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In this paper company co-mentions network is formed as a graph in which vertexes represent the world’s largest companies mentioned in financial and economic news flow. If two companies were mentioned in the same news report then the edge between two nodes is included in the co-mentions graph. The edge weight between any two nodes is calculated as the amount of news items that mentioned both companies in a certain period of time. We examine the changes of the structural properties of the company co-mentions graph over time. We analyze the distribution of the degrees of the vertices in this graph, the edge density of this graph as well as its connectivity. Based on the analysis, we make some conclusions regarding the dynamics of the evolution of the news flow.

We consider the problem of detecting the source of an epidemic that spreads in a network. The only information about the epidemic comes from a subset of nodes, which we call sensors, and which can reveal if and when they become infected. How many sensors do we need to guarantee that the epidemic source is correctly identified? The answer to this question is a known network property, called the double metric dimension (DMD); unfortunately, it is hard to compute. We compute tight bounds for the DMD of $\mathcal{G}(N, p)$ random networks. Interestingly, these bounds are non-monotonic functions of the edge density p: this implies in turn that the detectability of the source is influenced by the edge density p in a non-monotonic fashion in $\mathcal{G}(N,p)$ networks. We show empirically that this property applies to other topologies as well.

We study the maximum number $ex(n,e,H)$ of copies of a graph $H$ in graphs with given number of vertices and edges. We show that for any fixed graph $H$, $ex(n,e,H)$ is asymptotically realized by the quasi-clique provided that the edge density is sufficiently large. We also investigate a variant of this problem, when the host graph is bipartite.

We study the problem of representing topological graphs as polyline drawings with few bends per edge and such that the topology of the graph is either fully or partially preserved. More formally, let G be a simple topological graph and let Γ be a polyline drawing of G. Drawing Γ partially preserves the topology of G if it has the same external boundary, the same circular order of the edges around each vertex, and the same set of crossings as G, while it fully preserves the topology of G if the planarization of G and the planarization of Γ have the same planar embedding. We prove that if the set of crossing-free edges of G forms a biconnected (connected) spanning subgraph, then G admits a polyline drawing that partially preserves its topology and that has curve complexity at most one (three), i.e., with at most one (three) bend(s) per edge. If, however, the set of crossing-free edges of G is not a connected spanning subgraph, the curve complexity may be Ω ( n ) , while it is O ( 1 ) if the number of connected components is O ( 1 ) . Concerning drawings that fully preserve the topology, we show that if G is k-skew (i.e., it becomes planar after removing k suitably chosen edges), it admits one such drawing with curve complexity at most 2k; for 1-skew graphs, the curve complexity can be reduced to one, which is a tight bound. We also consider optimal 2-plane graphs (i.e., with at most two crossings per edge and maximum edge density), for which we discuss trade-offs between curve complexity and crossing angle resolution of drawings that fully preserve the topology.

An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical' properties are asymptotically equivalent and, thus, a graph $G$ possessing one such property automatically satisfies the others. In recent years, work in this area has focused on uncovering more quasirandom graph properties and on extending the known results to other discrete structures. In the context of hypergraphs, however, one may consider several different notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. We give short and purely combinatorial proofs of the main equivalences in Towsner's result., Comment: 19 pages

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the construction of the network, or in the network construction procedure itself, necessarily must propagate to any summary statistics reported. Here we study the problem of estimating the density of an arbitrary subgraph, given a noisy version of some underlying network as data. Under a simple model of network error, we show that consistent estimation of such densities is impossible when the rates of error are unknown and only a single network is observed. Accordingly, we develop method-of-moment estimators of network subgraph densities and error rates for the case where a minimal number of network replicates are available. These estimators are shown to be asymptotically normal as the number of vertices increases to infinity. We also provide confidence intervals for quantifying the uncertainty in these estimates based on the asymptotic normality. To construct the confidence intervals, a new and nonstandard bootstrap method is proposed to compute asymptotic variances, which is infeasible otherwise. We illustrate the proposed methods in the context of gene coexpression networks. Supplementary materials for this article are available online.

Given a simple graph and a constant $$\gamma \in (0,1]$$??(0,1], a $$\gamma $$?-quasi-clique is defined as a subset of vertices that induces a subgraph with an edge density of at least $$\gamma $$?. This well-known clique relaxation model arises in a variety of application domains. The maximum $$\gamma $$?-quasi-clique problem is to find a $$\gamma $$?-quasi-clique of maximum cardinality in the graph and is known to be NP-hard. This paper proposes new mixed integer programming (MIP) formulations for solving the maximum $$\gamma $$?-quasi-clique problem. The corresponding linear programming (LP) relaxations are analyzed and shown to be tighter than the LP relaxations of the MIP models available in the literature on sparse graphs. The developed methodology is naturally generalized for solving the maximum $$f(\cdot )$$f(·)-dense subgraph problem, which, for a given function $$f(\cdot )$$f(·), seeks for the largest k such that there is a subgraph induced by k vertices with at least f(k) edges. The performance of the proposed exact approaches is illustrated on real-life network instances with up to 10,000 vertices.

In the medium-sized heliotron device Heliotron J, edge density fluctuation has been measured simultaneously with a high-speed video camera and a Langmuir probe. Poloidally propagating, parallel elo...

The colouring number col ( G ) of a graph G is the minimum integer k such that there exists a linear ordering of the vertices of G in which each vertex v has back-degree at most k, i.e. v has at most k neighbours u with u v . The colouring number is a structural measure that measures the edge density of subgraphs of G. For r ≥ 1 , the numbers col r ( G ) and wcol r ( G ) generalise the colouring number, where col 1 ( G ) and wcol 1 ( G ) are equivalent to col ( G ) . For increasing values of r these measures converge to the well-known structural measures tree-width and tree-depth. For an n-vertex graph, col n ( G ) is equal to the tree-width of G and wcol n ( G ) is equal to the tree-depth of G. We show that if G excludes K t as a minor, then col r ( G ) ≤ ( t 2 ) ⋅ ( 2 r + 1 ) and wcol r ( G ) ≤ ( t 2 ) r ⋅ ( 2 r + 1 ) . It is easily observed that if G is planar, then col r ( G ) ≤ 5 r + 3 . The technically most demanding part of the paper is to show that for those graphs, wcol r ( G ) ≤ 5 r 5 . These results generalise to bounded genus graphs, i.e. if G is of genus g, then col r ( G ) ≤ ( 2 g + 3 ) ( 2 r + 1 ) and wcol r ( G ) ≤ 2 g ( 2 r + 1 ) + 5 r 5 .

 Abstract—The Medical Image can be understood by its visual features also known as image signatures. These features when modified or enhanced under certain geometrical functions, it improves the resultant retrieval by the increase of 94% in the performance with the Comparison of 85% in the case of the nearest neighbor and in the case of normal image Retrieval it comes out to be 75 %. This Research includes the approach of calculating edge density is applicable for the five human body parts- Hands, Pelvis, Breast, Brain and Chest and is cam parable to the system in the previous work in literatures. The Result acquired for the proposed system comprises of edge density concepts.

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once—for example, communication within a group rather than person to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental difference from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

Sidorenko's Conjecture asserts that every bipartite graph H has the Sidorenko property, i.e., a quasirandom graph minimizes the density of H among all graphs with the same edge density. We study a stronger property, which requires that a quasirandom multipartite graph minimizes the density of H among all graphs with the same edge densities between its parts; this property is called the step Sidorenko property. We show that many bipartite graphs fail to have the step Sidorenko property and use our results to show the existence of a bipartite edge-transitive graph that is not weakly norming; this answers a question of Hatami [Israel J. Math. 175 (2010), 125-150]., Comment: Minor correction on page 7

Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems. Here, we study the performance of two types of annealing machines--a commercially available quantum annealer built by D-Wave Systems, and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillator networks--on two classes of problems, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on regular graphs of degree 3. On denser problems, however, we observe an exponential penalty for the quantum annealer ($\exp(-\alpha_\textrm{DW} N^2)$) relative to CIMs ($\exp(-\alpha_\textrm{CIM} N)$) for fixed anneal times, on both the SK model and on 50%-edge-density MAX-CUT, where the coefficients $\alpha_\textrm{CIM}$ and $\alpha_\textrm{DW}$ are problem-class-dependent. On instances with over $50$ vertices, a several-orders-of-magnitude time-to-solution difference exists between CIMs and the D-Wave annealer. An optimal-annealing-time analysis is also consistent with a significant projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the measurement-feedback facilitated all-to-all connectivity of the CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers., Comment: 12 pages, 5 figures, 1 table (main text); 14 pages, 12 figures, 2 tables (supplementary)

A graph embedding is a representation of graph vertices in a low- dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear sequences of nodes to create embeddings using a neural network. In this paper, we propose diffusion graphs as a method to rapidly generate vertex sequences for network embedding. Its computational efficiency is superior to previous methods due to simpler sequence generation, and it produces more accurate results. In experiments, we found that the performance relative to other methods improves with increasing edge density in the graph. In a community detection task, clustering nodes in the embedding space produces better results compared to other sequence-based embedding methods.

The definition of community, usually, relies on the concept of edge density. Network motifs, however, have been recognized as fundamental building blocks of networks and, similarly to edges, may give insights for uncovering communities in complex networks. In this work, we propose a novel approach for identifying communities of network motifs. Differently from previous approaches, our method focuses on searching communities where nodes simultaneously participate in several types of motifs. Based on a genetic algorithm, the method finds a number of communities by minimizing the concept of multiple-motifs conductance. Simulations on a real-world network show that the proposed algorithm is able to better capture the real modular structure of the network, outperforming both motifs-based and classic community detection algorithms.

Anatomic differences on the toe pad epithelial cells of torrent and tree frogs (elongated versus regular geometry) are believed to account for superior ability of torrent frogs to attach to surfaces in the presence of running water. Here, the friction properties of artificial hexagonal arrays of polydimethylsiloxane (PDMS) pillars (elongated and regular) in the presence of water are compared. Elongated pillar patterns show significantly higher friction in a direction perpendicular to the long axis. A low bending stiffness of the pillars and a high edge density of the pattern in the sliding direction are the key design criteria for the enhanced friction. The elongated patterns also favor orientation-dependent friction. These findings have important implications for the development of new reversible adhesives for wet conditions.

We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community detection" algorithm's ability to correctly group nodes assigned to a planted partition, a problem which has been proven to be NP complete in a standard rendition. Our result does not rely on the use of any one particular algorithm nor on the analysis of the limitations of inference. Rather, we turn the problem on its head and work backwards to examine when, in the first place, well defined structure may exist in SBMs.The method that we introduce here could potentially be applied to other computational problems. The objective of community detection algorithms is to partition a given network into optimally disjoint subgraphs (or communities). Similar to k-SAT and other combinatorial optimization problems, "community detection" exhibits different phases. Networks that lie in the "unsolvable phase" lack well-defined structure and thus have no partition that is meaningful. Solvable systems splinter into two disparate phases: those in the "hard" phase and those in the "easy" phase. As befits its name, within the easy phase, a partition is easy to achieve by known algorithms. When a network lies in the hard phase, it still has an underlying structure yet finding a meaningful partition which can be checked in polynomial time requires an exhaustive computational effort that rapidly increases with the size of the graph. When taken together, (i) the rigorous results that we report here on when graphs have an underlying structure and (ii) recent results concerning the limits of rather general algorithms, suggest bounds on the hard phase., Comment: 21 pages, 9 figures

RESUMO A fragmentação florestal é um processo em que áreas contínuas de vegetação natural são subdivididas em manchas de tamanhos diversos, originado por atividades antrópicas ou causas naturais associadas a mudanças ambientais e eventos de grande magnitude. O presente trabalho tem por objetivo caracterizar e analisar a dinâmica da fragmentação florestal e a vulnerabilidade das manchas de distúrbios resultantes de deslizamentos ocasionados por chuvas intensas na região serrana do estado do Rio de Janeiro em 2011. Para tanto foi realizada uma avaliação do padrão espacial das manchas antes e após os eventos por meio de índices métricos de paisagem, estimados a partir de mapas de cobertura da terra e das cicatrizes dos deslizamentos, produzidos através da análise de imagens orbitais. Houve uma redução de 6% da área de floresta e um acréscimo de 107% no número de fragmentos, principalmente de pequenos. Ocorreu uma perda de 17% da área nuclear, um acréscimo de 43% do número de núcleos e de 28% da densidade de borda. A distância média do fragmento mais próximo diminuiu 46%, em virtude da forma das cicatrizes, alongadas e estreitas. Os resultados mostram que os deslizamentos ocasionaram uma intensificação do processo histórico de fragmentação florestal, promovendo um aumento da vulnerabilidade e instabilidade ecológica dos remanescentes florestais, evidenciando como eventos naturais de grande magnitude podem alterar rapidamente a paisagem. ABSTRACT Forest fragmentation is a process in which continuous natural vegetation areas are divided into patches of different sizes, originated by human activities or natural causes associated with environmental changes and high magnitude events. This work aims to characterize and to analyze the dynamics of forest fragmentation and the vulnerability of disturbance patches resulting from landslides, originated by heavy rainfall events that occurred in the mountain ranges of Rio de Janeiro state in the year 2011. The fragmentation pattern before and after the events was evaluated by the use of landscape metric indexes, extracted from land cover and landslide scars maps made by the analysis of satellite images. The indexes show a 6% reduction of the forest area and an increase of 107% in the number of forest patches, especially of small ones. A loss of 17% of forest core area and an increase of 43% in the number of forest cores and of 28% of edge density has occurred. The distance from the nearest neighbor decreased 46% due to the narrow and elongated shape of landslide scars. The overall results show that the rainfall events have caused an intensification of the historical process of forest fragmentation, promoting an increase of the ecological vulnerability and instability of the forest remnants, highlighting how high magnitude natural events can cause rapid landscape changes.

Given an integer $k \geq 2$ and a real number $\gamma\in [0, 1]$, which graphs of edge density $\gamma$ contain the largest number of $k$-edge stars? For $k=2$ Ahlswede and Katona proved that asymptotically there cannot be more such stars than in a clique or in the complement of a clique (depending on the value of $\gamma$). Here we extend their result to all integers $k\ge 2$., Comment: third version addresses changes arising from the referee reports

Reported reviews in the existing literature reveals that there is no significant work on the quality of thermal medical images. In the present scope, we briefed an overview on the quality measures of thermograms that should consider during processing and analysis of thermal medical images. Our analysis shows the effect of image qualities on the processing of breast thermograms using correlation coefficient of feature vectors. Features of left and right breast should be more correlated for normal thermograms than the abnormal one. The fact is based on the asymmetry analysis of breast thermograms. Based on the correlation coefficient the analysis is conducted in this present work. The result of analysis validates that image qualities are an important factor during thermogram analysis.

A construction of Alon yields a sequence of highly pseudorandom triangle-free graphs with edge density significantly higher than one might expect from comparison with random graphs. We give an alternative construction for such graphs., 6 pages

Patterned fabrics are generally constructed from the periodic repetition of a primitive pattern unit. Repeat pattern segmentation of printed fabrics has a very significant impact on the pattern retrieval and pattern defect detection. In this paper, we propose a new approach for repeat pattern segmentation by employing the adaptive template matching method. In contrast to the traditional method for template matching, the proposed algorithm first selects an adaptive size template image in the repeat pattern image based on the size of the original image and its local maximum edge density. Then it uses the sum of absolute differences as the matching features to identify the matched regions in the original image, and the minimum envelope border of the primitive pattern, typically as a parallelogram, can be determined from the results of the four adjacent matched templates. Finally, image traversal base on the obtained parallelogram is implemented over the original image using minimum information loss theory to produce a well-segmented primitive pattern with a complete edge structure. The results from the experiments conducted using an extensive database of real fabric images show that the proposed algorithm has the advantage of rotation invariance and scaling invariance and will not be affected when the background or foreground color is changed.

Let W"1,...,W"n be independent random subsets of [m]={1,...,m}. Assuming that each W"i is uniformly distributed in the class of d-subsets of [m] we study the uniform random intersection graph G"s(n,m,d) on the vertex set {W"1,...W"n}, defined by the adjacency relation: W"i~W"j whenever |W"[email protected]?W"j|>=s. We show that as n,m->~ the edge density threshold for the property that each vertex of G"s(n,m,d) has at least k neighbours is asymptotically the same as that for G"s(n,m,d) being k-connected.

Understanding the response of species to changes in landscape configuration is required to design adequate management and conservation strategies. Yet, the most appropriate spatial scale (i.e., landscape size) to assess the response of species to changes in landscape configuration (so-called “scale of effect”) is largely unknown. In this paper, we assess the impact of landscape forest cover, forest fragmentation, edge density, and inter-patch isolation distance on the diet and behavior of six communities of spider monkeys (Ateles geoffroyi) in the fragmented Lacandona rainforest, Mexico. We evaluated the strength of the relationship between each landscape predictor and each response variable within ten different-sized landscapes (range = 50–665 ha) to identify the landscape size that best predicted changes in diet and behavior. The strength of most associations varied across spatial scales, with the 126-ha landscape showing the strongest relationships between landscape predictors and response variables in many cases. Yet forest cover represented the main driver of the diet and behavior of spider monkeys, being positively associated with time traveling and time feeding on wood, but negatively related to time resting and time feeding on leaves. Although weaker, the impact of edge density was opposite to forest cover for most response variables. Forest fragmentation and isolation distance showed the weakest associations with the diet and behavior of this species. Our findings thus indicate that different landscape attributes operate on different response variables at different spatial scales. Therefore, the scale of effects cannot be generalized to all response variables and to all predictors, and a multi-scale analysis will be required to accurately assess the impact of landscape configuration on species' responses. Am. J. Primatol. 77:56–65, 2015. © 2014 Wiley Periodicals, Inc.

Let ?(G) denote the chromatic number of a graph G. We say that G is k-critical if ?(G)=k and ?(H) \left( {\tfrac{1} {2} - \tfrac{1} {{2^k - 1}}} \right)\left| D \right|^2$$. One corollary of our results is an explicit construction of an infinite family of k-critical digraphs of digirth l, for any pair of integers k,l?3. This extends a result by Bokal et al. who used a probabilistic approach to demonstrate the existence of one such digraph.

3rd International Geography Symposium (GEOMED) -- JUN 10-13, 2013 -- Antalya, TURKEY WOS: 000335821200003 The aim of this study is to analyze spatial variations of land cover using pattern metrics in the case of a Mediterranean coastal area. Various composition and configuration metrics were used to analyze characteristics of land cover and its spatial heterogeneity. Satellite images (i.e., SPOT) were used to classify land cover. Pattern analyses were conducted in Erdemli district of Mersin, Turkey, from coastline to about 200m ASL. Landscape patterns were quantified and mapped on the basis of number of patches (NP), edge density (ED), largest patch index (LPI), aggregation index (AI), Shannon's and Simpson's diversity and evenness indices (SHDI, SIDI, SHEI, STET). A relationship between observed patterns/calculated indices and current land uses were investigated. Results showed that many of the pattern features differed between the coast and upper lands due to varying composition and configuration characteristics of land cover types under investigation. (C) 2013 The Authors. Published by Elsevier Ltd.

Poloidally localized density fluctuation with applied and spontaneous 3-D fields in high-confinement mode (H-mode) plasma is observed by using poloidally distributed multichannel interferometer diagnostics in the experimental advanced superconducting tokamak. With the application of an n = 1 rotating nonaxisymmetric magnetic perturbation (NAMP) field, a density fluctuation appears on different interferometer channels sequentially. Evidence shows that this fluctuation is located at the plasma edge. When an n = 1 static NAMP field is applied, the density fluctuation amplitude increases in parts of channels but decreases in other channels, implying a poloidal localization. This localization is enhanced with the increase in the NAMP field. In addition, when a spontaneous n = 1 external kink mode with a frequency of ∼3.5 kHz appears in the plasma edge, the amplitude of density fluctuation is modulated by the n = 1 kink. This modulation could be attributed to the localization effect on fluctuation by the 3-D fields of the spontaneous kink mode.

Unfortunately in recent decades Central Zagros region has been changed adversely due to human activities. To analyze changes land cover maps produced using multi-temporal classification of Landsat satellite images of TM, ETM+ and OLI sensors, respectively for 1989, 2000 and 2013 years. Then derived maps used as input data in Land Change Modeler (LCM) to predict land cover changes on 2020, 2030, 2040 and 2050 based on a historical scenario. Results of classification and prediction were used to analyze landscape patterns and change processes. Five landscape pattern metrics as Normalized Entropy, Edge Density, Patch Area, Patch Compactness and Relative Richness were used to quantify landscape pattern and occurrence of ten landscape change processes as Attrition, Aggregation, Dissection, Creation, Shrinkage, Perforation, Shift, Deformation, Enlargement and Fragmentation were studied. Land cover maps showed great changes in central Zagros region in Lorestan province (Iran) whereas residential areas have destroyed about 5166.7 km2 of Zagros forests from 1989 to 2013. In this period residential areas are increased about 47.71 km2. Based on a “historical” scenario between 2013 up to 2050 about 4304.66 km2 of Zagros forests will lose and residential areas will increase about 244.51 km2 from. Results of landscape pattern analysis show increase of all studied landscape pattern metrics values; Normalized entropy from 0.001895 to 0.45236, Relative richness 11.12 to 22.89 percent, Edge density 0.002–0.44 m/ha, Patch area 92.04–193171.7 ha and Patch compactness 0.006 to 0.568 patches/100ha from 1989 to 2050. More over occurred change processes in different periods include: Shift, Enlargement, Attrition, Aggregation, Creation and Dissection. Results of this study present a clear perspective of future for managers and planners and can be used in natural resources management and environmental policy making, as well as creating mitigation measures in vulnerable areas.

Myanmar(Burma) has been preserved valuable environmental resources because of its political isolation. But recently, Myanmar has moved a capital city(Naypyidaw) at central forest area and it has been urbanized radically since 2005. In this paper, we built multi-temporal land cover map from Landsat images of 1970s to 2012 with ENVI 4.5 software. For a broad approach, administrative district Yamethin which includes Naypyidaw is classified into 3 classes and with only Naypyidaw region is classified with 4-5 classes to analyse specific changes. And with forest cover extracted by Object Oriented Classification, we evaluated forest fragmentation before and after the development using Patch Analyst(FRAGSTATs 3.3) at Yamethin area. For Yamethin area, there were significant forest cover change, 51% in 1999 to 48% in 2012, and for Naypyidaw area, 67% in 1999 to 57% in 2012 respectively. Also landscape indices resulted from Patch Analyst concluded that the total edge, edge density and mean shaped index of forest patches increased and total core area is decreased. It is attributed from land cover change with urbanization and agricultural land expansion.

A 1-planar drawing of a graph is such that each edge is crossed at most once. In 1997, Pach and Toth showed that any 1-planar drawing with n vertices has at most 4n-8 edges and that this bound is tight for n>=12. We show that, in fact, 1-planar drawings with n vertices have at most 4n-9 edges, if we require that the edges are straight-line segments. We also prove that this bound is tight for infinitely many values of n>=8. Furthermore, we investigate the density of 1-planar straight-line drawings with additional constraints on the vertex positions. We show that 1-planar drawings of bipartite graphs whose vertices lie on two distinct horizontal layers have at most 1.5n-2 edges, and we prove that 1-planar drawings such that all vertices lie on a circumference have at most 2.5n-4 edges; both these bounds are also tight.

International audience; Landscape composition and configuration are considered important factors influencing biodiversity in agricultural landscapes. Evaluating the relative importance of each component is complicated because they are often correlated. Overcoming this problem could lead to a better understanding of the mechanisms that drive biodiversity and help to determine effective actions. Usually, landscape-biodiversity relationships are studied at the local scale for a single habitat type (alpha diversity). However, for a better understanding of ecological processes at the landscape scale, it is also important to look at the overall diversity at the landscape level, including all habitat types. The present study was conducted to determine the relative effects of landscape composition and configuration on multi-habitat gamma diversity of carabid beetles and vascular plants in an agricultural region of western France. Twenty 1 km2 landscapes were sampled for plants and carabids. Data from 10 sampling sites representing crop fields, grasslands and woody covers in each landscape were pooled to obtain the total multi-habitat gamma diversity. Results showed that both landscape composition and configuration influenced carabid communities, while only landscape composition affected plant communities. Carabid species richness increased with increasing length of edge between crops and grasslands. Plant richness was negatively and positively affected by the percentage of crops and grasslands respectively. Carabid species composition was more dissimilar between landscapes with increasing difference in percentage of woody covers and crops, and length of grassy-crop edge. Plant species composition was more dissimilar between landscapes with a greater difference in percentage of crops. These results suggest grassy-crop adjacencies may enhance processes of resource complementation between habitats for carabids, while habitat availability and quality are the main factors for plants. This approach provided new insights for sustaining overall biodiversity in agricultural landscapes: e.g. encourage adjacencies between grasslands and crop fields and continue to subsidise grasslands for plant diversity.

Given a simple undirected graph G=(V,E) and a constant @[email protected]?(0,1), a subset of vertices is called a @c-quasi-clique or, simply, a @c-clique if it induces a subgraph with the edge density of at least @c. The maximum @c-clique problem consists in finding a @c-clique of largest cardinality in the graph. Despite numerous practical applications, this problem has not been rigorously studied from the mathematical perspective, and no exact solution methods have been proposed in the literature. This paper, for the first time, establishes some fundamental properties of the maximum @c-clique problem, including the NP-completeness of its decision version for any fixed @c satisfying 0

We characterize the set of properties of Boolean-valued functions on a finite domain $\mathcal{X}$ that are testable with a constant number of samples. Specifically, we show that a property $\mathcal{P}$ is testable with a constant number of samples if and only if it is (essentially) a $k$-part symmetric property for some constant $k$, where a property is {\em $k$-part symmetric} if there is a partition $S_1,\ldots,S_k$ of $\mathcal{X}$ such that whether $f:\mathcal{X} \to \{0,1\}$ satisfies the property is determined solely by the densities of $f$ on $S_1,\ldots,S_k$. We use this characterization to obtain a number of corollaries, namely: (i) A graph property $\mathcal{P}$ is testable with a constant number of samples if and only if whether a graph $G$ satisfies $\mathcal{P}$ is (essentially) determined by the edge density of $G$. (ii) An affine-invariant property $\mathcal{P}$ of functions $f:\mathbb{F}_p^n \to \{0,1\}$ is testable with a constant number of samples if and only if whether $f$ satisfies $\mathcal{P}$ is (essentially) determined by the density of $f$. (iii) For every constant $d \geq 1$, monotonicity of functions $f : [n]^d \to \{0, 1\}$ on the $d$-dimensional hypergrid is testable with a constant number of samples.

Signed networks remain relatively under explored despite the fact that many real networks are of this kind. Here, we study the problem of subgraph density in signed networks and show connections to the event detection task. Notions of density have been used in prior studies on anomaly detection, but all existing methods have been developed for unsigned networks. We develop the first algorithms for finding dense subgraphs in signed networks using semi-definite programming based rounding. We give rigorous guarantees for our algorithms, and develop a heuristic EGOSCAN which is significantly faster. We evaluate the performance of EGOSCAN for different notions of density, and observe that it performs significantly better than natural adaptations of prior algorithms for unsigned networks. In particular, the improvement in edge density over previous methods is as much as 85% and usually over 50%. These results are consistent across signed and unsigned networks in different domains. The improvement in performance is even more significant for a constrained version of the problem involving finding subgraphs containing a subset of query nodes. We also develop an event detection method for signed and unsigned networks based on subgraph density. We apply this to three different temporal datasets, and show that our method based on EGOSCAN significantly outperforms existing approaches and baseline methods in terms of the precision-recall tradeoff (by as much as 25-50% in some instances).

The next generation video coding standard, High Efficiency Video Coding (HEVC) has achieved great gains over the previous standards. However, the high efficiency brings huge computation complexity. In order to solve the problem of balance between complexity and performance, this paper presents a fast algorithm for the intra part in HEVC. The algorithm includes a pre-partitioning for CUs based on the edge density of the textures to simplify the partitioning and a new rough modes decision based on the most probable gradient angles to reduce candidate modes. Compared to HEVC reference software HM8.0, the proposed algorithm can save about 33% encoding time for all intra configurations with a slight loss of PSNR.

Among the most dangerous pollutants is PM2.5, which can directly pass through human lungs and move into the blood system. The use of nature-based solutions, such as increased vegetation cover in an urban landscape, is one of the possible solutions for reducing PM2.5 concentration. Our study objective was to understand the importance of green spaces in pollution reduction. Daily PM2.5 concentrations were manually collected at nine monitoring stations in Nanjing over a 534-day period from the air quality report of the China National Environmental Monitoring Center (CNEMC) to quantify the spatiotemporal change of PM2.5 concentration and its empirical relationship with vegetation and landscape structure in Nanjing. The daily average, minimum, and maximum PM2.5 concentrations from the nine stations were 74.0, 14.2, and 332.0 μg m−3, respectively. Out of the 534 days, the days recorded as “excellent” and “good” conditions were found mostly in the spring (30.7 %), autumn (25.6 %), and summer (24.5 %), with only 19.2 % of the days in the winter. High PM2.5 concentrations exceeding the safe standards of the CNEMC were recorded predominately during the winter (39.3–100.0 %). Our hypothesis that green vegetation had the potential to reduce PM2.5 concentration was accepted at specific seasons and scales. The PM2.5 concentration appeared very highly correlated (R 2 > 0.85) with green cover in spring at 1–2 km scales, highly correlated (R 2 > 0.6) in autumn and winter at 4 km scale, and moderately correlated in summer (R 2 > 0.4) at 2-, 5-, and 6-km scales. However, a non-significant correlation between green cover and PM2.5 concentration was found when its level was >75 μg m−3. Across the Nanjing urban landscape, the east and southwest parts had high pollution levels. Although the empirical models seemed significant for spring only, one should not devalue the importance of green vegetation in other seasons because the regulations are often complicated by vegetation, meteorological conditions, and human activities.

Let W 1,…,W n be independent random subsets of [m]={1,…,m}. Assuming that each W i is uniformly distributed in the class of d-subsets of [m] we study the uniform random intersection graph G s (n,m,d) on the vertex set {W 1,…W n }, defined by the adjacency relation: W i ∼W j whenever |W i ∩W j |≧s. For even n we show that as n,m→∞ the edge density threshold for the property that G s (n,m,d) contains a perfect matching is asymptotically the same as that for G s (n,m,d) being connected.

In this study we tested whether cotton fields contribute more than cereal fields to African elephant ( Loxodonta africana ) habitat loss through its effects on woodland fragmentation in the Mid-Zambezi Valley, Zimbabwe. In order to test this hypothesis, we first mapped cotton and cereal fields using MODIS remotely sensed data. Secondly, we analysed the effect of the area of cotton and cereal fields on woodland fragmentation using regression analysis. We then related the fragmentation indices, particularly edge density with elephant distribution data to test whether elephant distribution was significantly related with woodland fragmentation resulting from cotton fields. Our results showed that cotton fields contributed more to woodland fragmentation than cereal fields. In addition, results showed that the frequency of the African elephant increased where cotton fields were many and small relative to cereal fields. We concluded that cotton fields are the main driver of woodland fragmentation and therefore elephant habitat in the Mid-Zambezi Valley compared with cereal fields.

Turan's Theorem states that every graph of a certain edge density contains a complete graph $K^k$ and describes the unique extremal graphs. We give a similar Theorem for l-partite graphs. For large l, we find the minimal edge density $d^k_l$, such that every $\ell$-partite graph whose parts have pairwise edge density greater than $d^k_l$ contains a $K^k$. It turns out that $d^k_l=(k-2)/(k-1)$ for large enough l. We also describe the structure of the extremal graphs. For the case of triangles we show that $d^3_{13}=1/2$, disproving a conjecture by Bondy, Shen, Thomasse and Thomassen., Comment: 9 pages

Edge localized modes (ELMs), that are present in most tokamak H-(high confinement) modes, can cause significant damage to plasma facing components in fusion reactors. Controlling ELMs is considered necessary and hence it is vital to understand the underlying physics. The stability of ELMs is typically expressed in terms of the pressure gradient del p in the edge and the edge current density j(phi) Both del p and j(phi) are usually derived from profiles fitted to the measured edge density and temperature profiles, where for the calculation of j(phi) neoclassical theory is used. This paper presents direct measurements of the magnetic pitch angle gamma(m) evolution in the edge and the derived j(phi). These provide a method to validate the j(phi) as derived with neoclassical theory and they open up the possibility to find a complete, self-consistent set of edge profiles, that fit density, temperature and gamma(m) measurements, hence allowing for a more accurate stability analysis.

The aims of this research were to:(1) provide a theoretical basis for in-depth analysis of the influence of human activities on estuarine wetlands over a regional scale;(2) quantify the impact of anthropogenic interference on the landscape pattern index;and(3) establish a theoretical basis for the monitoring and evaluation of anthropogenic interference in estuarine wetlands.Based on aerial photographs from 1958,1970,and 1984(2 m resolution),and the spot5 image of 2008(5 m resolution),this study explored the spatiotemporal dynamics of hemeroby and the landscape pattern response scheme through hemeroby analysis,landscape pattern analysis,spatial patch analysis,and GIS spatial analysis in the Dayang estuary.The research evaluates: 1) the primary forcing landscape factors for spatial and temporal variation of hemeroby in an estuarine wetland;2) the response mechanism of landscape pattern index on the type of hemeroby;and 3) landscape indices associated with hemeroby in space.Results indicate that: 1) completely hemeroby regions increased from 4.16 km2 in 1958 to 9.16 km2 in 2008,while partially hemeroby regions increased from 115.82 km2 to 180.57 km2,and hemeroby regions declined from 291.23 km2 to 221.13 km2.Historically,hemeroby showed heterogeneous changes.The center of hemeroby moved gradually from land to ocean,and ocean aquaculture is the main driving factor in the change of hemeroby.Over time,hemeroby shows an upward trend,but the intensity of hemeroby changes are different at different historical periods,and hemeroby shows non-homogeneous characteristics at different historical periods.Comparing the change in different landscape types,we found paddy yield was the primary landscape type in 1958,aquaculture water in ocean and farmland showed upward increases in 1970,and after the 1980s aquaculture water in the ocean was the primary landscape type of human activities.Temporally,anthropogenic disturbance has led to an overall decrease in the number of patches(NP),edge density(ED),mean shape index(MSI),and area-weighted mean patch fractal dimension(AWMPFD) between 1958 and 2008.Through analysis of the landscape pattern index of different hemeroby types,we found that human disturbance has a certain effect on the landscape pattern index.Spatially,hemeroby is positively correlated with number of patches(NP),edge density(ED),and area-weighted mean patch fractal dimension(AWMPFD) in order of decreasing influence,while it is not significantly correlated with the mean shape index(MSI).The relationship between human disturbance activities and landscape pattern(four indices: number of patches(NP),edge density(ED),area-weighted mean patch fractal dimension(AWMPFD),mean shape index(MSI)) constituted differences in time and space within estuarine areas.Thus,heterogeneity and complexity of the landscape were greater in human disturbance areas over some time intervals,and heterogeneity and complexity of landscape showed declines in the continuing role of human disturbance with time.Therefore,the dimension of time and space should be distinguished in remote sensing monitoring responses of landscape patterns on human activities in estuarine wetlands.

We examined the effects of habitat change on Cerulean Warbler (Dendroica cerulea) populations at stops along Breeding Bird Survey (BBS) routes in the central Appalachians. We used aerial photographs to compare early (1967/1971), middle (1982/1985), and late (2000/2003) periods and compared 1992 and 2001 National Land Cover Data (NLCD). Mean Cerulean Warbler detections per stop decreased at 68 BBS stops between the early (0.05) and middle (0.01) time periods and their distribution became more restricted (15 vs. 3% of stops), but the amount of deciduous/mixed forest increased. Mean detections at 240 stops decreased from the middle (0.09) to the late (0.06) time periods, but the deciduous/mixed forest land cover and fragmentation metrics did not change. The amounts of deciduous/mixed forest, core forest area, and edge density in the NLCD analysis decreased from 1992 to 2001, whereas the amount of non-forest land cover increased. The number of Cerulean Warbler detections did not change (1992 = 0.08...

Water quality–landscape interaction were explored using multiple line regression in watershed, total stream corridor (200-m riparian buffer extending the entire stream length upstream of the site) and the local stream corridor (200-m riparian buffer extending 1000 m upstream of the site).The results showed that the catchment landscape characteristics appeared to have slightly greater influence on water quality than the total stream corridor and local stream corridor. The edge density of construction land and percent cultivated land had the greatest influence on water quality in watershed scale. The edge density of forest land and percent forest had the greatest influence on water quality in total stream corridor scale, but percent forest and PD had the greatest influence on water quality in the local stream corridor scale.

Fon-Der-Flaass (1988) presented a general construction that converts an arbitrary \(\vec C_4 \)-free oriented graph Γ into a Turan (3, 4)-graph. He observed that all Turan-Brown-Kostochka examples result from his construction, and proved the lower bound \(\tfrac{4} {9} \) (1 − o(1)) on the edge density of any Turan (3, 4)-graph obtainable in this way. In this paper we establish the optimal bound \(\tfrac{3} {7} \) (1 − o(1)) on the edge density of any Turan (3, 4)-graph resulting from the Fon-Der-Flaass construction under any of the following assumptions on the undirected graph G underlying the oriented graph Γ: (i) G is complete multipartite; (ii) the edge density of G is not less than \(\tfrac{2} {3} - \varepsilon \) for some absolute constant e > 0. We are also able to improve Fon-Der-Flaass’s bound to \(\tfrac{7} {{16}} \) (1 − o(1)) without any extra assumptions on Γ.

The application of lithium coatings on plasma facing components has been shown to profoundly affect plasma performance in the National Spherical Torus Experiment, improving energy confinement and eliminating edge-localized modes. The edge particle balance during these ELM-free discharges has been studied through 2-D plasma-neutrals modeling, constrained by measurements of the upstream plasma density and temperature profiles and the divertor heat flux and Dα emission. The calculations indicate that the reduction in divertor Dα emission with lithium coatings applied is consistent with a drop in recycling coefficient from R ∼ 0.98 to R ∼ 0.9. The change in recycling is not sufficient to account for the change in edge density profiles: interpretive modeling indicates similar transport coefficients within the edge transport barrier (D/χe ∼ 0.2/1.0 m2/s), but a widening of the barrier with lithium.