Control and stabilization of waves on 1-d networks

We present some recent results on control and stabilization of waves on 1-d networks.The fine time-evolution of solutions of wave equations on networks and, consequently, their control theoretical properties, depend in a subtle manner on the topology of the network under consideration and also on the number theoretical properties of the lengths of the strings entering in it. Therefore, the overall picture is quite complex.In this paper we summarize some of the existing results on the problem of controllability that, by classical duality arguments in control theory, can be reduced to that of observability of the adjoint uncontrolled system. The problem of observability refers to that of recovering the total energy of solutions by means of measurements made on some internal or external nodes of the network. They lead, by duality, to controllability results guaranteeing that L 2-controls located on those nodes may drive sufficiently smooth solutions to equilibrium at a final time. Most of our results in this context, obtained in collaboration with R. Dáger, refer to the problem of controlling the network from one single external node. It is, to some extent, the most complex situation since, obviously, increasing the number of controllers enhances the controllability properties of the system. Our methods of proof combine sidewise energy estimates (that in the particular case under consideration can be derived by simply applying the classical d'Alembert's formula), Fourier series representations, non-harmonic Fourier analysis, and number theoretical tools.These control results belong to the class of the so-called open-loop control systems.We then discuss the problem of closed-loop control or stabilization by feedback. We present a recent result, obtained in collaboration with J. Valein, showing that the observability results previously derived, regardless of the method of proof employed, can also be recast a posteriori in the context of stabilization, so to derive explicit decay rates (as) for the energy of smooth solutions. The decay rate depends in a very sensitive manner on the topology of the network and the number theoretical properties of the lengths of the strings entering in it.In the end of the article we also present some challenging open problems

Identification of genetic effects underlying Type 2 Diabetes in South Asian and European populations

South Asians are at high risk of developing type 2 diabetes (T2D). We carried out a genome-wide association meta-analysis with South Asian T2D cases (n=16,677) and controls (n=33,856), followed by combined analyses with Europeans (neff=231,420). We identify 21 novel genetic loci for significant association with T2D (P=4.7x10-8 to 5.2x10-12), to the best of our knowledge at the point of analysis. The loci are enriched for regulatory features, including DNA methylation and gene expression in relevant tissues, and highlight CHMP4B, PDHB, LRIG1 and other genes linked to adiposity and glucose metabolism. A polygenic risk score based on South Asian-derived summary statistics shows ~4-fold higher risk for T2D between the top and bottom quartile. Our results provide further insights into the genetic mechanisms underlying T2D, and highlight the opportunities for discovery from joint analysis of data from across ancestral populations

Transancestral fine-mapping of four type 2 diabetes susceptibility loci highlights potential causal regulatory mechanisms

To gain insight into potential regulatory mechanisms through which the effects of variants at four established type 2 diabetes (T2D) susceptibility loci (CDKAL1, CDKN2A-B, IGF2BP2 and KCNQ1) are mediated, we undertook transancestral fine-mapping in 22 086 cases and 42 539 controls of East Asian, European, South Asian, African American and Mexican American descent. Through high-density imputation and conditional analyses, we identified seven distinct association signals at these four loci, each with allelic effects on T2D susceptibility that were homogenous across ancestry groups. By leveraging differences in the structure of linkage disequilibrium between diverse populations, and increased sample size, we localised the variants most likely to drive each distinct association signal. We demonstrated that integration of these genetic fine-mapping data with genomic annotation can highlight potential causal regulatory elements in T2D-relevant tissues. These analyses provide insight into the mechanisms through which T2D association signals are mediated, and suggest future routes to understanding the biology of specific disease susceptibility loci

Large Scale Association Analysis Identifies Three Susceptibility Loci for Coronary Artery Disease

Genome wide association studies (GWAS) and their replications that have associated DNA variants with myocardial infarction (MI) and/or coronary artery disease (CAD) are predominantly based on populations of European or Eastern Asian descent. Replication of the most significantly associated polymorphisms in multiple populations with distinctive genetic backgrounds and lifestyles is crucial to the understanding of the pathophysiology of a multifactorial disease like CAD. We have used our Lebanese cohort to perform a replication study of nine previously identified CAD/MI susceptibility loci (LTA, CDKN2A-CDKN2B, CELSR2-PSRC1-SORT1, CXCL12, MTHFD1L, WDR12, PCSK9, SH2B3, and SLC22A3), and 88 genes in related phenotypes. The study was conducted on 2,002 patients with detailed demographic, clinical characteristics, and cardiac catheterization results. One marker, rs6922269, in MTHFD1L was significantly protective against MI (OR = 0.68, p = 0.0035), while the variant rs4977574 in CDKN2A-CDKN2B was significantly associated with MI (OR = 1.33, p = 0.0086). Associations were detected after adjustment for family history of CAD, gender, hypertension, hyperlipidemia, diabetes, and smoking. The parallel study of 88 previously published genes in related phenotypes encompassed 20,225 markers, three quarters of which with imputed genotypes The study was based on our genome-wide genotype data set, with imputation across the whole genome to HapMap II release 22 using HapMap CEU population as a reference. Analysis was conducted on both the genotyped and imputed variants in the 88 regions covering selected genes. This approach replicated HNRNPA3P1-CXCL12 association with CAD and identified new significant associations of CDKAL1, ST6GAL1, and PTPRD with CAD. Our study provides evidence for the importance of the multifactorial aspect of CAD/MI and describes genes predisposing to their etiology

Association of Six Single Nucleotide Polymorphisms with Gestational Diabetes Mellitus in a Chinese Population

To investigate whether the candidate genes that confer susceptibility to type 2 diabetes mellitus are also correlated with gestational diabetes mellitus (GDM) in pregnant Chinese women.In this study, 1764 unrelated pregnant women were recruited, of which 725 women had GDM and 1039 served as controls. Six single nucleotide polymorphisms (rs7754840 in CDKAL1, rs391300 in SRR, rs2383208 in CDKN2A/2B, rs4402960 in IGF2BP2, rs10830963 in MTNR1B, rs4607517 in GCK) were genotyped using TaqMan allelic discrimination assays. The genotype and allele distributions of each SNP between the GDM cases and controls and the combined effects of alleles for the risk of developing GDM were analyzed. We found that the rs4402960, rs2383208 and rs391300 were statistically associated with GDM (OR = 1.207, 95%CI = 1.029-1.417, p = 0.021; OR = 1.242, 95%CI = 1.077-1.432, p = 0.003; OR = 1.202, 95%CI = 1.020-1.416, P = 0.028, respectively). In addition, the effect was greater under a recessive model in rs391300 (OR = 1.820, 95%CI = 1.226-2.701, p = 0.003). Meanwhile, the joint effect of these three loci indicated an additive effect of multiple alleles on the risk of developing GDM with an OR of 1.196 per allele (p = 1.08×10(-4)). We also found that the risk alleles of rs2383208 (b = -0.085, p = 0.003), rs4402960 (b = -0.057, p = 0.046) and rs10830963 (b = -0.096, p = 0.001) were associated with HOMA-B, while rs7754840 was associated with decrease in insulin AUC during a 100 g OGTT given at the time of GDM diagnosis (b = -0.080, p = 0.007).Several risk alleles of type 2 diabetes were associated with GDM in pregnant Chinese women. The effects of these SNPs on GDM might be through the impairment of beta cell function and these risk loci contributed additively to the disease

Ancestral diversity improves discovery and fine-mapping of genetic loci for anthropometric traits — The Hispanic/Latino Anthropometry Consortium

Hispanic/Latinos have been underrepresented in genome-wide association studies (GWAS) for anthropometric traits despite their notable anthropometric variability, ancestry proportions, and high burden of growth stunting and overweight/obesity. To address this knowledge gap, we analyzed densely imputed genetic data in a sample of Hispanic/Latino adults to identify and fine-map genetic variants associated with body mass index (BMI), height, and BMI-adjusted waist-to-hip ratio (WHRadjBMI). We conducted a GWAS of 18 studies/consortia as part of the Hispanic/Latino Anthropometry (HISLA) Consortium (stage 1, n = 59,771) and generalized our findings in 9 additional studies (stage 2, n = 10,538). We conducted a trans-ancestral GWAS with summary statistics from HISLA stage 1 and existing consortia of European and African ancestries. In our HISLA stage 1 + 2 analyses, we discovered one BMI locus, as well as two BMI signals and another height signal each within established anthropometric loci. In our trans-ancestral meta-analysis, we discovered three BMI loci, one height locus, and one WHRadjBMI locus. We also identified 3 secondary signals for BMI, 28 for height, and 2 for WHRadjBMI in established loci. We show that 336 known BMI, 1,177 known height, and 143 known WHRadjBMI (combined) SNPs demonstrated suggestive transferability (nominal significance and effect estimate directional consistency) in Hispanic/Latino adults. Of these, 36 BMI, 124 height, and 11 WHRadjBMI SNPs were significant after trait-specific Bonferroni correction. Trans-ancestral meta-analysis of the three ancestries showed a small-to-moderate impact of uncorrected population stratification on the resulting effect size estimates. Our findings demonstrate that future studies may also benefit from leveraging diverse ancestries and differences in linkage disequilibrium patterns to discover novel loci and additional signals with less residual population stratification

Genetically defined elevated homocysteine levels do not result in widespread changes of DNA methylation in leukocytes

BACKGROUND:DNA methylation is affected by the activities of the key enzymes and intermediate metabolites of the one-carbon pathway, one of which involves homocysteine. We investigated the effect of the well-known genetic variant associated with mildly elevated homocysteine: MTHFR 677C>T independently and in combination with other homocysteine-associated variants, on genome-wide leukocyte DNA-methylation. METHODS:Methylation levels were assessed using Illumina 450k arrays on 9,894 individuals of European ancestry from 12 cohort studies. Linear-mixed-models were used to study the association of additive MTHFR 677C>T and genetic-risk score (GRS) based on 18 homocysteine-associated SNPs, with genome-wide methylation. RESULTS:Meta-analysis revealed that the MTHFR 677C>T variant was associated with 35 CpG sites in cis, and the GRS showed association with 113 CpG sites near the homocysteine-associated variants. Genome-wide analysis revealed that the MTHFR 677C>T variant was associated with 1 trans-CpG (nearest gene ZNF184), while the GRS model showed association with 5 significant trans-CpGs annotated to nearest genes PTF1A, MRPL55, CTDSP2, CRYM and FKBP5. CONCLUSIONS:Our results do not show widespread changes in DNA-methylation across the genome, and therefore do not support the hypothesis that mildly elevated homocysteine is associated with widespread methylation changes in leukocytes