Search

Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity conditions, also obey the Kirchhoff conditions, expressing the balance of tensions. In this paper, we propose a new look at quantum graphs as temporal networks, which means that the variable parametrizing the edges of a graph is interpreted as time, while each internal vertex is a branching point giving several different scenarios for the further trajectory of a process. Then Kirchhoff‐type conditions may also arise. Namely, they will be satisfied by such a trajectory of the process that is optimal with account of all the scenarios simultaneously. By employing the recent concept of global delay, we extend the problem of damping a first‐order control system with aftereffect, considered earlier only on an interval, to an arbitrary tree graph. The first means that the delay, imposed starting from the initial moment of time, associated with the root of the tree, propagates through all internal vertices. Bringing the system into the equilibrium and minimizing the energy functional with account of the anticipated probability of each scenario, we come to a variational problem. Then, we establish its equivalence to a self‐adjoint boundary value problem on the tree for some second‐order equations involving both the global delay and the global advance. The unique solvability of both problems is proved. We also illustrate that the interval case when the coefficients of the equation are discrete stochastic processes in discrete time can be viewed as the extension to a tree. [ABSTRACT FROM AUTHOR]

Background: Developmental delay happens when a child fails to attain age-appropriate milestones. Identification of developmental delay in children is important to initiate early intervention in them which will facilitate the children to have a productive life in their later years. Objectives: The objective was to study the prevalence of developmental delay among 12–36-month-old children from the area of Primary Health Centre, Bela, in rural Nagpur, Maharashtra. Materials and Methods: This was a community-based cross-sectional study design. A total of 314 children were selected through simple random sampling and assessed for delay using the Pediatric Development Screening Tool (PDST). Results: 14.9% had developmental delay in at least any one domain and 3.5% had global developmental delay. Domain-specific developmental delay was highest for language delay (10%) followed by fine motor (5%). Gross motor and personal social delays had the same prevalence (3.1%). On multivariable lower literacy, level of mother and Composite Index of Anthropometric Failure were significant variables for any developmental delay. Hospitalization of the child during the 1st month of life and lower parenting scores were the significant factors associated with global delay. Conclusion: Development delay is present in a sizeable proportion of children

We study a problem of damping a control system described by functional-differential equations of natural order and neutral type with nonsmooth complex coefficients on an arbitrary tree with global delay. The latter means that the delay propagates through internal vertices of the tree. Minimization of the energy functional of the system leads to a variational problem. We establish its equivalence to a certain self-adjoint boundary value problem on the tree for equations of order with nonlocal quasi-derivatives and multidirectional shifts of the argument as well as Kirchhoff-type conditions emerging at the internal vertices. The unique solvability of both problems is proved. [ABSTRACT FROM AUTHOR]

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, which is measured in the direction of a specific boundary vertex, called the root, propagates through the internal vertex to other edges. Now, we intend to recover the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except the root. For simplicity, we focus on star graphs with equal edges when the delay parameter is not less than their length. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained. [ABSTRACT FROM AUTHOR]

To delineate further the clinical phenotype of Lamb–Shaffer Syndrome (LSS) 16 unpublished patients with heterozygous variation in SOX5 were identified either through the UK Decipher database or the study team was contacted by clinicians directly. Clinical phenotyping tables were completed for each patient by their responsible clinical geneticist. Photos and clinical features were compared to assess key phenotypes and genotype–phenotype correlation. We report 16 SOX5 variants all of which meet American College of Medical Genetics/Association for Clinical Genomic Science ACMG/ACGS criteria class IV or V. 7/16 have intragenic deletions of SOX5 and 9/16 have single nucleotide variants (including both truncating and missense variants). The cohort includes two sets of monozygotic twins and parental gonadal mosaicism is noted in one family. This cohort of 16 patients is compared with the 71 previously reported cases and corroborates previous phenotypic findings. As expected, the most common findings include global developmental delay with prominent speech delay, mild to moderate intellectual disability, behavioral abnormalities and sometimes subtle characteristic facial features. We expand in more detail on the behavioral phenotype and observe that there is a greater tendency toward lower growth parameters and microcephaly in patients with single nucleotide variants. This cohort provides further evidence of gonadal mosaicism in SOX5 variants; this should be considered when providing genetic counseling for couples with one affected child and an apparently de novo variant. [ABSTRACT FROM AUTHOR]

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, which is measured in the direction of a specific boundary vertex, called the root, propagates through the internal vertex to other edges. Now, we intend to recover the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except the root. For simplicity, we focus on star graphs with equal edges when the delay parameter is not less than their length. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained.

Copy number variations (CNVs) are highly implicated in the etiology of neurodevelopmental disorders (NDDs), and chromosomal microarray analysis (CMA) has been recommended as a first-tier test for many NDDs. We undertook a study to identify clinically relevant CNVs and genes in an ethnically homogenous population of the United Arab Emirates. We genotyped 98 patients with NDDs using genome-wide chromosomal microarray analysis, and observed 47.1% deletion and 52.9% duplication CNVs, of which 11.8% are pathogenic, 23.5% are likely pathogenic, and 64.7% VOUS. The average size of copy number losses (3.9 Mb) was generally higher than of gains (738.4 kb). Analysis of VOUS CNVs for constrained genes (enrichment for brain critical exons and high pLI genes) yielded 7 unique genes. Among these 7 constrained genes, we propose FNTA and PXK as potential candidate genes for neurodevelopmental disorders, which warrants further investigation. Thirty-two overlapping CNVs (Decipher and ClinVar) containing the FNTA gene were previously identified in NDD patients and 6 overlapping CNVs (Decipher and ClinVar) containing the PXK gene were previously identified in NDD patients. Our study supports the utility of CMA for CNV profiling which aids in precise genetic diagnosis and its integration into therapeutics and management of NDD patients. [ABSTRACT FROM AUTHOR]

Global time delay is introduced to a bistable system driven by multiplicative and additive noises. Approximation of small delay and numerical simulations are employed to investigate the delay induced transition. The stationary probability distribution function $$P_{st}(x)$$ and the first order moment $$\langle x\rangle _{st}$$ are derived. Results indicate that with the increase of global time delay, $$P_{st}(x)$$ undergoes a transition from a bimodal structure to a unimodal shape and $$\langle x\rangle _{st}$$ as a function of the multiplicative noise intensity exhibits suppression-like and resonance-like behavior. For the case of multiplicative noise with delay, $$P_{st}(x)$$ undergoes a transition from a monostable to a bistable system. These results illustrate that global delay can control the transition of a bistable system effectively. [ABSTRACT FROM AUTHOR]

Well-intended efforts to diagnose a child's developmental delay may have unintended negative consequences for a child and his family. Consequently, clinicians may feel caught in a moral dilemma: between doing the good they seek and avoiding the harm they foresee. The dilemma is that when investigating global developmental delay it is not possible to avoid all the anticipated negative outcomes of genetic testing and concurrently fulfill our obligations to do the good from which these harmful effects result. It is imperative to recognize dilemmas especially where the moral questions or relevant facts are not as clear cut as in ethics textbooks and to bring their moral questions into a structured dialogue with the patient and his or her family. A modified principle of double effect is a useful method for deliberating about these moral cases. Three case examples illustrate the utility of the principle of double effect when investigating global developmental delay. [ABSTRACT FROM AUTHOR]