Extremal graphs for the sum of the two largest signless Laplacian eigenvalues

Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A, where A is the adjacency matrix and D is the diagonal matrix of the vertices degree of G. Let q1(G) and q2(G) be the first and the second largest eigenvalues of Q(G), respectively, and denote by S+ n the star graph with an additional edge. It is proved that inequality q1(G)+q2(G) e(G)+3 is tighter for the graph S+ n among all firefly graphs and also tighter to S+ n than to the graphs Kk _ Kn−k recently presented by Ashraf, Omidi and Tayfeh-Rezaie. Also, it is conjectured that S+ n minimizes f(G) = e(G) − q1(G) − q2(G) among all graphs G on n vertices.

Spectra and Laplacian spectra of arbitrary powers of lexicographic products of graphs

Consider two graphs G and H. Let H^k[G] be the lexicographic product of H^k and G, where H^k is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H^k[G]H and H^k when G and H are regular and the Laplacian spectrum of H^k[G] and H^k for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination of the spectrum (in case of regular graphs) and Laplacian spectrum (for arbitrary graphs) of huge graphs. As an example, the spectrum of the lexicographic power of the Petersen graph with the googol number (that is, 10^100 ) of vertices is determined. The paper finishes with the extension of some well known spectral and combinatorial invariant properties of graphs to its lexicographic powers.

On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.

Trade spectrum of K4-e

A K-4 - e trade consists of two disjoint decompositions of some simple graph H into copies of K-4 - e. The number of vertices of H is referred to as the foundation of the trade, while the number of copies of K-4 - e in each of the decompositions is called the volume of the trade. We determine the values of v and s for which there exists a K-4 - e trade of volume s and foundation v.

Altered structural connectivity in patients with medial temporal lobe epilepsy: A Diffusion Spectrum Imaging and Graph Analysis study

In this study we investigated the effect of medial temporal lobe epilepsy (MTLE) on the global characteristics of brain connectivity estimated by topological measures. We used DSI (Diffusion Spectrum Imaging) to construct a connectivity matrix where the nodes represents the anatomical ROIs and the edges are the connections between any pair of ROIs weighted by the mean GFA/FA values. A significant difference was found between the patient group vs control group in characteristic path length, clustering coefficient and small-worldness. This suggests that the MTLE network is less efficient compared to the network of the control group.

Dynamic polarizability, Cauchy moments, and the optical absorption spectrum of liquid water: A sequential molecular dynamics/quantum mechanical approach

The dynamic polarizability and optical absorption spectrum of liquid water in the 6-15 eV energy range are investigated by a sequential molecular dynamics (MD)/quantum mechanical approach. The MD simulations are based on a polarizable model for liquid water. Calculation of electronic properties relies on time-dependent density functional and equation-of-motion coupled-cluster theories. Results for the dynamic polarizability, Cauchy moments, S(-2), S(-4), S(-6), and dielectric properties of liquid water are reported. The theoretical predictions for the optical absorption spectrum of liquid water are in good agreement with experimental information.

Discrete approximation to the global spectrum of the tangent operator for flow past a circular cylinder

This paper deals with the calculation of the discrete approximation to the full spectrum for the tangent operator for the stability problem of the symmetric flow past a circular cylinder. It is also concerned with the localization of the Hopf bifurcation in laminar flow past a cylinder, when the stationary solution loses stability and often becomes periodic in time. The main problem is to determine the critical Reynolds number for which a pair of eigenvalues crosses the imaginary axis. We thus present a divergence-free method, based on a decoupling of the vector of velocities in the saddle-point system from the vector of pressures, allowing the computation of eigenvalues, from which we can deduce the fundamental frequency of the time-periodic solution. The calculation showed that stability is lost through a symmetry-breaking Hopf bifurcation and that the critical Reynolds number is in agreement with the value presented in reported computations. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Absorption spectrum of a strongly driven atom in a detuned squeezed vacuum

We present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mellow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed stales involving a probe field photon and a correlated photon pair from the squeezed vacuum field.

Spectrum of MMACHC mutations in Italian and Portuguese patients with combined methylmalonic aciduria and homocystinuria, cblC type

Methylmalonic aciduria (MMA) and homocystinuria, cblC type (MIM 277400) is the most frequent inborn error of vitamin B-12. The recent identification of the disease gene, MMACHC, has permitted preliminary genotype-phenotype correlations. We studied 24 Italian and 17 Portuguese patients with cblC defect to illustrate the spectrum of mutations in a southern European population and discuss the impact that mutation identification has on routine diagnostic procedures. Since the metabolic defect raises the serum levels of homocysteine, we also tested if variants in MTHFR-playing a key role in homocysteine remethylation pathway-could act as genetic modifier in cblC defect. We found that the c.271 dupA (accounting for 55% of the MMA CH alleles in our cohort) followed by c.394C > T (16%) and c.331C > T (9%) were the most frequent mutations. In our study we also identified a novel mutation (c.544T > C). On the other hand, the MTHFR genotype did not appear to influence age at onset, the clinical phenotype and outcome of patients with cblC defect. This study shows that mutation screening for the most common MMACH mutations occurring in early-onset forms (c.271dupA and c.331C > T) seems to have a high diagnostic yield in a southern European population with cblC defect. Although the identification of the gene defect per se does not predict completely time and severity of disease appearance, our data corroborate the importance of a molecular testing to offer accurate prenatal diagnosis to couples at high risk of having affected children. (C) 2007 Elsevier Inc. All rights reserved.

Resonance fluorescence spectrum of a two-level atom driven by a bichromatic field in a squeezed vacuum

The steady-state resonance fluorescence spectrum of a two-level atom driven by a bichromatic field in a broadband squeezed vacuum is studied. When the carrier frequency of the squeezed vacuum is tuned to the frequency of the central spectral line, anomalous spectral features, such as hole burning and dispersive profiles, can occur at the central line. We show that these features appear for wider, and experimentally more convenient, ranges of the parameters than in the case of monochromatic excitation. ?he absence of a coherent spectral component at the central line makes any experimental attempt to observe these features much easier. We also discuss the general features of the spectrum. When the carrier frequency of the squeezed vacuum is tuned to the first odd or even sidebands, the spectrum is asymmetric and only the sidebands an sensitive to phase. For appropriate choices of the phase the linewidths or only the odd or even sidebands can be reduced. A dressed-stale interpretation is provided.

Isotopically resolved (B)over-tilde<-(X)over-tilde electronic spectrum of Ag-3 and calculation of its Jahn-Teller effects

Ag-3 was produced by pulsed-nozzle laser vaporisation and jet-cooled in a Ne supersonic expansion. One-color resonant two-photon ionisation (R2PI) spectra of the (B) over tilde(2) E '' <-- (X) over tilde(2) E' transition of Ag-3 were separately measured for all four isotopic combinations. Long vibrational progressions are observed, involving clearly resolved bands at low energy, merging into a dense but resolvable spectrum up to 1000 cm(-1) above the origin. Both the ground (X) over tilde(2) E' and excited (B) over tilde(2) E '' states of Ag-3 are susceptible to Jahn-Teller distortion along the degenerate e' bending coordinate. The Jahn-Teller analysis includes both linear and quadratic terms, simultaneously with the spin-orbit coupling. Following extensive parameter fitting, the absorption spectrum is calculated, and bands assigned. The spin-orbit splitting is quenched below the localization energy, but becomes observable approximate to 300 cm(-1) above the origin.

The spectrum of autoantibodies in IPEX syndrome is broad and includes anti-mitochondrial autoantibodies

IPEX syndrome is a congenital disorder of immune regulation caused by mutations in the FOXP3 gene, which is required for the suppressive function of naturally arising CD4 + CD25 + regulatory T cells. In this case series we evaluated serum samples from 12 patients with IPEX syndrome for the presence of common autoantibodies associated with a broad range of autoimmune disorders. We note that 75% of patients (9/12) had 1 or more autoantibodies, an incidence far above the cumulative rate observed in the general population. The range of autoantibodies differed between patients and there was no predominant autoantibody or pattern of autoantibodies present in this cohort. Surprisingly, one patient had high-titer anti-mitochondrial antibodies (AMA) typically associated with primary biliary cirrhosis (PBC) although the patient had no signs of cholestasis. PBC is a well-characterized autoimmune disease that occurs primarily in women and includes the serological hallmarks of serum AMA and elevated IgM which were both present in this patient. PBC is virtually absent in children with the exception of one reported child with interleukin 2 receptor a (CD25) deficiency which is associated with an IPEX-like regulatory T cell dysfunction. Based on the present data and the available literature we suggest a direct role for CD4 + CD25 + regulatory T cells in restraining B cell autoantibody production and that defects in regulatory T cells may be crucial to the development of PBC. (C) 2010 Elsevier Ltd. All rights reserved.

A cross-sectional study on the clinical and immunological spectrum of human Leishmania (L.) infantum chagasi infection in the Brazilian Amazon region

The objectives of this study were to identify individuals with symptomatic and/or asymptomatic infection due to Leishmania (L.) infantum chagasi; to study the two types of infection, both clinically and immunologically, and to determine the prevalence rate of infection at the beginning of the study. This was a cross-sectional study with a cohort of 946 individuals, of both genders, from the age of 1 year, living in the municipality of Barcarena, PA, Brazil, an area endemic for American visceral leishmaniasis (AVL). The leishmanin skin test (LST) and the indirect fluorescent test (IFAT), were used for the diagnosis of infection. One hundred and twenty cases of infection were diagnosed, with a prevalence rate of 12.6%; eight cases showed high seroreactivity (1280-10240, IgG) in IFAT and no LST reaction; four of these cases were typical AVL and four had subclinical oligosymptomatic infection. Using two immunological methods with a clinical examination of the infected individuals enabled the identification of five clinical-immunological profiles which may promote a better understanding of the interaction between L. (L.) i. chagasi and the human immune response: asymptomatic infection (AI) 73.4%; subclinical resistant infection (SRI) 15%; subclinicat oligosymptomatic infection (SOI) 3%; symptomatic infection (AVL) 3% and indeterminate initial infection (III) 5%. (C) 2009 Royal Society of Tropical Medicine and Hygiene. Published by Elsevier Ltd. All rights reserved.

Systemic lupus erythematosus exhibits a dynamic and continuum spectrum of effector/regulatory T cells

Objective: The identification of regulatory T cells (Treg cells) as CD4(+)CD25(high) cells may be upset by the increased frequency of activated effector T cells (Teff cells) in inflammatory diseases such as systemic lupus erythematosus (SLE). This study aimed to evaluate the frequency of T-cell subsets according to the expression of CD25 and CD127 in active (A-SLE) and inactive SLE (I-SLE). Methods: Peripheral blood mononuclear cells (PBMCs) from 26 A-SLE patients (SLE Disease Activity Index (SLEDAI) = 10.17 +/- 3.7), 31 I-SLE patients (SLEDAI = 0), and 26 healthy controls (HC) were analysed by multicolour flow. cytometry. Results: CD25(high) cell frequency was increased in A-SLE (5.2 +/- 5.7%) compared to I-SLE (3.4 +/- 3.4%) and HC (1.73 +/- 0.8%) (p < 0.01). However, the percentage of FoxP3(+) cells in the CD25(high) subset was decreased in A-SLE (24.6 +/- 16.4%) compared to I-SLE (33.7 +/- 16) and HC (45 +/- 25.1%) (p < 0.01). This was partly due to the increased frequency of Teff cells (CD25(high)CD127(+)FoxP3(empty set)) in A-SLE (10.7 +/- 7.3%) compared to I-SLE (8.5 +/- 6.5) and HC (6.1 +/- 1.8%) (p = 0.02). Hence the frequency of Treg cells (CD25(+/high)CD127(low/empty set)FoxP3(+)) was equivalent in A-SLE (1.4 +/- 0.8%), I-SLE (1.37 +/- 1.0%), and HC (1.13 +/- 0.59%) (p = 0.42). A-SLE presented an increased frequency of CD25(+)CD127(+)FoxP3(+) and CD25(empty set)FoxP3(+)CD127(low/empty set) T cells, which may represent intermediate phenotypes between Treg and Teff cells. Conclusions: The present study has provided data supporting normal Treg cell frequency in A-SLE and I-SLE as well as increased frequency of Teff cells in A-SLE. This scenario reflects a Treg/Teff ratio imbalance that may favour the inflammatory phenotype of the disease. In addition, the increased frequency of T cells with putative intermediate phenotypes may be compatible with a highly dynamic immune system in SLE.

Fluorescence spectrum of a two-level atom driven by a multiple modulated field

We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving held is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mellow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving held. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are 180 degrees out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we shaw that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.