Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

Desplegament dels circuits dedicats de 1 i 10 Gbps entre el PIC i el CERN

Aquest projecte consisteix a realitzar el disseny i desplegament d'una connexió entre el Port d'Informació Científica (PIC) i el Consell Europeu per a la Recerca Nuclear (CERN) sobre un circuit dedicat amb una velocitat de transferència de 10 Gbps. En una primera fase el desplegament de la connexió es realitza sobre un circuit dedicat de 1 Gbps. El projecte implica la certificació dels circuits dedicats de 1 i 10 Gbps i el disseny dels plans d'actuació que han de permetre la integració de les noves connexions dins la xarxa i els serveis del PIC.

Combinatorial Synthesis and Biological Evaluation of Inhibitors of D-Ala-D-Ala-Ligase

Report for the scientific sojourn carried out at the Max Planck Institut of Molecular Phisiology, Germany, from 2006 to 2008.The work carried out during this postdoctoral stage was focused on two different projects. Firstly, identification of D-Ala D-Ala Inhibitors and the development of new synthethic approaches to obtain lipidated peptides and proteins and the use of these lipidated proteins in biological and biophysical studies. In the first project, new D-Ala D-Ala inhibitors were identified by using structural alignments of the ATP binding sites of the bacterial ligase DDl and protein and lipid kinases in complex with ATP analogs. We tested a series of commercially available kinase inhibitors and found LFM-A13 and Tyrphostine derivatives to inhibit DDl enzyme activity. Based on the initial screening results we synthesized a series of malononitrilamide and salicylamide derivatives and were able to confirm the validity of these scaffolds as inhibitors of DDl. From this investigation we gained a better understanding of the structural requirements and limitations necessary for the preparation of ATP competitive DDl inhibitors. The compounds in this study may serve as starting points for the development of bi-substrate inhibitors that incorporate both, an ATP competitive and a substrate competitive moiety. Bisubstrate inhibitors that block the ATP and D-Ala binding sites should exhibit enhanced selectivity and potency profiles by preferentially inhibiting DDl over kinases. In the second project, an optimized synthesis for tha alkylation of cysteins using the thiol ene reaction was establisehd. This new protocol allowed us to obtain large amounts of hexadecylated cysteine that was required for the synthesis of differently lipidated peptides. Afterwards the synthesis of various N-ras peptides bearing different lipid anchors was performed and the peptides were ligated to a truncated N-ras protein. The influence of this differently lipidated N-ras proteins on the partioning and association of N-Ras in model membrane subdomains was studied using Atomic Force Microscopy.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Cortical mapping of the neuronal circuits modulating the muscle tone. Introduction to the electrophysiological treatment of the spastic hand.

L’objectiu d’aquest estudi es investigar l’organització cortical junt amb la connectivitat còrtico-subcortical en subjectes sans, com a estudi preliminar. Els mapes corticals s’han fet per TMS navegada, i els punts motors obtinguts s’han exportant per estudi tractogràfic i anàlisi de las seves connexions. El coneixement precís de la localització de l’àrea cortical motora primària i les seves connexions es la base per ser utilitzada en estudis posteriors de la reorganització cortical i sub-cortical en pacients amb infart cerebral. Aquesta reorganització es deguda a la neuroplasticitat i pot ser influenciada per els efectes neuromoduladors de la estimulació cerebral no invasiva.

Pulse propagation sustained by noise in arrays of bistable electronic circuits

One-dimensional arrays of nonlinear electronic circuits are shown to support propagation of pulses when operating in a locally bistable regime, provided the circuits are under the influence of a global noise. These external random fluctuations are applied to the parameter that controls the transition between bistable and monostable dynamics in the individual circuits. As a result, propagating fronts become destabilized in the presence of noise, and the system self-organizes to allow the transmission of pulses. The phenomenon is also observed in weakly coupled arrays, when propagation failure arises in the absence of noise.

Identification of Ligands for the Tau Exon 10 Splicing Regulatory Element RNA Using Dynamic Combinatorial Chemistry

We describe the use of dynamic combinatorial chemistry (DCC) to identify ligands for the stem-loop structure located at the exon 10-5'-intron junction of Tau pre-mRNA, which is involved in the onset of several tauopathies including frontotemporal dementia with Parkinsonism linked to chromosome 17 (FTDP-17). A series of ligands that combine the small aminoglycoside neamine and heteroaromatic moieties (azaquinolone and two acridines) have been identified by using DCC. These compounds effectively bind the stem-loop RNA target (the concentration required for 50% RNA response (EC(50)): 2-58 μM), as determined by fluorescence titration experiments. Importantly, most of them are able to stabilize both the wild-type and the +3 and +14 mutated sequences associated with the development of FTDP-17 without producing a significant change in the overall structure of the RNA (as analyzed by circular dichroism (CD) spectroscopy), which is a key factor for recognition by the splicing regulatory machinery. A good correlation has been found between the affinity of the ligands for the target and their ability to stabilize the RNA secondary structure.

On the preservation of combinatorial types for maps on trees

We study the preservation of the periodic orbits of an A-monotone tree map f:T→T in the class of all tree maps g:S→S having a cycle with the same pattern as A. We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of ƒ into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved

Comments on "On resistor-induced thermal noise in linear circuits"

Correspondència referida a l'article de R. Giannetti, publicat ibid. vol.49 p.87-88

Error probability in synchronous digital circuits due to power supply noise

This paper presents a probabilistic approach to model the problem of power supply voltage fluctuations. Error probability calculations are shown for some 90-nm technology digital circuits.The analysis here considered gives the timing violation error probability as a new design quality factor in front of conventional techniques that assume the full perfection of the circuit. The evaluation of the error bound can be useful for new design paradigms where retry and self-recoveringtechniques are being applied to the design of high performance processors. The method here described allows to evaluate the performance of these techniques by means of calculating the expected error probability in terms of power supply distribution quality.

Improving the efficiency of PV low-power processing circuits by selecting an optimal inductor current of the DC/DC converter

In the context of autonomous sensors powered by small-size photovoltaic (PV) panels, this work analyses how the efficiency of DC/DC-converter-based power processing circuits can be improved by an appropriate selection of the inductor current that transfers the energy from the PV panel to a storage unit. Each component of power losses (fixed, conduction and switching losses) involved in the DC/DC converter specifically depends on the average inductor current so that there is an optimal value of this current that causes minimal losses and, hence, maximum efficiency. Such an idea has been tested experimentally using two commercial DC/DC converters whose average inductor current is adjustable. Experimental results show that the efficiency can be improved up to 12% by selecting an optimal value of that current, which is around 300-350 mA for such DC/DC converters.

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.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

Testing Cayley graph densities

We present a computer-assisted analysis of combinatorial properties of the Cayley graphs of certain finitely generated groups: Given a group with a finite set of generators, we study the density of the corresponding Cayley graph, that is, the least upper bound for the average vertex degree (= number of adjacent edges) of any finite subgraph. It is known that an m-generated group is amenable if and only if the density of the corresponding Cayley graph equals to 2m. We test amenable and non-amenable groups, and also groups for which amenability is unknown. In the latter class we focus on Richard Thompson’s group F.