Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

On the use of rotational splitting asymmetries to probe the internal rotation profile of stars: Application to beta Cephei stars

Rotationally-split modes can provide valuable information about the internal rotation profile of stars. This has been used for years to infer the internal rotation behavior of the Sun. The present work discusses the potential additional information that rotationally splitting asymmetries may provide when studying the internal rotation profile of stars. We present here some preliminary results of a method, currently under development, which intends: 1) to understand the variation of the rotational splitting asymmetries in terms of physical processes acting on the angular momentum distribution in the stellar interior, and 2) how this information can be used to better constrain the internal rotation profile of the stars. The accomplishment of these two objectives should allow us to better use asteroseismology as a test-bench of the different theories describing the angular momentum distribution and evolution in the stellar interiors. (C) 2010 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim

VALLEY SPLITTING AND g-FACTOR IN AlAs QUANTUM WELLS

Here we present the results of magneto resistance measurements in tilted magnetic field and compare them with calculations. The comparison between calculated and measured spectra for the case of perpendicular fields enable us to estimate the dependence of the valley splitting as a function of the magnetic field and the total Lande g-factor (which is assumed to be independent of the magnetic field). Since both the exchange contribution to the Zeeman splitting as well as the valley splitting are properties associated with the 2D quantum confinement, they depend only on the perpendicular component of the magnetic field, while the bare Zeeman splitting depends on the total magnetic field. This information aided by the comparison between experimental and calculated gray scale maps permits to obtain separately the values of the exchange and the bare contribution to the g-factor.

Enhancing an evolving tree-based text document visualization model with fuzzy c-Means clustering

An improved evolving model, i.e., Evolving Tree (ETree) with Fuzzy c-Means (FCM), is proposed for undertaking text document visualization problems in this study. ETree forms a hierarchical tree structure in which nodes (i.e., trunks) are allowed to grow and split into child nodes (i.e., leaves), and each node represents a cluster of documents. However, ETree adopts a relatively simple approach to split its nodes. Thus, FCM is adopted as an alternative to perform node splitting in ETree. An experimental study using articles from a flagship conference of Universiti Malaysia Sarawak (UNIMAS), i.e., Engineering Conference (ENCON), is conducted. The experimental results are analyzed and discussed, and the outcome shows that the proposed ETree-FCM model is effective for undertaking text document clustering and visualization problems.

Non-Zeeman splitting for a spin-resolved STM with a Kondo adatom in a spin-polarized two-dimensional electron gas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Macroscopic quantum tunneling in a dc SQUID: Instanton splitting

The theory of macroscopic quantum tunneling is applied to a current-biased dc SQUID which constitutes a system of two interacting quantum degrees of freedom coupled to the environment. The decay probability is obtained in the exponential approximation for the overdamped case. Close to the critical driving force of the system, the decay of the metastable state is determined by a unique instanton solution describing the symmetric decay of the phases in each of the two Josephson juctions. Upon reducing the external driving force a new regime is reached where the instanton splits. The doubling of the decay channels reduces the decreasing of the decay rate in the quantum regime. A current-temperature phase diagram is constructed based on the Landau theory of phase transitions. Depending on the external parameters the system develops either a first- or a second-order transition to the split-instanton regime. © 1994 The American Physical Society.

Photocatalytic hydrogen production by water splitting over Au-TiO2 commercial and home-made photocatalysts

[ES]Póster presentado en 3rd European Conference on Environmental Applications of Advanced Oxidation Processes.

El contenido del póster corresponde a parte del trabajo de tesis doctoral de la Dra. Cristina Rodríguez López.

The S-1/S-2 exciton interaction in 2-pyridone center dot 6-methyl-2-pyridone: Davydov splitting, vibronic coupling, and vibronic quenching

The excitonic splitting between the S-1 and S-2 electronic states of the doubly hydrogen-bonded dimer 2-pyridone center dot 6-methyl-2-pyridone (2PY center dot 6M2PY) is studied in a supersonic jet, applying two-color resonant two-photon ionization (2C-R2PI), UV-UV depletion, and dispersed fluorescence spectroscopies. In contrast to the C-2h symmetric (2-pyridone) 2 homodimer, in which the S-1 <- S-0 transition is symmetry-forbidden but the S-2 <- S-0 transition is allowed, the symmetry-breaking by the additional methyl group in 2PY center dot 6M2PY leads to the appearance of both the S-1 and S-2 origins, which are separated by Delta(exp) = 154 cm(-1). When combined with the separation of the S-1 <- S-0 excitations of 6M2PY and 2PY, which is delta = 102 cm(-1), one obtains an S-1/S-2 exciton coupling matrix element of V-AB, el = 57 cm(-1) in a Frenkel-Davydov exciton model. The vibronic couplings in the S-1/S-2 <- S-0 spectrum of 2PY center dot 6M2PY are treated by the Fulton-Gouterman single-mode model. We consider independent couplings to the intramolecular 6a' vibration and to the intermolecular sigma' stretch, and obtain a semi-quantitative fit to the observed spectrum. The dimensionless excitonic couplings are C(6a') = 0.15 and C(sigma') = 0.05, which places this dimer in the weak-coupling limit. However, the S-1/S-2 state exciton splittings Delta(calc) calculated by the configuration interaction singles method (CIS), time-dependent Hartree-Fock (TD-HF), and approximate second-order coupled-cluster method (CC2) are between 1100 and 1450 cm(-1), or seven to nine times larger than observed. These huge errors result from the neglect of the coupling to the optically active intra-and intermolecular vibrations of the dimer, which lead to vibronic quenching of the purely electronic excitonic splitting. For 2PY center dot 6M2PY the electronic splitting is quenched by a factor of similar to 30 (i.e., the vibronic quenching factor is Gamma(exp) = 0.035), which brings the calculated splittings into close agreement with the experimentally observed value. The 2C-R2PI and fluorescence spectra of the tautomeric species 2-hydroxypyridine center dot 6-methyl-2-pyridone (2HP center dot 6M2PY) are also observed and assigned. (C) 2011 American Institute of Physics.

Elderly age is not a negative predictive factor for virological response to therapy with pegylated interferon-α and ribavirin in chronic hepatitis C virus patients

BACKGROUND & AIMS: Age is frequently discussed as negative host factor to achieve a sustained virological response (SVR) to antiviral therapy of chronic hepatitis C. However, elderly patients often show advanced fibrosis/cirrhosis as known negative predictive factor. The aim of this study was to assess age as an independent predictive factor during antiviral therapy. METHODS: Overall, 516 hepatitis C patients were treated with pegylated interferon-α and ribavirin, thereof 66 patients ≥60 years. We analysed the impact of host factors (age, gender, fibrosis, haemoglobin, previous hepatitis C treatment) and viral factors (genotype, viral load) on SVR per therapy course by performing a generalized estimating equations (GEE) regression modelling, a matched pair analysis and a classification tree analysis. RESULTS: Overall, SVR per therapy course was 42.9 and 26.1%, respectively, in young and elderly patients with hepatitis C virus (HCV) genotypes 1/4/6. The corresponding figures for HCV genotypes 2/3 were 74.4 and 84%. In the GEE model, age had no significant influence on achieving SVR. In matched pair analysis, SVR was not different in young and elderly patients (54.2 and 55.9% respectively; P = 0.795 in binominal test). In classification tree analysis, age was not a relevant splitting variable. CONCLUSIONS: Age is not a significant predictive factor for achieving SVR, when relevant confounders are taken into account. As life expectancy in Western Europe at age 60 is more than 20 years, it is reasonable to treat chronic hepatitis C in selected elderly patients with relevant fibrosis or cirrhosis but without major concomitant diseases, as SVR improves survival and reduces carcinogenesis.

Measurement of kT splitting scales in W→lv events at sqrt(s)=7 TeV with the ATLAS detector

A measurement of splitting scales, as defined by the kT clustering algorithm, is presented for final states containing a W boson produced in proton-proton collisions at a centre-of-mass energy of 7 TeV. The measurement is based on the full 2010 data sample corresponding to an integrated luminosity of 36 pb(-1) which was collected using the ATLAS detector at the CERN Large Hadron Collider. Cluster splitting scales are measured in events containing W bosons decaying to electrons or muons. The measurement comprises the four hardest splitting scales in a k(T) cluster sequence of the hadronic activity accompanying the W boson, and ratios of these splitting scales. Backgrounds such as multi-jet and top-quark-pair production are subtracted and the results are corrected for detector effects. Predictions from various Monte Carlo event generators at particle level are compared to the data. Overall, reasonable agreement is found with all generators, but larger deviations between the predictions and the data are evident in the soft regions of the splitting scales.

The elusive S2 state, the S1/S2 splitting, and the excimer states of the benzene dimer

We observe the weak S 0 → S 2 transitions of the T-shaped benzene dimers (Bz)2 and (Bz-d 6)2 about 250 cm−1 and 220 cm−1 above their respective S 0 → S 1 electronic origins using two-color resonant two-photon ionization spectroscopy. Spin-component scaled (SCS) second-order approximate coupled-cluster (CC2) calculations predict that for the tipped T-shaped geometry, the S 0 → S 2 electronic oscillator strength f el (S 2) is ∼10 times smaller than f el (S 1) and the S 2 state lies ∼240 cm−1 above S 1, in excellent agreement with experiment. The S 0 → S 1 (ππ ∗) transition is mainly localized on the “stem” benzene, with a minor stem → cap charge-transfer contribution; the S 0 → S 2 transition is mainly localized on the “cap” benzene. The orbitals, electronic oscillator strengths f el (S 1) and f el (S 2), and transition frequencies depend strongly on the tipping angle ω between the two Bz moieties. The SCS-CC2 calculated S 1 and S 2 excitation energies at different T-shaped, stacked-parallel and parallel-displaced stationary points of the (Bz)2 ground-state surface allow to construct approximate S 1 and S 2 potential energy surfaces and reveal their relation to the “excimer” states at the stacked-parallel geometry. The f el (S 1) and f el (S 2) transition dipole moments at the C 2v -symmetric T-shape, parallel-displaced and stacked-parallel geometries are either zero or ∼10 times smaller than at the tipped T-shaped geometry. This unusual property of the S 0 → S 1 and S 0 → S 2 transition-dipole moment surfaces of (Bz)2 restricts its observation by electronic spectroscopy to the tipped and tilted T-shaped geometries; the other ground-state geometries are impossible or extremely difficult to observe. The S 0 → S 1/S 2 spectra of (Bz)2 are compared to those of imidazole ⋅ (Bz)2, which has a rigid triangular structure with a tilted (Bz)2 subunit. The S 0 → S 1/ S 2 transitions of imidazole-(benzene)2 lie at similar energies as those of (Bz)2, confirming our assignment of the (Bz)2 S 0 → S 2 transition.

Splitting monoidal stable model categories

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

Design principles for maximizing photovoltage in metal-oxide-protected water-splitting photoanodes

Metal oxide protection layers for photoanodes may enable the development of large-scale solar fuel and solar chemical synthesis, but the poor photovoltages often reported so far will severely limit their performance. Here we report a novel observation of photovoltage loss associated with a charge extraction barrier imposed by the protection layer, and, by eliminating it, achieve photovoltages as high as 630mV, the maximum reported so far for water-splitting silicon photoanodes. The loss mechanism is systematically probed in metal-insulator-semiconductor Schottky junction cells compared to buried junction p(+) n cells, revealing the need to maintain a characteristic hole density at the semiconductor/insulator interface. A leaky-capacitor model related to the dielectric properties of the protective oxide explains this loss, achieving excellent agreement with the data. From these findings, we formulate design principles for simultaneous optimization of built-in field, interface quality, and hole extraction to maximize the photovoltage of oxide-protected water-splitting anodes.

Engineering interfacial silicon dioxide for improved metal-insulator-semiconductor silicon photoanode water splitting performance

Silicon photoanodes protected by atomic layer deposited (ALD) TiO2 show promise as components of water splitting devices that may enable the large-scale production of solar fuels and chemicals. Minimizing the resistance of the oxide corrosion protection layer is essential for fabricating efficient devices with good fill factor. Recent literature reports have shown that the interfacial SiO2 layer, interposed between the protective ALD-TiO2 and the Si anode, acts as a tunnel oxide that limits hole conduction from the photoabsorbing substrate to the surface oxygen evolution catalyst. Herein, we report a significant reduction of bilayer resistance, achieved by forming stable, ultrathin (<1.3 nm) SiO2 layers, allowing fabrication of water splitting photoanodes with hole conductances near the maximum achievable with the given catalyst and Si substrate. Three methods for controlling the SiO2 interlayer thickness on the Si(100) surface for ALD-TiO2 protected anodes were employed: (1) TiO2 deposition directly on an HF-etched Si(100) surface, (2) TiO2 deposition after SiO2 atomic layer deposition on an HF-etched Si(100) surface, and (3) oxygen scavenging, post-TiO2 deposition to decompose the SiO2 layer using a Ti overlayer. Each of these methods provides a progressively superior means of reliably thinning the interfacial SiO2 layer, enabling the fabrication of efficient and stable water oxidation silicon anodes.