Asymptotic learning on Bayesian social networks

We study a standard model of economic agents on the nodes of a social network graph who learn a binary “state of the world” $S$ , from initial signals, by repeatedly observing each other’s best guesses. Asymptotic learning is said to occur on a family of graphs $G_n = (V_n,E_n)$ with $|V_n| \rightarrow \infty $ if with probability tending to $1$ as $n \rightarrow \infty $ all agents in $G_n$ eventually estimate $S$ correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.     

Robust learning in social networks via matrix scaling

The influence vanishing property in social networks states that the influence of the most influential agent vanishes as society grows. Removing this assumption causes a failure of learning of boundedly rational dynamics. We suggest a boundedly rational methodology that leads to learning in almost all networks. The methodology adjusts the agent's weights based on the Sinkhorn-Knopp matrix scaling algorithm. It is a simple, local, Markovian, and time-independent methodology that can be applied to multiple settings.     

House exchange and residential segregation in networks

This paper considers a Schelling model in an arbitrary fixed network where there are no vacant houses. Agents have preferences either for segregation or for mixed neighborhoods. Utility is non-transferable. Two agents exchange houses when the trade is mutually beneficial. We find that an allocation is stable when for two agents of opposite-color each black (white) agent has a higher proportion of neighbors who are black (white). This result holds irrespective of agents’ preferences. When all members of both groups prefer mixed neighborhoods, an allocation is also stable provided that if an agent belongs to the minority (majority), then any neighbor of opposite-color is in a smaller minority (larger majority).     

Viability in dynamic social networks

Two examples, Sampson's monks and Padgett and Ansell’ Florentines, illustrate the viability approach of dynamic networks. Notably, the relationship with centrality is studied. Historical processes involving networks are discussed.

Networks are presented as controls in controlled dynamic systems. Viability is the property for a state x that there exists a trajectory starting from x and satisfying the constraints until the time horizon. To obtain this, connection matrices must be selected at each time and each visited state among a specific set, the regulation map, which is carefully defined and built.     

Scale-invariant learning and convolutional networks

Multinomial logistic regression and other classification schemes used in conjunction with convolutional networks (convnets) were designed largely before the rise of the now standard coupling with convnets, stochastic gradient descent, and backpropagation. In the specific application to supervised learning for convnets, a simple scale-invariant classification stage is more robust than multinomial logistic regression, appears to result in somewhat lower errors on several standard test sets, has similar computational costs, and features precise control over the actual rate of learning. “Scale-invariant” means that multiplying the input values by any nonzero real number leaves the output unchanged.     

Activation clustering in neural and social networks

Questions related to the evolution of the structure of networks have received recently a lot of attention in the literature. But what is the state of the network given its structure? For example, there is the question of how the structures of neural networks make them behave? Or, in the case of a network of humans, the question could be related to the states of humans in general, given the structure of the social network. The models based on stochastic processes developed in this article, do not attempt to capture the fine details of social or neural dynamics. Rather they aim to describe the general relationship between the variables describing the network and the aggregate behavior of the network. A number of nontrivial results are obtained using computer simulations. © 2005 Wiley Periodicals, Inc. Complexity 10: 42–50, 2005     

New dominating sets in social networks

Motivated by applications in social networks, a new type of dominating set has been studied in the literature. In this paper, we present results regarding the complexity and approximation in general graphs.     

Unanimous opinions in social influence networks

In this paper, I show that persons reach unanimous opinions even when they have different initial opinions and different social influences in social influence networks. Friedkin and Johnsen introduced a model of social influence networks, and identified conditions for initially diverse opinions to converge. However, they did not examine conditions of “unanimous” convergence. Hence, I provide sufficient conditions of such unanimous consensus by focusing on three typical but conflicting social influences: the equal influence, the influence of the lowest opinion, and no influence. I show that unanimous opinions occur even when persons have antagonistic social influences such as the equal influence and the influence of the lowest opinion. I also demonstrate that the most cooperative type is the equal influence, but the most central type is the no influence.     

Knowledge management in semantic social networks

An object-oriented model of semantic social networks is proposed and formally analyzed. Methods for project, role, and team management based on the semantic model are defined and implemented in $\mathfrak{n}\mathfrak{i}\mathbf{K}\mathfrak{l}\mathfrak{a}\mathfrak{s}$ , a semantic wiki language based on frame logic developed by the author. The new approach to semantic social networks allows dynamic change of social network semantics and the establishment of the well known fishnet organization in a social network. In the end possible applications to knowledge management are presented.     

Generating and analyzing spatial social networks

In this paper, we propose a class of models for generating spatial versions of three classic networks: Erdös-Rényi (ER), Watts-Strogatz (WS), and Barabási-Albert (BA). We assume that nodes have geographical coordinates, are uniformly distributed over an m × m Cartesian space, and long-distance connections are penalized. Our computational results show higher clustering coefficient, assortativity, and transitivity in all three spatial networks, and imperfect power law degree distribution in the BA network. Furthermore, we analyze a special case with geographically clustered coordinates, resembling real human communities, in which points are clustered over k centers. Comparison between the uniformly and geographically clustered versions of the proposed spatial networks show an increase in values of the clustering coefficient, assortativity, and transitivity, and a lognormal degree distribution for spatially clustered ER, taller degree distribution and higher average path length for spatially clustered WS, and higher clustering coefficient and transitivity for the spatially clustered BA networks.     

Time-cost trade-off analysis of project networks in fuzzy environments

This paper proposes a novel approach for time-cost trade-off analysis of a project network in fuzzy environments. Different from the results of previous studies, in this paper the membership function of the fuzzy minimum total crash cost is constructed based on Zadeh’s extension principle and fuzzy solutions are provided. A pair of two-level mathematical programs parameterized by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy minimum total crash cost at α. By enumerating different values of α, the membership function of the fuzzy minimum total crash cost is constructed, and the corresponding optimal activity time for each activity is also obtained at the same time. An example of time-cost trade-off problem with several fuzzy parameters is solved successfully to demonstrate the validity of the proposed approach. Since the minimum total crash cost is expressed by a membership function rather than by a crisp value, the fuzziness of parameters is conserved completely, and more information is provided for time-cost trade-off analysis in project management. The proposed approach also can be applied to time-cost trade-off problems with other characteristics.     

Social roles and the evolution of networks in extreme and isolated environments

This article reports on the evolution of network structure as it relates to formal and informal social roles in well-bounded, isolated groups. Research was conducted at the Amundsen-Scott South Pole Station. Data were collected on crewmembers' networks of social interaction over each of three winter-over periods, when the station is completely isolated. In addition, data were collected on the informal roles played by crewmembers (e.g., instrumental leadership, expressive leadership). The study found that globally coherent networks in winter-over groups were associated with group consensus on the presence of critically important informal social roles (e.g., expressive leadership) where global coherence is the extent to which a network forms a single group composed of a unitary core and periphery as opposed to being factionalized into two or more subgroups. Conversely, the evolution of multiple subgroups was associated with the absence of consensus on critical informal social roles, above all the critically important role of instrumental leader.     

Social roles and the evolution of networks in extreme and isolated environments

This article reports on the evolution of network structure as it relates to formal and informal social roles in well-bounded, isolated groups. Research was conducted at the Amundsen-Scott South Pole Station. Data were collected on crewmembers' networks of social interaction over each of three winter-over periods, when the station is completely isolated. In addition, data were collectedon the informal roles played by crewmembers (e.g., instrumental leadership, expressive leadership). The study found that globally coherent networks in winter-over groups were associated with group consensus on the presence of critically important informal social roles (e.g., expressive leadership)where global coherence is the extent to which a network forms a single group composed of a unitary core and periphery as opposed to being factionalized into two or more subgroups. Conversely, the evolution of multiple subgroups was associated with the absence of consensus on critical informal social roles, above all the critically important role of instrumental leader.     

Microfinance in Sub-Saharan Africa: social efficiency,financial efficiency and institutional factors

Central European Journal of Operations Research - There are two natural efficiency measures associated with microfinance banking: social efficiency, measuring to what extent the micro-capital...     

Structural equivalence of individuals in social networks

The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ‘functorial’ mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the ‘theory of categories,’ a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach.     

How behaviors spread in dynamic social networks

In this paper, we explore how decentralized local interactions of autonomous agents in a network relate to collective behaviors. Earlier work in this area has modeled social networks with fixed agent relations. We instead focus on dynamic social networks in which agents can rationally adjust their neighborhoods based on their individual interests. We propose a new connection evaluation theory, the Highest Weighted Reward (HWR) rule: agents dynamically choose their neighbors in order to maximize their own utilities based on rewards from previous interactions. We prove that, in the two-action pure coordination game, our system would stabilize to a clustering state in which all relationships in the network are rewarded with an optimal payoff. Our experiments verify this theory and also reveal additional interesting patterns in the network.     

Approximation by neural networks and learning theory

We consider the problem of Learning Neural Networks from samples. The sample size which is sufficient for obtaining the almost-optimal stochastic approximation of function classes is obtained. In the terms of the accuracy confidence function, we show that the least-squares estimator is almost-optimal for the problem. These results can be used to solve Smale's network problem.     

Connecting social perspectives on mathematics teacher education in online environments

This article explores theoretical issues underpinning the design and use of online learning environments in mathematics teacher education. It considers the contribution of social theories of learning to conceptualising technology-mediated interaction, focusing specifically on community of practice models and the notion of digital mathematics performance. The article begins by introducing social perspectives on collaboration. Because of the diversity of theories within this broad research paradigm, the next section outlines networking strategies that have been proposed for connecting theoretical approaches. There follows a discussion of studies that illustrate the community of practice and performance-based approaches to research into online mathematics teacher education. The main purpose of the article is to show how these approaches could be connected by examining the same teaching and learning scenarios through different theoretical lenses. The final section identifies implications of this exploration for the design of online learning environments in mathematics teacher education to capitalise on the affordances of Web-based technologies.     

Inferring missing links in partially observed social networks

Determining the pattern of links within a large social network is often problematic due to the labour-intensive nature of the data collection and analysis process. With constrained data collection capabilities it is often only possible to either make detailed observations of a limited number of individuals in the network, or to make fewer observations of a larger number of people. Previously we have shown how detailed observation of a small network can be used, which infer where in the network previously unconnected individuals are likely to fit, thereby attempting to predict network growth as new people are considered for inclusion. Here, by contrast, we show how social network topology can be inferred following a limited observation of a large network. Essentially the issue is one of inferring the presence of links that are missed during a constrained data collection campaign on the network. It is particularly difficult to infer network structures for those organizations that actively seek to remain covert and undetected. However, it is often very useful to know if two given individuals are likely to be connected even though limited surveillance effort yields no evidence of a link. Specifically, we show how a statistical inference technique can be used to successfully predict the existence of links that are missed during network sampling. The procedure is demonstrated using network data obtained from open source publications.