Stone duality above dimension zero: Axiomatising the algebraic theory of C(X)

It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the category of sets. It follows that KH^op is equivalent to a possibly infinitary variety of algebras V in the sense of Slominski and Linton. Isbell showed in 1982 that the Lawvere-Linton algebraic theory of V can be generated using a finite number of finitary operations, together with a single operation of countably infinite arity. In 1983, Banaschewski and Rosicky independently proved a conjecture of Bankston, establishing a strong negative result on the axiomatisability of KH^op. In particular, V is not a finitary variety--Isbell's result is best possible. The problem of axiomatising V by equations has remained open. Using the theory of Chang's MV-algebras as a key tool, along with Isbell's fundamental insight on the semantic nature of the infinitary operation, we provide a finite axiomatisation of V.Comment: 26 pages. Presentation improve

Two isomorphism criteria for directed colimits

Using the general notions of finitely presentable and finitely generated object introduced by Gabriel and Ulmer in 1971, we prove that, in any (locally small) category, two sequences of finitely presentable objects and morphisms (or two sequences of finitely generated objects and monomorphisms) have isomorphic colimits (=direct limits) if, and only if, they are confluent. The latter means that the two given sequences can be connected by a back-and-forth chain of morphisms that is cofinal on each side, and commutes with the sequences at each finite stage. In several concrete situations, analogous isomorphism criteria are typically obtained by ad hoc arguments. The abstract results given here can play the useful r\^ole of discerning the general from the specific in situations of actual interest. We illustrate by applying them to varieties of algebras, on the one hand, and to dimension groups---the ordered $K_0$ of approximately finite-dimensional C*-algebras---on the other. The first application encompasses such classical examples as Kurosh's isomorphism criterion for countable torsion-free Abelian groups of finite rank. The second application yields the Bratteli-Elliott Isomorphism Criterion for dimension groups. Finally, we discuss Bratteli's original isomorphism criterion for approximately finite-dimensional C*-algebras, and show that his result does not follow from ours.Comment: 10 page

Pooling or sampling: Collective dynamics for electrical flow estimation

The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully decentralized way is implicit in a number of biological systems. Thus, a natural question is whether this task can provably be accomplished in an efficient way by a network of agents executing a simple protocol. We provide a positive answer, proposing two distributed approaches to electrical flow computation on a weighted network: a deterministic process mimicking Jacobi's iterative method for solving linear systems, and a randomized token diffusion process, based on revisiting a classical random walk process on a graph with an absorbing node. We show that both processes converge to a solution of Kirchhoff's node potential equations, derive bounds on their convergence rates in terms of the weights of the network, and analyze their time and message complexity

Entanglement entropy of two disjoint blocks in critical Ising models

We study the scaling of the Renyi and entanglement entropy of two disjoint blocks of critical Ising models, as function of their sizes and separations. We present analytic results based on conformal field theory that are quantitatively checked in numerical simulations of both the quantum spin chain and the classical two dimensional Ising model. Theoretical results match the ones obtained from numerical simulations only after taking properly into account the corrections induced by the finite length of the blocks to their leading scaling behavior.Comment: 4 pages, 5 figures. Revised version accepted for publication in PR

One-point statistics and intermittency of induced electric field in the solar wind

The interplanetary induced electric field e=vxb is studied, using solar wind time series. The probability distribution functions (PDFs) of the electric field components are measured from the data and their non-gaussianity is discussed. Moreover, for the first time we show that the electric field turbulence is characterized by intermittency. This point is addressed by studying, as usual, the scaling of the PDFs of field increments, which allows a quantitative characterization of intermittency.Comment: Accepted for publication on Europhysics Letters, April 22th, 200

Membrane-active derivatives of the frog skin peptide Esculentin-1 against relevant human pathogens

Candida albicans represents one of the most prevalent species causing life-threatening fungal infections. Current treatments to defeat Candida albicans have become quite difficult, due to their toxic side effects and the emergence of resistant strains. Antimicrobial peptides (AMPs) are fascinating molecules with a potential role as novel anti-infective agents. However, only a few studies have been performed on their efficacy towards the most virulent hyphal phenotype of this pathogen. The purpose of this work is to evaluate the anti-Candida activity of the N-terminal 1–18 fragment of the frog skin AMP esculentin- 1b, Esc(1–18), under both in vitro and in vivo conditions using Caenorhabditis elegans as a simple host model for microbial infections. Our results demonstrate that Esc(1–18) caused a rapid reduction in the number of viable yeast cells and killing of the hyphal population. Esc(1–18)revealed a membrane perturbing effect which is likely the basis of its mode of action. Esc(1-18) is able (1) to kill both growing stages of Candida; (2) to promote survival of Candida-infected living organisms and (3) to inhibit transition of these fungal cells from the roundish yeast shape to the more dangerous hyphal form at sub-inhibitory concentrations. Pseudomonas aeruginosa is an opportunistic bacterial pathogen that forms sessile communities, named biofilms. The non-motile forms are very difficult to eradicate and are often associated with the establishment of persistent infections, especially in patients with cystic fibrosis. The resistance of P. aeruginosa to conventional antibiotics has become a growing health concern worldwide and has prompted the search for new anti-infective agents with new modes of action. Naturally occurring antimicrobial peptides (AMPs) represent promising future template candidates. Here we report on the potent activity and membrane-perturbing effects of the amphibian AMP esculentin(1-21), on both the free-living and sessile forms of P. aeruginosa, as a possible mechanism for biofilm disruption. Furthermore, the findings that esculentin(1-21) is able to prolong survival of animals in models of sepsis and pulmonary infection indicate that this peptide can be a promising template for the generation of new antibiotic formulations to advance care of infections caused by P. aeruginosa

A three-arm current comparator bridge, for impedance comparisons over the complex plane

We present here the concept of three-arm current comparator impedance bridge, which allows comparisons among three unlike impedances. Its purpose is the calibration of impedances having arbitrary phase angles, against calibrated nearly-pure impedances. An analysis of the bridge optimal setting and proper operation is presented. To test the concept, a two terminal-pair digitally-assisted bridge has been realized; measurements of an air-core inductor and of an RC network versus decade resistance and capacitance standards, at kHz frequency, have been performed. The bridge measurements are compatible with previous knowledge of the standards' values with relative deviations in the 10^-5 -- 10^-6 range