New heuristics for the vertex coloring problem based on semidefinite programming

The Lovász theta number Lovász (IEEE Trans Inf Theory 25:1–7, 1979) is a well-known lower bound on the chromatic number of a graph \(G\), and \(\varPsi _K(G)\) is its impressive strengthening Gvozdenovi? and Laurent (SIAM J Optim 19(2):592–615, 2008). The bound \(\varPsi _K(G)\) was introduced in very specific and abstract setting which is tough to translate into usual mathematical programming framework. In the first part of this paper we unify the motivations and approaches to both bounds and rewrite them in a very similar settings which are easy to understand and straightforward to implement. In the second part of the paper we provide explanations how to solve efficiently the resulting semidefinite programs and how to use optimal solutions to get good coloring heuristics. We propose two vertex coloring heuristics based on \(\varPsi _K(G)\) and present numerical results on medium sized graphs.     

Generalized equivalent circuits for mixed conductors: silver sulfide as a model system

Abstract  The generalized equivalent circuit for Hebb–Wagner polarization in the frequency domain proposed by Jamnik and Maier (J Electrochem Soc 146:4183, 1999) includes the space-charge polarization that was previously neglected. In the present work, using a self-coded Fortran program, the completely generalized equivalent circuit is successfully applied to a mixed conducting silver sulfide with an AgI electrode that suppresses the electronic flow. A whole set of fit parameters, such as geometric capacitance, partial conductivities, chemical capacitance or diffusivity, and the blocking and shunting characteristics of electrodes are independently but self-consistently obtained over a range of silver activities, as controlled by a galvanic cell. The interfacial capacitance was found to be much larger than the diffuse space-charge double-layer capacitance and was thus ascribed to the adsorption capacitance at the core of the interface, which should be connected in parallel with the space-charge double-layer polarization. Two simplified equivalent circuits were shown to be good approximations for the spectra at the extreme low and high silver activity, respectively. Graphical abstract   It was belatedly learned that Derek Johnson, Scribner Ass. Inc., has implemented a “Jamink+Maier/Mixed Conductor” model in Zview 3.1.     

Generalized equivalent circuits for mixed conductors: silver sulfide as a model system

Abstract  

The generalized equivalent circuit for Hebb–Wagner polarization in the frequency domain proposed by Jamnik and Maier (J Electrochem Soc 146:4183, 1999) includes the space-charge polarization that was previously neglected. In the present work, using a self-coded Fortran program, the completely generalized equivalent circuit is successfully applied to a mixed conducting silver sulfide with an AgI electrode that suppresses the electronic flow. A whole set of fit parameters, such as geometric capacitance, partial conductivities, chemical capacitance or diffusivity, and the blocking and shunting characteristics of electrodes are independently but self-consistently obtained over a range of silver activities, as controlled by a galvanic cell. The interfacial capacitance was found to be much larger than the diffuse space-charge double-layer capacitance and was thus ascribed to the adsorption capacitance at the core of the interface, which should be connected in parallel with the space-charge double-layer polarization. Two simplified equivalent circuits were shown to be good approximations for the spectra at the extreme low and high silver activity, respectively.     

Hamilton cycles in graph bundles over a cycle with tree as a fibre

A sufficient and necessary condition for the existence of a Hamilton cycle in a graph bundle with a cycle as a base and a tree as a fibre is obtained.     

Ni speciation in tea infusions by monolithic chromatography—ICP-MS and Q-TOF-MS

For humans, Ni is not considered to be an essential trace element. Its compounds, at levels present in foodstuffs and drinks, are generally considered to be safe for consumption, but for individuals who already suffer from contact allergy to Ni and may be subject to develop systemic reactions from its dietary ingestion, dietary exposure to Ni must be kept under control. Being the second most popular beverage, tea is a potential source of dietary Ni. Present knowledge on its speciation in tea infusions is poor. Therefore, complete speciation analysis, consisting of separation by liquid chromatography using a weak CIM DEAE-1 monolithic column, “on-line” detection by inductively coupled plasma mass spectrometry (ICP-MS) and “off-line” identification of ligands by hybrid quadrupole time-of-flight mass spectrometry (Q-TOF MS), was implemented for the first time to study Ni speciation in tea infusions. Total concentrations of Ni in dry leaves of white, green, oolong and black tea (Camellia sinensis) and flowers of herbal chamomile (Matricaria chamomilla) and hibiscus (Hibiscus sabdariffa) tea were determined after microwave digestion by ICP-MS. They lay between 1.21 and 14.4 mg?kg^?1. Good agreement between the determined and the certified values of the Ni content in the standard reference material SRM 1573a tomato leaves confirmed the accuracy of the total Ni determination. During the infusion process, up to 85 % of Ni was extracted from tea leaves or flowers. Separation of Ni species was completed in 10 min by applying aqueous linear gradient elution with 0.6 mol?L^?1 NH₄NO₃. Ni was found to be present in the chromatographic fraction in which quinic acid was identified by Q-TOF in all the tea infusions analysed, which had pH values between 5.6 and 6.0. The only exception was the infusion of hibiscus tea with a pH of 2.7, where results of speciation analysis showed that Ni is present in its divalent ionic form.     

Energetic Basis of AGCGA‐Rich DNA Folding into a Tetrahelical Structure

It was recently discovered that, besides well‐known G‐quadruplexes and i‐motifs, DNA may adopt another type of noncanonical structure called AGCGA‐quadruplexes. Here, the folding of the VK2 fragment from the regulatory region of the PLEKHG3 gene is studied and, for the first time, the energetic contributions that stabilize this unique fold are described. Similarly to the B‐DNA, it is stabilized by hydrophobic desolvation and, in contrast to G‐quadruplexes, also by specific binding of water molecules. Compared to B‐DNA, VK2 folding is enthalpically less favorable due to poorer base‐stacking interactions, resulting in substantial conformational flexibility. This entropically favorable conformational “breathing” stabilizes the AGCGA‐quadruplexes. In conclusion, AGCGA‐quadruplexes have a distinguishing thermodynamic fingerprint and the corresponding driving forces enabling their folding are consistent with the observed structural features.     

Semidefinite approximations for quadratic programs over orthogonal matrices

Finding global optimum of a non-convex quadratic function is in general a very difficult task even when the feasible set is a polyhedron. We show that when the feasible set of a quadratic problem consists of orthogonal matrices from \mathbbR^n×k{\mathbb{R}^{n\times k}} , then we can transform it into a semidefinite program in matrices of order kn which has the same optimal value. This opens new possibilities to get good lower bounds for several problems from combinatorial optimization, like the Graph partitioning problem (GPP), the Quadratic assignment problem (QAP) etc. In particular we show how to improve significantly the well-known Donath-Hoffman eigenvalue lower bound for GPP by semidefinite programming. In the last part of the paper we show that the copositive strengthening of the semidefinite lower bounds for GPP and QAP yields the exact values.     

Small change in a G-rich sequence,a dramatic change in topology: new dimeric G-quadruplex folding motif with unique loop orientations

NMR study has shown that DNA oligonucleotide d(G(3)T(4)G(4)) adopts an asymmetric bimolecular G-quadruplex structure in solution. The structure of d(G(3)T(4)G(4))(2) is composed of three G-quartets, overhanging G11 residue and G3, which is part of the loop. Unique structural feature of d(G(3)T(4)G(4))(2) fold is the orientation of the two loops. Thymidine residues T4-T7 form a diagonal loop, whereas T15-T18 form an edge type loop. The G-quadruplex core of d(G(3)T(4)G(4))(2) consists of two stacked G-quartets with syn-anti-anti-anti alternation of dG residues and one G-quartet with syn-syn-anti-anti alternation. Another unusual structural feature of d(G(3)T(4)G(4))(2) is a leap between G19 and G20 over the middle G-quartet and chain reversal between G19 and G20 residues. The presence of one antiparallel and three parallel strands reveals the hitherto unknown G-quadruplex folding motif consisting of antiparallel/parallel strands and diagonal as well as edge type loops. Further examination of the influence of different monovalent cations on the folding of d(G(3)T(4)G(4)) showed that it forms a bimolecular G-quadruplex in the presence of K+, Na+, and NH4+ ions with the same general fold.