On Lyapunov and Upper Bohl Exponents of Diagonal Discrete Linear Time-Varying Systems

In this paper the necessary and sufficient conditions for two given functions to be the Lyapunov and the upper Bohl exponents of a certain discrete linear system with diagonal coefficients are presented. The obtained conditions are described in terms of easily verifiable properties

Genetic and Functional Analyses of SHANK2 Mutations Suggest a Multiple Hit Model of Autism Spectrum Disorders

Autism spectrum disorders (ASD) are a heterogeneous group of neurodevelopmental disorders with a complex inheritance pattern. While many rare variants in synaptic proteins have been identified in patients with ASD, little is known about their effects at the synapse and their interactions with other genetic variations. Here, following the discovery of two de novo SHANK2 deletions by the Autism Genome Project, we identified a novel 421 kb de novo SHANK2 deletion in a patient with autism. We then sequenced SHANK2 in 455 patients with ASD and 431 controls and integrated these results with those reported by Berkel et al. 2010 (n = 396 patients and n = 659 controls). We observed a significant enrichment of variants affecting conserved amino acids in 29 of 851 (3.4%) patients and in 16 of 1,090 (1.5%) controls (P = 0.004, OR = 2.37, 95% CI = 1.23-4.70). In neuronal cell cultures, the variants identified in patients were associated with a reduced synaptic density at dendrites compared to the variants only detected in controls (P = 0.0013). Interestingly, the three patients with de novo SHANK2 deletions also carried inherited CNVs at 15q11-q13 previously associated with neuropsychiatric disorders. In two cases, the nicotinic receptor CHRNA7 was duplicated and in one case the synaptic translation repressor CYFIP1 was deleted. These results strengthen the role of synaptic gene dysfunction in ASD but also highlight the presence of putative modifier genes, which is in keeping with the "multiple hit model" for ASD. A better knowledge of these genetic interactions will be necessary to understand the complex inheritance pattern of ASD

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

Genetic and Functional Analyses of SHANK2 Mutations Suggest a Multiple Hit Model of Autism Spectrum Disorders

Peer reviewe

Genetic and Functional Analyses of SHANK2 Mutations Suggest a Multiple Hit Model of Autism Spectrum Disorders

Autism spectrum disorders (ASD) are a heterogeneous group of neurodevelopmental disorders with a complex inheritance pattern. While many rare variants in synaptic proteins have been identified in patients with ASD, little is known about their effects at the synapse and their interactions with other genetic variations. Here, following the discovery of two de novo SHANK2 deletions by the Autism Genome Project, we identified a novel 421 kb de novo SHANK2 deletion in a patient with autism. We then sequenced SHANK2 in 455 patients with ASD and 431 controls and integrated these results with those reported by Berkel et al. 2010 (n = 396 patients and n = 659 controls). We observed a significant enrichment of variants affecting conserved amino acids in 29 of 851 (3.4%) patients and in 16 of 1,090 (1.5%) controls (P = 0.004, OR = 2.37, 95% CI = 1.23-4.70). In neuronal cell cultures, the variants identified in patients were associated with a reduced synaptic density at dendrites compared to the variants only detected in controls (P = 0.0013). Interestingly, the three patients with de novo SHANK2 deletions also carried inherited CNVs at 15q11-q13 previously associated with neuropsychiatric disorders. In two cases, the nicotinic receptor CHRNA7 was duplicated and in one case the synaptic translation repressor CYFIP1 was deleted. These results strengthen the role of synaptic gene dysfunction in ASD but also highlight the presence of putative modifier genes, which is in keeping with the "multiple hit model" for ASD. A better knowledge of these genetic interactions will be necessary to understand the complex inheritance pattern of ASD

Norm Estimates and Uncertainty Principles Associated with the Laguerre Integral Transform

In this paper we present some results concerning the action of the Laguerre integral transform over the class of polynomials and over the class of infinitely differentiable functions. We prove several uncertainty inequalities of Heisenberg-type, and we also indicate an explicit boundedness for two classes of generalized Laguerre integral transforms which include the classical Riemann Liouville fractional integral