The concentration-compactness principle for variable exponent spaces and applications

In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to the variable exponent case. We also give some applications to the existence problem for the $p(x)-$Laplacian with critical growth

H−H-convergence result for nonlocal elliptic-type problems via Tartar's method

In this work we obtain a compactness result for the $H-$convergence of a family of nonlocal and nonlinear monotone elliptic-type problems by means of Tartar's method of oscillating test functions.Comment: In this revision we added a new section that shows the Gamma-convergence of the associated energy functional

Existence of Eigenvalues for Anisotropic and Fractional Anisotropic Problems via Ljusternik-Schnirelmann Theory

In this work, our interest lies in proving the existence of critical values of the following Rayleigh-type quotients $$Q_{\mathbf p}(u) = \frac{\|\nabla u\|_{\mathbf p}}{\|u\|_{\mathbf p}},\quad\text{and}\quad Q_{\mathbf s,\mathbf p}(u) = \frac{[u]_{\mathbf s,\mathbf p}}{\|u\|_{\mathbf p}},$$ where $\mathbf p = (p_1,\dots,p_n)$, $\mathbf s=(s_1,\dots,s_n)$ and $$\|\nabla u\|_{\mathbf p} = \sum_{i=1}^n \|u_{x_i}\|_{p_i}$$ is an anisotropic Sobolev norm, $[u]_{\mathbf s,\mathbf p}$ is a fractional version of the same anisotropic norm, and $\|u\|_{\mathbf p}$ is an anisotropic Lebesgue norm. Using the Ljusternik-Schnirelmann theory, we prove the existence of a sequence of critical values and we also find an associated Euler-Lagrange equation for critical points. Additionally, we analyze the connection between the fractional critical values and its local counterparts.Comment: 18 pages, submitte

Silencing hepatic MCJ attenuates non-alcoholic fatty liver disease (NAFLD) by increasing mitochondrial fatty acid oxidation

Nonalcoholic fatty liver disease (NAFLD) is considered the next major health epidemic with an estimated 25% worldwide prevalence. No drugs have yet been approved and NAFLD remains a major unmet need. Here, we identify MCJ (Methylation-Controlled J protein) as a target for non-alcoholic steatohepatitis (NASH), an advanced phase of NAFLD. MCJ is an endogenous negative regulator of the respiratory chain Complex I that acts to restrain mitochondrial respiration. We show that therapeutic targeting of MCJ in the liver with nanoparticle- and GalNAc-formulated siRNA efficiently reduces liver lipid accumulation and fibrosis in multiple NASH mouse models. Decreasing MCJ expression enhances the capacity of hepatocytes to mediate beta -oxidation of fatty acids and minimizes lipid accumulation, which results in reduced hepatocyte damage and fibrosis. Moreover, MCJ levels in the liver of NAFLD patients are elevated relative to healthy subjects. Thus, inhibition of MCJ emerges as an alternative approach to treat NAFLD. Non-alcoholic fatty liver (NAFLD) disease causes degeneration of the liver, affects about 25% of people globally, and has no approved treatment. Here, the authors show that the therapeutic siRNA-driven silencing of MCJ in the liver is an effective and safe treatment for NAFLD in multiple mouse models.We thank Douglas Taatjes and Nicole Bouffard for help with confocal microscopy analysis (Microscopy Imaging Center) at the University of Vermont. We also thank the University of Vermont Medical Center's Department of Pathology and Laboratory Medicine Histology and Clinical Laboratories for assistance with liver section staining and AST/ALT measurement, respectively. This work was supported by NIH STTR R41DK112429 (M.R.), NIH PO GM103496 (M.R.), Mitotherapeutix LLC (M.R., K.F, and M.L.M.-C.), MINECO/Feder SAF2015-65327-R and RTI2018-096494-B-100 (J.A.), MINECO/Feder SAF2017-87301-R (M.L.M-C.), BIOEF (M.L.M.-C.), EITB Maratoia BIO15/CA/014 (M.L.M-C), BBVA (M.L.M.-C.), La Caixa Foundation (M.L.M.-C.), Basque Country Health Department 2013111114 (M.L.M-C), MINECO/Feder SAF2015-64352-R (P.A.) and MINECO-Feder RTI2018-095134-B-100 (P.A.). ISCIII-Feder PI17/00535 (C.G.-M.), ISCIII-Feder CP14/00181, and PI16/00823 (A.G-R.), and Francisco Cobos Foundation (A.G.-R.). CIC bioGUNE is the recipient of a Severo Ochoa Excellence Accreditation (SEV-2016-0644) by the Ministry of Science, Innovation and Universities

Is food addiction a predictor of treatment outcome among patients with eating disorder?

ObjectivesThe study aimed to examine whether food addiction (FA) was associated with greater severity in both binge eating disorders (BED) and bulimia nervosa and, therefore, to determine if FA was predictive of treatment outcome.MethodSeventy-one adult patients with bulimia nervosa and BED (42 and 29, respectively) participated in the study. FA was assessed by means of the Yale Food Addiction Scale.ResultsThe results confirmed a high prevalence of FA in patients with binge disorders (around 87%) and also its association with a greater severity of the disorder (i.e., related to an increased eating psychopathology and greater frequency of binge eating episodes). Although FA did not appear as a predictor of treatment outcome in general terms, when the diagnostic subtypes were considered separately, FA was associated with poor prognosis in the BED group. In this vein, FA appeared as a mediator in the relationship between ED severity and treatment outcome.DiscussionsOur findings suggest that FA may act as an indicator of ED severity, and it would be a predictor of treatment outcome in BED but not in BN.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152018/1/erv2705.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152018/2/erv2705_am.pd