Lower Bounds and Approximation Algorithms for Search Space Sizes in Contraction Hierarchies

Contraction hierarchies (CH) is a prominent preprocessing-based technique that accelerates the computation of shortest paths in road networks by reducing the search space size of a bidirectional Dijkstra run. To explain the practical success of CH, several theoretical upper bounds for the maximum search space size were derived in previous work. For example, it was shown that in minor-closed graph families search space sizes in ?(?n) can be achieved (with n denoting the number of nodes in the graph), and search space sizes in ?(h log D) in graphs of highway dimension h and diameter D. In this paper, we primarily focus on lower bounds. We prove that the average search space size in a so called weak CH is in ?(b_?) for ? ? 2/3 where b_? is the size of a smallest ?-balanced node separator. This discovery allows us to describe the first approximation algorithm for the average search space size. Our new lower bound also shows that the ?(?n) bound for minor-closed graph families is tight. Furthermore, we deeper investigate the relationship of CH and the highway dimension and skeleton dimension of the graph, and prove new lower bound and incomparability results. Finally, we discuss how lower bounds for strong CH can be obtained from solving a HittingSet problem defined on a set of carefully chosen subgraphs of the input network

Functional characterization of a novel arachidonic acid 12S-lipoxygenase in the halotolerant bacterium Myxococcus fulvus exhibiting complex social living patterns

Lipoxygenases are lipid peroxidizing enzymes, which frequently occur in higher plants and mammals. These enzymes are also expressed in lower multicellular organisms but here they are not widely distributed. In bacteria, lipoxygenases rarely occur and evaluation of the currently available bacterial genomes suggested that <0.5% of all sequenced bacterial species carry putative lipoxygenase genes. We recently rescreened the public bacterial genome databases for lipoxygenase‐like sequences and identified two novel lipoxygenase isoforms (MF‐LOX1 and MF‐LOX2) in the halotolerant Myxococcus fulvus. Both enzymes share a low degree of amino acid conservation with well‐characterized eukaryotic lipoxygenase isoforms but they involve the catalytically essential iron cluster. Here, we cloned the MF‐LOX1 cDNA, expressed the corresponding enzyme as N‐terminal hexa‐his‐tag fusion protein, purified the recombinant enzyme to electrophoretic homogeneity, and characterized it with respect to its protein‐chemical and enzymatic properties. We found that M. fulvus expresses a catalytically active intracellular lipoxygenase that converts arachidonic acid and other polyunsaturated fatty acids enantioselectively to the corresponding n‐9 hydroperoxy derivatives. The enzyme prefers C20‐ and C22‐polyenoic fatty acids but does not exhibit significant membrane oxygenase activity. The possible biological relevance of MF‐LOX1 will be discussed in the context of the suggested concepts of other bacterial lipoxygenases

Half-Metallic Ferromagnetism in the Heusler Compound Co2_2FeSi revealed by Resistivity, Magnetoresistance, and Anomalous Hall Effect measurements

We present electrical transport data for single-crystalline Co$_2$FeSi which provide clear-cut evidence that this Heusler compound is truly a half-metallic ferromagnet, i.e. it possesses perfect spin-polarization. More specifically, the temperature dependence of $\rho$ is governed by electron scattering off magnons which are thermally excited over a sizeable gap $\Delta\approx 100 K$ ($\sim 9 meV$) separating the electronic majority states at the Fermi level from the unoccupied minority states. As a consequence, electron-magnon scattering is only relevant at $T\gtrsim\Delta$ but freezes out at lower temperatures, i.e., the spin-polarization of the electrons at the Fermi level remains practically perfect for $T\lesssim\Delta$. The gapped magnon population has a decisive influence on the magnetoresistance and the anomalous Hall effect (AHE): i) The magnetoresistance changes its sign at $T\sim 100 K$, ii) the anomalous Hall coefficient is strongly temperature dependent at $T\gtrsim 100 K$ and compatible with Berry phase related and/or side-jump electronic deflection, whereas it is practically temperature-independent at lower temperatures

Low-temperature properties of single-crystal CrB2_{2}

We report the low-temperature properties of $^{11}$B-enriched single-crystal CrB$_{2}$ as prepared from high-purity Cr and B powder by a solid-state reaction and optical float zoning. The electrical resistivity, $\rho_{\rm xx}$, Hall effect, $\rho_{\rm xy}$, and specific heat, $C$, are characteristic of an exchange-enhanced Fermi liquid ground state, which develops a slightly anisotropic spin gap $\Delta \approx 220\,{\rm K}$ below $T_{\rm N}=88\,{\rm K}$. This observation is corroborated by the absence of a Curie dependence in the magnetization for $T\to0$ reported in the literature. Comparison of $C$ with $d\rho_{\rm xx}/dT$, where we infer lattice contributions from measurements of VB$_2$, reveals strong antiferromagnetic spin fluctuations with a characteristic spin fluctuation temperature $T_{\rm sf}\approx 257\,{\rm K}$ in the paramagnetic state, followed by a pronounced second-order mean-field transition at $T_{\rm N}$, and unusual excitations around $\approx T_{\rm N}/2$. The pronounced anisotropy of $\rho_{\rm xx}$ above $T_{\rm N}$ is characteristic of an easy-plane anisotropy of the spin fluctuations consistent with the magnetization. The ratio of the Curie-Weiss to the N$\acute{\rm{e}}$el temperatures, $f=-\Theta_{\rm CW}/T_{\rm N}\approx 8.5$, inferred from the magnetization, implies strong geometric frustration. All physical properties are remarkably invariant under applied magnetic fields up to $14\,\,{\rm T}$, the highest field studied. In contrast to earlier suggestions of local-moment magnetism our study identifies CrB$_{2}$ as a weak itinerant antiferromagnet par excellence with strong geometric frustration.Comment: 15 pages, 9 figure