Comparative performance of some popular ANN algorithms on benchmark and function approximation problems

We report an inter-comparison of some popular algorithms within the artificial neural network domain (viz., Local search algorithms, global search algorithms, higher order algorithms and the hybrid algorithms) by applying them to the standard benchmarking problems like the IRIS data, XOR/N-Bit parity and Two Spiral. Apart from giving a brief description of these algorithms, the results obtained for the above benchmark problems are presented in the paper. The results suggest that while Levenberg-Marquardt algorithm yields the lowest RMS error for the N-bit Parity and the Two Spiral problems, Higher Order Neurons algorithm gives the best results for the IRIS data problem. The best results for the XOR problem are obtained with the Neuro Fuzzy algorithm. The above algorithms were also applied for solving several regression problems such as cos(x) and a few special functions like the Gamma function, the complimentary Error function and the upper tail cumulative $\chi^2$-distribution function. The results of these regression problems indicate that, among all the ANN algorithms used in the present study, Levenberg-Marquardt algorithm yields the best results. Keeping in view the highly non-linear behaviour and the wide dynamic range of these functions, it is suggested that these functions can be also considered as standard benchmark problems for function approximation using artificial neural networks.Comment: 18 pages 5 figures. Accepted in Pramana- Journal of Physic

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Ancestral Components of Admixed Genomes in a Mexican Cohort

For most of the world, human genome structure at a population level is shaped by interplay between ancient geographic isolation and more recent demographic shifts, factors that are captured by the concepts of biogeographic ancestry and admixture, respectively. The ancestry of non-admixed individuals can often be traced to a specific population in a precise region, but current approaches for studying admixed individuals generally yield coarse information in which genome ancestry proportions are identified according to continent of origin. Here we introduce a new analytic strategy for this problem that allows fine-grained characterization of admixed individuals with respect to both geographic and genomic coordinates. Ancestry segments from different continents, identified with a probabilistic model, are used to construct and study “virtual genomes” of admixed individuals. We apply this approach to a cohort of 492 parent–offspring trios from Mexico City. The relative contributions from the three continental-level ancestral populations—Africa, Europe, and America—vary substantially between individuals, and the distribution of haplotype block length suggests an admixing time of 10–15 generations. The European and Indigenous American virtual genomes of each Mexican individual can be traced to precise regions within each continent, and they reveal a gradient of Amerindian ancestry between indigenous people of southwestern Mexico and Mayans of the Yucatan Peninsula. This contrasts sharply with the African roots of African Americans, which have been characterized by a uniform mixing of multiple West African populations. We also use the virtual European and Indigenous American genomes to search for the signatures of selection in the ancestral populations, and we identify previously known targets of selection in other populations, as well as new candidate loci. The ability to infer precise ancestral components of admixed genomes will facilitate studies of disease-related phenotypes and will allow new insight into the adaptive and demographic history of indigenous people

Genomic Ancestry of North Africans Supports Back-to-Africa Migrations

North African populations are distinct from sub-Saharan Africans based on cultural, linguistic, and phenotypic attributes; however, the time and the extent of genetic divergence between populations north and south of the Sahara remain poorly understood. Here, we interrogate the multilayered history of North Africa by characterizing the effect of hypothesized migrations from the Near East, Europe, and sub-Saharan Africa on current genetic diversity. We present dense, genome-wide SNP genotyping array data (730,000 sites) from seven North African populations, spanning from Egypt to Morocco, and one Spanish population. We identify a gradient of likely autochthonous Maghrebi ancestry that increases from east to west across northern Africa; this ancestry is likely derived from “back-to-Africa” gene flow more than 12,000 years ago (ya), prior to the Holocene. The indigenous North African ancestry is more frequent in populations with historical Berber ethnicity. In most North African populations we also see substantial shared ancestry with the Near East, and to a lesser extent sub-Saharan Africa and Europe. To estimate the time of migration from sub-Saharan populations into North Africa, we implement a maximum likelihood dating method based on the distribution of migrant tracts. In order to first identify migrant tracts, we assign local ancestry to haplotypes using a novel, principal component-based analysis of three ancestral populations. We estimate that a migration of western African origin into Morocco began about 40 generations ago (approximately 1,200 ya); a migration of individuals with Nilotic ancestry into Egypt occurred about 25 generations ago (approximately 750 ya). Our genomic data reveal an extraordinarily complex history of migrations, involving at least five ancestral populations, into North Africa

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

History Shaped the Geographic Distribution of Genomic Admixture on the Island of Puerto Rico

Contemporary genetic variation among Latin Americans human groups reflects population migrations shaped by complex historical, social and economic factors. Consequently, admixture patterns may vary by geographic regions ranging from countries to neighborhoods. We examined the geographic variation of admixture across the island of Puerto Rico and the degree to which it could be explained by historic and social events. We analyzed a census-based sample of 642 Puerto Rican individuals that were genotyped for 93 ancestry informative markers (AIMs) to estimate African, European and Native American ancestry. Socioeconomic status (SES) data and geographic location were obtained for each individual. There was significant geographic variation of ancestry across the island. In particular, African ancestry demonstrated a decreasing East to West gradient that was partially explained by historical factors linked to the colonial sugar plantation system. SES also demonstrated a parallel decreasing cline from East to West. However, at a local level, SES and African ancestry were negatively correlated. European ancestry was strongly negatively correlated with African ancestry and therefore showed patterns complementary to African ancestry. By contrast, Native American ancestry showed little variation across the island and across individuals and appears to have played little social role historically. The observed geographic distributions of SES and genetic variation relate to historical social events and mating patterns, and have substantial implications for the design of studies in the recently admixed Puerto Rican population. More generally, our results demonstrate the importance of incorporating social and geographic data with genetics when studying contemporary admixed populations

Multi-ancestry genome-wide association meta-analysis of Parkinson’s disease

Although over 90 independent risk variants have been identified for Parkinson’s disease using genome-wide association studies, most studies have been performed in just one population at a time. Here we performed a large-scale multi-ancestry meta-analysis of Parkinson’s disease with 49,049 cases, 18,785 proxy cases and 2,458,063 controls including individuals of European, East Asian, Latin American and African ancestry. In a meta-analysis, we identified 78 independent genome-wide significant loci, including 12 potentially novel loci (MTF2, PIK3CA, ADD1, SYBU, IRS2, USP8, PIGL, FASN, MYLK2, USP25, EP300 and PPP6R2) and fine-mapped 6 putative causal variants at 6 known PD loci. By combining our results with publicly available eQTL data, we identified 25 putative risk genes in these novel loci whose expression is associated with PD risk. This work lays the groundwork for future efforts aimed at identifying PD loci in non-European populations

Author Correction: Discovery of 42 genome-wide significant loci associated with dyslexia

Correction to: Nature Genetics https://doi.org/10.1038/s41588-022-01192-y. Published online 20 October 2022. In the version of this article originally published, a paragraph was omitted in the Methods section, reading “Genomic control. Top SNPs are reported from the more conservative GWAS results adjusted for genomic control (Fig. 1, Extended Data Figs. 1–4, and Supplementary Tables 1, 2, 9 and 10), whereas downstream analyses (including gene-set analysis, enrichment and heritability partitioning, genetic correlations, polygenic prediction, candidate gene replication) are based on GWAS results without genomic control.” The paragraph has now been included in the HTML and PDF versions of the article