A reconfigurations analogue of Brooks’ theorem.

Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show that from a k-colouring, k > Δ, a Δ-colouring of G can be obtained by a sequence of O(n 2) recolourings using only the original k colours unless G is a complete graph or a cycle with an odd number of vertices, or k = Δ + 1, G is Δ-regular and, for each vertex v in G, no two neighbours of v are coloured alike. We use this result to study the reconfiguration graph R k (G) of the k-colourings of G. The vertex set of R k (G) is the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. It is known that if k ≤ Δ(G), then R k (G) might not be connected and it is possible that its connected components have superpolynomial diameter, if k ≥ Δ(G) + 2, then R k (G) is connected and has diameter O(n 2). We complete this structural classification by settling the missing case: if k = Δ(G) + 1, then R k (G) consists of isolated vertices and at most one further component which has diameter O(n 2). We also describe completely the computational complexity classification of the problem of deciding whether two k-colourings of a graph G of maximum degree Δ belong to the same component of R k (G) by settling the case k = Δ(G) + 1. The problem is O(n 2) time solvable for k = 3, PSPACE-complete for 4 ≤ k ≤ Δ(G), O(n) time solvable for k = Δ(G) + 1, O(1) time solvable for k ≥ Δ(G) + 2 (the answer is always yes)

Oscillator strengths and line widths of dipole-allowed transitions in ¹⁴N₂ between 89.7 and 93.5 nm

Line oscillator strengths in the 20 electric dipole-allowed bands of ¹⁴N₂ in the 89.7–93.5nm (111480–106950cm⁻¹) region are reported from photoabsorptionmeasurements at an instrumental resolution of ∼6mÅ (0.7cm⁻¹) full width at half maximum. The absorptionspectrum comprises transitions to vibrational levels of the 3pσᵤc′₄¹Σᵤ⁺, 3pπᵤc³Πᵤ, and 3sσgo₃¹ΠᵤRydberg states and of the b′¹Σᵤ⁺ and b¹Πᵤ valence states. The J dependences of band f values derived from the experimental line f values are reported as polynomials in J′(J′+1) and are extrapolated to J′=0 in order to facilitate comparisons with results of coupled Schrödinger-equation calculations. Most bands in this study are characterized by a strong J dependence of the band f values and display anomalous P-, Q-, and R-branch intensity patterns. Predissociation line widths, which are reported for 11 bands, also exhibit strong J dependences. The f value and line width patterns can inform current efforts to develop comprehensive spectroscopic models that incorporate rotational effects and predissociation mechanisms, and they are critical for the construction of realistic atmospheric radiative-transfer models.This work was supported in part by NASA Grant No. NNG05GA03G to Wellesley College and Australian Research Council Discovery Program Grant No. DP0558962

Memory and chaos in an Ising spin glass

The non-equilibrium dynamics of the model 3d-Ising spin glass - Fe$_{0.55}$Mn$_{0.45}$TiO$_3$ - has been investigated from the temperature and time dependence of the zero field cooled magnetization recorded under certain thermal protocols. The results manifest chaos, rejuvenation and memory features of the equilibrating spin configuration that are very similar to those observed in corresponding studies of the archetypal RKKY spin glass Ag(Mn). The sample is rapidly cooled in zero magnetic field, and the magnetization recorded on re-heating. When a stop at constant temperature $T_s$ is made during the cooling, the system evolves toward its equilibrium state at this temperature. The equilibrated state established during the stop becomes frozen in on further cooling and is retrieved on re-heating. The memory of the aging at $T_s$ is not affected by a second stop at a lower temperature $T'_s$. Reciprocally, the first equilibration at $T_s$ has no influence on the relaxation at $T'_s$, as expected within the droplet model for domain growth in a chaotic landscape.Comment: REVTeX style; 4 pages, 4 figure

A family of tridiagonal pairs and related symmetric functions

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual eigenbasis are described. The overlap functions between the two dual basis are shown to satisfy a coupled system of recurrence relations and a set of discrete second-order $q-$difference equations which generalize the ones associated with the Askey-Wilson orthogonal polynomials with a discrete argument. Normalizing the fundamental solution to unity, the hierarchy of solutions are rational functions of one discrete argument, explicitly derived in some simplest examples. The weight function which ensures the orthogonality of the system of rational functions defined on a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition corrected compared to published versio

BPS Monopole Equation in Omega-background

We study deformed supersymmetries in N=2 super Yang-Mills theory in the Omega-backgrounds characterized by two complex parameters $\epsilon_1, \epsilon_2$. When one of the $\epsilon$-parameters vanishes, the theory has extended supersymmetries. We compute the central charge of the algebra and obtain the deformed BPS monopole equation. We examine supersymmetries preserved by the equation.Comment: 14 pages, typos corrected, published version in JHE

Fe-doping-induced evolution of charge-orbital ordering in a bicritical-state manganite

Impurity effects on the stability of a ferromagnetic metallic state in a bicritical-state manganite, (La0.7Pr0.3)0.65Ca0.35MnO3, on the verge of metal-insulator transition have been investigated by substituting a variety of transition-metal atoms for Mn ones. Among them, Fe doping exhibits the exceptional ability to dramatically decrease the ferromagnetic transition temperature. Systematic studies on the magnetotransport properties and x-ray diffraction for the Fe-doped crystals have revealed that charge-orbital ordering evolves down to low temperatures, which strongly suppresses the ferromagnetic metallic state. The observed glassy magnetic and transport properties as well as diffuse phase transition can be attributed to the phase-separated state where short-range charge-orbital-ordered clusters are embedded in the ferromagnetic metallic matrix. Such a behavior in the Fe-doped manganites form a marked contrast to the Cr-doping effects on charge-orbital-ordered manganites known as impurity-induced collapse of charge-orbital ordering.Comment: 8 pages, 7 figure

Oxidative stress dependent microRNA-34a activation via PI3Kα reduces the expression of sirtuin-1 and sirtuin-6 in epithelial cells

Sirtuin-1 (SIRT1) and SIRT6, NAD(+)-dependent Class III protein deacetylases, are putative anti-aging enzymes, down-regulated in patients with chronic obstructive pulmonary disease (COPD), which is characterized by the accelerated ageing of the lung and associated with increased oxidative stress. Here, we show that oxidative stress (hydrogen peroxide) selectively elevates microRNA-34a (miR-34a) but not the related miR-34b/c, with concomitant reduction of SIRT1/-6 in bronchial epithelial cells (BEAS2B), which was also observed in peripheral lung samples from patients with COPD. Over-expression of a miR-34a mimic caused a significant reduction in both mRNA and protein of SIRT1/-6, whereas inhibition of miR-34a (antagomir) increased these sirtuins. Induction of miR-34a expression with H2O2 was phosphoinositide-3-kinase (PI3K) dependent as it was associated with PI3Kα activation as well as phosphatase and tensin homolog (PTEN) reduction. Importantly, miR-34a antagomirs increased SIRT1/-6 mRNA levels, whilst decreasing markers of cellular senescence in airway epithelial cells from COPD patients, suggesting that this process is reversible. Other sirtuin isoforms were not affected by miR-34a. Our data indicate that miR-34a is induced by oxidative stress via PI3K signaling, and orchestrates ageing responses under oxidative stress, therefore highlighting miR-34a as a new therapeutic target and biomarker in COPD and other oxidative stress-driven aging diseases

A Note on the Picard-Fuchs Equations for N=2 Seiberg-Witten Theories

A concise presentation of the PF equations for N=2 Seiberg-Witten theories for the classical groups of rank r with N_f massless hypermultiplets in the fundamental representation is provided. For N_f=0, all r PF equations can be given in a generic form. For certain cases with N_f\neq zero, not all equations are generic. However, in all cases there are at least r-2 generic PF equations. For these cases the classical part of the equations is generic, while the quantum part can be formulated using a method described in a previous paper by the authors, which is well suited to symbolic computer calculations.Comment: 25 pages, Latex; some new references adde

A dual weighted residual method applied to complex periodic gratings

An extension of the dual weighted residual (DWR) method to the analysis of electromagnetic waves in a periodic diffraction grating is presented. Using the α,0-quasi-periodic transformation, an upper bound for the a posteriori error estimate is derived. This is then used to solve adaptively the associated Helmholtz problem. The goal is to achieve an acceptable accuracy in the computed diffraction efficiency while keeping the computational mesh relatively coarse. Numerical results are presented to illustrate the advantage of using DWR over the global a posteriori error estimate approach. The application of the method in biomimetic, to address the complex diffraction geometry of the Morpho butterfly wing is also discussed

A rejection-free Monte Carlo method for the hard-disk system

We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and this relationship is confirmed for our method by observing nonequilibrium relaxation of a bond-orientational order parameter. The rejection-free method gives a greater computational efficiency than the standard method at high densities. The rejection free method is implemented in a shrewd manner using optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density.Comment: 8 pages, 9 figures. This paper has been combined into the cond-mat/0508652, and published in Phys. Rev.