Backbone colorings along perfect matchings

Given a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $V\rightarrow \{1,2,\ldots\}$ of $G$ in which the colors assigned to adjacent vertices in $H$ differ by at least two. In a recent paper, backbone colorings were introduced and studied in cases were the backbone is either a spanning tree or a spanning path. Here we study the case where the backbone is a perfect matching. We show that for perfect matching backbones of $G$ the number of colors needed for a backbone coloring of $G$ can roughly differ by a multiplicative factor of at most $\frac{4}{3}$ from the chromatic number $\chi(G)$. We show that the computational complexity of the problem ``Given a graph $G$ with a perfect matching $M$, and an integer $\ell$, is there a backbone coloring for $G$ and $M$ with at most $\ell$ colors?'' jumps from polynomial to NP-complete between $\ell=3$ and $\ell=4$. Finally, we consider the case where $G$ is a planar graph

Noise Enhanced Stability in Fluctuating Metastable States

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential.Comment: 7 pages, 5 figures, to appear in Phys. Rev. E vol. 69 (6),200

Optical Absorption Study by Ab initio Downfolding Approach: Application to GaAs

We examine whether essence and quantitative aspects of electronic excitation spectra are correctly captured by an effective low-energy model constructed from an {\em ab initio} downfolding scheme. A global electronic structure is first calculated by {\em ab initio} density-functional calculations with the generalized gradient approximation. With the help of constrained density functional theory, the low-energy effective Hamiltonian for bands near the Fermi level is constructed by the downfolding procedure in the basis of maximally localized Wannier functions. The excited states of this low-energy effective Hamiltonian ascribed to an extended Hubbard model are calculated by using a low-energy solver. As the solver, we employ the Hartree-Fock approximation supplemented by the single-excitation configuration-interaction method considering electron-hole interactions. The present three-stage method is applied to GaAs, where eight bands are retained in the effective model after the downfolding. The resulting spectra well reproduce the experimental results, indicating that our downfolding scheme offers a satisfactory framework of the electronic structure calculation, particularly for the excitations and dynamics as well as for the ground state.Comment: 14 pages, 6 figures, and 1 tabl

Structural and dynamical properties of liquid Si. An orbital-free molecular dynamics study

Several static and dynamic properties of liquid silicon near melting have been determined from an orbital free {\em ab-initio} molecular dynamics simulation. The calculated static structure is in good agreement with the available X-ray and neutron diffraction data. The dynamical structure shows collective density excitations with an associated dispersion relation which closely follows recent experimental data. It is found that liquid silicon can not sustain the propagation of shear waves which can be related to the power spectrum of the velocity autocorrelation function. Accurate estimates have also been obtained for several transport coefficients. The overall picture is that the dynamic properties have many characteristics of the simple liquid metals although some conspicuous differences have been found.Comment: 12 pages, 11 figure

Evolutionary Relationships and Functional Diversity of Plant Sulfate Transporters

Sulfate is an essential nutrient cycled in nature. Ion transporters that specifically facilitate the transport of sulfate across the membranes are found ubiquitously in living organisms. The phylogenetic analysis of known sulfate transporters and their homologous proteins from eukaryotic organisms indicate two evolutionarily distinct groups of sulfate transport systems. One major group named Tribe 1 represents yeast and fungal SUL, plant SULTR, and animal SLC26 families. The evolutionary origin of SULTR family members in land plants and green algae is suggested to be common with yeast and fungal SUL and animal anion exchangers (SLC26). The lineage of plant SULTR family is expanded into four subfamilies (SULTR1–SULTR4) in land plant species. By contrast, the putative SULTR homologs from Chlorophyte green algae are in two separate lineages; one with the subfamily of plant tonoplast-localized sulfate transporters (SULTR4), and the other diverged before the appearance of lineages for SUL, SULTR, and SLC26. There also was a group of yet undefined members of putative sulfate transporters in yeast and fungi divergent from these major lineages in Tribe 1. The other distinct group is Tribe 2, primarily composed of animal sodium-dependent sulfate/carboxylate transporters (SLC13) and plant tonoplast-localized dicarboxylate transporters (TDT). The putative sulfur-sensing protein (SAC1) and SAC1-like transporters (SLT) of Chlorophyte green algae, bryophyte, and lycophyte show low degrees of sequence similarities with SLC13 and TDT. However, the phylogenetic relationship between SAC1/SLT and the other two families, SLC13 and TDT in Tribe 2, is not clearly supported. In addition, the SAC1/SLT family is absent in the angiosperm species analyzed. The present study suggests distinct evolutionary trajectories of sulfate transport systems for land plants and green algae

Yolk sac erythromyeloid progenitors expressing gain of function PTPN11 have functional features of JMML but are not sufficient to cause disease in mice

Background: Accumulating evidence suggests the origin of juvenile myelomonocytic leukemia (JMML) is closely associated with fetal development. Nevertheless, the contribution of embryonic progenitors to JMML pathogenesis remains unexplored. We hypothesized that expression of JMML-initiating PTPN11 mutations in HSC-independent yolk sac erythromyeloid progenitors (YS EMPs) would result in a mouse model of pediatric myeloproliferative neoplasm (MPN). Results: E9.5 YS EMPs from VavCre+;PTPN11D61Y embryos demonstrated growth hypersensitivity to granulocyte-macrophage colony-stimulating factor (GM-CSF) and hyperactive RAS-ERK signaling. Mutant EMPs engrafted the spleens of neonatal recipients, but did not cause disease. To assess MPN development during unperturbed hematopoiesis we generated CSF1R-MCM+;PTPN11E76K;ROSAYFP mice in which oncogene expression was restricted to EMPs. Yellow fluorescent protein-positive progeny of mutant EMPs persisted in tissues one year after birth and demonstrated hyperactive RAS-ERK signaling. Nevertheless, these mice had normal survival and did not demonstrate features of MPN. Conclusions: YS EMPs expressing mutant PTPN11 demonstrate functional and molecular features of JMML but do not cause disease following transplantation nor following unperturbed development

λ-backbone colorings along pairwise disjoint stars and matchings

Given an integer λ≥2, a graph G=(V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring of (G,H) is a proper vertex coloring V→{1,2,…} of G, in which the colors assigned to adjacent vertices in H differ by at least λ. We study the case where the backbone is either a collection of pairwise disjoint stars or a matching. We show that for a star backbone S of G the minimum number ℓ for which a λ-backbone coloring of (G,S) with colors in {1,…,ℓ} exists can roughly differ by a multiplicative factor of at most View the MathML source from the chromatic number χ(G). For the special case of matching backbones this factor is roughly View the MathML source. We also show that the computational complexity of the problem “Given a graph G with a star backbone S, and an integer ℓ, is there a λ-backbone coloring of (G,S) with colors in {1,…,ℓ}?” jumps from polynomially solvable to NP-complete between ℓ=λ+1 and ℓ=λ+2 (the case ℓ=λ+2 is even NP-complete for matchings). We finish the paper by discussing some open problems regarding planar graphs

Nanoscale buckling deformation in layered copolymer materials

In layered materials, a common mode of deformation involves buckling of the layers under tensile deformation in the direction perpendicular to the layers. The instability mechanism, which operates in elastic materials from geological to nanometer scales, involves the elastic contrast between different layers. In a regular stacking of "hard" and "soft" layers, the tensile stress is first accommodated by a large deformation of the soft layers. The inhibited Poisson contraction results in a compressive stress in the direction transverse to the tensile deformation axis. The hard layers sustain this transverse compression until buckling takes place and results in an undulated structure. Using molecular simulations, we demonstrate this scenario for a material made of triblock copolymers. The buckling deformation is observed to take place at the nanoscale, at a wavelength that depends on strain rate. In contrast to what is commonly assumed, the wavelength of the undulation is not determined by defects in the microstructure. Rather, it results from kinetic effects, with a competition between the rate of strain and the growth rate of the instability. http://www.pnas.org/content/early/2011/12/23/1111367109.abstrac

Localized thinning for strain concentration in suspended germanium membranes and optical method for precise thickness measurement

We deposited Ge layers on (001) Si substrates by molecular beam epitaxy and used them to fabricate suspended membranes with high uniaxial tensile strain. We demonstrate a CMOS-compatible fabrication strategy to increase strain concentration and to eliminate the Ge buffer layer near the Ge/Si hetero-interface deposited at low temperature. This is achieved by a two-steps patterning and selective etching process. First, a bridge and neck shape is patterned in the Ge membrane, then the neck is thinned from both top and bottom sides. Uniaxial tensile strain values higher than 3% were measured by Raman scattering in a Ge membrane of 76 nm thickness. For the challenging thickness measurement on micrometer-size membranes suspended far away from the substrate a characterization method based on pump-and-probe reflectivity measurements was applied, using an asynchronous optical sampling technique.EC/FP7/628197/EU/Heat Propagation and Thermal Conductivity in Nanomaterials for Nanoscale Energy Management/HEATPRONAN