Parameterized algorithm for eternal vertex cover

In this paper we initiate the study of a “dynamic” variant of the classical Vertex Cover problem, the Eternal Vertex Cover problem introduced by Klostermeyer and Mynhardt, from the perspective of parameterized algorithms. This problem consists in placing a minimum number of guards on the vertices of a graph such that these guards can protect the graph from any sequence of attacks on its edges. In response to an attack, each guard is allowed either to stay in his vertex, or to move to a neighboring vertex. However, at least one guard has to fix the attacked edge by moving along it. The other guards may move to reconfigure and prepare for the next attack. Thus at every step the vertices occupied by guards form a vertex cover. We show that the problem admits a kernel of size k⁴(k+1)+2k, which shows that the problem is fixed parameter tractable when parameterized by the number of available guards k. Finally, we also provide an algorithm with running time O(²O(k²)+nm) for Eternal Vertex Cover, where n is the number of vertices and m the number of edges of the input graph. In passing we also observe that Eternal Vertex Cover is NP-hard, yet it has a polynomial time 2-approximation algorithm.     

DECISION SUPPORT WITH LOGICAL AND FUZZY PETRI NETS

Modern knowledge representation is a very dynamic domain because of continuous research and development. This paper presents Logical Petri Nets (LPNs) and Fuzzy Petri Nets (FPNs) as models for knowledge representation. It is shown that knowledge propagation, described using logical and fuzzy Petri nets, terminates in a unique stable state. Based on this result, the paper introduces an algorithm for knowledge propagation in decision support systems.     

Solving Connected Dominating Set Faster than 2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In the connected dominating set problem we are given an n-node undirected graph, and we are asked to find a minimum cardinality connected subset S of nodes such that each node not in S is adjacent to some node in S. This problem is also equivalent to finding a spanning tree with maximum number of leaves. Despite its relevance in applications, the best known exact algorithm for the problem is the trivial Ω(2 ⁿ ) algorithm that enumerates all the subsets of nodes. This is not the case for the general (unconnected) version of the problem, for which much faster algorithms are available. Such a difference is not surprising, since connectivity is a global property, and non-local problems are typically much harder to solve exactly. In this paper we break the 2 ⁿ barrier, by presenting a simple O(1.9407 ⁿ ) algorithm for the connected dominating set problem. The algorithm makes use of new domination rules, and its analysis is based on the Measure and Conquer technique. An extended abstract of this paper appeared in the proceedings of FSTTCS’06. Fedor V. Fomin was additionally supported by the Research Council of Norway.     

Ultralow Dispersion Multicomponent Thin‐Film Chalcogenide Glass for Broadband Gradient‐Index Optics

A novel photothermal process to spatially modulate the concentration of sub‐wavelength, high‐index nanocrystals in a multicomponent Ge‐As‐Pb‐Se chalcogenide glass thin film resulting in an optically functional infrared grating is demonstrated. The process results in the formation of an optical nanocomposite possessing ultralow dispersion over unprecedented bandwidth. The spatially tailored index and dispersion modification enables creation of arbitrary refractive index gradients. Sub‐bandgap laser exposure generates a Pb‐rich amorphous phase transforming on heat treatment to high‐index crystal phases. Spatially varying nanocrystal density is controlled by laser dose and is correlated to index change, yielding local index modification to ≈+0.1 in the mid‐infrared.     

Dynamics of diamond nanoparticles in solution and cells

The fluorescence and motional dynamics of single diamond nanocrystals in buffer solution and in living cells is investigated. Stable hydrosols of nanodiamonds in buffer solutions are investigated by fluorescence correlation spectroscopy. Measurement of the effective hydrodynamic radius yields particles of 48 nm diameter, which is in excellent agreement with atomic force microscopy measurements made on the same particles. Fluorescence correlation spectroscopy measurements indicate that nanocrystals easily form aggregates when the buffer pH is changed. This tendency is reduced when the surface of the diamonds is covered with surfactants. Upon incubation, cells spontaneously take up nanocrystals that uniformly distribute in cells. Most of the particles get immobilized within a few minutes. The binding of streptavidin to biotinylated aggregates of 4 nm diameter nanodiamonds is demonstrated.     

ZnWO4 scintillators for cryogenic dark matter experiments

The scintillation properties of a zinc tungstate crystal, shaped as a hexagonal prism (height 40 mm, diagonal 40 mm) were determined. An energy resolution of 10.7% for the 662 keV γ-line of ¹³⁷Cs was measured with the scintillator placed in a light collection setup similar to that used by the CRESST dark matter search. The light output and decay kinetics of ZnWO₄ were examined over the temperature range 7–300 K and confirmed to be competitive with those of CaWO₄. The radioactive contaminations of the ZnWO₄ scintillator measured in the Solotvina Underground Laboratory do not exceed 0.1–10 mBq/kg (depending on radionuclide). Our study highlights the excellent feasibility of this ZnWO₄ scintillator for a cryogenic dark matter experiment.     

LSSmScarlet,dCyRFP2s,dCyOFP2s and CRISPRed2s,Genetically Encoded Red Fluorescent Proteins with a Large Stokes Shift

Genetically encoded red fluorescent proteins with a large Stokes shift (LSSRFPs) can be efficiently co-excited with common green FPs both under single- and two-photon microscopy, thus enabling dual-color imaging using a single laser. Recent progress in protein development resulted in a great variety of novel LSSRFPs; however, the selection of the right LSSRFP for a given application is hampered by the lack of a side-by-side comparison of the LSSRFPs’ performance. In this study, we employed rational design and random mutagenesis to convert conventional bright RFP mScarlet into LSSRFP, called LSSmScarlet, characterized by excitation/emission maxima at 470/598 nm. In addition, we utilized the previously reported LSSRFPs mCyRFP1, CyOFP1, and mCRISPRed as templates for directed molecular evolution to develop their optimized versions, called dCyRFP2s, dCyOFP2s and CRISPRed2s. We performed a quantitative assessment of the developed LSSRFPs and their precursors in vitro on purified proteins and compared their brightness at 488 nm excitation in the mammalian cells. The monomeric LSSmScarlet protein was successfully utilized for the confocal imaging of the structural proteins in live mammalian cells and multicolor confocal imaging in conjugation with other FPs. LSSmScarlet was successfully applied for dual-color two-photon imaging in live mammalian cells. We also solved the X-ray structure of the LSSmScarlet protein at the resolution of 1.4 Å that revealed a hydrogen bond network supporting excited-state proton transfer (ESPT). Quantum mechanics/molecular mechanics molecular dynamic simulations confirmed the ESPT mechanism of a large Stokes shift. Structure-guided mutagenesis revealed the role of R198 residue in ESPT that allowed us to generate a variant with improved pH stability. Finally, we showed that LSSmScarlet protein is not appropriate for STED microscopy as a consequence of LSSRed-to-Red photoconversion with high-power 775 nm depletion light.     

Dietary Docosahexaenoic Acid and <Emphasis Type="Italic">trans</Emphasis>-10, <Emphasis Type="Italic">cis</Emphasis>-12-Conjugated Linoleic Acid Differentially Alter Oxylipin Profiles in Mouse Periuterine Adipose Tissue

Diets containing high n-3 polyunsaturated fatty acids (PUFA) decrease inflammation and the incidence of chronic diseases including cardiovascular disease and nonalcoholic fatty liver disease while trans-fatty acids (TFA) intake increases the incidence of these conditions. Some health benefits of n-3 PUFA are mediated through the impact of their oxygenated metabolites, i.e. oxylipins. The TFA, trans-10, cis-12-conjugated linoleic acid (CLA; 18:2n-6) is associated with adipose tissue (AT) inflammation, oxidative stress, and wasting. We examined the impact of a 4-week feeding of 0, 0.5, and 1.5% docosahexaenoic acid (DHA; 22:6n-3) in the presence and absence of 0.5% CLA on AT oxylipin profiles in female C57BL/6N mice. Esterified oxylipins in AT derived from linoleic acid (LNA), alpha-linolenic acid (ALA), arachidonic acid (ARA), eicosapentaenoic acid (EPA), DHA, and putative from CLA were quantified. CLA containing diets reduced AT mass by ~62%. Compared with the control diet, the DHA diet elevated concentrations of EPA-and DHA-derived alcohols and epoxides and LNA-derived alcohols, reduced ARA-derived alcohols, ketones, epoxides, and 6-keto-prostaglandin (PG) F_1α (P < 0.05), and had mixed effects on ALA-derived alcohols. Dietary CLA lowered EPA-, DHA-, and ALA-derived epoxides, ARA-derived ketones and epoxides, and ALA-derived alcohols. While dietary CLA induced variable effects in EPA-, DHA-, and LNA-derived alcohols and LNA-derived ketones, it elevated ARA-derived alcohols and PGF_1α, PGF_2α, and F2-isoprostanes. DHA counteracted CLA-induced effects in 67, 57, 43, and 29% of total DHA-, ARA-, EPA-, and ALA-derived oxylipins, respectively. Thus, CLA elevated proinflammatory oxylipins while DHA increased anti-inflammatory oxylipins and diminished concentration of CLA-induced pro-inflammatory oxylipins in AT.