On faces of the Kunz cone and the numerical semigroups within them

A numerical semigroup is a cofinite subset of the non-negative integers that is closed under addition and contains 0. Each numerical semigroup $S$ with fixed smallest positive element $m$ corresponds to an integer point in a rational polyhedral cone $\mathcal C_m$, called the Kunz cone. Moreover, numerical semigroups corresponding to points in the same face $F \subseteq \mathcal C_m$ are known to share many properties, such as the number of minimal generators. In this work, we classify which faces of $\mathcal C_m$ contain points corresponding to numerical semigroups. Additionally, we obtain sharp bounds on the number of minimal generators of $S$ in terms of the dimension of the face of $\mathcal C_m$ containing the point corresponding to $S$

A generative flow for conditional sampling via optimal transport

Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a transport map that pushes forward a simple reference (e.g., a standard Gaussian) to a target distribution. While these approaches successfully describe many non-Gaussian problems, their performance is often limited by parametric bias and the reliability of gradient-based (adversarial) optimizers to learn these transformations. This work proposes a non-parametric generative model that iteratively maps reference samples to the target. The model uses block-triangular transport maps, whose components are shown to characterize conditionals of the target distribution. These maps arise from solving an optimal transport problem with a weighted $L^2$ cost function, thereby extending the data-driven approach in [Trigila and Tabak, 2016] for conditional sampling. The proposed approach is demonstrated on a two dimensional example and on a parameter inference problem involving nonlinear ODEs.Comment: 18 pages, 5 figure

Impaired oxysterol-liver X receptor signaling underlies aberrant cortical neurogenesis in a human stem cell model of neurodevelopmental disorder

The mechanisms by which genomic risks contribute to the onset of neuropsychiatric conditions remains a key challenge and a prerequisite for successful development of effective therapies. 15q11.2 CNV containing the CYFIP1 gene is associated with autism and schizophrenia. Using stem cell models we show that 15q11.2 deletion and CYFIP1-LoF leads to premature neuronal differentiation while CYFIP1-GoF favors neural progenitor maintenance. CYFIP1 dosage changes led to dysregulated cholesterol metabolism and altered levels of 24S,25-epoxycholesterol, which can mimic the 15q11.2del and CYFIP1-LoF phenotype by promoting cortical neuronal differentiation and restore the impaired neuronal differentiation of CYFIP1-GoF neural progenitors. Moreover, the neurogenic activity of 24S,25-epoxycholesterol is lost following genetic deletion of LXR while compound deletion of LXR in CYFIP1-/- background rescued their premature neurogenesis. This work delineates LXR mediated oxysterol regulation of neurogenesis as a pathological mechanism in neural cells carrying 15q11.2CNV and provides a potential target for therapeutic strategies for associated disorders

No Reliable Association between Runs of Homozygosity and Schizophrenia in a Well-Powered Replication Study

It is well known that inbreeding increases the risk of recessive monogenic diseases, but it is less certain whether it contributes to the etiology of complex diseases such as schizophrenia. One way to estimate the effects of inbreeding is to examine the association between disease diagnosis and genome-wide autozygosity estimated using runs of homozygosity (ROH) in genome-wide single nucleotide polymorphism arrays. Using data for schizophrenia from the Psychiatric Genomics Consortium (n = 21,868), Keller et al. (2012) estimated that the odds of developing schizophrenia increased by approximately 17% for every additional percent of the genome that is autozygous (β = 16.1, CI(β) = [6.93, 25.7], Z = 3.44, p = 0.0006). Here we describe replication results from 22 independent schizophrenia case-control datasets from the Psychiatric Genomics Consortium (n = 39,830). Using the same ROH calling thresholds and procedures as Keller et al. (2012), we were unable to replicate the significant association between ROH burden and schizophrenia in the independent PGC phase II data, although the effect was in the predicted direction, and the combined (original + replication) dataset yielded an attenuated but significant relationship between Froh and schizophrenia (β = 4.86,CI(β) = [0.90,8.83],Z = 2.40,p = 0.02). Since Keller et al. (2012), several studies reported inconsistent association of ROH burden with complex traits, particularly in case-control data. These conflicting results might suggest that the effects of autozygosity are confounded by various factors, such as socioeconomic status, education, urbanicity, and religiosity, which may be associated with both real inbreeding and the outcome measures of interest

Contribution of copy number variants to schizophrenia from a genome-wide study of 41,321 subjects

Copy number variants (CNVs) have been strongly implicated in the genetic etiology of schizophrenia (SCZ). However, genome-wide investigation of the contribution of CNV to risk has been hampered by limited sample sizes. We sought to address this obstacle by applying a centralized analysis pipeline to a SCZ cohort of 21,094 cases and 20,227 controls. A global enrichment of CNV burden was observed in cases (OR=1.11, P=5.7×10−15), which persisted after excluding loci implicated in previous studies (OR=1.07, P=1.7 ×10−6). CNV burden was enriched for genes associated with synaptic function (OR = 1.68, P = 2.8 ×10−11) and neurobehavioral phenotypes in mouse (OR = 1.18, P= 7.3 ×10−5). Genome-wide significant evidence was obtained for eight loci, including 1q21.1, 2p16.3 (NRXN1), 3q29, 7q11.2, 15q13.3, distal 16p11.2, proximal 16p11.2 and 22q11.2. Suggestive support was found for eight additional candidate susceptibility and protective loci, which consisted predominantly of CNVs mediated by non-allelic homologous recombination

Gene expression imputation across multiple brain regions provides insights into schizophrenia risk

Transcriptomic imputation approaches combine eQTL reference panels with large-scale genotype data in order to test associations between disease and gene expression. These genic associations could elucidate signals in complex genome-wide association study (GWAS) loci and may disentangle the role of different tissues in disease development. We used the largest eQTL reference panel for the dorso-lateral prefrontal cortex (DLPFC) to create a set of gene expression predictors and demonstrate their utility. We applied DLPFC and 12 GTEx-brain predictors to 40,299 schizophrenia cases and 65,264 matched controls for a large transcriptomic imputation study of schizophrenia. We identified 413 genic associations across 13 brain regions. Stepwise conditioning identified 67 non-MHC genes, of which 14 did not fall within previous GWAS loci. We identified 36 significantly enriched pathways, including hexosaminidase-A deficiency, and multiple porphyric disorder pathways. We investigated developmental expression patterns among the 67 non-MHC genes and identified specific groups of pre- and postnatal expression

Genetic correlation between amyotrophic lateral sclerosis and schizophrenia

A. Palotie on työryhmän Schizophrenia Working Grp Psychiat jäsen.We have previously shown higher-than-expected rates of schizophrenia in relatives of patients with amyotrophic lateral sclerosis (ALS), suggesting an aetiological relationship between the diseases. Here, we investigate the genetic relationship between ALS and schizophrenia using genome-wide association study data from over 100,000 unique individuals. Using linkage disequilibrium score regression, we estimate the genetic correlation between ALS and schizophrenia to be 14.3% (7.05-21.6; P = 1 x 10(-4)) with schizophrenia polygenic risk scores explaining up to 0.12% of the variance in ALS (P = 8.4 x 10(-7)). A modest increase in comorbidity of ALS and schizophrenia is expected given these findings (odds ratio 1.08-1.26) but this would require very large studies to observe epidemiologically. We identify five potential novel ALS-associated loci using conditional false discovery rate analysis. It is likely that shared neurobiological mechanisms between these two disorders will engender novel hypotheses in future preclinical and clinical studies.Peer reviewe

Mapping genomic loci implicates genes and synaptic biology in schizophrenia

Schizophrenia has a heritability of 60-80%1, much of which is attributable to common risk alleles. Here, in a two-stage genome-wide association study of up to 76,755 individuals with schizophrenia and 243,649 control individuals, we report common variant associations at 287 distinct genomic loci. Associations were concentrated in genes that are expressed in excitatory and inhibitory neurons of the central nervous system, but not in other tissues or cell types. Using fine-mapping and functional genomic data, we identify 120 genes (106 protein-coding) that are likely to underpin associations at some of these loci, including 16 genes with credible causal non-synonymous or untranslated region variation. We also implicate fundamental processes related to neuronal function, including synaptic organization, differentiation and transmission. Fine-mapped candidates were enriched for genes associated with rare disruptive coding variants in people with schizophrenia, including the glutamate receptor subunit GRIN2A and transcription factor SP4, and were also enriched for genes implicated by such variants in neurodevelopmental disorders. We identify biological processes relevant to schizophrenia pathophysiology; show convergence of common and rare variant associations in schizophrenia and neurodevelopmental disorders; and provide a resource of prioritized genes and variants to advance mechanistic studies

Age at first birth in women is genetically associated with increased risk of schizophrenia

Prof. Paunio on PGC:n jäsenPrevious studies have shown an increased risk for mental health problems in children born to both younger and older parents compared to children of average-aged parents. We previously used a novel design to reveal a latent mechanism of genetic association between schizophrenia and age at first birth in women (AFB). Here, we use independent data from the UK Biobank (N = 38,892) to replicate the finding of an association between predicted genetic risk of schizophrenia and AFB in women, and to estimate the genetic correlation between schizophrenia and AFB in women stratified into younger and older groups. We find evidence for an association between predicted genetic risk of schizophrenia and AFB in women (P-value = 1.12E-05), and we show genetic heterogeneity between younger and older AFB groups (P-value = 3.45E-03). The genetic correlation between schizophrenia and AFB in the younger AFB group is -0.16 (SE = 0.04) while that between schizophrenia and AFB in the older AFB group is 0.14 (SE = 0.08). Our results suggest that early, and perhaps also late, age at first birth in women is associated with increased genetic risk for schizophrenia in the UK Biobank sample. These findings contribute new insights into factors contributing to the complex bio-social risk architecture underpinning the association between parental age and offspring mental health.Peer reviewe

Schizophrenia-associated somatic copy-number variants from 12,834 cases reveal recurrent NRXN1 and ABCB11 disruptions

While germline copy-number variants (CNVs) contribute to schizophrenia (SCZ) risk, the contribution of somatic CNVs (sCNVs)—present in some but not all cells—remains unknown. We identified sCNVs using blood-derived genotype arrays from 12,834 SCZ cases and 11,648 controls, filtering sCNVs at loci recurrently mutated in clonal blood disorders. Likely early-developmental sCNVs were more common in cases (0.91%) than controls (0.51%, p = 2.68e−4), with recurrent somatic deletions of exons 1–5 of the NRXN1 gene in five SCZ cases. Hi-C maps revealed ectopic, allele-specific loops forming between a potential cryptic promoter and non-coding cis-regulatory elements upon 5′ deletions in NRXN1. We also observed recurrent intragenic deletions of ABCB11, encoding a transporter implicated in anti-psychotic response, in five treatment-resistant SCZ cases and showed that ABCB11 is specifically enriched in neurons forming mesocortical and mesolimbic dopaminergic projections. Our results indicate potential roles of sCNVs in SCZ risk