Oscillating Bispectra and Galaxy Clustering: A Novel Probe of Inflationary Physics with Large-Scale Structure

Many models of inflation predict oscillatory features in the bispectrum of primordial fluctuations. Since it has been shown that primordial non-Gaussianity can lead to a scale-dependent halo bias, we investigate the effect of oscillations in the three-point function on the clustering of dark-matter halos. Interestingly, we find that features in the inflaton potential such as oscillations or sharp steps get imprinted in the mass dependence of the non-Gaussian halo bias. In this paper, we focus on models displaying a sharp feature in the inflaton potential as well as Resonant non-Gaussianity. In both cases, we find a strong scale dependence for the non-Gaussian halo bias with a slope similar to that of the local model. In the resonant case, we find that the non-Gaussian bias oscillates with halo mass, a novel feature that is unique to this type of models. In the case of a sharp feature in the inflaton potential, we find that the clustering of halos is enhanced at the mass scale corresponding to the Fourier mode that exited the horizon when the inflaton was crossing the feature in the potential. Both of these are new effects that open the possibility of characterizing the inflationary potential with large-scale-structure surveys. We briefly discuss the prospects for detecting these non-Gaussian effects.Comment: 9 pages, 8 figures; v2 matching published versio

Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems.Comment: Neural Information Processing Systems (2011

Minimizing Finite Sums with the Stochastic Average Gradient

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. The convergence rate is improved from O(1/k^{1/2}) to O(1/k) in general, and when the sum is strongly-convex the convergence rate is improved from the sub-linear O(1/k) to a linear convergence rate of the form O(p^k) for p \textless{} 1. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.Comment: Revision from January 2015 submission. Major changes: updated literature follow and discussion of subsequent work, additional Lemma showing the validity of one of the formulas, somewhat simplified presentation of Lyapunov bound, included code needed for checking proofs rather than the polynomials generated by the code, added error regions to the numerical experiment

A simpler approach to obtaining an O(1/t) convergence rate for the projected stochastic subgradient method

In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an easy proof and an easy implementation. The new scheme is compared empirically to existing techniques, with similar performance behavior.Comment: 8 pages, 6 figures. Changes with previous version: Added reference to concurrently submitted work arXiv:1212.1824v1; clarifications added; typos corrected; title changed to 'subgradient method' as 'subgradient descent' is misnome

A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets

We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed method incorporates a memory of previous gradient values in order to achieve a linear convergence rate. In a machine learning context, numerical experiments indicate that the new algorithm can dramatically outperform standard algorithms, both in terms of optimizing the training error and reducing the test error quickly.Comment: The notable changes over the current version: - worked example of convergence rates showing SAG can be faster than first-order methods - pointing out that the storage cost is O(n) for linear models - the more-stable line-search - comparison to additional optimal SG methods - comparison to rates of coordinate descent methods in quadratic cas

L’apport d’Évelyne Patlagean à l’histoire et l’historiographie des Juifs et du judaïsme

Pour introduire ces quelques mots sur l’apport d’Évelyne Patlagean à l’histoire et l’historiographie des Juifs et du judaïsme, j’évoquerai un souvenir personnel que partagent sans doute tous les élèves, collègues ou amis qu’Évelyne Patlagean a invités chez elle pour « parler affaire », comme elle aimait à dire. Un dossier sur le judaïsme ancien dans les Annales C’est ainsi qu’à l’automne 1992, Évelyne m’avait invité Boulevard Raspail pour préciser les contours d’un dossier sur le judaïsme anc..

L’apport d’Évelyne Patlagean à l’histoire et l’historiographie des Juifs et du judaïsme

Pour introduire ces quelques mots sur l’apport d’Évelyne Patlagean à l’histoire et l’historiographie des Juifs et du judaïsme, j’évoquerai un souvenir personnel que partagent sans doute tous les élèves, collègues ou amis qu’Évelyne Patlagean a invités chez elle pour « parler affaire », comme elle aimait à dire. Un dossier sur le judaïsme ancien dans les Annales C’est ainsi qu’à l’automne 1992, Évelyne m’avait invité Boulevard Raspail pour préciser les contours d’un dossier sur le judaïsme anc..

Lattice fence and hedge barriers around an apiary increase honey bee flight height and decrease stings to people nearby

Urban beekeeping is becoming more popular in the UK. One of the challenges faced by urban beekeepers is finding a suitable apiary location. Honey bees are often perceived as a nuisance, mainly due to their stinging behaviour. Here, we experimentally test the assumption that barriers around an apiary such as walls or fences, force the bees to fly above human height, thereby reducing collisions with people and, consequently, stinging. The experiment was conducted in two apiaries using two common types of barrier: a lattice fence (trellis) and hedge. Barriers were 2 m high, which is taller than > 99% of humans and is also the maximum height allowed by UK planning regulations for garden fences or walls. We found that barriers were effective at both raising the mean honey bee flight height and reducing stinging. However, the effects were only seen when the barrier had been in place for a few days, not immediately after the barrier was put in place. Although this raises interesting questions regarding honey bee navigation and memory, it is not a problem for beekeepers, as any barrier placed around an apiary will be permanent. The effect of the barriers on raising bee flight height to a mean of c. 2.2-2.5 m was somewhat weak and inconsistent, probably because the bees flew high, mean of c. 1.6-2.0 m, even in the absence of a barrier. As barriers can also reduce wind exposure, improve security and are inexpensive, we recommend their use around urban apiaries in places such as private gardens or allotments, where nuisance to humans is likely to be a problem