Friendship selection

We model the formation of friendships as repeated cooperation within a set of heterogeneous players. The model is built around three of the most important facts about friendship: friends help each other, there is reciprocity in the relationship and people usually have only a few friends. In our results, we explain how similarity between people affects the friendship selection. We also characterize the long-run friendship network and illustrate how friendships emerge given the random process by which people meet each other.     

Network analysis: Understanding consumers' choice in the film industry and predicting pre‐released weekly box‐office revenue

Predicting weekly box‐office demand is an important yet challenging question. For theater exhibitors, such information will enhance negotiation options with distributers, and assist in planning weekly movie portfolio mix. Existing literature focuses on forecasts of pre‐released total gross revenue or on weekly predictions based on first‐weeks observations. This work adds to the literature in modeling the entire demand structure forecasts by utilizing information on movie similarity network. Specifically, we draw upon the assumption that aggregated consumers' choice in the film industry is the main key in understanding movies' demand. Therefore, similar movies, in terms of audience appeal, should yield similar demand structure. In this work, we propose an automated technique that derives measurements of demand structure. We demonstrate that our technique enables to analyze different aspects of demand structure, namely, decay rate, time of first demand peak, per‐screen gross value at peak time, existence of second demand wave, and time on screens. We deploy ideas from variable selection procedures, to investigate the prediction power of similarity network on demand dynamics. We show that not only our models perform significantly better than models that discard the similarity network but are also robust to new sets of box‐office movies. Copyright © 2016 John Wiley & Sons, Ltd.     

A multilevel network study of the effects of delinquent behavior on friendship evolution

A multilevel approach is proposed to the study of the evolution of multiple networks. In this approach, the basic evolution process is assumed to be the same, while parameter values may differ between different networks. For the network evolution process, stochastic actor-oriented models are used, of which the parameters are estimated by Markov chain Monte Carlo methods. This is applied to the study of effects of delinquent behavior on friendship formation, a question of long standing in criminology. The evolution of friendship is studied empirically in 19 school classes. It is concluded that there is evidence for an effect of similarity in delinquent behavior on friendship evolution. Similarity of the degree of delinquent behavior has a positive effect on tie formation but also on tie dissolution. The last result seems to contradict current criminological theories, and deserves further study.     

An agent-based model of the development of friendship links within Facebook

This paper investigates how local preferences and social structural constraints might affect the development of the friendship network in Facebook. We do this by analyzing a dataset of an American university, Caltech, and by building an agent-based simulation for comparison. Several different, but plausible, processes of friendship network development are proposed in which the structural information of the growing network and the student preferences are taken into account. ‘Network formation based on personal preference and social structure’ matches the data best, and is thus the preferred hypothesis for the way that students add “friends” on Facebook.     

Proximity relations in the fuzzy relational database model

The fuzzy relational model of Buckles and Petry is a rigorous scheme for incorporating non-ideal or fuzzy information in a relational database. In addition to providing a consistent scheme for representing fuzzy information in the relational structure, the model possesses two critical properties that hold for classical relational databases. These properties are that no two tuples have identical interpretations and each relational operation has a unique result.The fuzzy relational model relies on similarity relations for each scalar domain in the fuzzy database. These relations are reflexive, symmetric, and max-min transitive. In addition to introducing fuzziness into the relational model, each similarity relation induces equivalence classes in its domain. It is the existence of these equivalence classes that provides the model with the important properties possessed by classical relational databases.In this paper, we extend the fuzzy relational database model of Buckles and Petry to deal with proximity relations for scalar domains. Since reflexivity and symmetry are the only constraints placed on proximity relations, they generalize the notion of similarity relations. We show that it is possible to induce equivalence classes from proximity relations; thus, the ‘nice’ properties of the fuzzy relational model of Buckles and Petry are preserved. Furthermore, the removal of the max-min transitivity restriction also provides database users with more freedom to express their value structures.     

Friendship Networks Through Time: An Actor-Oriented Dynamic Statistical Network Model

We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.     

Temporally coherent conservative visibility

Efficiently identifying polygons that are visible from a changing synthetic viewpoint is an important problem in computer graphics. Even with hardware support, simple algorithms like depth-buffering cannot achieve interactive frame rates when applied to geometric models with many polygons. However, a visibility algorithm that exploits the occlusion properties of the scene to identify a superset of visible polygons, without touching most invisible polygons, could achieve fast frame rates while viewing such models.In this paper, we present a new approach to the visibility problem. The novel aspects of our algorithm are that it is temporally coherent and conservative; for all viewpoints the algorithm overestimates the set of visible polygons. As the synthetic viewpoint moves, the algorithm reuses visibility information computed for previous viewpoints. It does so by computing visual events at which visibility changes occur, and efficiently identifying and discarding these events as the viewpoint changes. In essence, the algorithm implicitly constructs and maintains a linearized portion of an aspect graph, a data structure for representing visual events. We demonstrate that the visibility algorithm significantly accelerates rendering of several test models.     

The rise,current position and future direction of asset management in utility industries

Ensuring the fitness for purpose of the UK's utility networks is vital to both the country and the network owners. Replacing these networks would cost many hundreds if not thousands of billions of pounds. As these assets age, high levels of investment are now required to maintain a satisfactory performance level. For example, the annual investment needed for the UK's electricity distribution network is over £1 billion. Hence, efficiently managing these assets is extremely important and ‘asset management’ is the core of the infrastructure companies' businesses. This paper reviews what is meant by the term ‘asset management’ and why it has risen in importance over the last few decades. The current position of asset management modelling is then described before the likely key future developments are considered.     

Network structure,perception level,and participants' welfares

Based on a market consisting of one monopoly and several customers who are embedded in an economic network, we study how the different perception levels about the network structure affect the two kinds of participants' welfares, and then provide some good strategies for the monopoly to mine the information of the network structure. The above question is the embodiment of the “complex structure and its corresponding functions” question often mentioned in the field of complexity science. We apply a two‐stage game to solve for the optimal pricing and consumption at different perception levels of the monopoly and further utilize simulation analysis to explore the influence patterns. We also discuss how this theoretic model can be applied to a real world problem by introducing the statistical exponential random graph model and its estimation method. Further, the main findings have specific policy implications on uncovering network information and demonstrate that it is possible for the policy‐maker to design some win–win mechanisms for uplifting both the monopoly's profit and the whole customers' welfare at the same time. © 2014 Wiley Periodicals, Inc. Complexity 21: 349–362, 2015     

Visibility of Shafarevich-Tate Groups of Abelian Varieties

We investigate Mazur's notion of visibility of elements of Shafarevich-Tate groups of abelian varieties. We give a proof that every cohomology class is visible in a suitable abelian variety, discuss the visibility dimension, and describe a construction of visible elements of certain Shafarevich-Tate groups. This construction can be used to give some of the first evidence for the Birch and Swinnerton-Dyer conjecture for abelian varieties of large dimension. We then give examples of visible and invisible Shafarevich-Tate groups.     

The Dynamics of Closeness and Betweenness

Although both betweenness and closeness centrality are claimed to be important for the effectiveness of someone's network position, it has not been comprehensively studied which networks emerge if actors strive to optimize their centrality in the network in terms of betweenness and closeness. We study each of these centrality measures separately, but we also analyze what happens if actors value betweenness and closeness simultaneously. Network dynamics differ considerably in a scenario with either betweenness or closeness incentives compared with a scenario in which closeness and betweenness incentives are combined. There are not only more stable networks if actors’ betweenness and closeness are combined, but also these stable networks are less stylized.     

On a question of Sós about 3‐uniform friendship hypergraphs

The well‐known Friendship Theorem states that if G is a graph in which every pair of vertices has exactly one common neighbor, then G has a single vertex joined to all others (a “universal friend”). V. Sós defined an analogous friendship property for 3‐uniform hypergraphs, and gave a construction satisfying the friendship property that has a universal friend. We present new 3‐uniform hypergraphs on 8, 16, and 32 vertices that satisfy the friendship property without containing a universal friend. We also prove that if n ≤ 10 and n ≠ 8, then there are no friendship hypergraphs on n vertices without a universal friend. These results were obtained by computer search using integer programming. © 2008 Wiley Periodicals, Inc. J Combin Designs 16: 253–261, 2008     

A deductive approach to friendship networks

Based on a simple actor model, I derive theory concerning satisfied networks of close, reciprocal friendships. By satisfied networks I mean networks of actors who would be unhappier with more or fewer close friends. Deductions concern characteristics of such networks, such as that a satisfied network component (connected subnetwork) containing an actor with only one friend must be a dyad. I show that the model of satisfied friendship networks fits eight empirical friendship networks significantly better than a random model. Finally, I show the theory's usefulness by making five additional predictions, including two involving intervention.     

Infinite generalized friendship graphs

We give necessary and sufficient conditions for the existence of infinite generalized friendship graphs and show that there are 2° non-isomorphic ones of each admissible order c and chromatic number. Further we prove that such graphs and their complements are almost always regular of degree equal to the order and that various generalizations of the Friendship Theorem do not hold for infinite generalized friendship graphs.     

Prisoner's dilemma and clusters on small‐world networks

The structure of interaction plays an important role in the outcome of evolutionary games. This study investigates the evolution of stochastic strategies of the prisoner's dilemma played on structures ranging from lattices to small world networks. Strategies and payoffs are analyzed as a function of the network characteristics of the node they are playing on. Nodes with lattice‐like neighborhoods tend to perform better than the nodes modified during the rewiring process of the construction of the small‐world network. © 2007 Wiley Periodicals, Inc. Complexity 12:22–36, 2006     

灰色面板数据视域下的相似性和接近性关联度模型拓展

灰色面板数据包含研究对象诸多信息,由于数据类型和结构较为复杂,目前还没有测度其相似性和接近性的关联度模型,针对这一问题。首先,通过投影方法将灰色面板数据转化为样本关于指标的时间序列行为矩阵,矩阵每行为指标的时间序列;然后,定义一般灰数的距离测度和运算法则;最后,基于两折线间斜率与面积的视角,测度相似性和接近性关联系数。进而构建灰色面板数据的相似性和接近性关联度模型,并研究了该模型的性质。实例表明该模型在测度面板数据类型为一般灰数时的相似性和接近性方面具有良好的效果。     

Some asymptotic results for the combination of evidence problem

The combination of evidence problem is treated here as the construction of a posterior possibility function (or probability function, as a special case) describing an unknown state parameter vector of interest. This function exhibits the appropriate components contributing to knowledge of the parameter, including conditions or inference rules, relating the parameter with observable characteristics or attributes, and errors or confidences of observed or reported data. Multivalued logic operators - in particular, disjunction, conjunction, and implication operators, where needed – are used to connect these components and structure the posterior function. Typically, these operators are well-defined for only a finite number of arguments. Yet, often in the problem at hand, a number of observable attributes represent probabilistic concepts in the form of probability density functions. This occur, for example, for attributes representing ordinary numerical measurements- as opposed to those attributes representing linguistic-based information, where non-probabilistic possibility functions are used. Thus the problem of discretization of probabilistic attributes arises, where p.d.f.'s are truncated and discretized to probability functions. As the discretization process becomes finer and finer, intuitively the posterior function should better and better represent the information available. Hence, the basic question that arises is: what is the limiting behavior of the resulting posterior functions when the level of discretization becomes infinitely fine, and, in effect, the entire p.d.f.'s are used?It is shown in this paper that under mild analytic conditions placed upon the relevant functions and operators involved, nontrivial limits in the above sense do exist and involve monotone transforms of statistical expectations of functions of random variable corresponding to the p.d.f.'s for the probabilistic attributes.     

Coverage problems and visibility regions on topographic surfaces

The viewshed of a point on an irregular topographic surface is defined as the area visible from the point. The area visible from a set of points is the union of their viewsheds. We consider the problems of locating the minimum number of viewpoints to see the entire surface, and of locating a fixed number of viewpoints to maximize the area visible, and possible extensions. We discuss alternative methods of representing the surface in digital form, and adopt a TIN or triangulated irregular network as the most suitable data structure. The space is tesselated into a network of irregular triangles whose vertices have known elevations and whose edges join vertices which are Thiessen neighbours, and the surface is represented in each one by a plane. Visibility is approximated as a property of each triangle: a triangle is defined as visible from a point if all of its edges are fully visible. We present algorithms for determination of visibility, and thus reduce the problems to variants of the location set covering and maximal set covering problems. We examine the performance of a variety of heuristics.     

Friendship Two-Graphs

A friendship graph is a graph in which every two distinct vertices have exactly one common neighbor. All finite friendship graphs are known, each of them consists of triangles having a common vertex. We extend friendship graphs to two-graphs, a two-graph being an ordered pair G = (G ₀, G ₁) of edge-disjoint graphs G ₀ and G ₁ on the same vertex-set V(G ₀) = V(G ₁). One may think that the edges of G are colored with colors 0 and 1. In a friendship two-graph, every unordered pair of distinct vertices u, v is connected by a unique bicolored 2-path. The pairs of adjacency matrices of friendship two-graphs are solutions to the matrix equation AB + BA = J − I, where A and B are n × n symmetric 0 − 1 matrices, J is an n × n matrix with every entry being 1, and I is the identity n × n matrix. We show that there is no finite friendship two-graph with minimum vertex degree at most two. However, we construct an infinite such graph, and this construction can be extended to an infinite (uncountable) family. Also, we find a finite friendship two-graph, conjecture that it is unique, and prove this conjecture for the two-graphs that have a dominating vertex.