different failure envelopes and the conservative design is evaluated, with respect to the designs obtained by using only one failure criteria. The design approach is recommended for structures where composites are the key load-carrying members such as helicopter rotor blades.

A self-adaptive migration model genetic algorithm for data mining applications

Data mining involves nontrivial process of extracting knowledge or patterns from large databases. Genetic Algorithms are efficient and robust searching and optimization methods that are used in data mining. In this paper we propose a Self-Adaptive Migration Model GA (SAMGA), where parameters of population size, the number of points of crossover and mutation rate for each population are adaptively fixed. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions and a set of actual classification datamining problems. Michigan style of classifier was used to build the classifier and the system was tested with machine learning databases of Pima Indian Diabetes database, Wisconsin Breast Cancer database and few others. The performance of our algorithm is better than others.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Genetic programming metamodel for rotating beams

This paper investigates the use of Genetic Programming (GP) to create an approximate model for the non-linear relationship between flexural stiffness, length, mass per unit length and rotation speed associated with rotating beams and their natural frequencies. GP, a relatively new form of artificial intelligence, is derived from the Darwinian concept of evolution and genetics and it creates computer programs to solve problems by manipulating their tree structures. GP predicts the size and structural complexity of the empirical model by minimizing the mean square error at the specified points of input-output relationship dataset. This dataset is generated using a finite element model. The validity of the GP-generated model is tested by comparing the natural frequencies at training and at additional input data points. It is found that by using a non-dimensional stiffness, it is possible to get simple and accurate function approximation for the natural frequency. This function approximation model is then used to study the relationships between natural frequency and various influencing parameters for uniform and tapered beams. The relations obtained with GP model agree well with FEM results and can be used for preliminary design and structural optimization studies.

A Haplotype at the UCP1 Gene Locus Contributes to Genetic Risk for Type 2 Diabetes in Asian Indians (CURES-72)

Background: The gene encoding for uncoupling protein-1 (UCP1) is considered to be a candidate gene for type 2 diabetes because of its role in thermogenesis and energy expenditure. The objective of the study was to examine whether genetic variations in the UCP1 gene are associated with type 2 diabetes and its related traits in Asian Indians. Methods: The study subjects, 810 type 2 diabetic subjects and 990 normal glucose tolerant (NGT) subjects, were chosen from the Chennai Urban Rural Epidemiological Study (CURES), an ongoing population-based study in southern India. The polymorphisms were genotyped using the polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) method. Linkage disequilibrium (LD) was estimated from the estimates of haplotypic frequencies. Results: The three polymorphisms, namely -3826A -> G, an A -> C transition in the 5'-untranslated region (UTR) and Met229Leu, were not associated with type 2 diabetes. However, the frequency of the A-C-Met (-3826A -> G-5'UTR A -> C-Met229Leu) haplotype was significantly higher among the type 2 diabetic subjects (2.67%) compared with the NGT subjects (1.45%, P < 0.01). The odds ratio for type 2 diabetes for the individuals carrying the haplotype A-C-Met was 1.82 (95% confidence interval, 1.29-2.78, P = 0.009). Conclusions: The haplotype, A-C-Met, in the UCP1 gene is significantly associated with the increased genetic risk for developing type 2 diabetes in Asian Indians.

Real-coded genetic algorithm for machining condition optimization

In this paper, we consider the machining condition optimization models presented in earlier studies. Finding the optimal combination of machining conditions within the constraints is a difficult task. Hence, in earlier studies standard optimization methods are used. The non-linear nature of the objective function, and the constraints that need to be satisfied makes it difficult to use the standard optimization methods for the solution. In this paper, we present a real coded genetic algorithm (RCGA), to find the optimal combination of machining conditions. We present various issues related to real coded genetic algorithm such as solution representation, crossover operators, and repair algorithm in detail. We also present the results obtained for these models using real coded genetic algorithm and discuss the advantages of using real coded genetic algorithm for these problems. From the results obtained, we conclude that real coded genetic algorithm is reliable and accurate for solving the machining condition optimization models.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

A Dynamic Migration Model for Self-adaptive Genetic Algorithms

In this paper, we propose a self Adaptive Migration Model for Genetic Algorithms, where parameters of population size, the number of points of crossover and mutation rate for each population are fixed adaptively. Further, the migration of individuals between populations is decided dynamically. This paper gives a mathematical schema analysis of the method stating and showing that the algorithm exploits previously discovered knowledge for a more focused and concentrated search of heuristically high yielding regions while simultaneously performing a highly explorative search on the other regions of the search space. The effective performance of the algorithm is then shown using standard testbed functions, when compared with Island model GA(IGA) and Simple GA(SGA).