Weak lensing, dark matter and dark energy

Weak gravitational lensing is rapidly becoming one of the principal probes of dark matter and dark energy in the universe. In this brief review we outline how weak lensing helps determine the structure of dark matter halos, measure the expansion rate of the universe, and distinguish between modified gravity and dark energy explanations for the acceleration of the universe. We also discuss requirements on the control of systematic errors so that the systematics do not appreciably degrade the power of weak lensing as a cosmological probe.Comment: Invited review article for the GRG special issue on gravitational lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). V3: subsection on three-point function and some references added. Matches the published versio

Human genetics and neuropathology suggest a link between miR-218 and amyotrophic lateral sclerosis pathophysiology

Motor neuron–specific microRNA-218 (miR-218) has recently received attention because of its roles in mouse development. However, miR-218 relevance to human motor neuron disease was not yet explored. Here, we demonstrate by neuropathology that miR-218 is abundant in healthy human motor neurons. However, in amyotrophic lateral sclerosis (ALS) motor neurons, miR-218 is down-regulated and its mRNA targets are reciprocally up-regulated (derepressed). We further identify the potassium channel Kv10.1 as a new miR-218 direct target that controls neuronal activity. In addition, we screened thousands of ALS genomes and identified six rare variants in the human miR-218-2 sequence. miR-218 gene variants fail to regulate neuron activity, suggesting the importance of this small endogenous RNA for neuronal robustness. The underlying mechanisms involve inhibition of miR-218 biogenesis and reduced processing by DICER. Therefore, miR-218 activity in motor neurons may be susceptible to failure in human ALS, suggesting that miR-218 may be a potential therapeutic target in motor neuron disease

Weak Lensing and CMB: Parameter forecasts including a running spectral index

We use statistical inference theory to explore the constraints from future galaxy weak lensing (cosmic shear) surveys combined with the current CMB constraints on cosmological parameters, focusing particularly on the running of the spectral index of the primordial scalar power spectrum, $\alpha_s$. Recent papers have drawn attention to the possibility of measuring $\alpha_s$ by combining the CMB with galaxy clustering and/or the Lyman-$\alpha$ forest. Weak lensing combined with the CMB provides an alternative probe of the primordial power spectrum. We run a series of simulations with variable runnings and compare them to semi-analytic non-linear mappings to test their validity for our calculations. We find that a ``Reference'' cosmic shear survey with $f_{sky}=0.01$ and $6.6\times 10^8$ galaxies per steradian can reduce the uncertainty on $n_s$ and $\alpha_s$ by roughly a factor of 2 relative to the CMB alone. We investigate the effect of shear calibration biases on lensing by including the calibration factor as a parameter, and show that for our Reference Survey, the precision of cosmological parameter determination is only slightly degraded even if the amplitude calibration is uncertain by as much as 5%. We conclude that in the near future weak lensing surveys can supplement the CMB observations to constrain the primordial power spectrum.Comment: 12 pages, 10 figures, revtex4. Final form to appear in Phys Rev

Fractional-Order Regularization and Wavelet Approximation to the Inverse Estimation Problem for Random Fields

AbstractThe least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of prior information in the form of a fractional stochastic model, with covariance operator bicontinuous with respect to a certain fractional Sobolev norm, leads to a regularization of this problem. Third, a multiresolution approximation to the class of linear inverse problems considered is obtained from a wavelet-based orthogonal expansion of the input and output random models. The least-squares linear estimate of the input random field is then computed using these orthogonal wavelet decompositions. The results are applied to solving two important cases of linear inverse problems defined in terms of fractional integral operators