{"results":[{"id":"crossref_10.3390/genes13071120","title":"Gene-Based Association Tests Using New Polygenic Risk Scores and Incorporating Gene Expression Data","authors":[{"name":"Shijia Yan"},{"name":"Qiuying Sha"},{"name":"Shuanglin Zhang"}],"abstract":"Recently, gene-based association studies have shown that integrating genome-wide association studies (GWAS) with expression quantitative trait locus (eQTL) data can boost statistical power and that the genetic liability of traits can be captured by polygenic risk scores (PRSs). In this paper, we propose a new gene-based statistical method that leverages gene-expression measurements and new PRSs to identify genes that are associated with phenotypes of interest. We used a generalized linear model to associate phenotypes with gene expression and PRSs and used a score-test statistic to test the association between phenotypes and genes. Our simulation studies show that the newly developed method has correct type I error rates and can boost statistical power compared with other methods that use either gene expression or PRS in association tests. A real data analysis figure based on UK Biobank data for asthma shows that the proposed method is applicable to GWAS.","source":"CrossRef","year":2022,"language":"en","subjects":null,"doi":"10.3390/genes13071120","url":"https://doi.org/10.3390/genes13071120","is_open_access":true,"citations":5,"published_at":"","score":66.15},{"id":"ss_a4a358b0546fe50b28315cf1a1a08e0adb5698a3","title":"Improved Approximation of Maximum Vertex Coverage Problem on Bipartite Graphs","authors":[{"name":"N. Apollonio"},{"name":"B. Simeone"}],"abstract":"","source":"Semantic Scholar","year":2014,"language":"en","subjects":["Mathematics","Computer Science"],"doi":"10.1137/130931059","url":"https://www.semanticscholar.org/paper/a4a358b0546fe50b28315cf1a1a08e0adb5698a3","is_open_access":true,"citations":14,"published_at":"","score":58.42},{"id":"ss_681404c48c84ebbf712a7b39fd9c6545f1ed84d0","title":"d-COS-R is FPT via Interval Deletion","authors":[{"name":"N. Narayanaswamy"},{"name":"R. Subashini"}],"abstract":"A binary matrix $M$ has the Consecutive Ones Property (COP) if there exists a permutation of columns that arranges the ones consecutively in all the rows. Given a matrix, the $d$-COS-R problem is to determine if there exists a set of at most $d$ rows whose deletion results in a matrix with COP. We consider the parameterized complexity of this problem with respect to the number $d$ of rows to be deleted as the parameter. The closely related Interval Deletion problem has recently shown to be FPT [Y. Cao and D. Marx, Interval Deletion is Fixed-Parameter Tractable, arXiv:1211.5933 [cs.DS],2012]. In this work, we describe a recursive depth-bounded search tree algorithm in which the problems at the leaf-level are solved as instances of Interval Deletion. The running time of the algorithm is dominated by the running time of Interval Deletion, and therefore we show that $d$-COS-R is fixed-parameter tractable and has a run-time of $O^*(10^d)$.","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Computer Science","Mathematics"],"url":"https://www.semanticscholar.org/paper/681404c48c84ebbf712a7b39fd9c6545f1ed84d0","is_open_access":true,"citations":1,"published_at":"","score":57.03},{"id":"doaj_10.46298/dmtcs.2995","title":"Adaptive compression against a countable alphabet","authors":[{"name":"Dominique Bontemps"},{"name":"Stephane Boucheron"},{"name":"Elisabeth Gassiat"}],"abstract":"This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and non-decreasing hazard rate. We prove that the auto-censuring (AC) code introduced by Bontemps (2011) is adaptive with respect to the collection of such classes. The analysis builds on the tight characterization of universal redundancy rate in terms of metric entropy by Haussler and Opper (1997) and on a careful analysis of the performance of the AC-coding algorithm. The latter relies on non-asymptotic bounds for maxima of samples from discrete distributions with finite and non-decreasing hazard rate.","source":"DOAJ","year":2012,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2995","url":"https://dmtcs.episciences.org/2995/pdf","pdf_url":"https://dmtcs.episciences.org/2995/pdf","is_open_access":true,"published_at":"","score":56},{"id":"doaj_10.46298/dmtcs.2984","title":"Additive tree functionals with small toll functions and subtrees of random trees","authors":[{"name":"Stephan Wagner"}],"abstract":"Many parameters of trees are additive in the sense that they can be computed recursively from the sum of the branches plus a certain toll function. For instance, such parameters occur very frequently in the analysis of divide-and-conquer algorithms. Here we are interested in the situation that the toll function is small (the average over all trees of a given size $n$ decreases exponentially with $n$). We prove a general central limit theorem for random labelled trees and apply it to a number of examples. The main motivation is the study of the number of subtrees in a random labelled tree, but it also applies to classical instances such as the number of leaves.","source":"DOAJ","year":2012,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.2984","url":"https://dmtcs.episciences.org/2984/pdf","pdf_url":"https://dmtcs.episciences.org/2984/pdf","is_open_access":true,"published_at":"","score":56},{"id":"doaj_10.46298/dmtcs.3012","title":"Infinite Systems of Functional Equations and Gaussian Limiting Distributions","authors":[{"name":"Michael Drmota"},{"name":"Bernhard Gittenberger"},{"name":"Johannes F. Morgenbesser"}],"abstract":"In this paper infinite systems of functional equations in finitely or infinitely many random variables arising in combinatorial enumeration problems are studied. We prove sufficient conditions under which the combinatorial random variables encoded in the generating function of the system tend to a finite or infinite dimensional limiting distribution.","source":"DOAJ","year":2012,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3012","url":"https://dmtcs.episciences.org/3012/pdf","pdf_url":"https://dmtcs.episciences.org/3012/pdf","is_open_access":true,"published_at":"","score":56},{"id":"ss_9dd3c66d07a4b0e3beb41dc63019f6520f5add20","title":"Greedy Algorithms for Multi-Queue Buffer Management with Class Segregation (New Trends in Algorithms and Theory of Computation)","authors":[{"name":"T. Itoh"},{"name":"Seiji Yoshimoto"}],"abstract":"In this paper, we focus on a multi-queue buffer management in which packets of different values are segregated in different queues. Our model consists of m packets values and m queues. Recently, Al-Bawani and Souza (arXiv:1103.6049v2 [cs.DS] 30 Mar 2011) presented an online multi-queue buffer management algorithm Greedy and showed that it is 2-competitive for the general m-valued case, i.e., m packet values are 0 \u003c v_{1} \u003c v_{2} \u003c ... \u003c v_{m}, and (1+v_{1}/v_{2})-competitive for the two-valued case, i.e., two packet values are 0 \u003c v_{1} \u003c v_{2}. For the general m-valued case, let c_i = (v_{i} + \\sum_{j=1}^{i-1} 2^{j-1} v_{i-j})/(v_{i+1} + \\sum_{j=1}^{i-1}2^{j-1}v_{i-j}) for 1 \\leq i \\leq m-1, and let c_{m}^{*} = \\max_{i} c_{i}. In this paper, we precisely analyze the competitive ratio of Greedy for the general m-valued case, and show that the algorithm Greedy is (1+c_{m}^{*})-competitive.","source":"Semantic Scholar","year":2011,"language":"en","subjects":["Computer Science","Mathematics"],"url":"https://www.semanticscholar.org/paper/9dd3c66d07a4b0e3beb41dc63019f6520f5add20","is_open_access":true,"citations":1,"published_at":"","score":55.03},{"id":"ss_2f32b2fc535edd755ae14014e984b2f3af05fe06","title":"Greedy Algorithms for Multi-Queue Buffer Management Policies with Class Segregation","authors":[{"name":"T. Itoh"},{"name":"Seiji Yoshimoto"}],"abstract":"","source":"Semantic Scholar","year":2011,"language":"en","subjects":["Mathematics","Computer Science"],"url":"https://www.semanticscholar.org/paper/2f32b2fc535edd755ae14014e984b2f3af05fe06","is_open_access":true,"published_at":"","score":55},{"id":"ss_f713732c9320eb6cc9b46d339f43578b3829d319","title":"HIM Trimester Program on Analysis and Numerics for High Dimensional Problems","authors":[{"name":"M. Hegland"},{"name":"V. Pestov"},{"name":"I. Sloan"}],"abstract":"","source":"Semantic Scholar","year":2011,"language":"en","subjects":null,"url":"https://www.semanticscholar.org/paper/f713732c9320eb6cc9b46d339f43578b3829d319","is_open_access":true,"published_at":"","score":55},{"id":"ss_890e807f3bf75f6d15136cc11304abcf30da207f","title":"N A ] 1 4 M ay 2 00 7 Nearly-Linear Time Algorithms for Preconditioning and Solving Symmetric , Diagonally Dominant Linear Systems ∗","authors":[{"name":"D. Spielman"},{"name":"S. Teng"}],"abstract":"","source":"Semantic Scholar","year":2009,"language":"en","subjects":null,"url":"https://www.semanticscholar.org/paper/890e807f3bf75f6d15136cc11304abcf30da207f","is_open_access":true,"published_at":"","score":53},{"id":"ss_b82d6cb2d0ee6622a10d7cca439be300ce720666","title":"Smoothed analysis of termination of linear programming algorithms","authors":[{"name":"D. Spielman"},{"name":"S. Teng"}],"abstract":"","source":"Semantic Scholar","year":2003,"language":"en","subjects":["Mathematics","Computer Science"],"doi":"10.1007/s10107-003-0448-9","url":"https://www.semanticscholar.org/paper/b82d6cb2d0ee6622a10d7cca439be300ce720666","is_open_access":true,"citations":56,"published_at":"","score":51.68},{"id":"doaj_10.46298/dmtcs.3518","title":"Expected values of statistics on permutation tableaux","authors":[{"name":"Sylvie Corteel"},{"name":"Pawel Hitczenko"}],"abstract":"Permutation tableaux are new objects that were introduced by Postnikov in the context of enumeration of the totally positive Grassmannian cells. They are known to be in bijection with permutations and recently, they have been connected to PASEP model used in statistical physics. Properties of permutation tableaux became a focus of a considerable research activity. In this paper we study properties of basic statistics defined on permutation tableaux. We present a simple and unified approach based on probabilistic techniques and use it to compute the expected values of basic statistics defined on permutation tableaux. We also provide a non―bijective and very simple proof that there are n! permutation tableaux of length n.","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3518","url":"https://dmtcs.episciences.org/3518/pdf","pdf_url":"https://dmtcs.episciences.org/3518/pdf","is_open_access":true,"published_at":"","score":51},{"id":"doaj_10.46298/dmtcs.3547","title":"On expected number of maximal points in polytopes","authors":[{"name":"Yu. Baryshnikov"}],"abstract":"We answer an old question: what are possible growth rates of the expected number of vector-maximal points in a uniform sample from a polytope.","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3547","url":"https://dmtcs.episciences.org/3547/pdf","pdf_url":"https://dmtcs.episciences.org/3547/pdf","is_open_access":true,"published_at":"","score":51},{"id":"doaj_10.46298/dmtcs.3528","title":"Distributional asymptotics in the analysis of algorithms: Periodicities and discretization","authors":[{"name":"Rudolf Grübel"}],"abstract":"It is well known that many distributions that arise in the analysis of algorithms have an asymptotically fluctuating behaviour in the sense that we do not have 'full' convergence, but only convergence along suitable subsequences as the size of the input to the algorithm tends to infinity. We are interested in constructions that display such behaviour via an ordinarily convergent background process in the sense that the periodicities arise from this process by deterministic transformations, typically involving discretization as a decisive step. This leads to structural representations of the resulting family of limit distributions along subsequences, which in turn may give access to their properties, such as the tail behaviour (unsuccessful search in digital search trees) or the dependence on parameters of the algorithm (success probability in a selection algorithm).","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3528","url":"https://dmtcs.episciences.org/3528/pdf","pdf_url":"https://dmtcs.episciences.org/3528/pdf","is_open_access":true,"published_at":"","score":51},{"id":"doaj_10.46298/dmtcs.3521","title":"Degree distribution of random Apollonian network structures and Boltzmann sampling","authors":[{"name":"Alexis Darrasse"},{"name":"Michèle Soria"}],"abstract":"Random Apollonian networks have been recently introduced for representing real graphs. In this paper we study a modified version: random Apollonian network structures (RANS), which preserve the interesting properties of real graphs and can be handled with powerful tools of random generation. We exhibit a bijection between RANS and ternary trees, that transforms the degree of nodes in a RANS into the size of particular subtrees. The distribution of degrees in RANS can thus be analysed within a bivariate Boltzmann model for the generation of random trees, and we show that it has a Catalan form which reduces to a power law with an exponential cutoff: $α ^k k^{-3/2}$, with $α = 8/9$. We also show analogous distributions for the degree in RANS of higher dimension, related to trees of higher arity.","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3521","url":"https://dmtcs.episciences.org/3521/pdf","pdf_url":"https://dmtcs.episciences.org/3521/pdf","is_open_access":true,"published_at":"","score":51},{"id":"doaj_10.46298/dmtcs.3551","title":"Coherent random permutations with record statistics","authors":[{"name":"Alexander Gnedin"}],"abstract":"A two-parameter family of random permutations of $[n]$ is introduced, with distribution conditionally uniform given the counts of upper and lower records. The family interpolates between two versions of Ewens' distribution. A distinguished role of the family is determined by the fact that every sequence of coherent permutations $(π _n,n=1,2,\\ldots)$ with the indicated kind of sufficiency is obtainable by randomisation of the parameters. Generating algorithms and asymptotic properties of the permutations follow from the representation via initial ranks.","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3551","url":"https://dmtcs.episciences.org/3551/pdf","pdf_url":"https://dmtcs.episciences.org/3551/pdf","is_open_access":true,"published_at":"","score":51},{"id":"doaj_10.46298/dmtcs.3523","title":"The average position of the first maximum in a sample of geometric random variables","authors":[{"name":"Margaret Archibald"},{"name":"Arnold Knopfmacher"}],"abstract":"We consider samples of n geometric random variables $(Γ _1, Γ _2, \\dots Γ _n)$ where $\\mathbb{P}\\{Γ _j=i\\}=pq^{i-1}$, for $1≤j ≤n$, with $p+q=1$. The parameter we study is the position of the first occurrence of the maximum value in a such a sample. We derive a probability generating function for this position with which we compute the first two (factorial) moments. The asymptotic technique known as Rice's method then yields the main terms as well as the Fourier expansions of the fluctuating functions arising in the expected value and the variance.","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3523","url":"https://dmtcs.episciences.org/3523/pdf","pdf_url":"https://dmtcs.episciences.org/3523/pdf","is_open_access":true,"published_at":"","score":51},{"id":"doaj_10.46298/dmtcs.3534","title":"Random permutations and their discrepancy process","authors":[{"name":"Guillaume Chapuy"}],"abstract":"Let $\\sigma$ be a random permutation chosen uniformly over the symmetric group $\\mathfrak{S}_n$. We study a new \"process-valued\" statistic of $\\sigma$, which appears in the domain of computational biology to construct tests of similarity between ordered lists of genes. More precisely, we consider the following \"partial sums\": $Y^{(n)}_{p,q} = \\mathrm{card} \\{1 \\leq i \\leq p : \\sigma_i  \\leq q \\}$ for $0 \\leq p,q \\leq n$. We show that a suitable normalization of $Y^{(n)}$ converges weakly to a bivariate tied down brownian bridge on $[0,1]^2$, i.e. a continuous centered gaussian process $X^{\\infty}_{s,t}$ of covariance: $\\mathbb{E}[X^{\\infty}_{s,t}X^{\\infty}_{s',t'}] = (min(s,s')-ss')(min(t,t')-tt')$.","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3534","url":"https://dmtcs.episciences.org/3534/pdf","pdf_url":"https://dmtcs.episciences.org/3534/pdf","is_open_access":true,"published_at":"","score":51},{"id":"doaj_10.46298/dmtcs.3542","title":"On the Ehrenfeucht-Mycielski Balance Conjecture","authors":[{"name":"John C. Kieffer"},{"name":"W. Szpankowski"}],"abstract":"In 1992, A. Ehrenfeucht and J. Mycielski defined a seemingly pseudorandom binary sequence which has since been termed the EM-sequence. The balance conjecture for the EM-sequence, still open, is the conjecture that the sequence of EM-sequence initial segment averages converges to $1/2$. In this paper, we do not prove the balance conjecture but we do make some progress concerning it, namely, we prove that every limit point of the aforementioned sequence of averages lies in the interval $[1/4,3/4]$, improving the best previous result that every such limit point belongs to the interval $[0.11,0.89]$. Our approach is novel and exploits an analysis of the growth behavior as $n \\to \\infty$ of the rooted tree formed by the binary strings appearing at least twice as substrings of the length $n$ initial segment of the EM-sequence.","source":"DOAJ","year":2007,"language":"","subjects":["Mathematics"],"doi":"10.46298/dmtcs.3542","url":"https://dmtcs.episciences.org/3542/pdf","pdf_url":"https://dmtcs.episciences.org/3542/pdf","is_open_access":true,"published_at":"","score":51},{"id":"ss_4dfd12720c3057870bbab5fbda21bd6602fd7bc9","title":"On the Satisfiability of Random k-Horn Formulae","authors":[{"name":"Gabriel Istrate"}],"abstract":"We determine the asymptotical satisfiability probability of a random at-most-k-Horn formula, via a probabilistic analysis of a simple version, called PUR, of positive unit resolution. We show that for $k=k(n)\\rightarrow \\infty$ the problem can be ``reduced''to the case k(n)=n, that was solved in cs.DS/9912001. On the other hand, in the case k= a constant the behavior of PUR is modeled by a simple queuing chain, leading to a closed-form solution when $k=2$. Our analysis predicts an ``easy-hard-easy''pattern in this latter case. Under a rescaled parameter, the graphs of satisfaction probability corresponding to finite values of k converge to the one for the uniform case, a ``dimension-dependent behavior''similar to the one found experimentally by Kirkpatrick and Selman (Science'94) for k-SAT. The phenomenon is qualitatively explained by a threshold property for the number of iterations of PUR makes on random satisfiable Horn formulas.","source":"Semantic Scholar","year":2000,"language":"en","subjects":["Computer Science","Mathematics"],"doi":"10.1090/dimacs/063/09","url":"https://www.semanticscholar.org/paper/4dfd12720c3057870bbab5fbda21bd6602fd7bc9","is_open_access":true,"citations":4,"published_at":"","score":50.12}],"total":109120,"page":1,"page_size":20,"sources":["DOAJ","CrossRef","Semantic Scholar"],"query":"cs.DS"}