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**1 - 6**of**6**### Local coordination and global congestion in random networks

"... Abstract This paper analyzes the impact of local and global interactions on individuals' action choices. Players are located in a network and interact with each other with perfect knowledge of their neighborhood and probabilistic knowledge of the complete network topology. Each player chooses ..."

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Abstract This paper analyzes the impact of local and global interactions on individuals' action choices. Players are located in a network and interact with each other with perfect knowledge of their neighborhood and probabilistic knowledge of the complete network topology. Each player chooses an action, from some finite set, which imposes an externality on their neighbors as well as an externality on the complete network. Players deal with two opposing forces: they obtain utility from sharing their choices with their neighbors (positive local externality) but suffer disutility from sharing the same choice with all members of the network (negative global externality). Economic and social phenomena exhibiting these features are: the adoption of cost-reducing innovations, clusters of firms, time schedule choices, the adoption of subcultures and fads, among others. We find the conditions for the existence of all Bayesian Nash equilibria and translate them to a characterization in terms of the main properties of the network topology. The balance between local satisfaction and global dissatisfaction partially explains the equilibrium outcome. The players who finally decide the type of equilibria are those that are either highly connected (hubs) or poorly connected (peripherals) to the others. On the one hand, hubs try to coordinate their action choices, which will depend on the perceived congestion. On the other, peripherals are only worried about congestion and play the less selected actions of the network. Some examples illustrate our main results as well as the failure of equilibirum existence for some congestion costs.

### Small-World Networks: Links with long-tailed distributions.

, 2008

"... Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing an AL depends on the chemical distance between the connecte ..."

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Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing an AL depends on the chemical distance between the connected sites. We assume a power-law probability distribution and study random walkers on the network, focussing especially on their probability of being at the origin. We connect the results to Lévy Flights, which follow from a mean field variant of our model. PACS numbers: 05.40Fb, 05.60.-k, 71.55.Jv. 1

### Geometry and Physics on w ∞ Orbits. ∗

, 1993

"... We apply the coadjoint orbit technique to the group of area preserving diffeomorphisms (APD) of a 2D manifold, particularly to the APD of the semi-infinite cylinder which is identified with w∞. The geometrical action obtained is relevant to both w gravity and 2D turbulence. For the latter we describ ..."

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We apply the coadjoint orbit technique to the group of area preserving diffeomorphisms (APD) of a 2D manifold, particularly to the APD of the semi-infinite cylinder which is identified with w∞. The geometrical action obtained is relevant to both w gravity and 2D turbulence. For the latter we describe the hamiltonian, which appears to be given by the Schwinger mass term, and discuss some possible developments within our approach. Next we show that the set of highest weight orbits of w ∞ splits into subsets, each of which consists of highest weight orbits of ¯wN for a given N. We specify the general APD geometric action to an orbit of ¯wN and describe an appropriate set of observables, thus getting an action and observables for ¯wN gravity. We compute also the Ricci form on the ¯wN orbits, what gives us the critical central charge of the ¯wN string, which appears to be the same as the one of the WN string.

### Major: Maternal/Child Nursing Thesis: Spanish Translation of an Instrument Measuring Parental Stressors in the Neonatal Intensive Care Unit

"... School of Nursing ..."

### Number Sense: The Underpinning Understanding for Early Quantitative Literacy

"... The fundamental meaning of Quantitative Literacy (QL) as the application of quantitative knowledge or reasoning in new/unfamiliar contexts is problematic because how we acquire knowledge, and transfer it to new situations, is not straightforward. This article argues that in the early development of ..."

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The fundamental meaning of Quantitative Literacy (QL) as the application of quantitative knowledge or reasoning in new/unfamiliar contexts is problematic because how we acquire knowledge, and transfer it to new situations, is not straightforward. This article argues that in the early development of QL, there is a specific corpus of numerical knowledge which learners need to integrate into their thinking, and to which teachers should attend. The paper is a rebuttal to historically prevalent (and simplistic) views that the terrain of early numerical understanding is little more than simple counting devoid of cognitive complexity. Rather, the knowledge upon which early QL develops comprises interdependent dimensions: Number Knowledge, Counting Skills and Principles, Nonverbal Calculation, Number Combinations and Story Problems- summarised as Number Sense. In order to derive the findings for this manuscript, a realist synthesis of recent Education and Psychology literature was conducted. The findings are of use not only when teaching very young children, but also when teaching learners who are experiencing learning difficulties through the absence of prerequisite numerical knowledge. As well, distilling fundamental quantitative knowledge for teachers to integrate into practice, the review emphasises that improved pedagogy is less a function of literal applications of reported interventions, on the grounds of perceived efficacy elsewhere, but based in refinements of teachers'

### I hereby recommend that this dissertation prepared under my

"... Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the aut ..."

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Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Downloaded 6-Mar-2016 01:44:30 Link to item