New C*-completions of discrete groups and related spaces

Let $\Gamma$ be a discrete group. To every ideal in \ell^{\infty}(\G) we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general framework we develop unifies some classical results and leads to new insights. For example, we give the first C$^*$-algebraic characterization of a-T-menability; a new characterization of property (T); new examples of "exotic" quantum groups; and, after extending our construction to transformation groupoids, we improve and simplify a recent result of Douglas and Nowak.Comment: 13 page

The Evolutionary Unfolding of Complexity

We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. Our approach---statistical dynamics---combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current ``landscape'' models of evolutionary optimization. We describe the population dynamics on the macroscopic level of fitness classes or phenotype subbasins, while averaging out the genotypic variation that is consistent with a macroscopic state. Metastability in epochal evolution occurs solely at the macroscopic level of the fitness distribution. While a balance between selection and mutation maintains a quasistationary distribution of fitness, individuals diffuse randomly through selectively neutral subbasins in genotype space. Sudden innovations occur when, through this diffusion, a genotypic portal is discovered that connects to a new subbasin of higher fitness genotypes. In this way, we identify innovations with the unfolding and stabilization of a new dimension in the macroscopic state space. The architectural view of subbasins and portals in genotype space clarifies how frozen accidents and the resulting phenotypic constraints guide the evolution to higher complexity.Comment: 28 pages, 5 figure

Hispanic Ethnicity Is Associated With Increased Hospital Charges After Radical Cystectomy in the United States

Objective: To examine the impact of race and ethnicity on financial charges associated with radical cystectomy (RC). Data Sources/Study Setting: The Nationwide Inpatient Sample was used to identify patients who underwent RC for bladder cancer between 1998 and 2010. Study Design: The primary outcome was total hospital charges adjusted for inflation. Multivariate analysis was performed using a generalized linear model on the logarithmically transformed outcome variable (total hospital charges) after adjusting for age, sex, race, Elixhauser comorbidities, surgical approach, year, primary payer, hospital and surgeon annual RC volume, hospital characteristics, and postoperative complications. Principle findings: A total of 14,873 patients were identified. Hispanic and black patients were more likely to be treated by low-volume surgeons and/or institutions (both P=.07). Conclusions: Hispanic ethnicity but not black race predicts higher hospital charges after RC

Metastable Evolutionary Dynamics: Crossing Fitness Barriers or Escaping via Neutral Paths?

We analytically study the dynamics of evolving populations that exhibit metastability on the level of phenotype or fitness. In constant selective environments, such metastable behavior is caused by two qualitatively different mechanisms. One the one hand, populations may become pinned at a local fitness optimum, being separated from higher-fitness genotypes by a {\em fitness barrier} of low-fitness genotypes. On the other hand, the population may only be metastable on the level of phenotype or fitness while, at the same time, diffusing over {\em neutral networks} of selectively neutral genotypes. Metastability occurs in this case because the population is separated from higher-fitness genotypes by an {\em entropy barrier}: The population must explore large portions of these neutral networks before it discovers a rare connection to fitter phenotypes. We derive analytical expressions for the barrier crossing times in both the fitness barrier and entropy barrier regime. In contrast with ``landscape'' evolutionary models, we show that the waiting times to reach higher fitness depend strongly on the width of a fitness barrier and much less on its height. The analysis further shows that crossing entropy barriers is faster by orders of magnitude than fitness barrier crossing. Thus, when populations are trapped in a metastable phenotypic state, they are most likely to escape by crossing an entropy barrier, along a neutral path in genotype space. If no such escape route along a neutral path exists, a population is most likely to cross a fitness barrier where the barrier is {\em narrowest}, rather than where the barrier is shallowest.Comment: 32 pages, 7 figures, 1 table; http://www.santafe.edu/projects/evca/med.ps.g

Observational Signatures of Quantum Gravity in Interferometers

We consider the uncertainty in the arm length of an interferometer due to metric fluctuations from the quantum nature of gravity, proposing a concrete microscopic model of energy fluctuations in holographic degrees of freedom on the surface bounding a causally connected region of spacetime. In our model, fluctuations longitudinal to the beam direction accumulate in the infrared and feature strong long distance correlation in the transverse direction. This leads to a signal that could be observed in a gravitational wave interferometer. We connect the positional uncertainty principle arising from our calculations to the 't Hooft gravitational S-matrix.Comment: 6 pages, 1 figur