Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws

We define a large class of continuous time multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk (MRW) [Bacry-Delour-Muzy] and the log-Poisson "product of cynlindrical pulses" [Barral-Mandelbrot]. Our construction is based on some ``continuous stochastic multiplication'' from coarse to fine scales that can be seen as a continuous interpolation of discrete multiplicative cascades. We prove the stochastic convergence of the defined processes and study their main statistical properties. The question of genericity (universality) of limit multifractal processes is addressed within this new framework. We finally provide some methods for numerical simulations and discuss some specific examples.Comment: 24 pages, 4 figure

Cylindrical fractional Brownian motion in Banach spaces

In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures. The developed stochastic integral for deterministic operator valued integrands is based on a series representation of the cylindrical fractional Brownian motion, which is analogous to the Karhunen-Loève expansion for genuine stochastic processes. In the last part we apply our results to study the abstract stochastic Cauchy problem in a Banach space driven by cylindrical fractional Brownian motion

DNA Damage, Somatic Aneuploidy, and Malignant Sarcoma Susceptibility in Muscular Dystrophies

Albeit genetically highly heterogeneous, muscular dystrophies (MDs) share a convergent pathology leading to muscle wasting accompanied by proliferation of fibrous and fatty tissue, suggesting a common MD–pathomechanism. Here we show that mutations in muscular dystrophy genes (Dmd, Dysf, Capn3, Large) lead to the spontaneous formation of skeletal muscle-derived malignant tumors in mice, presenting as mixed rhabdomyo-, fibro-, and liposarcomas. Primary MD–gene defects and strain background strongly influence sarcoma incidence, latency, localization, and gender prevalence. Combined loss of dystrophin and dysferlin, as well as dystrophin and calpain-3, leads to accelerated tumor formation. Irrespective of the primary gene defects, all MD sarcomas share non-random genomic alterations including frequent losses of tumor suppressors (Cdkn2a, Nf1), amplification of oncogenes (Met, Jun), recurrent duplications of whole chromosomes 8 and 15, and DNA damage. Remarkably, these sarcoma-specific genetic lesions are already regularly present in skeletal muscles in aged MD mice even prior to sarcoma development. Accordingly, we show also that skeletal muscle from human muscular dystrophy patients is affected by gross genomic instability, represented by DNA double-strand breaks and age-related accumulation of aneusomies. These novel aspects of molecular pathologies common to muscular dystrophies and tumor biology will potentially influence the strategies to combat these diseases

Haploinsufficiency of SOX5 at 12p12.1 is associated with developmental delays with prominent language delay, behavior problems, and mild dysmorphic features

SOX5 encodes a transcription factor involved in the regulation of chondrogenesis and the development of the nervous system. Despite its important developmental roles, SOX5 disruption has yet to be associated with human disease. We report one individual with a reciprocal translocation breakpoint within SOX5, eight individuals with intragenic SOX5 deletions (four are apparently de novo and one inherited from an affected parent), and seven individuals with larger 12p12 deletions encompassing SOX5. Common features in these subjects include prominent speech delay, intellectual disability, behavior abnormalities, and dysmorphic features. The phenotypic impact of the deletions may depend on the location of the deletion and consequently which of the three major SOX5 protein isoforms are affected. One intragenic deletion involving only untranslated exons was present in a more mildly affected subject, was inherited from a healthy parent and grandparent, and is similar to a deletion found in a control cohort. Therefore, some intragenic SOX5 deletions may have minimal phenotypic effect. Based on the location of the deletions in the subjects compared to the controls, the de novo nature of most of these deletions, and the phenotypic similarities among cases, SOX5 appears to be a dosage-sensitive, developmentally important gene

Loss of TNR causes a nonprogressive neurodevelopmental disorder with spasticity and transient opisthotonus.

PURPOSE: TNR, encoding Tenascin-R, is an extracellular matrix glycoprotein involved in neurite outgrowth and neural cell adhesion, proliferation and migration, axonal guidance, myelination, and synaptic plasticity. Tenascin-R is exclusively expressed in the central nervous system with highest expression after birth. The protein is crucial in the formation of perineuronal nets that ensheath interneurons. However, the role of Tenascin-R in human pathology is largely unknown. We aimed to establish TNR as a human disease gene and unravel the associated clinical spectrum. METHODS: Exome sequencing and an online matchmaking tool were used to identify patients with biallelic variants in TNR. RESULTS: We identified 13 individuals from 8 unrelated families with biallelic variants in TNR sharing a phenotype consisting of spastic para- or tetraparesis, axial muscular hypotonia, developmental delay, and transient opisthotonus. Four homozygous loss-of-function and four different missense variants were identified. CONCLUSION: We establish TNR as a disease gene for an autosomal recessive nonprogressive neurodevelopmental disorder with spasticity and transient opisthotonus and highlight the role of central nervous system extracellular matrix proteins in the pathogenicity of spastic disorders

Chromosomal contacts connect loci associated with autism, BMI and head circumference phenotypes

Copy number variants (CNVs) are major contributors to genomic imbalance disorders. Phenotyping of 137 unrelated deletion and reciprocal duplication carriers of the distal 16p11.2 220 kb BP2-BP3 interval showed that these rearrangements are associated with autism spectrum disorders and mirror phenotypes of obesity/underweight and macrocephaly/microcephaly. Such phenotypes were previously associated with rearrangements of the non-overlapping proximal 16p11.2 600 kb BP4-BP5 interval. These two CNV-prone regions at 16p11.2 are reciprocally engaged in complex chromatin looping, as successfully confirmed by 4C-seq, fluorescence in situ hybridization and Hi-C, as well as coordinated expression and regulation of encompassed genes. We observed that genes differentially expressed in 16p11.2 BP4-BP5 CNV carriers are concomitantly modified in their chromatin interactions, suggesting that disruption of chromatin interplays could participate in the observed phenotypes. We also identified cis- and trans-acting chromatin contacts to other genomic regions previously associated with analogous phenotypes. For example, we uncovered that individuals with reciprocal rearrangements of the trans-contacted 2p15 locus similarly display mirror phenotypes on head circumference and weight. Our results indicate that chromosomal contacts’ maps could uncover functionally and clinically related genes.Molecular Psychiatry advance online publication, 31 May 2016; doi:10.1038/mp.2016.84

Interstitial deletions and intrachromosomal amplification initiated from a double-strand break targeted to a mammalian chromosome.

Interstitial deletions of tumour suppressor genes and amplification of oncogenes are two major manifestations of chromosomal instability in tumour cells. The development of model systems allowing the study of the events triggering these processes is of major clinical importance. Using the properties of the I-SceI nuclease to introduce a localized double-strand break (DSB) in a mammalian chromosome carrying its target sequence, we demonstrate here that both types of mutations can be initiated by non-conservative DSB repair pathways. In our system, I-SceI activity dissociates a transfected gpt gene from its promoter, allowing the isolation of gpt- clones. Our results show that intrachromatid single-strand annealing events occur frequently, giving rise to interstitial deletions not accompanied by other chromosomal rearrangements. We also observed that, when present in the cells, extrachromosomal DNA molecules are integrated preferentially at the broken locus. Taking advantage of the insertion of the I-SceI recognition sequence telomeric to and close to the dihydrofolate reductase gene, we show that a less frequent outcome of I-SceI activity is the initiation of cycles of intrachromosomal amplification of this marker, from breaks at a site merging with the enzyme target

has attracted interest. For a motivation and further references, we refer the reader to Barczy and Pap

Abstract: Let α,T> 0. We study the asymptotic properties of a least squares estimator for the parameter α of a fractional bridge defined as dXt = −α Xt T−t dt + dBt, 0 � t < T, where B is a fractional Brownian motion of Hurst parameter H> 1 2. Depending on the value of α, we prove that we may have strong consistency or not as t → T. When we have consistency, we obtain the rate of this convergence as well. Also, we compare our results to the (known) case where B is replaced by a standard Brownian motion W. It is great pleasure for us to dedicate this paper to our friend David Nualart, in celebration of his 60th birthday and with all our admiration. hal-00560815, version 3- 2 Aug 2013