Adjacency labeling schemes and induced-universal graphs

We describe a way of assigning labels to the vertices of any undirected graph on up to $n$ vertices, each composed of $n/2+O(1)$ bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an $n/2+O(\log n)$ bound of Moon. As a consequence, we obtain an induced-universal graph for $n$-vertex graphs containing only $O(2^{n/2})$ vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs

Free radical scavenging and formation by multi-walled carbon nanotubes in cell free conditions and in human bronchial epithelial cells

Background: Certain multi-walled carbon nanotubes (MWCNTs) have been shown to elicit asbestos-like toxicological effects. To reduce needs for risk assessment it has been suggested that the physicochemical characteristics or reactivity of nanomaterials could be used to predict their hazard. Fibre-shape and ability to generate reactive oxygen species (ROS) are important indicators of high hazard materials. Asbestos is a known ROS generator, while MWCNTs may either produce or scavenge ROS. However, certain biomolecules, such as albumin – used as dispersants in nanomaterial preparation for toxicological testing in vivo and in vitro - may reduce the surface reactivity of nanomaterials. Methods: Here, we investigated the effect of bovine serum albumin (BSA) and cell culture medium with and without BEAS 2B cells on radical formation/scavenging by five MWCNTs, Printex 90 carbon black, crocidolite asbestos, and glass wool, using electron spin resonance (ESR) spectroscopy and linked this to cytotoxic effects measured by trypan blue exclusion assay. In addition, the materials were characterized in the exposure medium (e.g. for hydrodynamic size-distribution and sedimentation rate). Results: The test materials induced highly variable cytotoxic effects which could generally be related to the abundance and characteristics of agglomerates/aggregates and to the rate of sedimentation. All carbon nanomaterials were found to scavenge hydroxyl radicals (•OH) in at least one of the solutions tested. The effect of BSA was different among the materials. Two types of long, needle-like MWCNTs (average diameter >74 and 64.2 nm, average length 5.7 and 4.0 µm, respectively) induced, in addition to a scavenging effect, a dose-dependent formation of a unique, yet unidentified radical in both absence and presence of cells, which also coincided with cytotoxicity. Conclusions: Culture medium and BSA affects scavenging/production of •OH by MWCNTs, Printex 90 carbon black, asbestos and glass-wool. An unidentified radical is generated by two long, needle-like MWCNTs and these two CNTs were more cytotoxic than the other CNTs tested, suggesting that this radical could be related to the adverse effects of MWCNTs

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

Fingerprints in Compressed Strings

The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string S of size N compressed by a context-free grammar of size n that answers fingerprint queries. That is, given indices i and j, the answer to a query is the fingerprint of the substring S[i,j]. We present the first O(n) space data structures that answer fingerprint queries without decompressing any characters. For Straight Line Programs (SLP) we get O(logN) query time, and for Linear SLPs (an SLP derivative that captures LZ78 compression and its variations) we get O(log log N) query time. Hence, our data structures has the same time and space complexity as for random access in SLPs. We utilize the fingerprint data structures to solve the longest common extension problem in query time O(log N log l) and O(log l log log l + log log N) for SLPs and Linear SLPs, respectively. Here, l denotes the length of the LCE

Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)

In this paper, a compressed membership problem for finite automata, both deterministic and non-deterministic, with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, such recompression induces only small changes in the automaton, in particular, the size of the automaton remains polynomial. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter and extending the partial result of Lohrey and Mathissen; as it is already known, that this problem is NP-hard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P; for this problem, only trivial upper-bound PSPACE was known

Comparison of dust released from sanding conventional and nanoparticle-doped wall and wood coatings

Introduction of engineered nanoparticles (ENPs) into traditional surface coatings (e.g., paints, lacquers, fillers) may result in new exposures to both workers and consumers and possibly also a new risk to their health. During finishing and renovation, such products may also be a substantial source of exposure to ENPs or aggregates thereof. This study investigates the particle size distributions (5.6 nm–19.8 μm) and the total number of dust particles generated during sanding of ENP-doped paints, lacquers, and fillers as compared to their conventional counterparts. In all products, the dust emissions from sanding were found to consist of five size modes: three modes under 1 μm and two modes around 1 and 2 μm. Corrected for the emission from the sanding machine, the sanding dust, was dominated by 100–300 nm size particles, whereas the mass and surface area spectra were dominated by the micrometer modes. Adding ENPs to the studied products only vaguely affected the geometric mean diameters of the particle modes in the sanding dust when compared to their reference products. However, we observed considerable differences in the number concentrations in the different size modes, but still without revealing a clear effect of ENPs on dust emissions from sanding

A Simple Linear-Space Data Structure for Constant-Time Range Minimum Query

Abstract. We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution that is simple, intuitive, and practical without increasing asymptotic costs for query time or space