Continuity of Optimal Control Costs and its application to Weak KAM Theory

We prove continuity of certain cost functions arising from optimal control of affine control systems. We give sharp sufficient conditions for this continuity. As an application, we prove a version of weak KAM theorem and consider the Aubry-Mather problems corresponding to these systems.Comment: 23 pages, 1 figures, added explanations in the proofs of the main theorem and the exampl

Barium alginate capsules for 3D immobilisation of living cells: morphology, membrane properties and permeability

Encapsulation in a barium alginate membrane is a promising strategy to obtain a three dimensional culture of living cells: membrane properties are crucial for a realistic clinical application. A one-step encapsulation technique, recently developed for controlled release of boar semen, was employed to prepare barium alginate and protamine-alginate membranes: permeability to two model molecules (haemoglobin and glucose) was evaluated. Capsules were evaluated for technological properties and scanning electron microscopy was used to examine the external morphology of the capsules and the 3D distribution of the cells within the core. The results indicate that 3D arrangement and cell shape are maintained, capsule dimensions and mechanical properties can be modulated, as well as their permeability to model molecules such as haemoglobin and glucose

Media use during adolescence: the recommendations of the Italian Pediatric Society.

BACKGROUND: The use of media device, such as smartphone and tablet, is currently increasing, especially among the youngest. Adolescents spend more and more time with their smartphones consulting social media, mainly Facebook, Instagram and Twitter because. Adolescents often feel the necessity to use a media device as a means to construct a social identity and express themselves. For some children, smartphone ownership starts even sooner as young as 7 yrs, according to internet safety experts. MATERIAL AND METHODS: We analyzed the evidence on media use and its consequences in adolescence. RESULTS: In literature, smartphones and tablets use may negatively influences the psychophysical development of the adolescent, such as learning, sleep and sigh. Moreover, obesity, distraction, addiction, cyberbullism and Hikikomori phenomena are described in adolescents who use media device too frequently. The Italian Pediatric Society provide action-oriented recommendations for families and clinicians to avoid negative outcomes. CONCLUSIONS: Both parents and clinicians should be aware of the widespread phenomenon of media device use among adolescents and try to avoid psychophysical consequences on the youngest

On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a few minor technical fixes. Modified title slightl

Lipid metabolism in development and progression of hepatocellular carcinoma

Metabolic reprogramming is critically involved in the development and progression of cancer. In particular, lipid metabolism has been investigated as a source of energy, micro-environmental adaptation, and cell signalling in neoplastic cells. However, the specific role of lipid metabolism dysregulation in hepatocellular carcinoma (HCC) has not been widely described yet. Alterations in fatty acid synthesis, β-oxidation, and cellular lipidic composition contribute to initiation and progression of HCC. The aim of this review is to elucidate the mechanisms by which lipid metabolism is involved in hepatocarcinogenesis and tumour adaptation to different conditions, focusing on the transcriptional aberrations with new insights in lipidomics and lipid zonation. This will help detect new putative therapeutic approaches in the second most frequent cause of cancer-related death

Effective dynamics using conditional expectations

The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(x)$, where $x$ describes the configuration of the system in a high-dimensional space $\R^n$, and $\xi$ is a smooth function with value in $\R$ (typically a reaction coordinate). It is well known that, given a Boltzmann-Gibbs distribution on $x \in \R^n$, the equilibrium properties on $\xi(x)$ are completely determined by the free energy. On the other hand, the question of the effective dynamics on $\xi(x)$ is much more difficult to address. Starting from an overdamped Langevin equation on $x \in \R^n$, we propose an effective dynamics for $\xi(x) \in \R$ using conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones. We check numerically on some toy examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarse-grained dynamics

Proteolytic and lipolytic starter cultures and their effect on traditional fermented sausages ripening and sensory traits

In this study, three starter formulations including Lactobacillus curvatus and Staphylococcus xylosus strains selected in vitro on the basis of their lipolytic and proteolytic activities were employed for the manufacture of traditional fermented sausages of southern Italy. Microbial population, proteolysis, lipolysis, changes in free amino acids (FAA) and free fatty acids (FFA) and development of characteristic taste and flavor of the final product were investigated. Proteolysis and lipolysis were observed in sausages inoculated with proteolytic and lipolytic S. xylosus coupled with L. curvatus, while the sausage started with only S. xylosus without lactobacilli was identical to the non-inoculated control, indicating that the proteolysis could be due to both microbial activity and endogenous proteases activated by the decrease in pH. The statistical analysis applied to the instrumental and sensory data showed that there was an effect of the starter used on the characteristics of the sausage obtained. In particular, the control samples showed very close features different from the sausages obtained by adding starter cultures. Finally, analyzing the sensory parameters the sausages ripened without starter addition and those started without the L. curvatus AVL3 showed similar features indicating an influence of the presence of the lactobacilli on the final organoleptic quality of the sausages. An appropriate choice of a combination of strains in a starter formulation is fundamental to obtain products of the expected quality

Corneal involvement in rheumatoid arthritis: an vivo confocal study

PURPOSE. To analyze the in vivo morphology of corneal cells and nerves in patients with rheumatoid arthritis (RA), with or without secondary Sj\uf6gren\u2019s syndrome (SSII), and to investigate the correlations between corneal alterations and RA activity. METHODS. Fifty patients with RA and 30 age- and gender-matched control subjects were studied. SSII was diagnosed according to the American-European Consensus Group criteria, and RA activity was evaluated by the Lansbury index (LI). Confocal microscopy was used to investigate corneal thickness, the number of epithelial and stromal cells, and keratocyte hyperreflectivity. In addition, the sub-basal plexus was assessed for the number, tortuosity, and reflectivity of the nerve fibers and the presence of beadlike formations. RESULTS. Sixteen percent of patients with RA also had SSII. Between the SSII and non-SSII groups, no significant differences were found in the LI or in the clinical and confocal variables. Significant differences were present between patients with RA and control subjects for all the variables studied except nerve reflectivity. In patients with RA with and without SSII, LI correlated significantly with the number of beadlike formations and the number of hyperreflective, activated keratocytes. CONCLUSIONS. Confocal microscopy of patients with RA showed several changes in corneal cells and nerves. The number of beadlike formations and the number of activated keratocytes could be interpreted as confocal signs of ocular surface disease activity. These correlations with the index of systemic disease activity, LI, may provide insight regarding the pathogenic mechanisms of dry eye in patients with RA

Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde