Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Caldarelli et al. (2002). Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.Comment: 5 figure

Training needs and recommendations for Citizen Science participants, facilitators and designers

In this report, we aimed to systematise and elaborate on the ideas discussed during the COST Action WG2 workshop “Systematic review on training requirements and recommendations for Citizen Science” that took place in Riga on 12-13th November 2018. Building on the input from the workshop participants’ broad range of different perspectives and expertise in citizen science and education, we compiled a list of training needs for project participants, project facilitators and project designers in citizen science and categorised them into core, operational and engagement needs. Based on our experience we discussed challenges that may need to be considered when designing training in citizen science. We then addressed the needs by formulating recommendations and pointing out available resources that have been proven to be useful in our own citizen science research and practice. While we acknowledge that these training needs and training recommendations may not be complete, we believe that our approach from needs to recommendations can act as a helpful working model when designing training and the list of resources provides a starting point to delve deeper into the topic and good training examples to build on. We invite the community to provide further insights into training needs and recommendations and to contribute further resources to the listThis is an open access publication. The attached file is the published version of the article

Recognizing Chordal-Bipartite Probe Graphs

A graph G is chordal-bipartite probe if its vertices can be partitioned into two sets P (probes) and N (non-probes) where N is a stable set and such that G can be extended to a chordal-bipartite graph by adding edges between non-probes. A bipartite graph is called chordal-bipartite if it contains no chordless cycle of length strictly greater than 5. Such probe/non-probe completion problems have been studied previously on other families of graphs, such as interval graphs and chordal graphs. In this paper, we give a characterization of chordal-bipartite probe graphs, in the case of a fixed given partition of the vertices into probes and nonprobes. Our results are obtained by solving first the more general case without assuming that N is a stable set, and then this can be applied to the more specific case. Our characterization uses an edge elimination ordering which also implies a polynomial time recognition algorithm for the class. This research was conducted in the context of a France-Israel Binational project, while the French team visited Haifa in March 2007

Parameterized Domination in Circle Graphs

A circle graph is the intersection graph of a set of chords in a circle. Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that Dominating Set, Connected Dominating Set, and Total Dominating Set are NP-complete in circle graphs. To the best of our knowledge, nothing was known about the parameterized complexity of these problems in circle graphs. In this paper we prove the following results, which contribute in this direction: Dominating Set, Independent Dominating Set, Connected Dominating Set, Total Dominating Set, and Acyclic Dominating Set are W[1]-hard in circle graphs, parameterized by the size of the solution. Whereas both Connected Dominating Set and Acyclic Dominating Set are W[1]-hard in circle graphs, it turns out that Connected Acyclic Dominating Set is polynomial-time solvable in circle graphs. If T is a given tree, deciding whether a circle graph has a dominating set isomorphic to T is NP-complete when T is in the input, and FPT when parameterized by |V(T)|. We prove that the FPT algorithm is subexponential

Rainbow domination and related problems on some classes of perfect graphs

Let $k \in \mathbb{N}$ and let $G$ be a graph. A function $f: V(G) \rightarrow 2^{[k]}$ is a rainbow function if, for every vertex $x$ with $f(x)=\emptyset$, $f(N(x)) =[k]$. The rainbow domination number $\gamma_{kr}(G)$ is the minimum of $\sum_{x \in V(G)} |f(x)|$ over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs

Separating Hierarchical and General Hub Labelings

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is a class of labels that has been extensively studied. Performance of the hub label query depends on the label size. Hierarchical labels are a natural special kind of hub labels. These labels are related to other problems and can be computed more efficiently. This brings up a natural question of the quality of hierarchical labels. We show that there is a gap: optimal hierarchical labels can be polynomially bigger than the general hub labels. To prove this result, we give tight upper and lower bounds on the size of hierarchical and general labels for hypercubes.Comment: 11 pages, minor corrections, MFCS 201

Tuning of Human Modulation Filters Is Carrier-Frequency Dependent

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