Max-Coloring Paths: Tight Bounds and Extensions

The max-coloring problem is to compute a legal coloring of the vertices of a graph G = (V, E) with a non-negative weight function w on V such that Sigma(k)(i=1) max(v epsilon Ci) w(v(i)) is minimized, where C-1, ... , C-k are the various color classes. Max-coloring general graphs is as hard as the classical vertex coloring problem, a special case where vertices have unit weight. In fact, in some cases it can even be harder: for example, no polynomial time algorithm is known for max-coloring trees. In this paper we consider the problem of max-coloring paths and its generalization, max-coloring abroad class of trees and show it can be solved in time O(vertical bar V vertical bar+time for sorting the vertex weights). When vertex weights belong to R, we show a matching lower bound of Omega(vertical bar V vertical bar log vertical bar V vertical bar) in the algebraic computation tree model.

Angelica archengelica extract induced perturbation of rat skin and tight junctional protein (ZO-1) of HaCaT cells

Background and purpose of the study: Herbal enhancers compared to the synthetic ones have shown less toxis effects. Coumarins have been shown at concentrations inhibiting phospoliphase C-Y (Phc-Y) are able to enhance tight junction (TJ) permeability due to hyperpoalation of Zonolous Occludense-1 (ZO-1) proteins. The purpose of this study was to evaluate the influence of ethanolic extract of Angelica archengelica (AA-E) which contain coumarin on permeation of repaglinide across rat epidermis and on the tight junction plaque protein ZO-1 in HaCaT cells. Methods: Transepidermal water loss (TEWL) from the rat skin treated with different concentrations of AA-E was assessed by Tewameter. Scanning and Transmission Electron Microscopy (TEM) on were performed on AA-E treated rat skin portions. The possibility of AA-E influence on the architecture of tight junctions by adverse effect on the cytoplasmic ZO-1 in HaCaT cells was investigated. Finally, the systemic delivery of repaglinide from the optimized transdermal formulation was investigated in rats. Results: The permeation of repaglinide across excised rat epidermis was 7-fold higher in the presence of AA-E (5% w/v) as compared to propylene glycol:ethanol (7:3) mixture. The extract was found to perturb the lipid microconstituents in both excised and viable rat skin, although, the effect was less intense in the later. The enhanced permeation of repaglinide across rat epidermis excised after treatment with AA-E (5% w/v) for different periods was in concordance with the high TEWL values of similarly treated viable rat skin. Further, the observed increase in intercellular space, disordering of lipid structure and corneocyte detachment indicated considerable effect on the ultrastructure of rat epidermis. Treatment of HaCaT cell line with AA-E (0.16% w/v) for 6 hrs influenced ZO-1 as evidenced by reduced immunofluorescence of anti-TJP1 (ZO-1) antibody in Confocal Laser Scanning Microscopy studies (CLSM) studies. The plasma concentration of repaglinide from transdermal formulation was maintained higher and for longer time as compared to oral administration of repaglinide. Major conclusion: Results suggest the overwhelming influence of Angelica archengelica in enhancing the percutaneous permeation of repaglinide to be mediated through perturbation of skin lipids and tight junction protein (ZO-1).

Tight co-degree condition for perfect matchings in 4-graphs

We will give a tight minimum co-degree condition for a 4-uniform hypergraph to contain a perfect matching.

An infinite family of tight triangulations of manifolds

We give explicit construction of vertex-transitive tight triangulations of d-manifolds for d >= 2. More explicitly, for each d >= 2, we construct two (d(2) + 5d + 5)-vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated d-manifolds with 2d + 3 vertices constructed by Kuhnel. The manifolds we construct are strongly minimal. For d >= 3, they are also tight neighborly as defined by Lutz, Sulanke and Swartz. Like Kuhnel complexes, our manifolds are orientable in even dimensions and non-orientable in odd dimensions. (c) 2013 Elsevier Inc. All rights reserved.

Non-existence of tight neighborly triangulated manifolds with beta(1)=2

All triangulated d-manifolds satisfy the inequality ((f0-d-1)(2)) >= ((d+2)(2))beta(1) for d >= 3. A triangulated d-manifold is called tight neighborly if it attains equality in this bound. For each d >= 3, a (2d + 3)-vertex tight neighborly triangulation of the Sd-1-bundle over S-1 with beta(1) = 1 was constructed by Kuhnel in 1986. In this paper, it is shown that there does not exist a tight neighborly triangulated manifold with beta(1) = 2. In other words, there is no tight neighborly triangulation of (Sd-1 x S-1)(#2) or (Sd-1 (sic) S-1)(#2) for d >= 3. A short proof of the uniqueness of K hnel's complexes for d >= 4 under the assumption beta(1) not equal 0 is also presented.

A provably tight delay-driven concurrently congestion mitigating global routing algorithm

Routing is a very important step in VLSI physical design. A set of nets are routed under delay and resource constraints in multi-net global routing. In this paper a delay-driven congestion-aware global routing algorithm is developed, which is a heuristic based method to solve a multi-objective NP-hard optimization problem. The proposed delay-driven Steiner tree construction method is of O(n(2) log n) complexity, where n is the number of terminal points and it provides n-approximation solution of the critical time minimization problem for a certain class of grid graphs. The existing timing-driven method (Hu and Sapatnekar, 2002) has a complexity O(n(4)) and is implemented on nets with small number of sinks. Next we propose a FPTAS Gradient algorithm for minimizing the total overflow. This is a concurrent approach considering all the nets simultaneously contrary to the existing approaches of sequential rip-up and reroute. The algorithms are implemented on ISPD98 derived benchmarks and the drastic reduction of overflow is observed. (C) 2014 Elsevier Inc. All rights reserved.

1D Tight-Binding Models Render Quantum First Passage Time ``Speakable''

The calculation of First Passage Time (moreover, even its probability density in time) has so far been generally viewed as an ill-posed problem in the domain of quantum mechanics. The reasons can be summarily seen in the fact that the quantum probabilities in general do not satisfy the Kolmogorov sum rule: the probabilities for entering and non-entering of Feynman paths into a given region of space-time do not in general add up to unity, much owing to the interference of alternative paths. In the present work, it is pointed out that a special case exists (within quantum framework), in which, by design, there exists one and only one available path (i.e., door-way) to mediate the (first) passage -no alternative path to interfere with. Further, it is identified that a popular family of quantum systems - namely the 1d tight binding Hamiltonian systems - falls under this special category. For these model quantum systems, the first passage time distributions are obtained analytically by suitably applying a method originally devised for classical (stochastic) mechanics (by Schroedinger in 1915). This result is interesting especially given the fact that the tight binding models are extensively used in describing everyday phenomena in condense matter physics.

Tight triangulations of closed 3-manifolds

A triangulation of a closed 2-manifold is tight with respect to a field of characteristic two if and only if it is neighbourly; and it is tight with respect to a field of odd characteristic if and only if it is neighbourly and orientable. No such characterization of tightness was previously known for higher dimensional manifolds. In this paper, we prove that a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked. In consequence, the Kuhnel-Lutz conjecture is valid in dimension three for fields of odd characteristic. Next let F be a field of characteristic two. It is known that, in this case, any neighbourly and stacked triangulation of a closed 3-manifold is F-tight. For closed, triangulated 3-manifolds with at most 71 vertices or with first Betti number at most 188, we show that the converse is true. But the possibility of the existence of an F-tight, non-stacked triangulation on a larger number of vertices remains open. We prove the following upper bound theorem on such triangulations. If an F-tight triangulation of a closed 3-manifold has n vertices and first Betti number beta(1), then (n - 4) (617n - 3861) <= 15444 beta(1). Equality holds here if and only if all the vertex links of the triangulation are connected sums of boundary complexes of icosahedra. (C) 2015 Elsevier Ltd. All rights reserved.

Nanometer scale thermal drift of 4Gbit/s uncooled laser for tight-channel-spacing low-cost WDM

A 4Gbit/s directly modulated DBR laser is demonstrated with nanometre scale thermal tuning over an extended 20-70°C temperature range. >40dB side mode suppression over the entire temperature range is achieved. © 2005 Optical Society of America.

Coherent scattering of light by Bose-Einstein condensation in a tight confinement

We have observed strong scattering of a probe light by dilute Bose-Einstein condensate (BEC) Rb-87 gas in a tight magnetic trap. The scattering light forms fringes at the image plane. It is found that we can infer the real size of the condensation and the number of the atoms by modelling the imaging system. We present a quantitative calculation of light scattering by the condensed atoms. The calculation shows that the experimental results agree well with the prediction of the generalized diffraction theory, and thus we can directly observe the phase transition of BEC in a tight trap.

The meta-converse bound is tight

We show that the meta-converse bound derived by Polyanskiy et al. provides the exact error probability for a fixed joint source-channel code and an appropriate choice of the bound parameters. While the expression is not computable in general, it identifies the weaknesses of known converse bounds to the minimum achievable error probability. © 2013 IEEE.