On the independence number and Hamiltonicity of uniform random intersection graphs

AbstractIn the uniform random intersection graphs model, denoted by Gn,m,λ, to each vertex v we assign exactly λ randomly chosen labels of some label set M of m labels and we connect every pair of vertices that has at least one label in common. In this model, we estimate the independence number α(Gn,m,λ), for the wide range m=⌊nα⌋,α<1 and λ=O(m1/4). We also prove the Hamiltonicity of this model by an interesting combinatorial construction. Finally, we give a brief note concerning the independence number of Gn,m,p random intersection graphs, in which each vertex chooses labels with probability p

Maximum Cliques in Graphs with Small Intersection Number and Random Intersection Graphs

In this paper, we relate the problem of finding a maximum clique to the intersection number of the input graph (i.e. the minimum number of cliques needed to edge cover the graph). In particular, we consider the maximum clique problem for graphs with small intersection number and random intersection graphs (a model in which each one of $m$ labels is chosen independently with probability $p$ by each one of $n$ vertices, and there are edges between any vertices with overlaps in the labels chosen). We first present a simple algorithm which, on input $G$ finds a maximum clique in $O(2^{2^m + O(m)} + n^2 \min\{2^m, n\})$ time steps, where $m$ is an upper bound on the intersection number and $n$ is the number of vertices. Consequently, when $m \leq \ln{\ln{n}}$ the running time of this algorithm is polynomial. We then consider random instances of the random intersection graphs model as input graphs. As our main contribution, we prove that, when the number of labels is not too large ($m=n^{\alpha}, 0< \alpha <1$), we can use the label choices of the vertices to find a maximum clique in polynomial time whp. The proof of correctness for this algorithm relies on our Single Label Clique Theorem, which roughly states that whp a "large enough" clique cannot be formed by more than one label. This theorem generalizes and strengthens other related results in the state of the art, but also broadens the range of values considered. As an important consequence of our Single Label Clique Theorem, we prove that the problem of inferring the complete information of label choices for each vertex from the resulting random intersection graph (i.e. the \emph{label representation of the graph}) is \emph{solvable} whp. Finding efficient algorithms for constructing such a label representation is left as an interesting open problem for future research

Determining Majority in Networks with Local Interactions and Very Small Local Memory

We study here the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types (states). The vertices may have a few additional possible states and can interact in pairs only if they share an edge. Any (population) protocol is required to stabilize in the initial majority, i.e. its output function must interpret the local state of each vertex so that each vertex outputs the initial majority type. We first provide a protocol with 4 states per vertex that always computes the initial majority value, under any fair scheduler. Under the uniform probabilistic scheduler of pairwise interactions, we prove that our protocol stabilizes in expected polynomial time for any network and is quite fast on the clique. As we prove, this protocol is optimal, in the sense that there does not exist any population protocol that always computes majority with fewer than 4 states per vertex. However this does not rule out the existence of a protocol with 3 states per vertex that is correct with high probability (whp). To this end, we examine an elegant and very natural majority protocol with 3 states per vertex, introduced in [2] where its performance has been analyzed for the clique graph. In particular, it determines the correct initial majority type in the clique very fast and whp under the uniform probabilistic scheduler. We study the performance of this protocol in arbitrary networks. We prove that, when the two initial states are put uniformly at random on the vertices, the protocol of [2] converges to the initial majority with probability higher than the probability of converging to the initial minority. In contrast, we present an infinite family of graphs, on which the protocol of [2] can fail, i.e. it can converge to the initial minority type whp, even when the difference between the initial majority and the initial minority is n − Θ(ln n). We also present another infinite family of graphs in which the protocol of [2] takes an expected exponential time to converge. These two negative results build upon a very positive result concerning the robustness of the protocol of [2] on the clique, namely that if the initial minority is at most n7, the protocol fails with exponentially small probability. Surprisingly, the resistance of the clique to failure causes the failure in general graphs. Our techniques use new domination and coupling arguments for suitably defined processes whose dynamics capture the antagonism between the states involved

The temporal explorer who returns to the base

We study here the problem of exploring a temporal graph when the underlying graph is a star. The aim of the exploration problem in a temporal star is finding a temporal walk which starts and finishes at the center of the star, and visits all leaves. We present a systematic study of the computational complexity of this problem, depending on the number k of time points where each edge can be present in the graph. We distinguish between the decision version StarExp(k), asking whether a complete exploration exists, and the maximization version MaxStarExp(k), asking for an exploratkion of the greatest possible number of edges. We fully characterize MaxStarExp(k) in terms of complexity. We also partially characterize StarExp(k), showing that it is in P for k 5 . Finally, we partially characterize classes of “random” temporal stars which are, asymptotically almost surely, yes-instances and no-instances for StarExp(k)

Improving sensor network performance with wireless energy transfer

Through recent technology advances in the field of wireless energy transmission Wireless Rechargeable Sensor Networks have emerged. In this new paradigm for wireless sensor networks a mobile entity called mobile charger (MC) traverses the network and replenishes the dissipated energy of sensors. In this work we first provide a formal definition of the charging dispatch decision problem and prove its computational hardness. We then investigate how to optimise the trade-offs of several critical aspects of the charging process such as: a) the trajectory of the charger; b) the different charging policies; c) the impact of the ratio of the energy the Mobile Charger may deliver to the sensors over the total available energy in the network. In the light of these optimisations, we then study the impact of the charging process to the network lifetime for three characteristic underlying routing protocols; a Greedy protocol, a clustering protocol and an energy balancing protocol. Finally, we propose a mobile charging protocol that locally adapts the circular trajectory of the MC to the energy dissipation rate of each sub-region of the network. We compare this protocol against several MC trajectories for all three routing families by a detailed experimental evaluation. The derived findings demonstrate significant performance gains, both with respect to the no charger case as well as the different charging alternatives; in particular, the performance improvements include the network lifetime, as well as connectivity, coverage and energy balance properties

Natural models for evolution on networks

Evolutionary dynamics has been traditionally studied in the context of homogeneous populations, mainly described by the Moran process [P. Moran, Random processes in genetics, Proceedings of the Cambridge Philosophical Society 54 (1) (1958) 60–71]. Recently, this approach has been generalized in [E. Lieberman, C. Hauert, M.A. Nowak, Evolutionary dynamics on graphs, Nature 433 (2005) 312–316] by arranging individuals on the nodes of a network (in general, directed). In this setting, the existence of directed arcs enables the simulation of extreme phenomena, where the fixation probability of a randomly placed mutant (i.e., the probability that the offspring of the mutant eventually spread over the whole population) is arbitrarily small or large. On the other hand, undirected networks (i.e., undirected graphs) seem to have a smoother behavior, and thus it is more challenging to find suppressors/amplifiers of selection, that is, graphs with smaller/greater fixation probability than the complete graph (i.e., the homogeneous population). In this paper we focus on undirected graphs. We present the first class of undirected graphs which act as suppressors of selection, by achieving a fixation probability that is at most one half of that of the complete graph, as the number of vertices increases. Moreover, we provide some generic upper and lower bounds for the fixation probability of general undirected graphs. As our main contribution, we introduce the natural alternative of the model proposed in [E. Lieberman, C. Hauert, M.A. Nowak, Evolutionary dynamics on graphs, Nature 433 (2005) 312–316]. In our new evolutionary model, all individuals interact simultaneously and the result is a compromise between aggressive and non-aggressive individuals. We prove that our new model of mutual influences admits a potential function, which guarantees the convergence of the system for any graph topology and any initial fitness vector of the individuals. Furthermore, we prove fast convergence to the stable state for the case of the complete graph, as well as we provide almost tight bounds on the limit fitness of the individuals. Apart from being important on its own, this new evolutionary model appears to be useful also in the abstract modeling of control mechanisms over invading populations in networks. We demonstrate this by introducing and analyzing two alternative control approaches, for which we bound the time needed to stabilize to the “healthy” state of the system

Synthesis and structural characterization of poly(dicyclopentadiene) gels obtained with a novel ditungsten versus conventional W and Ru mononuclear catalysts

Poly(dicyclopentadiene) (PDCPD) gels were prepared via ring opening metathesis polymerization (ROMP) of dicyclopentadiene (DCPD), which is known to provide highly crosslinked insoluble polymers. Two catalytic systems were employed, both based on W compounds. The first one was based on the ditungsten complex Na[W2(μ-Cl)3 Cl4(THF)2] (THF)3 ({W3W}6+, a&apos;2e&apos;4) and the second one on commercially available WCl6. Both catalysts require activation by small amounts of phenylacetylene (PA). Drygels were characterized with TGA, FTIR-ATR, FT-Raman and solid-state NMR, and were compared with PDCPD aerogels synthesized using the well-established first and second generation Ru-based Grubbs’ catalysts (Ru-I and Ru-II). Emphasis is given on the determination of the cis/trans ratio of the polymeric chain. Data confirmed that Ru-based catalysts favor the trans-configuration, while W-based catalysts favor the cis-configuration, in accord with the stereoselectivity that has been observed with those catalytic systems in other ROMP reactions of substrates that yield soluble polymers. Most importantly, it is also shown that the configuration of the polymeric chain plays a key role in the swelling behavior of those PDCPD dry-gels in toluene. High-cis PDCPD gels obtained from the ditungsten catalytic system increased their volume by more than 100 times, while gels obtained with the other catalytic systems swelled to a much lesser extent (WCl6/PA, Ru-II), or did not swell at all (Ru-I). It is evident that swelling strongly depends on the configuration of the polymeric chain and increases together with the content of the cis configuration. Therefore, the ditungsten catalytic system shows unique advantages in terms of stereochemistry and properties of PDCPD gels over the mononuclear W- and Ru-based catalytic systems

Benchmarking of measurement and performance evaluation methods for third sector organizations

Organizações do Terceiro Setor são financiadas por recursos públicos e privados. Entretanto, para que possam receber essesrecursos, necessitam demonstrar os resultados gerados, com base nos objetivos e metas pactuados com seus financiadores. Logo,a adoção de melhores práticas de mensuração de desempenho é importante para assegurar maior transparência e aderência aosresultados esperados. Portanto, o objetivo deste ensaio teórico é apresentar as práticas de mensuração de desempenho adotadaspelo setor e determinar aquelas que podem ser consideradas benchmarkings internacionais. Este trabalho apresenta contribuiçõesao estabelecer um referencial teórico para avaliação de desempenho que pode ser adotado como instrumento de comparação comos modelos atuais. Desta forma, foi realizada uma pesquisa exploratória qualitativa cujos dados foram tratados por meio de análisede conteúdo. Os achados demonstraram que as melhores práticas de avaliação de desempenho estão relacionadas à mensuração deeficácia e à apuração dos resultados e impactos gerados aos diversos beneficiários.info:eu-repo/semantics/publishedVersio

Poly(urethane-norbornene) Aerogels via Ring Opening Metathesis Polymerization of Dendritic Urethane-Norbornene Monomers: Structure-Property Relationships as a Function of an Aliphatic Versus an Aromatic Core and the Number of Peripheral Norbornene Moieties

We report the synthesis and characterization of synthetic polymer aerogels based on dendritic-type urethane-norbornene monomers. The core of those monomers is based either on an aromatic/rigid (TIPM/Desmodur RE), or an aliphatic/flexible (Desmodur N3300) triisocyanate. The terminal norbornene groups (three at the tip of each of the three branches) were polymerized via ROMP using the inexpensive 1st generation Grubbs catalyst. The polymerization/gelation conditions were optimized by varying the amount of the catalyst. The resulting wet-gels were dried either from pentane under ambient pressure at 50 oC, or from t-butanol via freeze-drying, or by using supercritical fluid (SCF) CO2. Monomers were characterized with high resolution mass spectrometry (HRMS), 1H- and solid-state 13C-NMR. Aerogels were characterized with ATR-FTIR and solid-state 13C-NMR. The porous network was probed with N2-sorption and SEM. The thermal stability of monomers and aerogels was studied with TGA, which also provides evidence for the number of norbornene groups that reacted via ROMP. At low densities (&lt;0.1 g cm-3) all aerogels were highly porous (porosity &gt; 90%), mostly macroporous materials; aerogels based on the aliphatic/flexible core were fragile, whereas aerogels containing the aromatic/rigid core were plastic, and at even lower densities (0.03 g cm-3) foamy. At higher densities (0.2–0.7 g cm-3) all materials were stiff, strong, and hard. At low monomer concentrations all aerogels consisted of discrete primary particles that formed spherical secondary aggregates. At higher monomer concentrations the structure consisted of fused particles with the size of the previous secondary aggregates, due to the low solubility of the developing polymer, which phase-separated and formed a primary particle network. Same-size fused aggregates were observed for both aliphatic and aromatic triisocyanate-derived aerogels, leading to the conclusion that it is not the aliphatic or aromatic core that determines phase separation, but rather the solubility of the polymeric backbone (polynorbornene) that is in both cases the same. The material properties were compared to those of analogous aerogels bearing only one norbornene moiety at the tip of each branch deriving from the same cores