Infinite energy solutions to the homogeneous Boltzmann equation

The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of probability measures defined via the Fourier transform. In that space, the second moment of a measure is not assumed to be finite, so infinite energy solutions are not {\it a priori} excluded from our considerations. Moreover, we study the large time asymptotics of solutions and, in a particular case, we give an elementary proof of the asymptotic stability of self-similar solutions obtained by A.V. Bobylev and C. Cercignani [J. Stat. Phys. {\bf 106} (2002), 1039--1071]

A trace theorem in kinetic theory

AbstractA mathematical assumption made in a recent paper by Cercignani on the traces of the solutions of initial-boundary value problems for the Boltzmann Equation is shown here to be true in the case of a domain whose boundary is a Lyapunoff surface with purely diffusing boundary conditions

Well-posedness of the boundary layer equations

We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. The proof is achieved applying the abstract Cauchy-Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433-461], as we do not require analyticity of the data with respect to the normal variable

Modeling Human Muscular Dystrophies in Zebrafish: Mutant Lines, Transgenic Fluorescent Biosensors, and Phenotyping Assays

: Muscular dystrophies (MDs) are a heterogeneous group of myopathies characterized by progressive muscle weakness leading to death from heart or respiratory failure. MDs are caused by mutations in genes involved in both the development and organization of muscle fibers. Several animal models harboring mutations in MD-associated genes have been developed so far. Together with rodents, the zebrafish is one of the most popular animal models used to reproduce MDs because of the high level of sequence homology with the human genome and its genetic manipulability. This review describes the most important zebrafish mutant models of MD and the most advanced tools used to generate and characterize all these valuable transgenic lines. Zebrafish models of MDs have been generated by introducing mutations to muscle-specific genes with different genetic techniques, such as (i) N-ethyl-N-nitrosourea (ENU) treatment, (ii) the injection of specific morpholino, (iii) tol2-based transgenesis, (iv) TALEN, (v) and CRISPR/Cas9 technology. All these models are extensively used either to study muscle development and function or understand the pathogenetic mechanisms of MDs. Several tools have also been developed to characterize these zebrafish models by checking (i) motor behavior, (ii) muscle fiber structure, (iii) oxidative stress, and (iv) mitochondrial function and dynamics. Further, living biosensor models, based on the expression of fluorescent reporter proteins under the control of muscle-specific promoters or responsive elements, have been revealed to be powerful tools to follow molecular dynamics at the level of a single muscle fiber. Thus, zebrafish models of MDs can also be a powerful tool to search for new drugs or gene therapies able to block or slow down disease progression

Human Mutated MYOT and CRYAB Genes Cause a Myopathic Phenotype in Zebrafish

Myofibrillar myopathies (MFMs) are a group of hereditary neuromuscular disorders sharing common histological features, such as myofibrillar derangement, Z-disk disintegration, and accumulation of degradation products into protein aggregates. They are caused by mutations in several genes that encode either structural proteins or molecular chaperones. Nevertheless, the mechanisms by which mutated genes result in protein aggregation are still unknown. To unveil the role of myotilin and αB-crystallin in the pathogenesis of MFM, we injected zebrafish fertilized eggs at one-cell stage with expression plasmids harboring cDNA sequences of human wildtype or mutated MYOT (p.Ser95Ile) and human wildtype or mutated CRYAB (p.Gly154Ser). We evaluated the effects on fish survival, motor behavior, muscle structure and development. We found that transgenic zebrafish showed morphological defects that were more severe in those overexpressing mutant genes which developed a myopathic phenotype consistent with that of human myofibrillar myopathy including the formation of protein aggregates. Results indicate that pathogenic mutations in myotilin and αB-crystallin genes associated with MFM cause a structural and functional impairment of the skeletal muscle in zebrafish, thereby making this non-mammalian organism a powerful model to dissect disease pathogenesis and find possible druggable targets

Understanding Limits of Parametrial Resection in RadicalHysterectomy: A Randomized Controlled Trial

Cervical cancer treatment has always represented a challenge for surgeons, radiotherapist, radiologist and medical oncologist..

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

A novel in-frame deletion in MYOT causes an early adult onset distal myopathy

Missense mutations in MYOT encoding the sarcomeric Z-disk protein myotilin cause three main myopathic phenotypes including proximal limb-girdle muscular dystrophy, spheroid body myopathy, and late-onset distal myopathy. We describe a family carrying a heterozygous MYOT deletion (Tyr4_His9del) that clinically was characterized by an early-adult onset distal muscle weakness and pathologically by a myofibrillar myopathy (MFM). Molecular modeling of the full-length myotilin protein revealed that the 4-YERPKH-9 amino acids are involved in local interactions within the N-terminal portion of myotilin. Injection of in vitro synthetized mutated human MYOT RNA or of plasmid carrying its cDNA sequence in zebrafish embryos led to muscle defects characterized by sarcomeric disorganization of muscle fibers and widening of the I-band, and severe motor impairments. We identify MYOT novel Tyr4_His9 deletion as the cause of an early-onset MFM with a distal myopathy phenotype and provide data supporting the importance of the amino acid sequence for the structural role of myotilin in the sarcomeric organization of myofibers