Complexity of integration, special values, and recent developments

Two questions often come up when the author discusses integration: what is the complexity of the integration process, and for what special values of parameters is an unintegrable function actually integrable. These questions have not been much considered in the formal literature, and where they have been, there is one recent development indicating that the question is more delicate than had been supposed

Power analysis for genome-wide association studies

Abstract Background Genome-wide association studies are a promising new tool for deciphering the genetics of complex diseases. To choose the proper sample size and genotyping platform for such studies, power calculations that take into account genetic model, tag SNP selection, and the population of interest are required. Results The power of genome-wide association studies can be computed using a set of tag SNPs and a large number of genotyped SNPs in a representative population, such as available through the HapMap project. As expected, power increases with increasing sample size and effect size. Power also depends on the tag SNPs selected. In some cases, more power is obtained by genotyping more individuals at fewer SNPs than fewer individuals at more SNPs. Conclusion Genome-wide association studies should be designed thoughtfully, with the choice of genotyping platform and sample size being determined from careful power calculations.</p

Satisfiability Checking and Symbolic Computation

Symbolic Computation and Satisfiability Checking are viewed as individual research areas, but they share common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite these commonalities, the two communities are currently only weakly connected. We introduce a new project SC-square to build a joint community in this area, supported by a newly accepted EU (H2020-FETOPEN-CSA) project of the same name. We aim to strengthen the connection between these communities by creating common platforms, initiating interaction and exchange, identifying common challenges, and developing a common roadmap. This abstract and accompanying poster describes the motivation and aims for the project, and reports on the first activities.Comment: 3 page Extended Abstract to accompany an ISSAC 2016 poster. Poster available at http://www.sc-square.org/SC2-AnnouncementPoster.pd

The Genetic Interpretation of Area under the ROC Curve in Genomic Profiling

Genome-wide association studies in human populations have facilitated the creation of genomic profiles which combine the effects of many associated genetic variants to predict risk of disease. The area under the receiver operator characteristic (ROC) curve is a well established measure for determining the efficacy of tests in correctly classifying diseased and non-diseased individuals. We use quantitative genetics theory to provide insight into the genetic interpretation of the area under the ROC curve (AUC) when the test classifier is a predictor of genetic risk. Even when the proportion of genetic variance explained by the test is 100%, there is a maximum value for AUC that depends on the genetic epidemiology of the disease, i.e. either the sibling recurrence risk or heritability and disease prevalence. We derive an equation relating maximum AUC to heritability and disease prevalence. The expression can be reversed to calculate the proportion of genetic variance explained given AUC, disease prevalence, and heritability. We use published estimates of disease prevalence and sibling recurrence risk for 17 complex genetic diseases to calculate the proportion of genetic variance that a test must explain to achieve AUC = 0.75; this varied from 0.10 to 0.74. We provide a genetic interpretation of AUC for use with predictors of genetic risk based on genomic profiles. We provide a strategy to estimate proportion of genetic variance explained on the liability scale from estimates of AUC, disease prevalence, and heritability (or sibling recurrence risk) available as an online calculator

Considering Trauma Exposure in the Context of Genetics Studies of Posttraumatic Stress Disorder: A Systematic Review

Background: Posttraumatic stress disorder (PTSD) is a debilitating anxiety disorder. Surveys of the general population suggest that while 50-85% of Americans will experience a traumatic event in their lifetime, only 2-50% will develop PTSD. Why some individuals develop PTSD following trauma exposure while others remain resilient is a central question in the field of trauma research. For more than half a century, the role of genetic influences on PTSD has been considered as a potential vulnerability factor. However, despite the exponential growth of molecular genetic studies over the past decade, limited progress has been made in identifying true genetic variants for PTSD. Methods: In an attempt to aid future genome wide association studies (GWAS), this paper presents a systematic review of 28 genetic association studies of PTSD. Inclusion criteria required that 1) all participants were exposed to Criterion A traumatic events, 2) polymorphisms of relevant genes were genotyped and assessed in relation to participants’ PTSD status, 3) quantitative methods were used, and 4) articles were published in English and in peer-reviewed journals. In the examination of these 28 studies, particular attention was given to variables related to trauma exposure (e.g. number of traumas, type of trauma). Results: Results indicated that most articles did not report on the GxE interaction in the context of PTSD or present data on the main effects of E despite having data available. Furthermore, some studies that did consider the GxE interaction had significant findings, underscoring the importance of examining how genotypes can modify the effect of trauma on PTSD. Additionally, results indicated that only a small number of genes continue to be studied and that there were marked differences in methodologies across studies, which subsequently limited robust conclusions. Conclusions: As trauma exposure is a necessary condition for the PTSD diagnosis, this paper identifies gaps in the current literature as well as provides recommendations for how future GWAS studies can most effectively incorporate trauma exposure data in both the design and analysis phases of studies

Replicating genotype-phenotype associations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62757/1/447655a.pd

A linkage study of candidate loci in familial Parkinson's Disease

BACKGROUND: Parkinson's disease is the second most common neurodegenerative disorder after Alzheimer's disease. Most cases are sporadic, however familial cases do exist. We examined 12 families with familial Parkinson's disease ascertained at the Movement Disorder clinic at the Oregon Health Sciences University for genetic linkage to a number of candidate loci. These loci have been implicated in familial Parkinson's disease or in syndromes with a clinical presentation that overlaps with parkinsonism, as well as potentially in the pathogenesis of the disease. METHODS: The examined loci were PARK3, Parkin, DRD (dopa-responsive dystonia), FET1 (familial essential tremor), BDNF (brain-derived neurotrophic factor), GDNF (glial cell line-derived neurotrophic factor), Ret, DAT1 (the dopamine transporter), Nurr1 and Synphilin-1. Linkage to the α-synuclein gene and the Frontotemporal dementia with parkinsonism locus on chromosome 17 had previously been excluded in the families included in this study. Using Fastlink, Genehunter and Simwalk both parametric and model-free non-parametric linkage analyses were performed. RESULTS: In the multipoint parametric linkage analysis lod scores were below -2 for all loci except FET1 and Synphilin-1 under an autosomal dominant model with incomplete penetrance. Using non-parametric linkage analysis there was no evidence for linkage, although linkage could not be excluded. A few families showed positive parametric and non-parametric lod scores indicating possible genetic heterogeneity between families, although these scores did not reach any degree of statistical significance. CONCLUSIONS: We conclude that in these families there was no evidence for linkage to any of the loci tested, although we were unable to exclude linkage with both parametric and non-parametric methods

Early onset torsion dystonia (Oppenheim's dystonia)

Early onset torsion dystonia (EOTD) is a rare movement disorder characterized by involuntary, repetitive, sustained muscle contractions or postures involving one or more sites of the body. A US study estimated the prevalence at approximately 1 in 30,000. The estimated prevalence in the general population of Europe seems to be lower, ranging from 1 in 330,000 to 1 in 200,000, although precise numbers are currently not available. The estimated prevalence in the Ashkenazi Jewish population is approximately five to ten times higher, due to a founder mutation. Symptoms of EOTD typically develop first in an arm or leg in middle to late childhood and progress in approximately 30% of patients to other body regions (generalized dystonia) within about five years. Distribution and severity of symptoms vary widely between affected individuals. The majority of cases from various ethnic groups are caused by an autosomal dominantly inherited deletion of 3 bp (GAG) in the DYT1 gene on chromosome 9q34. This gene encodes a protein named torsinA, which is presumed to act as a chaperone protein associated with the endoplasmic reticulum and the nuclear envelope. It may interact with the dopamine transporter and participate in intracellular trafficking, although its precise function within the cell remains to be determined. Molecular genetic diagnostic and genetic counseling is recommended for individuals with age of onset below 26 years, and may also be considered in those with onset after 26 years having a relative with typical early onset dystonia. Treatment options include botulinum toxin injections for focal symptoms, pharmacological therapy such as anticholinergics (most commonly trihexiphenydil) for generalized dystonia and surgical approaches such as deep brain stimulation of the internal globus pallidus or intrathecal baclofen application in severe cases. All patients have normal cognitive function, and despite a high rate of generalization of dystonia, 75% of those patients are able to maintain ambulation and independence, and therefore a comparatively good quality of life, with modern treatment modalities