Infinite products involving binary digit sums

Let $(u_n)_{n\ge 0}$ denote the Thue-Morse sequence with values $\pm 1$. The Woods-Robbins identity below and several of its generalisations are well-known in the literature \begin{equation*}\label{WR}\prod_{n=0}^\infty\left(\frac{2n+1}{2n+2}\right)^{u_n}=\frac{1}{\sqrt 2}.\end{equation*} No other such product involving a rational function in $n$ and the sequence $u_n$ seems to be known in closed form. To understand these products in detail we study the function \begin{equation*}f(b,c)=\prod_{n=1}^\infty\left(\frac{n+b}{n+c}\right)^{u_n}.\end{equation*} We prove some analytical properties of $f$. We also obtain some new identities similar to the Woods-Robbins product.Comment: Accepted in Proc. AMMCS 2017, updated according to the referees' comment

Algorithmic Randomness and Capacity of Closed Sets

We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets K which have nonempty intersection with Q. We prove an effective version of Choquet's capacity theorem by showing that every computable capacity may be obtained from a computable measure in this way. We establish conditions on the measure m that characterize when the capacity of an m-random closed set equals zero. This includes new results in classical probability theory as well as results for algorithmic randomness. For certain computable measures, we construct effectively closed sets with positive capacity and with Lebesgue measure zero. We show that for computable measures, a real q is upper semi-computable if and only if there is an effectively closed set with capacity q

Approccio alla lingua italiana per allievi stranieri - ALIAS

Contiene, di P. E. Balboni, - "Approccio alla lingua italiana per allievi stranieri", pp. 55-71 - "Problemi interculturali nei rapporti con allievi stranieri e con le loro famiglie", pp. 73-90 - "La fomrazione dei docenti: i contenuti e gli strumenti di base", pp. 181-184

Immunosuppressive Exosomes: A New Approach for Treating Arthritis

Rheumatoid arthritis (RA) is a chronic autoimmune disease and one of the leading causes of disability in the USA. Although certain biological therapies, including protein and antibodies targeting inflammatory factors such as the tumor necrosis factor, are effective in reducing symptoms of RA, these treatments do not reverse disease. Also, although novel gene therapy approaches have shown promise in preclinical and clinical studies to treat RA, it is still unclear whether gene therapy can be readily and safely applied to treat the large number of RA patients. Recently, nanosized, endocytic-derived membrane vesicles “exosomes” were demonstrated to function in cell-to-cell communication and to possess potent immunoregulatory properties. In particular, immunosuppressive DC-derived exosomes and blood plasma- or serum-derived exosomes have shown potent therapeutic effects in animal models of inflammatory and autoimmune disease including RA. This paper discusses the current knowledge on the production, efficacy, mechanism of action, and potential therapeutic use of immunosuppressive exosomes for arthritis therapy

The Roles of Tumor-Derived Exosomes in Cancer Pathogenesis

Exosomes are endosome-derived, 30–100 nm small membrane vesicles released by most cell types including tumor cells. They are enriched in a selective repertoire of proteins and nucleic acids from parental cells and are thought to be actively involved in conferring intercellular signals. Tumor-derived exosomes have been viewed as a source of tumor antigens that can be used to induce antitumor immune responses. However, tumor-derived exosomes also have been found to possess immunosuppressive properties and are able to facilitate tumor growth, metastasis, and the development of drug resistance. These different effects of tumor-derived exosomes contribute to the pathogenesis of cancer. This review will discuss the roles of tumor-derived exosomes in cancer pathogenesis, therapy, and diagnostics

Ground-state properties of a supersymmetric fermion chain

We analyze the ground state of a strongly interacting fermion chain with a supersymmetry. We conjecture a number of exact results, such as a hidden duality between weak and strong couplings. By exploiting a scale free property of the perturbative expansions, we find exact expressions for the order parameters, yielding the critical exponents. We show that the ground state of this fermion chain and another model in the same universality class, the XYZ chain along a line of couplings, are both written in terms of the same polynomials. We demonstrate this explicitly for up to N = 24 sites, and provide consistency checks for large N. These polynomials satisfy a recursion relation related to the Painlev\'e VI differential equation, and using a scale-free property of these polynomials, we derive a simple and exact formula for their limit as N goes to infinity.Comment: v2: added more information on scaling function, fixed typo

Methane metabolism in the archaeal phylum Bathyarchaeota revealed by genome-centric metagenomics

Methanogenic and methanotrophic archaea play important roles in the global flux of methane. Culture-independent approaches are providing deeper insight into the diversity and evolution of methane-metabolizing microorganisms, but, until now, no compelling evidence has existed for methane metabolism in archaea outside the phylum Euryarchaeota. We performed metagenomic sequencing of a deep aquifer, recovering two near-complete genomes belonging to the archaeal phylum Bathyarchaeota (formerly known as the Miscellaneous Crenarchaeotal Group). These genomes contain divergent homologs of the genes necessary for methane metabolism, including those that encode the methyl–coenzyme M reductase (MCR) complex. Additional non-euryarchaeotal MCR-encoding genes identified in a range of environments suggest that unrecognized archaeal lineages may also contribute to global methane cycling. These findings indicate that methane metabolism arose before the last common ancestor of the Euryarchaeota and Bathyarchaeota

Amplification of Fluctuations in Unstable Systems with Disorder

We study the early-stage kinetics of thermodynamically unstable systems with quenched disorder. We show analytically that the growth of initial fluctuations is amplified by the presence of disorder. This is confirmed by numerical simulations of morphological phase separation (MPS) in thin liquid films and spinodal decomposition (SD) in binary mixtures. We also discuss the experimental implications of our results.Comment: 15 pages, 4 figure