A note on the application of integrals involving cyclic products kernels

A l'estadística de processos estocàstics i camps aleatoris, una funció de moments o un cumulant d'un estimador de la funció de correlació o de la densitat espectral sovint pot contenir una integral amb un producte cíclic de nuclis. En aquest treball es defineix i s'investiga aquesta classe d'integrals i es demostra la desigualtat de Young-Hölder que permet estudiar el comportament asimptòtic de les esmentades integrals en la situació quan els nuclis depenen d'un pàràmetre. Es considera una aplicació al problema d'estimació de la funció de resposta en un sistema de Volterra.

The automorphism group of a free-by-cyclic group in rank 2

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Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

Quasi-Potency and Cyclic subgroup separability

We study the profinite topology on discrete groups and in particular the property of cyclic subgroup separability. We investigate the class of quasi-potent, cyclic subgroup separable groups, producing many examples and showing how it behaves with respect to certain group constructions.

Statistical evidences of cyclic changes in volcanic gas chemistry composition by inverse modelling

The identification of compositional changes in fumarolic gases of active and quiescent volcanoes is one of the mostimportant targets in monitoring programs. From a general point of view, many systematic (often cyclic) and randomprocesses control the chemistry of gas discharges, making difficult to produce a convincing mathematical-statisticalmodelling.Changes in the chemical composition of volcanic gases sampled at Vulcano Island (Aeolian Arc, Sicily, Italy) fromeight different fumaroles located in the northern sector of the summit crater (La Fossa) have been analysed byconsidering their dependence from time in the period 2000-2007. Each intermediate chemical composition has beenconsidered as potentially derived from the contribution of the two temporal extremes represented by the 2000 and 2007samples, respectively, by using inverse modelling methodologies for compositional data. Data pertaining to fumarolesF5 and F27, located on the rim and in the inner part of La Fossa crater, respectively, have been used to achieve theproposed aim. The statistical approach has allowed us to highlight the presence of random and not random fluctuations,features useful to understand how the volcanic system works, opening new perspectives in sampling strategies and inthe evaluation of the natural risk related to a quiescent volcano

The Molecular Basis for Antimicrobial Activity of Pore-Forming Cyclic Peptides

The mechanism of action of antimicrobial peptides is, to our knowledge, still poorly understood. To probe the biophysical characteristics that confer activity, we present here a molecular-dynamics and biophysical study of a cyclic antimicrobial peptide and its inactive linear analog. In the simulations, the cyclic peptide caused large perturbations in the bilayer and cooperatively opened a disordered toroidal pore, 1–2 nm in diameter. Electrophysiology measurements confirm discrete poration events of comparable size. We also show that lysine residues aligning parallel to each other in the cyclic but not linear peptide are crucial for function. By employing dual-color fluorescence burst analysis, we show that both peptides are able to fuse/aggregate liposomes but only the cyclic peptide is able to porate them. The results provide detailed insight on the molecular basis of activity of cyclic antimicrobial peptides

Seasonality and cyclic tendency of mortality in a Pyrenean population

Las características de la mortalidad Influyen decisivamente en la estructura demográfica de las poblaciones, regida por diferentes factores: internos (rasgos específicos genéticos y culturales), externos (características del ecosistema) e intermedios (capacidad de la población de autoajustarse al ambiente). El estudio de la distribución estacional de las 3313 defunciones registradas en la Villa de El Pont de Suert (Alta Ribagorça, Cataluña) desde 1664 evidencia la importancia de todos estos factores. Los patrones de distribución muestran el Influjo de las condiciones climáticas, de los ambientes epidemiológicos, así como de las transformaciones socioeconómicas y demográficas. El modelo de tendencia cíclica en la mortalidad, común a muchas poblaciones ibéricas de montaña, no se evidencia en esta población.

Spin-Peierls vs Peierls distortions in a family of conjugated polymers

Distortions in a family of conjugated polymers are studied using two complementary approaches: within a many-body valence bond approach using a transfer-matrix technique to treat the Heisenberg model of the systems, and also in terms of the tight-binding band-theoretic model with interactions limited to nearest neighbors. The computations indicate that both methods predict the presence or absence of the same distortions in most of the polymers studied.

Valence-bond treatment of distortions in polyacene polymers

Distortions of polyacene polymers are studied within a many-body valence-bond framework using a powerful transfer-matrix technique for the valence-bond (or Heisenberg) model of the system. The computations suggest that the ground-state geometry is either totally symmetric or possibly exhibits a slight (A2 or B2 symmetry) bond-alternation distortion. The lowest-energy (nonsymmetric, in-plane) distortions are the A2 and B2 modes, which, within our approximations, are degenerate.

Reliability of the density functional approximation to describe the charge transfer and electrostatic complexes involved in the modeling of organic conducting polymers

Both the intermolecular interaction energies and the geometries for M ̄ thiophene, M ̄ pyrrole, M n+ ̄ thiophene, and M n+ ̄ pyrrole ͑with M = Li, Na, K, Ca, and Mg; and M n+ = Li+ , Na+ , K+ , Ca2+, and Mg2+͒ have been estimated using four commonly used density functional theory ͑DFT͒ methods: B3LYP, B3PW91, PBE, and MPW1PW91. Results have been compared to those provided by HF, MP2, and MP4 conventional ab initio methods. The PBE and MPW1PW91 are the only DFT methods able to provide a reasonable description of the M ̄ complexes. Regarding M n+ ̄ ␲ complexes, the four DFT methods have been proven to be adequate in the prediction of these electrostatically stabilized systems, even though they tend to overestimate the interaction energies.

Comparing and taming the reactivity of HWE and Wittig reagents with cyclic hemiacetals

A practical solution to the formation of mixtures of E/Z and open/cyclic isomers in the reaction of (2R,4S)-4-hydroxy-2-methylpentanal (as its hemiacetal, a lactol) with conjugated phosphoranes (stabilised Wittig reagents) and Horner-Wadsworth-Emmons reagents is disclosed. The HWE reaction has a strong bias to give oxolanes. On the other hand, stabilised Wittig reagents give unsaturated carboxyl derivatives of configuration E (major) and oxolanes (minor); the latter can be avoided by addition of CF3CH2OH or using morpholine amide phosphorane.

The role of intramolecular barriers on the glass transition of polymers: computer simulations versus mode coupling theory

We present computer simulations of a simple bead-spring model for polymer melts with intramolecular barriers. By systematically tuning the strength of the barriers, we investigate their role on the glass transition. Dynamic observables are analyzed within the framework of the mode coupling theory (MCT). Critical nonergodicity parameters, critical temperatures, and dynamic exponents are obtained from consistent fits of simulation data to MCT asymptotic laws. The so-obtained MCT λ-exponent increases from standard values for fully flexible chains to values close to the upper limit for stiff chains. In analogy with systems exhibiting higher-order MCT transitions, we suggest that the observed large λ-values arise form the interplay between two distinct mechanisms for dynamic arrest: general packing effects and polymer-specific intramolecular barriers. We compare simulation results with numerical solutions of the MCT equations for polymer systems, within the polymer reference interaction site model (PRISM) for static correlations. We verify that the approximations introduced by the PRISM are fulfilled by simulations, with the same quality for all the range of investigated barrier strength. The numerical solutions reproduce the qualitative trends of simulations for the dependence of the nonergodicity parameters and critical temperatures on the barrier strength. In particular, the increase in the barrier strength at fixed density increases the localization length and the critical temperature. However the qualitative agreement between theory and simulation breaks in the limit of stiff chains. We discuss the possible origin of this feature.

Straightforward synthesis of cyclic and bicyclic peptides

Cyclic peptide architectures can be easily synthesized from cysteine-containing peptides with appending maleimides, free or protected, through an intramolecular Michael-type reaction. After peptide assembly, the peptide can cyclize either during the trifluoroacetic acid treatment, if the maleimide is not protected, or upon deprotection of the maleimide. The combination of free and protected maleimide moieties and two orthogonally protected cysteines gives access to structurally different bicyclic peptides with isolated or fused cycles.