A Subdivision Solver for Systems of Large Dense Polynomials

We describe here the package {\tt subdivision\\_solver} for the mathematical software {\tt SageMath}. It provides a solver on real numbers for square systems of large dense polynomials. By large polynomials we mean multivariate polynomials with large degrees, which coefficients have large bit-size. While staying robust, symbolic approaches to solve systems of polynomials see their performances dramatically affected by high degree and bit-size of input polynomials.Available numeric approaches suffer from the cost of the evaluation of large polynomials and their derivatives.Our solver is based on interval analysis and bisections of an initial compact domain of $\R^n$ where solutions are sought. Evaluations on intervals with Horner scheme is performed by the package {\tt fast\\_polynomial} for {\tt SageMath}.The non-existence of a solution within a box is certified by an evaluation scheme that uses a Taylor expansion at order 2, and existence and uniqueness of a solution within a box is certified with krawczyk operator.The precision of the working arithmetic is adapted on the fly during the subdivision process and we present a new heuristic criterion to decide if the arithmetic precision has to be increased

Consumer Values of Health-Related Food Symbols and Chemical Food Additives - The Case of Breakfast Cereals

In this paper we analyze consumers’ revealed values of food symbols indicating nutritious and organic food, as well as consumers’ revealed values for chemical food additives. We do so by estimating a hedonic price function based on a rich data set on breakfast cereal purchases. Our findings suggest that consumers positively value chemical food additives in breakfast cereals, suggesting that the positive taste effect from e.g. chemical taste enhancers, emulsifiers, colourings and preservatives outweighs consumers’ health concerns regarding such additives. We find no evidence that consumers positively value the symbol indicating nutritious food. In addition, surprisingly enough, our results imply that consumers have a negative willingness-to-pay for the symbol indicating organic food.consumer economics; hedonic pricing; food labelling; food additives

Frequency Following Imaging of Electric Fields from Resonant Superconducting Devices using a Scanning Near-Field Microwave Microscope

We have developed a scanning near-field microwave microscope that operates at cryogenic temperatures. Our system uses an open-ended coaxial probe with a 200 mm inner conductor diameter and operates from 77 to 300 K in the 0.01-20 GHz frequency range. In this paper, we present microwave images of the electric field distribution above a Tl2Ba2CaCu2O8 microstrip resonator at 77 K, measured at several heights. In addition, we describe the use of a frequency-following circuit to study the influence of the probe on the resonant frequency of the device.Comment: 4 pages, postscript file with 6 figures conference proceeding for the Applied Superconductivity Conference 199

The effect of AGN feedback on the halo mass function

[Abridged.] We investigate baryon effects on the halo mass function (HMF), with emphasis on the role played by AGN feedback. Halos are identified with both Friends-of-Friends (FoF) and Spherical Overdensity (SO) algorithms. We embed the standard SO algorithm into a memory-controlled frame program and present the {\bf P}ython spher{\bf I}c{\bf A}l {\bf O}verdensity code --- {\small PIAO}. For both FoF and SO halos, the effect of AGN feedback is that of suppressing the HMFs to a level even below that of Dark Matter simulations. The ratio between the HMFs in the AGN and in the DM simulations is $\sim 0.8$ at overdensity $\Delta_c=500$, a difference that increases at higher overdensity $\Delta_c=2500$, with no significant redshift and mass dependence. A decrease of the halo masses ratio with respect to the DM case induces the decrease of the HMF in the AGN simulation. The shallower inner density profiles of halos in the AGN simulation witnesses that mass reduction is induced by the sudden displacement of gas induced by thermal AGN feedback. We provide fitting functions to describe halo mass variations at different overdensities, which can recover the HMFs with a residual random scatter $\lt 5$ per cent for halo masses larger than $10^{13} ~h^{-1}{\rm M_\odot}$.Comment: 16 pages, 11 figures. Matches to MNRAS published version, typo corrected in the fitting functio

The contributions of matter inside and outside of haloes to the matter power spectrum

Halo-based models have been successful in predicting the clustering of matter. However, the validity of the postulate that the clustering is fully determined by matter inside haloes remains largely untested, and it is not clear a priori whether non-virialised matter might contribute significantly to the non-linear clustering signal. Here, we investigate the contribution of haloes to the matter power spectrum as a function of both scale and halo mass by combining a set of cosmological N-body simulations to calculate the contributions of different spherical overdensity regions, Friends-of-Friends (FoF) groups and matter outside haloes to the power spectrum. We find that matter inside spherical overdensity regions of size R200,mean cannot account for all power for 1<k<100 h/Mpc, regardless of the minimum halo mass. At most, it accounts for 95% of the power (k>20 h/Mpc). For 2<k<10 h/Mpc, haloes with mass M200,mean<10^11 Msun/h contribute negligibly to the power spectrum, and our results appear to be converged with decreasing halo mass. When haloes are taken to be regions of size R200,crit, the amount of power unaccounted for is larger on all scales. Accounting also for matter inside FoF groups but outside R200,mean increases the contribution of halo matter on most scales probed here by 5-15%. Matter inside FoF groups with M200,mean>10^9 Msun/h accounts for essentially all power for 3<k<100 h/Mpc. We therefore expect halo models that ignore the contribution of matter outside R200,mean to overestimate the contribution of haloes of any mass to the power on small scales (k>1 h/Mpc).Comment: 13 pages, 9 figures. Replaced to match the version accepted by MNRA

Analysis-of-marginal-Tail-Means (ATM): a robust method for discrete black-box optimization

We present a new method, called Analysis-of-marginal-Tail-Means (ATM), for effective robust optimization of discrete black-box problems. ATM has important applications to many real-world engineering problems (e.g., manufacturing optimization, product design, molecular engineering), where the objective to optimize is black-box and expensive, and the design space is inherently discrete. One weakness of existing methods is that they are not robust: these methods perform well under certain assumptions, but yield poor results when such assumptions (which are difficult to verify in black-box problems) are violated. ATM addresses this via the use of marginal tail means for optimization, which combines both rank-based and model-based methods. The trade-off between rank- and model-based optimization is tuned by first identifying important main effects and interactions, then finding a good compromise which best exploits additive structure. By adaptively tuning this trade-off from data, ATM provides improved robust optimization over existing methods, particularly in problems with (i) a large number of factors, (ii) unordered factors, or (iii) experimental noise. We demonstrate the effectiveness of ATM in simulations and in two real-world engineering problems: the first on robust parameter design of a circular piston, and the second on product family design of a thermistor network

One year of monitoring the Vela pulsar using a Phased Array Feed

We have observed the Vela pulsar for one year using a Phased Array Feed (PAF) receiver on the 12-metre antenna of the Parkes Test-Bed Facility. These observations have allowed us to investigate the stability of the PAF beam-weights over time, to demonstrate that pulsars can be timed over long periods using PAF technology and to detect and study the most recent glitch event that occurred on 12 December 2016. The beam-weights are shown to be stable to 1% on time scales on the order of three weeks. We discuss the implications of this for monitoring pulsars using PAFs on single dish telescopes.Comment: 6 pages, 4 figures, 2 tables. Accepted for publication in PAS