Hardness of Exact Distance Queries in Sparse Graphs Through Hub Labeling

A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. An important class of distance labeling schemes is that of hub labelings, where a node $v \in G$ stores its distance to the so-called hubs $S_v \subseteq V$, chosen so that for any $u,v \in V$ there is $w \in S_u \cap S_v$ belonging to some shortest $uv$ path. Notice that for most existing graph classes, the best distance labelling constructions existing use at some point a hub labeling scheme at least as a key building block. Our interest lies in hub labelings of sparse graphs, i.e., those with $|E(G)| = O(n)$, for which we show a lowerbound of $\frac{n}{2^{O(\sqrt{\log n})}}$ for the average size of the hubsets. Additionally, we show a hub-labeling construction for sparse graphs of average size $O(\frac{n}{RS(n)^{c}})$ for some $0 < c < 1$, where $RS(n)$ is the so-called Ruzsa-Szemer{\'e}di function, linked to structure of induced matchings in dense graphs. This implies that further improving the lower bound on hub labeling size to $\frac{n}{2^{(\log n)^{o(1)}}}$ would require a breakthrough in the study of lower bounds on $RS(n)$, which have resisted substantial improvement in the last 70 years. For general distance labeling of sparse graphs, we show a lowerbound of $\frac{1}{2^{O(\sqrt{\log n})}} SumIndex(n)$, where $SumIndex(n)$ is the communication complexity of the Sum-Index problem over $Z_n$. Our results suggest that the best achievable hub-label size and distance-label size in sparse graphs may be $\Theta(\frac{n}{2^{(\log n)^c}})$ for some $0<c < 1$

Cokebildung und Entcoking während der Methanbildung und des Methanzerfalls auf Ni-Cu-Trägerkatalysatoren

The effect of the composition of silica supported Ni-Cu alloy catalysts on the process of coking and decoking during methane decomposition and during methanation was considered. The kinetics of methanation was studied and compared to those of carbon deposition and of strong adsorption of hydrogen. Initiation of the formation of filamentous carbon formation on mono-metallic surfaces may take place if the ratio of the partial pressures, pCO/pH2, is larger than 2 (T 673 K). Once the process starts, the chemical potential of the gas phase may be reduced to lower values without interruption of filament growth. Besides, it was concluded that the methanation reaction includes two steps: the dissociative adsorption of CO and the hydrogenation of the adsorbed species. It was possible to establish the mechanism through which Cu affects the activity of Ni. The effect of the composition of the alloy catalysts on the methane formation and on the simultaneous carbon deposition indicates that those reactions belong to group I and to group II, respectively, following Ponec's classification. It was possible to find the optimal Cu concentration that maximises methanation and minimises carbon deposition. The kinetics of methane decomposition was also considered and is well described by adapting a model developed by other authors for Fe catalysts

A simpler and more efficient algorithm for the next-to-shortest path problem

Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path length. In this paper we show that the problem can be solved in linear time if the distances from $s$ and $t$ to all other vertices are given. Particularly our new algorithm runs in $O(|V|\log |V|+|E|)$ time for general graphs, which improves the previous result of $O(|V|^2)$ time for sparse graphs, and takes only linear time for unweighted graphs, planar graphs, and graphs with positive integer edge lengths.Comment: Partial result appeared in COCOA201

Kohlenstoffbildung auf Nickel und Nickel-Kupfer-Legierungskatalysatoren

Equilibrium, kinetic and morphological studies of carbon formation in CH4+H2, CO, and CO+H2 gases on silica supported nickel and nickel-copper catalysts are reviewed. The equilibrium deviates in all cases from graphite equilibrium and more so in CO+CO2 than in CH4+H2. A kinetic model based on information from surface science results with chemisorption of CH4 and possibly also the first dehydrogenation step as rate controlling describes carbon formation on nickel catalyst in CH4+H2 well. The kinetics of carbon formation in CO and CO+H2 gases are in agreement with CO disproportionation as rate determining step. The presence of hydrogen influences strongly the chemisorption of CO. Carbon filaments are formed when hydrogen is present in the gas while encapsulating carbon dominates in pure CO. Small amounts of Cu alloying promotes while larger amounts (Cu : Ni ≥ 0.1) inhibits carbon formation and changes the morphology of the filaments ("octopus" carbon formation). Adsorption induced nickel segregation changes the kinetics of the alloy catalysts at high carbon activities. Modifications suggested in some very recent papers on the basis of new results are also briefly discussed.Center for Surface Reactivity

Bioaccumulation and ecotoxicity of carbon nanotubes

Carbon nanotubes (CNT) have numerous industrial applications and may be released to the environment. In the aquatic environment, pristine or functionalized CNT have different dispersion behavior, potentially leading to different risks of exposure along the water column. Data included in this review indicate that CNT do not cross biological barriers readily. When internalized, only a minimal fraction of CNT translocate into organism body compartments. The reported CNT toxicity depends on exposure conditions, model organism, CNT-type, dispersion state and concentration. In the ecotoxicological tests, the aquatic organisms were generally found to be more sensitive than terrestrial organisms. Invertebrates were more sensitive than vertebrates. Single-walled CNT were found to be more toxic than double-/multi-walled CNT. Generally, the effect concentrations documented in literature were above current modeled average environmental concentrations. Measurement data are needed for estimation of environmental no-effect concentrations. Future studies with benchmark materials are needed to generate comparable results. Studies have to include better characterization of the starting materials, of the dispersions and of the biological fate, to obtain better knowledge of the exposure/effect relationships