The large scale distribution of galaxies in the Shapley Supercluster

We present new results of our wide-field redshift survey of galaxies in a 182 square degree region of the Shapley Supercluster (SSC) based on observations with the FLAIR-II spectrograph on the UK Schmidt Telescope (UKST). In this paper we present new measurements to give a total sample of redshifts for 710 bright (R less than or equal to 16.6) galaxies, of which 464 are members of the SSC (8000 < υ < 18 000 km s(-1)). Our data reveal that the main plane of the SSC (upsilon approximate to 14 500 km s(-1)) extends further than previously realised, filling the whole extent of our survey region of 10 degrees by 20 degrees on the sky (35 Mpc by 70 Mpc, for H-0 = 75 km s(-1) Mpc(-1)). There is also a significant structure associated with the slightly nearer Abell 3571 cluster complex (upsilon approximate to 12 000 km s(-1)) with a caustic structure evident out to a radius of 6 Mpc. These galaxies seem to link two previously identified sheets of galaxies and establish a connection with a third one at (V) over bar = 15 000 km s(-1) near RA = 13(h). They also tend to fill the gap of galaxies between the foreground Hydra-Centaurus region and the more distant SSC. We calculate galaxy overdensities of 5.0+/-0.1 over the 182 square degree region surveyed and 3.3+.-0.1 in a 159 square degree region excluding rich clusters. Over the large region of our survey the inter-cluster galaxies make up 46 per cent of all galaxies in the SSC region and may contribute a similar amount of mass to the cluster galaxies.

Structure and dynamics of the Shapley Supercluster - Velocity catalogue, general morphology and mass

We present results of our wide-field redshift survey of galaxies in a 285 square degree region of the Shapley Supercluster (SSC), based on a set of 10 529 velocity measurements (including 1201 new ones) on 8632 galaxies obtained from various telescopes and from the literature. Our data reveal that the main plane of the SSC (v approximate to 14 500 km s(-1)) extends further than previous estimates, filling the whole extent of our survey region of 12 degrees by 30 degrees on the sky (30 x 75 h(-1) Mpc). There is also a connecting structure associated with the slightly nearer Abell 3571 cluster complex (v approximate to 12 000 km s(-1)). These galaxies seem to link two previously identified sheets of galaxies and establish a connection with a third one at v = 15 000 km s(-1) near RA = 13(h). They also tend to fill the gap of galaxies between the foreground Hydra-Centaurus region and the more distant SSC. In the velocity range of the Shapley Supercluster (9000 km s(-1) < cz < 18 000 km s(-1)), we found redshift-space overdensities with b(j) < 17.5 of similar or equal to 5.4 over the 225 square degree central region and similar or equal to 3.8 in a 192 square degree region excluding rich clusters. Over the large region of our survey, we find that the intercluster galaxies make up 48 per cent of the observed galaxies in the SSC region and, accounting for the different completeness, may contribute nearly twice as much mass as the cluster galaxies. In this paper, we discuss the completeness of the velocity catalogue, the morphology of the supercluster, the global overdensity, and some properties of the individual galaxy clusters in the Supercluster.

Large-scale velocity structures in the Horologium-Reticulum supercluster

We present 547 optical redshifts obtained for galaxies in the region of the Horologium-Reticulum supercluster (HRS) using the 6 degrees field (6dF) multifiber spectrograph on the UK Schmidt Telescope at the Anglo-Australian Observatory. The HRS covers an area of more than 12 degrees x 12 degrees on the sky centered at approximately alpha = 03(h)19(m), delta = 50 degrees 02'. Our 6dF observations concentrate on the intercluster regions of the HRS, from which we describe four primary results. First, the HRS spans at least the redshift range from 17,000 to 22,500 km s(-1). Second, the overdensity of galaxies in the intercluster regions of the HRS in this redshift range is estimated to be 2.4, or delta rho/(rho) over bar similar to 1: 4. Third, we find a systematic trend of increasing redshift along a southeast-northwest spatial axis in the HRS, in that the mean redshift of HRS members increases by more than 1500 km s(-1) from southeast to northwest over a 12 degrees region. Fourth, the HRS is bimodal in redshift with a separation of similar to 2500 km s(-1) (35 Mpc) between the higher and lower redshift peaks. This fact is particularly evident if the above spatial-redshift trend is fitted and removed. In short, the HRS appears to consist of two components in redshift space, each one exhibiting a similar systematic spatial-redshift trend along a southeast-northwest axis. Lastly, we compare these results from the HRS with the Shapley supercluster and find similar properties and large-scale features.

Redshifts and velocity dispersions of galaxy clusters in the horologium-reticulum supercluster

We present 118 new optical redshifts for galaxies in 12 clusters in the Horologium-Reticulum supercluster (HRS) of galaxies. For 76 galaxies, the data were obtained with the Dual Beam Spectrograph on the 2.3 m telescope of the Australian National University at Siding Spring Observatory. After combining 42 previously unpublished redshifts with our new sample, we determine mean redshifts and velocity dispersions for 13 clusters in which previous observational data were sparse. In 6 of the 13 clusters, the newly determined mean redshifts differ by more than 750 km s(-1) from the published values. In three clusters, A3047, A3109, and A3120, the redshift data indicate the presence of multiple components along the line of sight. The new cluster redshifts, when combined with other reliable mean redshifts for clusters in the HRS, are found to be distinctly bimodal. Furthermore, the two redshift components are consistent with the bimodal redshift distribution found for the intercluster galaxies in the HRS by Fleenor and coworkers.

A study of extended radio galaxies in the Shapley concentration core

Extended cluster radio galaxies show different morphologies com- pared to those found isolated in the field. Indeed, symmetric double radio galaxies are only a small percentage of the total content of ra- dio loud cluster galaxies, which show mainly tailed morphologies (e.g. O’Dea & Owen, 1985). Moreover, cluster mergers can deeply affect the statistical properties of their radio activity. In order to better understand the morphological and radio activity differences of the radio galaxies in major mergeing and non/tidal-merging clusters, we performed a multifrequency study of extended radio galax- ies inside two cluster complexes, A3528 and A3558. They belong to the innermost region of the Shapley Concentration, the most massive con- centration of galaxy clusters (termed supercluster) in the local Universe, at average redshift z ≈ 0.043. We analysed low frequency radio data performed at 235 and 610 MHz with Giant Metrewave Radio Telescope (GMRT) and we combined them with proprietary and literature observations, in order to have a wide frequency range (150 MHz to 8.4 GHz) to perform the spectral analysis. The low frequency images allowed us to carry out a detailed study of the radio tails and diffuse emission found in some cases. The results in the radio band were also qualitatively compared with the X-ray information coming from XMM-Newton observations, in order to test the interaction between radio galaxies and cluster weather. We found that the brightest central galaxies (BCGs) in the A3528 cluster complex are powerful and present substantial emission from old relativistic plasma characterized by a steep spectrum (α > 2). In the light of observational pieces of evidence, we suggest they are possible re-started radio galaxies. On the other hand, the tailed radio galaxies trace the host galaxy motion with respect to the ICM, and our find- ings is consistent with the dynamical interpretation of a tidal interaction (Gastaldello et al. 2003). On the contrary, the BCGs in the A3558 clus- ter complex are either quiet or very faint radio galaxies, supporting the hypothesis that clusters mergers quench the radio emission from AGN.

A Shapley value analysis to coordinate the formation of procurement

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Recent research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of Procurement Network Formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

The core and shapley value analysis for cooperative formation of procurement networks

Formation of high value procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions, where suppliers are intelligent and rational agents who act strategically. In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged We model the problem of Procurement Network Formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a stable and fair manner We first investigate the stability of such networks by examining the conditions under which the core of the game is non-empty. We then present a protocol, based on the extensive form game realization of the core, for forming such networks so that the resulting network is stable. We also mention a key result when the Shapley value is applied as a solution concept.

A Shapley Value-Based Approach to Discover Influential Nodes in Social Networks

Our study concerns an important current problem, that of diffusion of information in social networks. This problem has received significant attention from the Internet research community in the recent times, driven by many potential applications such as viral marketing and sales promotions. In this paper, we focus on the target set selection problem, which involves discovering a small subset of influential players in a given social network, to perform a certain task of information diffusion. The target set selection problem manifests in two forms: 1) top-k nodes problem and 2) lambda-coverage problem. In the top-k nodes problem, we are required to find a set of k key nodes that would maximize the number of nodes being influenced in the network. The lambda-coverage problem is concerned with finding a set of k key nodes having minimal size that can influence a given percentage lambda of the nodes in the entire network. We propose a new way of solving these problems using the concept of Shapley value which is a well known solution concept in cooperative game theory. Our approach leads to algorithms which we call the ShaPley value-based Influential Nodes (SPINs) algorithms for solving the top-k nodes problem and the lambda-coverage problem. We compare the performance of the proposed SPIN algorithms with well known algorithms in the literature. Through extensive experimentation on four synthetically generated random graphs and six real-world data sets (Celegans, Jazz, NIPS coauthorship data set, Netscience data set, High-Energy Physics data set, and Political Books data set), we show that the proposed SPIN approach is more powerful and computationally efficient. Note to Practitioners-In recent times, social networks have received a high level of attention due to their proven ability in improving the performance of web search, recommendations in collaborative filtering systems, spreading a technology in the market using viral marketing techniques, etc. It is well known that the interpersonal relationships (or ties or links) between individuals cause change or improvement in the social system because the decisions made by individuals are influenced heavily by the behavior of their neighbors. An interesting and key problem in social networks is to discover the most influential nodes in the social network which can influence other nodes in the social network in a strong and deep way. This problem is called the target set selection problem and has two variants: 1) the top-k nodes problem, where we are required to identify a set of k influential nodes that maximize the number of nodes being influenced in the network and 2) the lambda-coverage problem which involves finding a set of influential nodes having minimum size that can influence a given percentage lambda of the nodes in the entire network. There are many existing algorithms in the literature for solving these problems. In this paper, we propose a new algorithm which is based on a novel interpretation of information diffusion in a social network as a cooperative game. Using this analogy, we develop an algorithm based on the Shapley value of the underlying cooperative game. The proposed algorithm outperforms the existing algorithms in terms of generality or computational complexity or both. Our results are validated through extensive experimentation on both synthetically generated and real-world data sets.

Determining Top K Nodes in Social Networks using the Shapley Value

In this paper, we consider the problem of selecting, for any given positive integer k, the top-k nodes in a social network, based on a certain measure appropriate for the social network. This problem is relevant in many settings such as analysis of co-authorship networks, diffusion of information, viral marketing, etc. However, in most situations, this problem turns out to be NP-hard. The existing approaches for solving this problem are based on approximation algorithms and assume that the objective function is sub-modular. In this paper, we propose a novel and intuitive algorithm based on the Shapley value, for efficiently computing an approximate solution to this problem. Our proposed algorithm does not use the sub-modularity of the underlying objective function and hence it is a general approach. We demonstrate the efficacy of the algorithm using a co-authorship data set from e-print arXiv (www.arxiv.org), having 8361 authors.

A Shapley Value Analysis to Coordinate the Formation of Procurement Networks

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of procurement network formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

Influence limitation in multi-campaign social networks: A Shapley value based approach

We investigate the problem of influence limitation in the presence of competing campaigns in a social network. Given a negative campaign which starts propagating from a specified source and a positive/counter campaign that is initiated, after a certain time delay, to limit the the influence or spread of misinformation by the negative campaign, we are interested in finding the top k influential nodes at which the positive campaign may be triggered. This problem has numerous applications in situations such as limiting the propagation of rumor, arresting the spread of virus through inoculation, initiating a counter-campaign against malicious propaganda, etc. The influence function for the generic influence limitation problem is non-submodular. Restricted versions of the influence limitation problem, reported in the literature, assume submodularity of the influence function and do not capture the problem in a realistic setting. In this paper, we propose a novel computational approach for the influence limitation problem based on Shapley value, a solution concept in cooperative game theory. Our approach works equally effectively for both submodular and non-submodular influence functions. Experiments on standard real world social network datasets reveal that the proposed approach outperforms existing heuristics in the literature. As a non-trivial extension, we also address the problem of influence limitation in the presence of multiple competing campaigns.

Algoritmo de Gale-Shapley. Variaciones y alternativas

En esta memoria se trata el problema de encontrar un algoritmo que construya un emparejamiento entre dos grupos, entendiendo por emparejamiento la asignacion a cada individuo, de cada grupo, otro individuo. La situaci on inicial de la que parte el problema es la siguiente: Dos grupos, los proponentes y los propuestos, que est an formados por n individuos cada uno, siendo n la dimensi on del problema. El grupo de los proponentes es el encargado de hacer las propuestas a la hora de construir el emparejamiento. El grupo de los propuestos es el encargado de recibir y gestionar las propuestas a la hora de construir el emparejamiento. Cada individuo de cada grupo ordena en una lista, de manera decreciente, a individuos del otro grupo atendiendo a su preferencia a la hora de ser emparejado, a esta lista la llamaremos lista de preferencia del individuo, considerando el quedarse solo la opci on menos preferida de entre las aceptables. El objetivo del problema es crear un emparejamiento en el que cada pareja sea satisfactoria para los individuos que la crean en base a las preferencias de cada uno.

Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

We reconsider the following cost-sharing problem: agent i = 1,...,n demands a quantity xi of good i; the corresponding total cost C(x1,...,xn) must be shared among the n agents. The Aumann-Shapley prices (p1,...,pn) are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann-Shapley cost-sharing method assigns the cost share pixi to agent i. When goods come in indivisible units, we show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or merge their demands.

Evaluation de la valeur de Shapley et son application au calcul du pouvoir des provinces canadiennes dans le vote d'un projet de loi au parlement.

Rapport de recherche