The Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory

Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the process and the time $t_{\rm max}$ at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting $H=1/2 + \varepsilon$. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of $H$ test these analytical predictions and show excellent agreement, even for large $\varepsilon$.Comment: 5 pages, 7 figure

Perturbative Expansion for the Maximum of Fractional Brownian Motion

Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst exponent $H$. For $H=1/2$, Brownian motion is recovered. We develop a perturbative approach to treat the non-locality in time in an expansion in $\varepsilon = H-1/2$. This allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics: The maximum $m$ of the process and the time $t_{\text{max}}$ at which this maximum is reached, as well as their joint distribution. We test our analytical predictions with extensive numerical simulations for different values of $H$. They show excellent agreement, even for $H$ far from $1/2$.Comment: 28 pages, 9 figure

Transcriptional and translational expression of calbindin-D9k in the duodenum, kidney and uterus of a female canine model

Calbindin-D9k (CaBP-9k) is a cytosolic calcium-binding protein expressed in tissues in the intestine, uterus, placenta, kidney, pituitary gland and bone. Its exact function is unknown, but it is considered to regulate intracytoplasmic concentration and transport of free ions (Ca2+). CaBP-9k protein is involved in intestinal calcium absorption in the intestine and in the regulation of myometrial activity by intracellular calcium in the uterus. Renal CaBP-9k protein is expressed at the site of calcium re-absorption in the kidney and expressed in distal convoluted tubules, where it is thought to facilitate calcium re-absorption. Expression of the CaBP-9k gene has been explored in most mammalians except in a canine model. Presently, we elucidated the expression of CaBP-9k mRNA and protein in the duodenum, kidney and uterus in a canine model involving two adult (2.5-year-old) female beagles. To collect tissues, the dogs were euthanized and then the abdominal cavity was exposed by midline incision. The proximal duodenum, cortex of kidney and uterine horn were collected. Expression of CaBP-9k mRNA was confirmed by reverse transcription-polymerase chain reaction (RT-PCR) and real-time PCR. CaBP-9k protein expression and localization were ascertained by Western blot analysis and immunohistochemistry, respectively. CaBP-9k mRNA was detected in the duodenum, but not in the kidney and uterus. Its protein was expressed only in the enterocytes of the duodenum. Taken together, the results indicate that CaBP-9k mRNA and protein are highly expressed in the enterocytes of the duodenum of a canine model, consistent with findings in other mammalian species

Exploratory analysis of obsessive compulsive symptom dimensions in children and adolescents: a Prospective follow-up study

BACKGROUND: Recent statistical approaches based on factor analysis of obsessive compulsive (OC) symptoms in adult patients have identified dimensions that seem more effective in symptom-based taxonomies and appear to be more stable over time. Although a phenotypic continuum from childhood to adulthood has been hypothesized, no factor analytic studies have been performed in juvenile patients, and the stability of OC dimensions in children and adolescents has not been assessed. METHODS: This study was designed to perform an exploratory factor analysis of OC symptoms in a sample of children and adolescents with OC disorder (OCD) and to investigate the course of factors over time (mean follow-up period: four years). RESULTS: We report for the first time that four symptom dimensions, remarkably similar to those previously described in adults, underlined the heterogeneity of OC symptoms in children and adolescents. Moreover, after follow-up, the symptom dimensions identified remained essentially unmodified. The changes observed concerned the intensity of dimensions rather than shifts from one dimension to another. CONCLUSION: These findings reinforce the hypothesis of a phenotypic continuum of OC symptoms from childhood to adulthood. They also strengthen the interest for investigating the clinical, neurobiological and genetic heterogeneity of OCD using a dimension-based approach

CNTN6 mutations are risk factors for abnormal auditory sensory perception in autism spectrum disorders

Contactin genes CNTN5 and CNTN6 code for neuronal cell adhesion molecules that promote neurite outgrowth in sensory-motor neuronal pathways. Mutations of CNTN5 and CNTN6 have previously been reported in individuals with autism spectrum disorders (ASDs), but very little is known on their prevalence and clinical impact. In this study, we identified CNTN5 and CNTN6 deleterious variants in individuals with ASD. Among the carriers, a girl with ASD and attention-deficit/hyperactivity disorder was carrying five copies of CNTN5. For CNTN6, both deletions (6/1534 ASD vs 1/8936 controls; P=0.00006) and private coding sequence variants (18/501 ASD vs 535/33480 controls; P=0.0005) were enriched in individuals with ASD. Among the rare CNTN6 variants, two deletions were transmitted by fathers diagnosed with ASD, one stop mutation CNTN6W923X was transmitted by a mother to her two sons with ASD and one variant CNTN6P770L was found de novo in a boy with ASD. Clinical investigations of the patients carrying CNTN5 or CNTN6 variants showed that they were hypersensitive to sounds (a condition called hyperacusis) and displayed changes in wave latency within the auditory pathway. These results reinforce the hypothesis of abnormal neuronal connectivity in the pathophysiology of ASD and shed new light on the genes that increase risk for abnormal sensory perception in ASD

A novel microdeletion syndrome at 3q13.31 characterised by developmental delay, postnatal overgrowth, hypoplastic male genitals, and characteristic facial features

Item does not contain fulltextBACKGROUND: Congenital deletions affecting 3q11q23 have rarely been reported and only five cases have been molecularly characterised. Genotype-phenotype correlation has been hampered by the variable sizes and breakpoints of the deletions. In this study, 14 novel patients with deletions in 3q11q23 were investigated and compared with 13 previously reported patients. METHODS: Clinical data were collected from 14 novel patients that had been investigated by high resolution microarray techniques. Molecular investigation and updated clinical information of one cytogenetically previously reported patient were also included. RESULTS: The molecular investigation identified deletions in the region 3q12.3q21.3 with different boundaries and variable sizes. The smallest studied deletion was 580 kb, located in 3q13.31. Genotype-phenotype comparison in 24 patients sharing this shortest region of overlapping deletion revealed several common major characteristics including significant developmental delay, muscular hypotonia, a high arched palate, and recognisable facial features including a short philtrum and protruding lips. Abnormal genitalia were found in the majority of males, several having micropenis. Finally, a postnatal growth pattern above the mean was apparent. The 580 kb deleted region includes five RefSeq genes and two of them are strong candidate genes for the developmental delay: DRD3 and ZBTB20. CONCLUSION: A newly recognised 3q13.31 microdeletion syndrome is delineated which is of diagnostic and prognostic value. Furthermore, two genes are suggested to be responsible for the main phenotype.1 februari 201

Meta-analysis of SHANK Mutations in Autism Spectrum Disorders: A Gradient of Severity in Cognitive Impairments.

International audienceSHANK genes code for scaffold proteins located at the post-synaptic density of glutamatergic synapses. In neurons, SHANK2 and SHANK3 have a positive effect on the induction and maturation of dendritic spines, whereas SHANK1 induces the enlargement of spine heads. Mutations in SHANK genes have been associated with autism spectrum disorders (ASD), but their prevalence and clinical relevance remain to be determined. Here, we performed a new screen and a meta-analysis of SHANK copy-number and coding-sequence variants in ASD. Copy-number variants were analyzed in 5,657 patients and 19,163 controls, coding-sequence variants were ascertained in 760 to 2,147 patients and 492 to 1,090 controls (depending on the gene), and, individuals carrying de novo or truncating SHANK mutations underwent an extensive clinical investigation. Copy-number variants and truncating mutations in SHANK genes were present in ∼1% of patients with ASD: mutations in SHANK1 were rare (0.04%) and present in males with normal IQ and autism; mutations in SHANK2 were present in 0.17% of patients with ASD and mild intellectual disability; mutations in SHANK3 were present in 0.69% of patients with ASD and up to 2.12% of the cases with moderate to profound intellectual disability. In summary, mutations of the SHANK genes were detected in the whole spectrum of autism with a gradient of severity in cognitive impairment. Given the rare frequency of SHANK1 and SHANK2 deleterious mutations, the clinical relevance of these genes remains to be ascertained. In contrast, the frequency and the penetrance of SHANK3 mutations in individuals with ASD and intellectual disability-more than 1 in 50-warrant its consideration for mutation screening in clinical practice

Phenotypic effects of genetic variants associated with autism

While over 100 genes have been associated with autism, little is known about the prevalence of variants affecting them in individuals without a diagnosis of autism. Nor do we fully appreciate the phenotypic diversity beyond the formal autism diagnosis. Based on data from more than 13,000 individuals with autism and 210,000 undiagnosed individuals, we estimated the odds ratios for autism associated to rare loss-of-function (LoF) variants in 185 genes associated with autism, alongside 2,492 genes displaying intolerance to LoF variants. In contrast to autism-centric approaches, we investigated the correlates of these variants in individuals without a diagnosis of autism. We show that these variants are associated with a small but significant decrease in fluid intelligence, qualification level and income and an increase in metrics related to material deprivation. These effects were larger for autism-associated genes than in other LoF-intolerant genes. Using brain imaging data from 21,040 individuals from the UK Biobank, we could not detect significant differences in the overall brain anatomy between LoF carriers and non-carriers. Our results highlight the importance of studying the effect of the genetic variants beyond categorical diagnosis and the need for more research to understand the association between these variants and sociodemographic factors, to best support individuals carrying these variants