No stratification without representation

Sortition is an alternative approach to democracy, in which representatives are not elected but randomly selected from the population. Most electoral democracies fail to accurately represent even a handful of protected groups. By contrast, sortition guarantees that every subset of the population will in expectation fill their fair share of the available positions. This fairness property remains satisfied when the sample is stratified based on known features. Moreover, stratification can greatly reduce the variance in the number of positions filled by any unknown group, as long as this group correlates with the strata. Our main result is that stratification cannot increase this variance by more than a negligible factor, even in the presence of indivisibilities and rounding. When the unknown group is unevenly spread across strata, we give a guarantee on the reduction in variance with respect to uniform sampling. We also contextualize stratification and uniform sampling in the space of fair sampling algorithms. Finally, we apply our insights to an empirical case study.Accepted manuscrip

Robust ecological pattern formation induced by demographic noise

We demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing instability in mean field theory, demographic noise greatly enlarges the region of parameter space where pattern formation occurs. To distinguish between patterns generated by fluctuations and those present at the mean field level in real ecosystems, we calculate the power spectrum in the noise-driven case and predict the presence of fat tails not present in the mean field case. These results may account for the prevalence of large-scale ecological patterns, beyond that expected from traditional non-stochastic approaches.Comment: Revised version. Supporting simulation at: http://guava.physics.uiuc.edu/~tom/Netlogo

Stable Mode Sorting by Two-Dimensional Parity of Photonic Transverse Spatial States

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG_nm input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG modes depending upon whether they have an even or odd value of their orbital angular momentum. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m=1) spatial states, covering the entire Poincare sphere of first-order transverse modes.Comment: 11 pages, 12 figures, 2 appendice

The Discovery of a Twelfth Wolf-Rayet Star in the Small Magellanic Cloud

We report the discovery of a relatively faint (V=15.5) early-type WN star in the SMC. The line strength and width of He II lambda 4686 emission is similar to that of the other SMC WNs, and the presense of N V lambda 4603,19 emission (coupled with the lack of N III) suggests this star is of spectral type WN3-4.5, and thus is similar in type to the other SMC WRs. Also like the other SMC WN stars, an early-type absorption spectrum is weakly present. The absolute magnitude is comparable to that of other (single) Galactic early-type WNs. The star is located in the Hodge 53 OB association, which is also the home of two other SMC WNs. This star, which we designate SMC-WR12, was actually detected at a high significance level in an earlier interference-filter survey, but the wrong star was observed as part of a spectroscopic followup, and this case of mistaken identity resulted in its Wolf-Rayet nature not being recognized until now.Comment: Accepted by PASP (November 2003 issue

Narratives of therapeutic art-making in the context of marital breakdown: Older women reflect on a significant mid-life experience

This paper explores the narratives of three women aged 65-72 years. They reflected on an episode of therapeutic art-making in midlife, which addressed depression associated with marital crisis and breakdown. The narrative analysis focused upon on the ways in which participants narrated the events leading up to their participation in therapeutic art-making; the aspects of therapeutic art-making that continued to be given significance; the characters given primacy in the stories they told about their journey through therapy and marital breakdown; meanings, symbolic and otherwise, that participants ascribed to their artwork made during this turning point in their lives; and aspects of the narratives that conveyed present-day identities and artistic endeavors. The narratives revealed the complexity of the journey through marital breakdown and depression into health, and showed that therapeutic art-making could best be understood, not as a stand-alone experience, but as given meaning within the context of wider personal and social resources. Participants looked back on therapeutic art-making that occurred two decades earlier and still described this as a significant turning point in their personal development. Art as an adjunct to counselling/therapy was not only symbolically self-expressive but provided opportunity for decision-making, agency and a reformulated self-image

Flow in linearly sheared two dimensional foams: from bubble to bulk scale

We probe the flow of two dimensional foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate dependent and inhomogeneous (shear banded) velocity profiles, while monodisperse, ordered foams are also shear banded, but essentially rate independent. Second, we introduce a simple model based on balancing the averaged drag forces between the bubbles and the top plate and the averaged bubble-bubble drag forces. This model captures the observed rate dependent flows, and the rate independent flows. Third, we perform independent rheological measurements, both for ordered and disordered systems, and find these to be fully consistent with the scaling forms of the drag forces assumed in the simple model, and we see that disorder modifies the scaling. Fourth, we vary the packing fraction $\phi$ of the foam over a substantial range, and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, our model describes flow profiles and rate dependence over the whole range of packing fractions with the same power law exponents -- only a dimensionless number $k$ which measures the ratio of the pre-factors of the viscous drag laws is seen to vary with packing fraction. We find that $k \sim (\phi-\phi_c)^{-1}$, where $\phi_c \approx 0.84$, corresponding to the 2d jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power law) rheology observed in a wide range of disordered materials.Comment: 16 pages, 14 figures, submitted to Phys. Rev. E. High quality version available at: http://www.physics.leidenuniv.nl/sections/cm/gr

A two-parameter random walk with approximate exponential probability distribution

We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the number of reversals of direction k are used to estimate eps_r and eps_l. We calculate the joint probability distribution p_n(x,k) in closed form and show that, approximately, it belongs to the exponential family.Comment: 12 pages, updated reference to companion paper cond-mat/060126