Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

The recently proposed map [arXiv:2011.01415] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [Phys. Rev. X 9, 021035 (2019)] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial ($t=0$) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times $t<0$. A similar singularity appears at $t = T/4$, where $T$ is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at $t > T/4$. Here, we first map -- using the scale invariance of the problem -- the trapped motion to an untrapped one. Then we show that in the new representation, the solution [arXiv:2011.01415] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [Phys. Rev. A 69, 043610 (2004)]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers' equation, a nonlinear transport equation. More specifically, under the Damski map, the $t=0$ singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [Ballistic Research Laboratory Report No. 423 (1943)]. At $t=T/8$, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [arXiv:2011.01415] and the Damski-Chandrasekhar shock wave becomes invalid.Comment: 13 pages, 2 figures. Submission to SciPos

Common and Rare Variant Analysis in Early-Onset Bipolar Disorder Vulnerability

Bipolar disorder is one of the most common and devastating psychiatric disorders whose mechanisms remain largely unknown. Despite a strong genetic contribution demonstrated by twin and adoption studies, a polygenic background influences this multifactorial and heterogeneous psychiatric disorder. To identify susceptibility genes on a severe and more familial sub-form of the disease, we conducted a genome-wide association study focused on 211 patients of French origin with an early age at onset and 1,719 controls, and then replicated our data on a German sample of 159 patients with early-onset bipolar disorder and 998 controls. Replication study and subsequent meta-analysis revealed two genes encoding proteins involved in phosphoinositide signalling pathway (PLEKHA5 and PLCXD3). We performed additional replication studies in two datasets from the WTCCC (764 patients and 2,938 controls) and the GAIN-TGen cohorts (1,524 patients and 1,436 controls) and found nominal P-values both in the PLCXD3 and PLEKHA5 loci with the WTCCC sample. In addition, we identified in the French cohort one affected individual with a deletion at the PLCXD3 locus and another one carrying a missense variation in PLCXD3 (p.R93H), both supporting a role of the phosphatidylinositol pathway in early-onset bipolar disorder vulnerability. Although the current nominally significant findings should be interpreted with caution and need replication in independent cohorts, this study supports the strategy to combine genetic approaches to determine the molecular mechanisms underlying bipolar disorder

Genetic and functional abnormalities of the melatonin biosynthesis pathway in patients with bipolar disorder

Patients affected by bipolar disorder (BD) frequently report abnormalities in sleep/wake cycles. In addition, they showed abnormal oscillating melatonin secretion, a key regulator of circadian rhythms and sleep patterns. The acetylserotonin O-methyltransferase (ASMT) is a key enzyme of the melatonin biosynthesis and has recently been associated with psychiatric disorders such as autism spectrum disorders and depression. In this paper, we analysed rare and common variants of ASMT in patients with BD and unaffected control subjects and performed functional analysis of these variants by assaying the ASMT activity in their B-lymphoblastoid cell lines. We sequenced the coding and the regulatory regions of the gene in a discovery sample of 345 patients with BD and 220 controls. We performed an association study on this discovery sample using common variants located in the promoter region and showed that rs4446909 was significantly associated with BD (P= 0.01) and associated with a lower mRNA level (P< 10(-4)) and a lower enzymatic activity (P< 0.05) of ASMT. A replication study and a meta-analysis using 480 independent patients with BD and 672 controls confirmed the significant association between rs4446909 and BD (P= 0.002). These results correlate with the general lower ASMT enzymatic activity observed in patients with BD (P= 0.001) compared with controls. Finally, several deleterious ASMT mutations identified in patients were associated with low ASMT activity (P= 0.01). In this study, we determined how rare and common variations in ASMT might play a role in BD vulnerability and suggest a general role of melatonin as susceptibility factor for BD