Seminar Abstracts - 2010

Tuesday, September 14, 2010
David Rand, Harvard
"Reward, punishment and the evolution of cooperation"
5670 Haven Hall *Note room change*

Cooperation, where one individual incurs a cost to benefit others, is a fundamental aspect of all levels of the natural world as well as human society. Yet cooperation poses a challenge to evolutionairy biologists and social scientists: How can the fundamentally selfish process of natural selection favor "altruistic" cooperation, and why are humans, as strategic decision-makers, often willing to help others at a cost to themselves? In my talk, I will explore this question using a combination of evolutionary computer simulations and behavioral experiments involving economic games. I will focus particularly on the role of punishment and reward in discouraging free-riding and fostering cooperation. In the realistic context of repeated interactions where reputation is in play, I show that denial of reward promotes cooperation as effectively as costly punishment. Yet costly punishment is destructive and reduces the payoffs of both players, while denial of reward does not. Thus the use of costly punishment is detrimental to both the individual punisher and to the group as a whole. These results raise serious questions about the role of costly punishment in promoting cooperation, and emphasize the importance of developing opportunities for constructive interactions between individuals to help prevent "tragedies of the commons".

Tuesday, September 21, 2010
Evelyn Sander, Mathematics, George Mason University
"Connecting period-doubling cascades to chaos"

The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a parameter often reveal a complicated intermingling of period- doubling cascades and chaos. This talk describes recent research in which we are able to link cascades and chaos in a new way.

Period doubling can be studied at three levels of complexity. The first is an individual period-doubling bifurcation. The second is an infinite collection of period doublings that are connected together by periodic orbits in a pattern called a cascade. The third level of complexity involves a transition from simple behavior at one parameter value through infinitely-many cascades until it reaches a larger parameter value at which there is chaos. In this talk, we describe recent work using topological methods showing that often virtually all (i.e., all but finitely many) ``regular'' periodic orbits in the chaotic regime are each connected to exactly one cascade by a path of regular periodic orbits; and virtually all cascades are either paired -- connected to exactly one other cascade, or solitary -- connected to exactly one regular periodic orbit in the chaotic regime Furthermore, solitary cascades are robust to large perturbations. Hence the investigation of infinitely many cascades is essentially reduced to studying the regular periodic orbits of a one-parameter family. Examples discussed include the forced-damped pendulum and the double-well Duffing equation. This talk will not assume prior knowledge of either topology or cascades.

Tuesday, September 28, 2010
Dan Lathrop, University of Maryland
"Quantum Turbulence"

Long range quantum order underlies a number of related physical phenomena including superfluidity, superconductivity, the Higgs mechanism, Bose-Einstein condensates, and spin systems. While superfluidity in Helium-4 was one of the earliest discovered of these, it is not the best understood, owing to the strong interactions (making theoretical progress difficult) and the lack of local experimental probes. Approximately three years ago, our group discovered that micron-sized hydrogen particles may be used to label quantized vortices in flows of superfluid helium. Particles not on vortices trace the motion of the normal component of the superfluid. This ability has given a new perspective on an old subject. By directly observing and tracking these particles, we have directly confirmed the two-fluid model, observed vortex rings and reconnection, characterized thermal counterflows, and taken local observations of the very peculiar nature of quantum turbulence. One of many surprising observations is the existence of power law tails in the probability distribution of velocity for these flows. That is easily understood as stemming from the reconnection on quantized vortices. Our summary conclusions are that quantum turbulence is dominated by reconnection and ring vortex collapse, making turbulence in a quantum liquid distinct from classical turbulence of a Newtonian fluid.

Tuesday, October 5, 2010
Prof. L. Mahadevan, Applied Mathematics, Harvard University
"On growth and form: geometry, physics and biology"

The growth and form of a soft solid pose a range of problems that combine aspects of mathematics, physics and biology. I will discuss some examples of growth and form in the plant and animal world motivated by qualitative and quantitative biological observations. The problems include the shape of a polymerizing microtubule, and that of a freely growing pollen tube, the undulating fringes on a leaf or petal, and the loops in the vertebrate gut . In each case, we will see how a combination of biological and physical experiments, mathematical models and simple computations allow us to unravel the basis for the diversity and complexity of biological form, while suggesting a rich new lode of problems in geometry and analysis.

Tuesday, October 12, 2010
Dan McShea, Duke University
"Biology's First Law"

In modern evolutionary theory, natural selection explains adaptation, the fit of organisms to their environments, but what explains complexity? What explains the fact that modern organisms consist of many different part types, while ancient organisms were simpler? Drawing on recent work with my colleague Robert Brandon (Philosophy, Duke), I argue that there is a spontaneous tendency for parts in organisms to differentiate, a tendency that does not depend on natural selection and could in principle be opposed by selection. This tendency is predicted by what we call the Zero Force Evolutionary Law, or ZFEL. The law is analogous to Newton's First Law in that it tells us what to expect when no forces act. Newton's First Law says that when no forces act, velocities remain unchanged. The ZFEL says that when no forces act, complexity tends to increase. In this talk, I will: 1) explain the logic behind the ZFEL; 2) argue that the ZFEL applies universally, to life at all times, everywhere it occurs; 3) defend the understanding of complexity on which the law is based; 4) offer a simple empirical test; and 5) show how the ZFEL points to a new way to understand the history of complexity change in evolution.

Monday, October 25, 2010
Joel Miller, Harvard School of Public Health
"Edge compartmental infectious disease models"

The structure of social interactions along which disease spreads can be represented using a network. When we investigate disease spreading in a network we find that many of the assumptions of mass action mixing fail. Individuals with many contacts tend to become infected earlier, and in turn infect more individuals, leading to faster initial growth. However, the remaining population has fewer contacts than average, and so the growth rate decreases more rapidly and the epidemic eventually dies out sooner than mass action predicts. Unfortunately mathematical models of infectious disease tend to require (arbitrarily) many differential equations. Recent work by Erik Volz (SIR dynamics in random networks with heterogeneous connectivity, JMB 2008) showed that it is possible to capture the dynamics exactly with a low-dimensional system. My own work (A note on a paper by Erik Volz: SIR dynamics in random networks, JMB 2010) has shown that it is possible to simplify this derivation and in so doing arrive at an even simpler system. Our more recent unpublished work simplifies the derivation further, and allows easy generalization to a wide range of (SI or SIR) diseases and population structures, including populations whose contacts change in time. The key simplification comes from focusing our attention to the fraction of edges that connect to susceptible, infected, or recovered individuals rather than the fraction of the population with given infection status. I will show how to derive these systems and compare the resulting predictions with simulation.

Tuesday, October 26, 2010
Eric Smith, Santa Fe Institute
"Opportunities in quantitative historical linguistics and lexical semantics"

Historical linguists identify relations due to descent among modern languages, and reconstruct past language forms, using a system known as the Classical Comparative Method (CCM). Like most systems in linguistics, the CCM is rule-based and non-quantitative, loosely akin to formal logic. The frontiers of deep reconstruction, however, will require the interpretation of heterogeneous evidence, much of it diffuse within the lexicon and phonology. Only with properly-formulated likelihood or Bayesian probability methods do we stand a chance of interpreting such diffuse signatures. I will describe recent trends of work in quantitative and computational historical reconstruction, and the enormous range of opportunities that exist, to create a quantitative historical linguistics. I will discuss how far one can get by plugging language data into molecular phylogeny codes, the systematic errors that result, and the need to base systematics on the proper probability model for language change. This will bring us to the role of forward models in maximum-likelihood and Bayesian algorithms, and to the intriguing problem of what meanings are, how words relate to them, and how they may be quantitatively compared across languages and through time.

Tuesday, November 2, 2010
Damon Centola, MIT
"The Spread of Health Behaviors in Social Networks"

The strength of weak ties is that they tend to be long - they connect socially distant locations. Research on "small worlds" shows that these long ties can dramatically reduce the "degrees of separation" of a social network, thereby allowing ideas and behaviors to rapidly diffuse. However, I show that the opposite can also be true. Increasing the frequency of long ties in a clustered social network can also inhibit the diffusion of collective behavior across a population. For health related behaviors that require strong social reinforcement, such as dieting, exercising, smoking cessation, or even condom use, successful diffusion may depend primarily on the width of bridges between otherwise distant locations, not just their length. I present results from an Internet experiment that uses artificially structured on-line communities to empirically test the effects of social network topology on the diffusion of health behavior.

Tuesday, November 9, 2010
Keith Julien, University of Colorado/Boulder

"Reduced Models for Astrophysical Accretion Disks"

Astrophysical accretion disks are known and observed to form about massivecentral objects (e.g. young stars and black holes). The primary forcebalance within these disks results in Keplerian velocity profiles that areknown to be stable to pure hydrodynamic perturbations. However, inferredaccretion rates onto the central objects indicate enhanced transport ratesthat must result from turbulent processes. Turbulent processes are alsorequired to aid planetary formation on timescales shorter than theexistence time for protoplanetary disks. In this talk I will overview someof our recent modeling efforts addressing these issues.

The magnetorotational instability is a linear instability in the presenceof an imposed magnetic field and shear (or differential rotation) in anelectrically conducting fluid. Presently, this instability serves as theleading mechanism for the efficient transport of angular momentumnecessary for turbulent accretion in astrophysical disks. The level ofangular momentum transport is determined by the saturated state ofsustained turbulence generated by the instability. However, the mechanism of nonlinear saturation of this instability is not well understood. Here,I shall discuss an asymptotically exact nonlinear feedback mechanismleading to saturation.

For cold disks such as protoplanetary disks, the magnetorotationalinstability is absent. One possible enhancement mechanism is baroclinicvortex formation. I will provide an overview of our reduced modelingefforts in this situation.

Tuesday, November 16, 2010
Mark Dykman, Michigan State University
"Fragility, Scaling, and Control of the Rates of Rare Events"

We show that the rates of rare events display several universal, model-independent features. They include scaling behavior of the switching rates, which occurs close to bifurcation points where the number of stable states of the system changes. Another feature is fragility. Here, the logarithm of the rate calculated in the limit where the control parameter goes to zero differs from the result obtained for the parameter equal to zero. The occurrence of fragility will be illustrated using the problem of extinction in a broadly used model of population dynamics. We will also discuss the recent demonstration that, in a rare event like fluctuation-induced switching, the system follows a well-defined trajectory. The occurrence of such a trajectory makes it possible to control the rates with exponential efficiency. An example that will be discussed is control of disease extinction with limited vaccine.

Tuesday, December 7, 2010
Comsa Shalizi, Statistics Dept., Carnegie Melon University
"Homophily, Contagion and Confounding: Pick Any Three"

One person's behavior can often be predicted from that of their neighbors in a social network. This is sometimes explained by homophily, the tendency to form social ties with others because we resemble them. It is also sometimes explained by social contagion or social influence, the tendency to act like someone because they are our neighbor. We show that, generically, these two mechanisms are confounded with each other, and with the causal effect of an individual's attributes on their behavior. Distinguishing them requires strong assumptions on the parametrization of the social process or on the adequacy of the covariates used (or both). In particular, simple examples show that asymmetries in regression coefficients cannot identify causal effects, and that imitation (a form of social contagion) can produce substantial correlations between an individual's enduring traits and their choices, even when there is no intrinsic affinity between them. We also suggest some possible constructive responses to these non-identifiability results. (Joint work with Andrew Thomas)