Social Learning in Social Networks

This paper analyzes a model of social learning in a social network. Agents decide whether or not to adopt a new technology with unknown payoffs based on their prior beliefs and the experiences of their neighbors in the network. Using a mean-field approximation, I prove that the diffusion process always has at least one stable equilibrium, and I examine the dependence of the set of equilibria on the model parameters and the structure of the network. In particular, I show how first and second order stochastic dominance shifts in the degree distribution of the network impact diffusion. I find that the relationship between equilibrium diffusion levels and network structure depends on the distribution of payoffs to adoption and the distribution of agents' prior beliefs regarding those payoffs, and I derive the precise conditions characterizing those relationships

The geometry of reaction norms yields insights on classical fitness functions for Great Lakes salmon.

Life history theory examines how characteristics of organisms, such as age and size at maturity, may vary through natural selection as evolutionary responses that optimize fitness. Here we ask how predictions of age and size at maturity differ for the three classical fitness functions-intrinsic rate of natural increase r, net reproductive rate R0, and reproductive value Vx-for semelparous species. We show that different choices of fitness functions can lead to very different predictions of species behavior. In one's efforts to understand an organism's behavior and to develop effective conservation and management policies, the choice of fitness function matters. The central ingredient of our approach is the maturation reaction norm (MRN), which describes how optimal age and size at maturation vary with growth rate or mortality rate. We develop a practical geometric construction of MRNs that allows us to include different growth functions (linear growth and nonlinear von Bertalanffy growth in length) and develop two-dimensional MRNs useful for quantifying growth-mortality trade-offs. We relate our approach to Beverton-Holt life history invariants and to the Stearns-Koella categorization of MRNs. We conclude with a detailed discussion of life history parameters for Great Lakes Chinook Salmon and demonstrate that age and size at maturity are consistent with predictions using R0 (but not r or Vx) as the underlying fitness function

The power of teams that disagree:team formation in large action spaces

Recent work has shown that diverse teams can outperform a uniform team made of copies of the best agent. However, there are fundamental questions that were never asked before. When should we use diverse or uniform teams? How does the performance change as the action space or the teams get larger? Hence, we present a new model of diversity, where we prove that the performance of a diverse team improves as the size of the action space increases. Moreover, we show that the performance converges exponentially fast to the optimal one as we increase the number of agents. We present synthetic experiments that give further insights: even though a diverse team outperforms a uniform team when the size of the action space increases, the uniform team will eventually again play better than the diverse team for a large enough action space. We verify our predictions in a system of Go playing agents, where a diverse team improves in performance as the board size increases, and eventually overcomes a uniform team

Social Learning in Social Networks

This paper analyzes a model of social learning in a social network. Agents decide whether or not to adopt a new technology with unknown payoffs based on their prior beliefs and the experiences of their neighbors in the network. Using a mean-field approximation, we prove that the diffusion process always has at least one stable equilibrium, and we examine the dependence of the set of equilibria on the model parameters and the structure of the network. In particular, we show how first and second order stochastic dominance shifts in the degree distribution of the network impact diffusion. We find that the relationship between equilibrium diffusion levels and network structure depends on the distribution of payoffs to adoption and the distribution of agents' prior beliefs regarding those payoffs, and we derive the precise conditions characterizing those relationships. For example, in contrast to contagion models of diffusion, we find that a first order stochastic dominance shift in the degree distribution can either increase or decrease equilibrium diffusion levels depending on the relationship between agents' prior beliefs and the payoffs to adoption. Surprisingly, adding more links can decrease diffusion even when payoffs from the new technology exceed those of the status quo in expectation.

Tipping points

Shaun Murray, ENIAtype The Tipping Points in architecture and design as an ineffaceable illumination as materialism ossifies architecture in boundless creativity as a mirror of our age. This issue will challenge the idea of tipping points through three factions. Firstly, Bifurcations – on how does the tipping point phenomena arise and was there a pinch point, break-off as too where the tipping point occurred. Secondly, Fault lines – on what did the tipping point leave exposed? Was it an open chasm? Is there a shift between two factions that caused this tipping point? Thirdly, Consequences – on what are the consequences of the tipping point? Was there an impact on the current condition? Each contribution to this issue will offer a different perspective on current tipping points in fashion, designing architecture and making models, computing in architecture, post-cinema and communication design through to the practicing of architecture and the allure of objects that cause fault lines in our relational ecologies

The geometry of reaction norms yields insights on classical fitness functions for Great Lakes salmon.

Life history theory examines how characteristics of organisms, such as age and size at maturity, may vary through natural selection as evolutionary responses that optimize fitness. Here we ask how predictions of age and size at maturity differ for the three classical fitness functions-intrinsic rate of natural increase r, net reproductive rate R0, and reproductive value Vx-for semelparous species. We show that different choices of fitness functions can lead to very different predictions of species behavior. In one's efforts to understand an organism's behavior and to develop effective conservation and management policies, the choice of fitness function matters. The central ingredient of our approach is the maturation reaction norm (MRN), which describes how optimal age and size at maturation vary with growth rate or mortality rate. We develop a practical geometric construction of MRNs that allows us to include different growth functions (linear growth and nonlinear von Bertalanffy growth in length) and develop two-dimensional MRNs useful for quantifying growth-mortality trade-offs. We relate our approach to Beverton-Holt life history invariants and to the Stearns-Koella categorization of MRNs. We conclude with a detailed discussion of life history parameters for Great Lakes Chinook Salmon and demonstrate that age and size at maturity are consistent with predictions using R0 (but not r or Vx) as the underlying fitness function