A nullstellensatz for sequences over F_p

Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for l < p. The critical case l=p is of particular interest. In this context, we prove that whenever l=p and A is nonconstant, the above equation has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case l=p-1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem.Comment: 23 page

Flares in Open Clusters with K2. I. M45 (Pleiades), M44 (Praesepe) and M67

The presence and strength of a stellar magnetic field and activity is rooted in a star's fundamental parameters such as mass and age. Can flares serve as an accurate stellar "clock"? To explore if we can quantify an activity-age relation in the form of a flaring-age relation, we measured trends in the flaring rates and energies for stars with different masses and ages. We investigated the time-domain photometry provided by Kepler's follow-up mission K2 and searched for flares in three solar metallicity open clusters with well-known ages, M45 (0.125 Gyr), M44 (0.63 Gyr), and M67 (4.3 Gyr). We updated and employed the automated flare finding and analysis pipeline Appaloosa, originally designed for Kepler. We introduced a synthetic flare injection and recovery subroutine to ascribe detection and energy recovery rates for flares in a broad energy range for each light curve. We collected a sample of 1 761 stars, mostly late-K to mid-M dwarfs and found 751 flare candidates with energies ranging from $4\cdot10^{32}$ erg to $6\cdot10^{34}$ erg, of which 596 belong to M45, 155 to M44, and none to M67. We find that flaring activity depends both on $T_\mathrm{eff}$, and age. But all flare frequency distributions have similar slopes with $\alpha \approx2.0-2.4$, supporting a universal flare generation process. We discuss implications for the physical conditions under which flares occur, and how the sample's metallicity and multiplicity affect our results.Comment: 17 pages, 11 figures, appendix. Accepted to A&

The Pros and Cons of Compressive Sensing for Wideband Signal Acquisition: Noise Folding vs. Dynamic Range

Compressive sensing (CS) exploits the sparsity present in many signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in the design of a wideband radio receiver in a noisy environment. We formulate the problem statement for such a receiver and establish a reasonable set of requirements that a receiver should meet to be practically useful. We then evaluate the performance of a CS-based receiver in two ways: via a theoretical analysis of its expected performance, with a particular emphasis on noise and dynamic range, and via simulations that compare the CS receiver against the performance expected from a conventional implementation. On the one hand, we show that CS-based systems that aim to reduce the number of acquired measurements are somewhat sensitive to signal noise, exhibiting a 3dB SNR loss per octave of subsampling, which parallels the classic noise-folding phenomenon. On the other hand, we demonstrate that since they sample at a lower rate, CS-based systems can potentially attain a significantly larger dynamic range. Hence, we conclude that while a CS-based system has inherent limitations that do impose some restrictions on its potential applications, it also has attributes that make it highly desirable in a number of important practical settings

Cooling with heat recovery for electrical cable tunnels in cities

Within cities, electrical power is often distributed by means of underground cable tunnels, frequently extending for many kilometres. Cables can generate significant heat, with the quantity of heat being directly related to the electrical load carried. Tunnel air temperatures are generally controlled by ventilation using outside air; preventing the cables from overheating. If active cooling was provided, tunnel air temperatures could be further reduced, permitting higher electrical loadings to be used. Using an air/water heat exchanger to cool the outside air entering the ventilation shaft has been investigated. The temperature of the heat extracted (to water) was increased using a heat pump before transfer to a heat network. Benefits identified included reduction in cable temperatures, and carbon and cost savings compared to conventional heat delivery

Phase separation and electron pairing in repulsive Hubbard clusters

Exact thermal studies of small (4-site, 5-site and 8-site) Hubbard clusters with local electron repulsion yield intriguing insight into phase separation, charge-spin separation, pseudogaps, condensation, in particular, pairing fluctuations away from half filling (near optimal doping). These exact calculations, carried out in canonical (i.e. for fixed electron number N) and grand canonical (i.e. fixed chemical potential $\mu$) ensembles, monitoring variations in temperature T and magnetic field h, show rich phase diagrams in a T-$\mu$ space consisting of pairing fluctuations and signatures of condensation. These electron pairing instabilities are seen when the onsite Coulomb interaction U is smaller than a critical value U$_c$(T) and they point to a possible electron pairing mechanism. The specific heat, magnetization, charge pairing and spin pairing provide strong support for the existence of competing (paired and unpaired) phases near optimal doping in these clusters as observed in recent experiments in doped La$_{2-x}$Sr$_x$CuO$_{4+y}$ high T$_c$ superconductors.Comment: 5 pages, 5 figure

The current progress of the ALICE Ring Imaging Cherenkov Detector

Recently, the last two modules (out of seven) of the ALICE High Momentum Particle Identification detector (HMPID) were assembled and tested. The full detector, after a pre-commissioning phase, has been installed in the experimental area, inside the ALICE solenoid, at the end of September 2006. In this paper we review the status of the ALICE/HMPID project and we present a summary of the series production of the CsI photo-cathodes. We describe the key features of the production procedure which ensures high quality photo-cathodes as well as the results of the quality assessment performed by means of a specially developed 2D scanner system able to produce a detailed map of the CsI photo-current over the entire photo-cathode surface. Finally we present our recent R&D efforts toward the development of a novel generation of imaging Cherenkov detectors with the aim to identify, in heavy ions collisions, hadrons up to 30 GeV/c.Comment: Presented at the Imaging-2006 Conference, Stockholm, Sweden, June 200