Dictionary Matching with One Gap

The dictionary matching with gaps problem is to preprocess a dictionary $D$ of $d$ gapped patterns $P_1,\ldots,P_d$ over alphabet $\Sigma$, where each gapped pattern $P_i$ is a sequence of subpatterns separated by bounded sequences of don't cares. Then, given a query text $T$ of length $n$ over alphabet $\Sigma$, the goal is to output all locations in $T$ in which a pattern $P_i\in D$, $1\leq i\leq d$, ends. There is a renewed current interest in the gapped matching problem stemming from cyber security. In this paper we solve the problem where all patterns in the dictionary have one gap with at least $\alpha$ and at most $\beta$ don't cares, where $\alpha$ and $\beta$ are given parameters. Specifically, we show that the dictionary matching with a single gap problem can be solved in either $O(d\log d + |D|)$ time and $O(d\log^{\varepsilon} d + |D|)$ space, and query time $O(n(\beta -\alpha )\log\log d \log ^2 \min \{ d, \log |D| \} + occ)$, where $occ$ is the number of patterns found, or preprocessing time and space: $O(d^2 + |D|)$, and query time $O(n(\beta -\alpha ) + occ)$, where $occ$ is the number of patterns found. As far as we know, this is the best solution for this setting of the problem, where many overlaps may exist in the dictionary.Comment: A preliminary version was published at CPM 201

Optimal discovery of subword associations in strings

Given a textstring x of n symbols and an integer constant d, we consider the problem of finding, for any pair (y, z) of subwords of x the number of times that y and z occur in tandem (i.e., with no intermediate occurrence of either one of them) within a distance of d symbols of x. Although in principle there might be n(4) distinct subword pairs in x, we show that it suffices to consider a family of only n(2) such pairs, with the property that for any neglected pair (y', z'), there is a corresponding pair (y, z) contained in our family and such that: (i) y' is a prefix of y and z' is a prefix of z, and (ii) the tandem index of (y', z') equals that of (y, z). We show that an algorithm for the construction of the table of all such tandem indices can be built to run in optimal O(n(2)) time and space

Viridoxins a and B: Novel Toxins From the Fungus, Metarhizium Flavoviridae

Abstract. Relational methods are gaining growing acceptance for specifying and verifying properties defined in terms of the execution of two programs—notions such as simulation, observational equivalence, non-interference, and continuity can be elegantly casted in this setting. In previous work, we have proposed program product construction as a technique to reduce relational verification to standard verification. This method hinges on the ability to interpret relational assertions as traditional predicates, which becomes problematic when considering assertions from relational separation logic. We report in this article an alternative method that overcomes this difficulty, defined as a relational weakest precondition calculus based on separation logic and formalized in the Coq proof assistant. The formalization includes an application to the formal verification of the Schorr-Waite graph marking algorithm. We discuss additional variants of relational separation logic inspired by the standard notions of partial and total correctness, and extensions of the logic to handle non-structurally equivalent programs.

Genome-wide study identifies association between HLA-B∗55:01 and Self-Reported Penicillin Allergy

Hypersensitivity reactions to drugs are often unpredictable and can be life threatening, underscoring a need for understanding their underlying mechanisms and risk factors. The extent to which germline genetic variation influences the risk of commonly reported drug allergies such as penicillin allergy remains largely unknown. We extracted data from the electronic health records of more than 600,000 participants from the UK, Estonian, and Vanderbilt University Medical Center’s BioVU biobanks to study the role of genetic variation in the occurrence of self-reported penicillin hypersensitivity reactions. We used imputed SNP to HLA typing data from these cohorts to further fine map the human leukocyte antigen (HLA) association and replicated our results in 23andMe’s research cohort involving a total of 1.12 million individuals. Genome-wide meta-analysis of penicillin allergy revealed two loci, including one located in the HLA region on chromosome 6. This signal was further fine-mapped to the HLA-B∗55:01 allele (OR 1.41 95% CI 1.33–1.49, p value 2.04 × 10−31) and confirmed by independent replication in 23andMe’s research cohort (OR 1.30 95% CI 1.25–1.34, p value 1.00 × 10−47). The lead SNP was also associated with lower lymphocyte counts and in silico follow-up suggests a potential effect on T-lymphocytes at HLA-B∗55:01. We also observed a significant hit in PTPN22 and the GWAS results correlated with the genetics of rheumatoid arthritis and psoriasis. We present robust evidence for the role of an allele of the major histocompatibility complex (MHC) I gene HLA-B in the occurrence of penicillin allergy

Overlapping genetic architecture between Parkinson disease and melanoma

Epidemiologic studies have reported inconsistent results regarding an association between Parkinson disease (PD) and cutaneous melanoma (melanoma). Identifying shared genetic architecture between these diseases can support epidemiologic findings and identify common risk genes and biological pathways. Here, we apply polygenic, linkage disequilibrium-informed methods to the largest available case-control, genome-wide association study summary statistic data for melanoma and PD. We identify positive and significant genetic correlation (correlation: 0.17, 95% CI 0.10-0.24; P = 4.09 x 10(-06)) between melanoma and PD. We further demonstrate melanoma and PD-inferred gene expression to overlap across tissues (correlation: 0.14, 95% CI 0.06 to 0.22; P = 7.87 x 10(-04)) and highlight seven genes including PIEZO1, TRAPPC2L, and SOX6 as potential mediators of the genetic correlation between melanoma and PD. These findings demonstrate specific, shared genetic architecture between PD and melanoma that manifests at the level of gene expression.Hereditary cancer genetic