A Lower-Bound Result on the Power of a Genetic Algorithm

This paper presents a lower-bound result on the computational power of a genetic algorithm in the context of combinatorial optimization. We describe a new genetic algorithm, the merged genetic algorithm, and prove that for the class of monotonic functions, the algorithm finds the optimal solution, and does so with an exponential convergence rate. The analysis pertains to the ideal behavior of the algorithm where the main task reduces to showing convergence of probability distributions over the search space of combinatorial structures to the optimal one. We take exponential convergence to be indicative of efficient solvability for the sample-bounded algorithm, although a sampling theory is needed to better relate the limit behavior to actual behavior. The paper concludes with a discussion of some immediate problems that lie ahead.

Geometric Generalizations of the Power of Two Choices

A well-known paradigm for load balancing in distributed systems is the``power of two choices,''whereby an item is stored at the less loaded of two (or more) random alternative servers. We investigate the power of two choices in natural settings for distributed computing where items and servers reside in a geometric space and each item is associated with the server that is its nearest neighbor. This is in fact the backdrop for distributed hash tables such as Chord, where the geometric space is determined by clockwise distance on a one-dimensional ring. Theoretically, we consider the following load balancing problem. Suppose that servers are initially hashed uniformly at random to points in the space. Sequentially, each item then considers d candidate insertion points also chosen uniformly at random from the space,and selects the insertion point whose associated server has the least load. For the one-dimensional ring, and for Euclidean distance on the two-dimensional torus, we demonstrate that when n data items are hashed to n servers,the maximum load at any server is log log n / log d + O(1) with high probability. While our results match the well-known bounds in the standard setting in which each server is selected equiprobably, our applications do not have this feature, since the sizes of the nearest-neighbor regions around servers are non-uniform. Therefore, the novelty in our methods lies in developing appropriate tail bounds on the distribution of nearest-neighbor region sizes and in adapting previous arguments to this more general setting. In addition, we provide simulation results demonstrating the load balance that results as the system size scales into the millions.

Bounds on the Power of Constant-Depth Quantum Circuits

We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 ⊆ P, where EQNC^0 is the constant-depth analog of the class EQP. On the other hand, we adapt and extend ideas of Terhal and DiVincenzo [?] to show that, for any family

Genetic correlates of longevity and selected age-related phenotypes: a genome-wide association study in the Framingham Study

BACKGROUND: Family studies and heritability estimates provide evidence for a genetic contribution to variation in the human life span. METHODS:We conducted a genome wide association study (Affymetrix 100K SNP GeneChip) for longevity-related traits in a community-based sample. We report on 5 longevity and aging traits in up to 1345 Framingham Study participants from 330 families. Multivariable-adjusted residuals were computed using appropriate models (Cox proportional hazards, logistic, or linear regression) and the residuals from these models were used to test for association with qualifying SNPs (70, 987 autosomal SNPs with genotypic call rate [greater than or equal to]80%, minor allele frequency [greater than or equal to]10%, Hardy-Weinberg test p [greater than or equal to] 0.001).RESULTS:In family-based association test (FBAT) models, 8 SNPs in two regions approximately 500 kb apart on chromosome 1 (physical positions 73,091,610 and 73, 527,652) were associated with age at death (p-value < 10-5). The two sets of SNPs were in high linkage disequilibrium (minimum r2 = 0.58). The top 30 SNPs for generalized estimating equation (GEE) tests of association with age at death included rs10507486 (p = 0.0001) and rs4943794 (p = 0.0002), SNPs intronic to FOXO1A, a gene implicated in lifespan extension in animal models. FBAT models identified 7 SNPs and GEE models identified 9 SNPs associated with both age at death and morbidity-free survival at age 65 including rs2374983 near PON1. In the analysis of selected candidate genes, SNP associations (FBAT or GEE p-value < 0.01) were identified for age at death in or near the following genes: FOXO1A, GAPDH, KL, LEPR, PON1, PSEN1, SOD2, and WRN. Top ranked SNP associations in the GEE model for age at natural menopause included rs6910534 (p = 0.00003) near FOXO3a and rs3751591 (p = 0.00006) in CYP19A1. Results of all longevity phenotype-genotype associations for all autosomal SNPs are web posted at http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007. CONCLUSION: Longevity and aging traits are associated with SNPs on the Affymetrix 100K GeneChip. None of the associations achieved genome-wide significance. These data generate hypotheses and serve as a resource for replication as more genes and biologic pathways are proposed as contributing to longevity and healthy aging.