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A freely walking fly visits roughly 100 stereotyped states in a strongly non-Markovian sequence. To explore these dynamics, we develop a generalization of the information bottleneck method, compressing the large number of behavioral states into a more compact description that maximally preserves the correlations between successive states. Surprisingly, preserving these short time correlations with a compression into just two states captures the long ranged correlations seen in the raw data. Having reduced the behavior to a binary sequence, we describe the distribution of these sequences by an Ising model with pairwise interactions, which is the maximum entropy model that matches the two-point correlations. Matching the correlation function at longer and longer times drives the resulting model toward the Ising model with inverse square interactions and near zero magnetic field. The emergence of this statistical physics problem from the analysis real data on animal behavior is unexpected.

Organismal phenotypes emerge from a complex set of genotypic interactions. While technological advances in sequencing provide a quantitative description of an organism's genotype, characterization of an organism's physical phenotype lags far behind. Here, we relate genotype to the complex and multi-dimensional phenotype of an anatomical structure using the Drosophila wing as a model system. We develop a mathematical approach that enables a robust description of biologically salient phenotypic variation. Analysing natural phenotypic variation, and variation generated by weak perturbations in genetic and environmental conditions during development, we observe a highly constrained set of wing phenotypes. In a striking ex-ample of dimensionality reduction, the nature of varieties produced by the Drosophila developmental pro-gram is constrained to a single integrated mode of variation in the wing. Our strategy demonstrates the emergent simplicity manifest in the genotype-to-phenotype map in the Drosophila wing and may represent a general approach for interrogating a variety of genotype-phenotype relationships., Comment: 32 pages, 5 figures, 8 supplementary figures

We consider the primordial gravity wave background produced by inflation. We compute the small anisotropy produced by the primordial scalar fluctuations., Comment: 5 pages, 2 figures, references corrected

We study unitary conformal field theories with a unique stress tensor and at least one higher-spin conserved current in d>3 dimensions. We prove that every such theory contains an infinite number of higher-spin conserved currents of arbitrarily high spin, and that Ward identities generated by the conserved charges of these currents imply that the correlators of the stress tensor and the conserved currents of the theory must coincide with one of the following three possibilities: a) a theory of n free bosons (for some integer n), b) a theory of n free fermions, or c) a theory of n (d-2)/2-forms. For d even, all three structures exist, but for d odd, it may be the case that the third structure (c) does not; if it does exist, it is unclear what theory, if any, realizes it. This is a generalization of the result proved in three dimensions by Maldacena and Zhiboedov [arXiv:1112.1016]. This paper supersedes the previous paper by the authors [arXiv:1307.8092], Comment: 40 pages, This paper supersedes the previous paper arXiv:1307.8092 by the authors