Some new well-posedness results for continuity and transport equations, and applications to the chromatography system

We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly having a blow-up of the BV norm at the initial time. We apply these results (valid in any space dimension) to the k x k chromatography system of conservation laws and to the k x k Keyfitz and Kranzer system, both in one space dimension.Comment: 33 pages, minor change

Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials

System identification (SI) is the discipline of inferring mathematical models from unknown dynamic systems using the input/output observations of such systems with or without prior knowledge of some of the system parameters. Many valid algorithms are available in the literature, including Volterra series expansion, Hammerstein–Wiener models, nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) and its derivatives (NARX, NARMA). Different nonlinear estimators can be used for those algorithms, such as polynomials, neural networks or wavelet networks. This paper uses a different approach, named particle-Bernstein polynomials, as an estimator for SI. Moreover, unlike the mentioned algorithms, this approach does not operate in the time domain but rather in the spectral components of the signals through the use of the discrete Karhunen–Loève transform (DKLT). Some experiments are performed to validate this approach using a publicly available dataset based on ground vibration tests recorded from a real F-16 aircraft. The experiments show better results when compared with some of the traditional algorithms, especially for large, heterogeneous datasets such as the one used. In particular, the absolute error obtained with the prosed method is 63% smaller with respect to NARX and from 42% to 62% smaller with respect to various artificial neural network-based approaches

Evidence for a continuum limit in causal set dynamics

We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single ``coupling constant'' $p$ and is easy to simulate on a computer. The model in question is a stochastic process that can also be interpreted as 1-dimensional directed percolation, or in terms of random graphs.Comment: 24 pages, 19 figures, LaTeX, adjusted terminolog

A Diffusion Tensor Imaging Study on the Auditory System and Tinnitus

Tinnitus is an auditory percept in the absence of an external sound source. Mechanisms in the central nervous system are believed to be key in the pathophysiology of tinnitus. Diffusion tensor imaging (DTI) is an MR imaging technique that allows in vivo exploration of white matter tissue in the human brain. Using a probabilistic DTI approach, we determined the characteristics of fiber tracts from the inferior colliculus to the medial geniculate body up to the primary auditory cortex. We also investigated the connections between the auditory system and the amygdala, which may be involved in some forms of tinnitus. White matter tracts were characterized by three quantities: the mean fractional anisotropy, the weighted mean fractional anisotropy and the path strength. All these quantities are measures of the patency of white matter tracts. The most important finding is an increased patency of the white matter tracts between the auditory cortex and the amygdala in tinnitus patients as compared to healthy controls

Generalized Wasserstein distance and its application to transport equations with source

In this article, we generalize the Wasserstein distance to measures with different masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences. We use this generalized Wasserstein distance to study a transport equation with source, in which both the vector field and the source depend on the measure itself. We prove existence and uniqueness of the solution to the Cauchy problem when the vector field and the source are Lipschitzian with respect to the generalized Wasserstein distance

Clearance of the mutant androgen receptor in motoneuronal models of spinal and bulbar muscular atrophy.

Spinal and bulbar muscular atrophy (SBMA) is an X-linked motoneuron disease caused by an abnormal expansion of a tandem CAG repeat in exon 1 of the androgen receptor (AR) gene that results in an abnormally long polyglutamine tract (polyQ) in the AR protein. As a result, the mutant AR (ARpolyQ) misfolds, forming cytoplasmic and nuclear aggregates in the affected neurons. Neurotoxicity only appears to be associated with the formation of nuclear aggregates. Thus, improved ARpolyQ cytoplasmic clearance, which indirectly decreases ARpolyQ nuclear accumulation, has beneficial effects on affected motoneurons. In addition, increased ARpolyQ clearance contributes to maintenance of motoneuron proteostasis and viability, preventing the blockage of the proteasome and autophagy pathways that might play a role in the neuropathy in SBMA. The expression of heat shock protein B8 (HspB8), a member of the small heat shock protein family, is highly induced in surviving motoneurons of patients affected by motoneuron diseases, where it seems to participate in the stress response aimed at cell protection. We report here that HspB8 facilitates the autophagic removal of misfolded aggregating species of ARpolyQ. In addition, though HspB8 does not influence p62 and LC3 (two key autophagic molecules) expression, it does prevent p62 bodies formation, and restores the normal autophagic flux in these cells. Interestingly, trehalose, a well-known autophagy stimulator, induces HspB8 expression, suggesting that HspB8 might act as one of the molecular mediators of the proautophagic activity of trehalose. Collectively, these data support the hypothesis that treatments aimed at restoring a normal autophagic flux that result in the more efficient clearance of mutant ARpolyQ might produce beneficial effects in SBMA patients