Beyond the Death of Linear Response: 1/f optimal information transport

Non-ergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. We show that it is possible to go beyond the ``death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating non-ergodic renewal processes, by taking as stimulus a similar non-ergodic process. The ideal condition of 1/f-noise corresponds to a singularity that is expected to be relevant in several experimental conditions.Comment: 4 pages, 2 figures, 1 table, in press on Phys. Rev. Let

Calibrated embeddings in the special Lagrangian and coassociative cases

Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of self-dual 2-forms is trivial can be isometrically embedded as a coassociative submanifold in a G_2-manifold, even as the fixed locus of an anti-G_2 involution. These results, when coupled with McLean's analysis of the moduli spaces of such calibrated submanifolds, yield a plentiful supply of examples of compact calibrated submanifolds with nontrivial deformation spaces.Comment: AMS-TeX v. 2.1, 26 pages, uses amsppt.sty (2.1h), minor typos correcte

Consistency of a method of moments estimator based on numerical solutions to asset pricing models

This paper considers the properties of estimators based on numerical solutions to a class of economic models. In particular, the numerical methods discussed are those applied in the solution of linear integral equations, specifically Fredholm equations of the second kind. These integral equations arise out of economic models in which endogenous variables appear linearly in the Euler equations, but for which easily characterized solutions do not exist. Tauchen and Hussey [24] have proposed the use of these methods in the solution of the consumption-based asset pricing model. In this paper, these methods are used to construct method of moments estimators where the population moments implied by a model are approximated by the population moments of numerical solutions. These estimators are shown to be consistent if the accuracy of the approximation is increased with the sample size. This result depends on the solution method having the property that the moments of the approximate solutions converge uniformly in the model parameters to the moments of the true solutions

G2G_2-monopoles with singularities (examples)

$G_2$-monopoles are solutions to gauge theoretical equations on $G_2$-manifolds. If the $G_2$-manifolds under consideration are compact, then any irreducible $G_2$-monopole must have singularities. It is then important to understand which kind of singularities $G_2$-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles whose singularities are not of that type. We also give an existence result for Abelian monopoles with Dirac type singularities on compact manifolds. This should be one of the building blocks in a gluing construction aimed at constructing non-Abelian ones.Comment: Lett Math Phys (2016

High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noise modulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. Eye-diagram and signal-to-noise ratio (SNR) analysis show that this new broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR compared to a previous slow-modulation method

Task-Driven Adaptive Statistical Compressive Sensing of Gaussian Mixture Models

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity

A solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields

We give a complete list of normal forms for the 2-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.Comment: This is an extended version of the paper that will appear in Math. Annalen. Some typos were corrected, references were updated, title was changed (as in the journal version). 31 page

Synthetic lethal analysis of Caenorhabditis elegans posterior embryonic patterning genes identifies conserved genetic interactions

Phenotypic robustness is evidenced when single-gene mutations do not result in an obvious phenotype. It has been suggested that such phenotypic stability results from 'buffering' activities of homologous genes as well as non-homologous genes acting in parallel pathways. One approach to characterizing mechanisms of phenotypic robustness is to identify genetic interactions, specifically, double mutants where buffering is compromised. To identify interactions among genes implicated in posterior patterning of the Caenorhabditis elegans embryo, we measured synthetic lethality following RNA interference of 22 genes in 15 mutant strains. A pair of homologous T-box transcription factors (tbx-8 and tbx-9) is found to interact in both C. elegans and C. briggsae, indicating that their compensatory function is conserved. Furthermore, a muscle module is defined by transitive interactions between the MyoD homolog hlh-1, another basic helix-loop-helix transcription factor, hnd-1, and the MADS-box transcription factor unc-120. Genetic interactions within a homologous set of genes involved in vertebrate myogenesis indicate broad conservation of the muscle module and suggest that other genetic modules identified in C. elegans will be conserved

Enhancing Light-Atom Interactions via Atomic Bunching

There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here, we show theoretically that sub-Doppler-cooled, two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonant saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all atomic temperature regimes and simultaneously accounts for the back-action of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only a limited range of temperatures. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices

Etiology of Severe Non-malaria Febrile Illness in Northern Tanzania: A Prospective Cohort Study.

The syndrome of fever is a commonly presenting complaint among persons seeking healthcare in low-resource areas, yet the public health community has not approached fever in a comprehensive manner. In many areas, malaria is over-diagnosed, and patients without malaria have poor outcomes. We prospectively studied a cohort of 870 pediatric and adult febrile admissions to two hospitals in northern Tanzania over the period of one year using conventional standard diagnostic tests to establish fever etiology. Malaria was the clinical diagnosis for 528 (60.7%), but was the actual cause of fever in only 14 (1.6%). By contrast, bacterial, mycobacterial, and fungal bloodstream infections accounted for 85 (9.8%), 14 (1.6%), and 25 (2.9%) febrile admissions, respectively. Acute bacterial zoonoses were identified among 118 (26.2%) of febrile admissions; 16 (13.6%) had brucellosis, 40 (33.9%) leptospirosis, 24 (20.3%) had Q fever, 36 (30.5%) had spotted fever group rickettsioses, and 2 (1.8%) had typhus group rickettsioses. In addition, 55 (7.9%) participants had a confirmed acute arbovirus infection, all due to chikungunya. No patient had a bacterial zoonosis or an arbovirus infection included in the admission differential diagnosis. Malaria was uncommon and over-diagnosed, whereas invasive infections were underappreciated. Bacterial zoonoses and arbovirus infections were highly prevalent yet overlooked. An integrated approach to the syndrome of fever in resource-limited areas is needed to improve patient outcomes and to rationally target disease control efforts