Parrondo's Paradox for Games with Three Players

Parrondo’s paradox appears in game theory which asserts that playing two losing games, A and B (say) randomly or periodically may result in a winning expectation. In the original paradox the strategy of game B was capital-dependent. Some extended versions of the original Parrondo’s game as history dependent game, cooperative Parrondo’s game and others have been introduced. In all of these methods, games are played by two players. In this paper, we introduce a generalized version of this paradox by considering three players. In our extension, two games are played among three players by throwing a three-sided dice. Each player will be in one of three places in the game. We set up the conditions for parameters under which player one is in the third place in two games A and B. Then paradoxical property is obtained by combining these two games periodically and chaotically and (s)he will be in the first place when (s)he plays the games in one of the mentioned fashions. Mathematical analysis of the generalized strategy is presented and the results are also justified by computer simulations

Global haplotype partitioning for maximal associated SNP pairs

<p>Abstract</p> <p>Background</p> <p>Global partitioning based on pairwise associations of SNPs has not previously been used to define haplotype blocks within genomes. Here, we define an association index based on LD between SNP pairs. We use the Fisher's exact test to assess the statistical significance of the LD estimator. By this test, each SNP pair is characterized as associated, independent, or not-statistically-significant. We set limits on the maximum acceptable proportion of independent pairs within all blocks and search for the partitioning with maximal proportion of associated SNP pairs. Essentially, this model is reduced to a constrained optimization problem, the solution of which is obtained by iterating a dynamic programming algorithm.</p> <p>Results</p> <p>In comparison with other methods, our algorithm reports blocks of larger average size. Nevertheless, the haplotype diversity within the blocks is captured by a small number of tagSNPs. Resampling HapMap haplotypes under a block-based model of recombination showed that our algorithm is robust in reproducing the same partitioning for recombinant samples. Our algorithm performed better than previously reported models in a case-control association study aimed at mapping a single locus trait, based on simulation results that were evaluated by a block-based statistical test. Compared to methods of haplotype block partitioning, we performed best on detection of recombination hotspots.</p> <p>Conclusion</p> <p>Our proposed method divides chromosomes into the regions within which allelic associations of SNP pairs are maximized. This approach presents a native design for dimension reduction in genome-wide association studies. Our results show that the pairwise allelic association of SNPs can describe various features of genomic variation, in particular recombination hotspots.</p

Site Specific Ground Response and Liquefaction Analyses for a Project Site in New Madrid Seismic Zone

ABSTRACT: With the rapid pace of industrialization, structures are being designed and constructed in the flood plains of major rivers. In high seismicity areas, such as the New Madrid seismic zone (NMSZ), International Building Code (IBC) recommends that a site specific ground response analysis be performed if the site soils have potential for liquefaction. For projects in the NMSZ one of the major challenges for performing site specific seismic analysis is the lack of recorded ground motion data. Therefore, synthetic time histories need to be generated using the attenuation models applicable to the region. This paper provides detailed information about site specific shear wave velocity measurements using downhole method and development of site specific seismic parameters to be used for the design of structures at a project site in the bootheel area of Missouri, USA which is located in the NMSZ

An empirical method to estimate shear wave velocity of soils in the New Madrid seismic zone

In this study, a set of charts are developed to estimate shear wave velocity of soils in the New Madrid seismic zone (NMSZ), using the standard penetration test (SPT) N values and soil depths. Laboratory dynamic test results of soil samples collected from the NMSZ showed that the shear wave velocity of soils is related to the void ratio and the effective confining pressure applied to the soils. The void ratio of soils can be estimated from the SPT N values and the effective confining pressure depends on the depth of soils. Therefore, the shear wave velocity of soils can be estimated from the SPT N value and the soil depth. To make the methodology practical, two corrections should be made. One is that field SPT N values of soils must be adjusted to an unified SPT N′ value to account the effects of overburden pressure and equipment. The second is that the effect of water table to effective overburden pressure of soils must be considered. To verify the methodology, shear wave velocities of five sites in the NMSZ are estimated and compared with those obtained from field measurements. The comparison shows that our approach and the field tests are consistent with an error of less than of 15%. Thus, the method developed in this study is useful for dynamic study and practical designs in the NMSZ region. Copyright © 1996 Elsevier Science Limited