Corrigendum for "Almost vanishing polynomials and an application to the Hough transform"

In this note we correct a technical error occurred in [M. Torrente and M.C. Beltrametti, "Almost vanishing polynomials and an application to the Hough transform", J. Algebra Appl. 13(8), (2014)]. This affects the bounds given in that paper, even though the structure and the logic of all proofs remain fully unchanged.Comment: 30 page

The emerging role of the inwardly rectifying K+ channels in autism spectrum disorders and epilepsy

Autism is a complex behavioral disorder that develops prior to age three years and is distinguished by high heritability. Many genes predisposing to autism spectrum disorders (ASDs) have been identified. These findings have demonstrated that ASDs are etiologically heterogeneous; although, the mutations underlying ASDs are identifiable only in a minority of patients. Indeed, the causes of ASDs are unknown in more than 70% of patients. Recently, we have described two unrelated families whose affected individuals display a characteristic triad of symptoms of autism; such as impairments in social interaction, impairments in communication, restricted interests and repetitive behavior. They also displayed other symptoms commonly observed in autistic individuals; such as gait imbalance, clumsiness, mental retardation and epilepsy. The genetic analysis of these families resulted in the identification of new heterozygous point mutations in the KCNJ10 gene that encodes the inwardly-rectifying K+ channel Kir4.1 expressed predominantly, but not exclusively, in astrocytes. Functionally, the mutated channels exhibited a phenotype consistent with gain-of-function defects. These new findings highlight the emerging role of inwardly-rectifying K+ channels and astrocyte dysfunction in autism spectrum disorders associated with epilepsy.peer-reviewe

Long Term and Short Term Effects of Perturbations in a Immune Network Model

In this paper we review the trajectory of a model proposed by Stauffer and Weisbuch in 1992 to describe the evolution of the immune repertoire and present new results about its dynamical behavior. Ten years later this model, which is based on the ideas of the immune network as proposed by Jerne, has been able to describe a multi-connected network and could be used to reproduce immunization and aging experiments performed with mice. Besides its biological implications, the physical aspects of the complex dynamics of this network is very interesting {\it per se}. The immunization protocol is simulated by introducing small and large perturbations (damages), and in this work we discuss the role of both. In a very recent paper we studied the aging effects by using auto-correlation functions, and the results obtained apparently indicated that the small perturbations would be more important than the large ones, since their cumulative effects may change the attractor of the dynamics. However our new results indicate that both types of perturbations are important. It is the cooperative effects between both that lead to the complex behavior which allows to reproduce experimental results.Comment: 15 pages, 5 figure

On the optimization of conservation law models at a junction with inflow and flow distribution controls

The paper proposes a general framework to analyze control problems for conservation law models on a network. Namely we consider a general class of junction distribution controls and inflow controls and we establish the compactness in $L^1$ of a class of flux-traces of solutions. We then derive the existence of solutions for two optimization problems: (I) the maximization of an integral functional depending on the flux-traces of solutions evaluated at points of the incoming and outgoing edges; (II) the minimization of the total variation of the optimal solutions of problem (I). Finally we provide an equivalent variational formulation of the min-max problem (II) and we discuss some numerical simulations for a junction with two incoming and two outgoing edges.Comment: 29 pages, 14 figure

Promising approaches to optimize the biological properties of the antimicrobial peptide esculentin-1a(1-21)NH2. amino acids substitution and conjugation to nanoparticles

Antimicrobial peptides (AMPs) represent an interesting class of molecules with expanding biological properties which make them a viable alternative for the development of future antibiotic drugs. However, for this purpose, some limitations must be overcome: (i) the poor biostability due to enzymatic degradation; (ii) the cytotoxicity at concentrations slightly higher than the therapeutic dosages; and (iii) the inefficient delivery to the target site at effective concentrations. Recently, a derivative of the frog skin AMP esculentin-1a, named esculentin-1a(1-21)NH2, [Esc(1-21): GIFSKLAGKKIKNLLISGLKG-NH2] has been found to have a potent activity against the Gram-negative bacterium Pseudomonas aeruginosa; a slightly weaker activity against Gram-positive bacteria and interesting immunomodulatory properties. With the aim to optimize the antimicrobial features of Esc(1-21) and to circumvent the limitations described above, two different approaches were followed: (i) substitutions by non-coded amino acids, i.e., α-aminoisobutyric acid or d-amino acids; and (ii) peptide conjugation to gold nanoparticles. In this mini-review, we summarized the structural and functional properties of the resulting Esc(1-21)-derived compounds. Overall, our data may assist researchers in the rational design and optimization of AMPs for the development of future drugs to fight the worldwide problem of antibiotic resistance

Bilocal Dynamics for Self-Avoiding Walks

We introduce several bilocal algorithms for lattice self-avoiding walks that provide reasonable models for the physical kinetics of polymers in the absence of hydrodynamic effects. We discuss their ergodicity in different confined geometries, for instance in strips and in slabs. A short discussion of the dynamical properties in the absence of interactions is given.Comment: 38 LaTeX2e pages with 9 postscript figure