On the integrability conditions for some structures related to evolution differential equations

Using the result by D.Gessler (Differential Geom. Appl. 7 (1997) 303-324, DIPS-9/98, http://diffiety.ac.ru/preprint/98/09_98abs.htm), we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp., symplectic).Comment: 5 pages, AMS-LaTeX. v2: minor correction

A geometric study of the dispersionless Boussinesq type equation

We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney-Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in . The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators that send conservation laws and symmetries to each other but are neither Hamiltonian, nor symplectic. These operators give rise to a noncommutative infinite-dimensional algebra of recursion operators

On integrability of the Camassa-Holm equation and its invariants. A geometrical approach

Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local and nonlocal).Comment: 24 page

Long-Read Sequencing Emerging in Medical Genetics

The wide implementation of next-generation sequencing (NGS) technologies has revolutionized the field of medical genetics. However, the short read lengths of currently used sequencing approaches pose a limitation for the identification of structural variants, sequencing repetitive regions, phasing of alleles and distinguishing highly homologous genomic regions. These limitations may significantly contribute to the diagnostic gap in patients with genetic disorders who have undergone standard NGS, like whole exome or even genome sequencing. Now, the emerging long-read sequencing (LRS) technologies may offer improvements in the characterization of genetic variation and regions that are difficult to assess with the prevailing NGS approaches. LRS has so far mainly been used to investigate genetic disorders with previously known or strongly suspected disease loci. While these targeted approaches already show the potential of LRS, it remains to be seen whether LRS technologies can soon enable true whole genome sequencing routinely. Ultimately, this could allow the de novo assembly of individual whole genomes used as a generic test for genetic disorders. In this article, we summarize the current LRS-based research on human genetic disorders and discuss the potential of these technologies to facilitate the next major advancements in medical genetics

In Situ Laser Light Scattering for Temporally and Locally Resolved Studies on Nanoparticle Trapping in a Gas Aggregation Source

Gas phase synthesis of nanoparticles (NPs) via magnetron sputtering in a gas aggregation source (GAS) has become a well-established method since its conceptualization three decades ago. NP formation is commonly described in terms of nucleation, growth, and transport alongside the gas stream. However, the NP formation and transport involve complex non-equilibrium processes, which are still the subject of investigation. The development of in situ investigation techniques such as UV–Vis spectroscopy and small angle X-ray scattering enabled further insights into the dynamic processes inside the GAS and have recently revealed NP trapping at different distances from the magnetron source. The main drawback of these techniques is their limited spatial resolution. To understand the spatio-temporal behavior of NP trapping, an in situ laser light scattering technique is applied in this study. By this approach, silver NPs are made visible inside the GAS with good spatial and temporal resolution. It is found that the argon gas pressure, as well as different gas inlet configurations, have a strong impact on the trapping behavior of NPs inside the GAS. The different gas inlet configurations not only affect the trapping of NPs, but also the size distribution and deposition rate of NPs

Retinal diffusion restrictions in acute branch retinal arteriolar occlusion

This study sought to investigate the occurrence of retinal diffusion restrictions (RDR) in branch retinal arteriolar occlusion (BRAO) using standard brain diffusion-weighted imaging (DWI). Two radiologists assessed DWI MRI scans of BRAO patients for RDR in a retrospective cohort study. Inter- and intrarater reliability were calculated using Kappa statistics. Detection rates of RDR were compared among MRI scans with varying field strength, sequence type and onset-to-DWI time intervals. 85 BRAO patients (63.1 +/- 16.5 years) and 89 DWI scans were evaluated. Overall sensitivity of RDR in BRAO was 46.1% with visually correlating low ADC signal in 56.1% of cases. Localization of RDR matched distribution of fundoscopic retinal edema in 85% of patients. Inter- and intra-rater agreement for RDR in BRAO was kappa(inter) = 0.64 (95% CI 0.48-0.80) and kappa(intra) = 0.87 (95% CI 0.76-0.96), respectively. RDR detection rate tended to be higher for 3T, when compared to 1.5T MRI scans (53.7% vs. 34.3%%; p = 0.07). RDR were identified within 24 h up to 2 weeks after onset of visual impairment. RDR in BRAO can be observed by means of standard stroke DWI in a substantial proportion of cases, although sensitivity and interrater reliability were lower than previously reported for complete central retinal artery occlusion

Geometry of jet spaces and integrable systems

An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with constraints (on a PDE) are discussed. Analogs of tangent and cotangent bundles to a differential equation are introduced and the variational Schouten bracket is defined. General theoretical constructions are illustrated by a series of examples.Comment: 54 pages; v2-v6 : minor correction