Odd order cases of the logarithmically averaged Chowla conjecture

A famous conjecture of Chowla states that the Liouville function $\lambda(n)$ has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd order cases of the logarithmically averaged Chowla conjecture. In this note, we give a new and shorter proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular, this proof avoids all mention of ergodic theory, which had an important role in the previous proof.Comment: 15 pages, no figures, submitted, J. Numb. Thy. Bordeau

Multichannel sparse recovery of complex-valued signals using Huber's criterion

In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. This requires careful characterization of robust complex-valued loss functions as well as Huber's criterion function for the multivariate sparse regression problem. We devise a greedy algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Unlike the conventional SNIHT method, our algorithm, referred to as HUB-SNIHT, is robust under heavy-tailed non-Gaussian noise conditions, yet has a negligible performance loss compared to SNIHT under Gaussian noise. Usefulness of the method is illustrated in source localization application with sensor arrays.Comment: To appear in CoSeRa'15 (Pisa, Italy, June 16-19, 2015). arXiv admin note: text overlap with arXiv:1502.0244

Cooling and Heating Functions of Photoionized Gas

Cooling and heating functions of cosmic gas are a crucial ingredient for any study of gas dynamics and thermodynamics in the interstellar and intergalactic medium. As such, they have been studied extensively in the past under the assumption of collisional ionization equilibrium. However, for a wide range of applications, the local radiation field introduces a non-negligible, often dominant, modification to the cooling and heating functions. In the most general case, these modifications cannot be described in simple terms, and would require a detailed calculation with a large set of chemical species using a radiative transfer code (the well-known code Cloudy, for example). We show, however, that for a sufficiently general variation in the spectral shape and intensity of the incident radiation field, the cooling and heating functions can be approximated as depending only on several photoionization rates, which can be thought of as representative samples of the overall radiation field. This dependence is easy to tabulate and implement in cosmological or galactic-scale simulations, thus economically accounting for an important but rarely-included factor in the evolution of cosmic gas. We also show a few examples where the radiation environment has a large effect, the most spectacular of which is a quasar that suppresses gas cooling in its host halo without any mechanical or non-radiative thermal feedback.Comment: replaced with the accepted version; note that the revised version differs substantially from the original draf

Central dark matter trends in early-type galaxies from strong lensing, dynamics and stellar populations

We analyze the correlations between central dark matter (DM) content of early-type galaxies and their sizes and ages, using a sample of intermediate-redshift (z ~ 0.2) gravitational lenses from the SLACS survey, and by comparing them to a larger sample of z ~ 0 galaxies. We decompose the deprojected galaxy masses into DM and stellar components using combinations of strong lensing, stellar dynamics, and stellar populations modeling. For a given stellar mass, we find that for galaxies with larger sizes, the DM fraction increases and the mean DM density decreases, consistently with the cuspy halos expected in cosmological formation scenarios. The DM fraction also decreases with stellar age, which can be partially explained by the inverse correlation between size and age. The residual trend may point to systematic dependencies on formation epoch of halo contraction or stellar initial mass functions. These results are in agreement with recent findings based on local galaxies by Napolitano, Romanowsky & Tortora (2010) and suggest negligible evidence of galaxy evolution over the last ~ 2.5 Gyr other than passive stellar aging.Comment: 5 pages, 3 figures, accepted for publication on ApJL. Version including further updates and a complementary note added in proo

Application of MARSplines Method for Failure Rate Prediction

In this paper MARSplines method was presented to model failure rate of water pipes in years 2015-2016 in the selected Polish city. The output parameters were chosen as three dependent variables - three values of failure rate of water mains, distribution pipes and house connections. Diameter, season, material and kind of the conduit were selected as independent variables. At the beginning of modelling 21 basis (splines) function were assumed. On a final note two functions were selected (after reduction of negligible functions). The model consists of three factors: β0, β1 and β2. The penalty for adding basis function was assumed at the level of 2. The correlation was equalled to 0.44. Relatively huge discrepancies between real and predicted values of failure rate of water mains and house connections were observed. In the future investigations concerning this problem the three separated models for each kind of conduit should be created. The calculations using MARSplines method were carried out in the program Statistica 13.1

Top quark mass determination from the energy peaks of b-jets and B-hadrons at NLO QCD

We analyze the energy spectra of $single$ b-jets and B-hadrons resulting from the production and decay of top quarks within the SM at the LHC at the NLO QCD. For both hadrons and jets, we calculate the correlation of the peak of the spectrum with the top quark mass, considering the "energy-peak" as an observable to determine the top quark mass. Such a method is motivated by our previous work where we argued that this approach can have reduced sensitivity to the details of the production mechanism of the top quark, whether it is higher-order QCD effects or new physics contributions. As part of the NLO improvement over the original proposal, we assess the residual sensitivity of the extracted top quark mass to perturbative effects both in top quark production and decay. For a 1% jet energy scale uncertainty (and assuming negligible statistical error), the top quark mass can then be extracted using the energy-peak of b-jets with an error +- (1.2 (exp) + 0.6(th)) GeV. We note that recently the CMS collaboration reported a top quark mass measurement based on the original proposal (with b-jets) so that our result contributes to a precise evaluation of the associated theory uncertainty. In view of the dominant jet energy scale uncertainty in the measurement using b-jets, we also investigate the extraction of the top quark mass from the energy-peak of the corresponding B-hadrons which, in principle, can be measured without this uncertainty. The calculation of the B-hadron energy spectrum is carried out using fragmentation functions at NLO. The dependence on the fragmentation scale turns out to be the largest theoretical uncertainty in this extraction of top quark mass. Future improvement of the treatment of bottom quark hadronization can reduce this uncertainty, rendering methods based on the B-hadron energy-peak competitive for the top quark mass measurement.Comment: 5 figures, 12 page

Odd order cases of the logarithmically averaged chowla conjecture

A famous conjecture of Chowla states that the Liouville function λ(n) has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of multiplicative functions, which in turn implied all the odd order cases of the logarithmically averaged Chowla conjecture. In this note, we give a new proof of the odd order cases of the logarithmically averaged Chowla conjecture. In particular, this proof avoids all mention of ergodic theory, which had an important role in the previous proof. </p