Nearly optimal solutions for the Chow Parameters Problem and low-weight approximation of halfspaces

The \emph{Chow parameters} of a Boolean function $f: \{-1,1\}^n \to \{-1,1\}$ are its $n+1$ degree-0 and degree-1 Fourier coefficients. It has been known since 1961 (Chow, Tannenbaum) that the (exact values of the) Chow parameters of any linear threshold function $f$ uniquely specify $f$ within the space of all Boolean functions, but until recently (O'Donnell and Servedio) nothing was known about efficient algorithms for \emph{reconstructing} $f$ (exactly or approximately) from exact or approximate values of its Chow parameters. We refer to this reconstruction problem as the \emph{Chow Parameters Problem.} Our main result is a new algorithm for the Chow Parameters Problem which, given (sufficiently accurate approximations to) the Chow parameters of any linear threshold function $f$, runs in time \tilde{O}(n^2)\cdot (1/\eps)^{O(\log^2(1/\eps))} and with high probability outputs a representation of an LTF $f'$ that is \eps-close to $f$. The only previous algorithm (O'Donnell and Servedio) had running time \poly(n) \cdot 2^{2^{\tilde{O}(1/\eps^2)}}. As a byproduct of our approach, we show that for any linear threshold function $f$ over $\{-1,1\}^n$, there is a linear threshold function $f'$ which is \eps-close to $f$ and has all weights that are integers at most \sqrt{n} \cdot (1/\eps)^{O(\log^2(1/\eps))}. This significantly improves the best previous result of Diakonikolas and Servedio which gave a \poly(n) \cdot 2^{\tilde{O}(1/\eps^{2/3})} weight bound, and is close to the known lower bound of $\max\{\sqrt{n},$ (1/\eps)^{\Omega(\log \log (1/\eps))}\} (Goldberg, Servedio). Our techniques also yield improved algorithms for related problems in learning theory

Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion

We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation, gives results which stay close to the exact solution for longer than previous methods. It provides a promising basis for extension to a full field theoretic treatment.Comment: 12 pages, including 4 figure

Aspects of Magnetic Field Configurations in Planar Nonlinear Electrodynamics

In the framework of three-dimensional Born-Infeld Electrodynamics, we pursue an investigation of the consequences of the space-time dimensionality on the existence of magnetostatic fields generated by electric charges at rest in an inertial frame, which are present in its four-dimensional version. Our analysis reveals interesting features of the model. In fact, a magnetostatic field associated with an electric charge at rest does not appear in this case. Interestingly, the addition of the topological term (Chern-Simons) to Born-Infeld Electrodynamics yields the appearance of the magnetostatic field. We also contemplate the fields associated to the would-be-magnetic monopole in three dimensions.Comment: 8 page

Optimizing training adaptations by manipulating glycogen

For decades, glycogen has been recognized as a storage form of glucose within the liver and muscles. Only recently has a greater role for glycogen as a regulator of metabolic signalling been suggested. Glycogen either directly or indirectly regulates a number of signalling proteins, including the adenosine-5\u27-phosphate- (AMP-) activated protein kinase (AMPK) and p38 mitogen-activated protein kinase (MAPK). AMPK and p38 MAPK play a significant role in controlling the expression and activity of the peroxisome proliferator activated receptor &gamma; coactivators (PGCs), respectively. The PGCs can directly increase muscle mitochondrial mass and endurance exercise performance. As low muscle glycogen is generally associated with greater activation of these pathways, the concept of training with low glycogen to maximize the physiological adaptations to endurance exercise is gaining acceptance in the scientific community. In this review, we evaluate the scientific basis for this philosophy and propose some practical applications of this philosophy for the general population as well as elite endurance athletes.<br /

Design, development and verification of the 30 and 44 GHz front-end modules for the Planck Low Frequency Instrument

We give a description of the design, construction and testing of the 30 and 44 GHz Front End Modules (FEMs) for the Low Frequency Instrument (LFI) of the Planck mission to be launched in 2009. The scientific requirements of the mission determine the performance parameters to be met by the FEMs, including their linear polarization characteristics. The FEM design is that of a differential pseudo-correlation radiometer in which the signal from the sky is compared with a 4-K blackbody load. The Low Noise Amplifier (LNA) at the heart of the FEM is based on indium phosphide High Electron Mobility Transistors (HEMTs). The radiometer incorporates a novel phase-switch design which gives excellent amplitude and phase match across the band. The noise temperature requirements are met within the measurement errors at the two frequencies. For the most sensitive LNAs, the noise temperature at the band centre is 3 and 5 times the quantum limit at 30 and 44 GHz respectively. For some of the FEMs, the noise temperature is still falling as the ambient temperature is reduced to 20 K. Stability tests of the FEMs, including a measurement of the 1/f knee frequency, also meet mission requirements. The 30 and 44 GHz FEMs have met or bettered the mission requirements in all critical aspects. The most sensitive LNAs have reached new limits of noise temperature for HEMTs at their band centres. The FEMs have well-defined linear polarization characteristcs.Comment: 39 pages, 33 figures (33 EPS files), 12 tables. Planck LFI technical papers published by JINST: http://www.iop.org/EJ/journal/-page=extra.proc5/1748-022

How the central domain of dystrophin acts to bridge F-actin to sarcolemmal lipids

Dystrophin is a large intracellular protein that prevents sarcolemmal ruptures by providing a mechanical link between the intracellular actin cytoskeleton and the transmembrane dystroglycan complex. Dystrophin deficiency leads to the severe muscle wasting disease Duchenne Muscular Dystrophy and the milder allelic variant, Becker Muscular Dystrophy (DMD and BMD). Previous work has shown that concomitant interaction of the actin binding domain 2 (ABD2) comprising spectrin like repeats 11 to 15 (R11-15) of the central domain of dystrophin, with both actin and membrane lipids, can greatly increase membrane stiffness. Based on a combination of SAXS and SANS measurements, mass spectrometry analysis of cross-linked complexes and interactive low-resolution simulations, we explored in vitro the molecular properties of dystrophin that allow the formation of ABD2-F-actin and ABD2-membrane model complexes. In dystrophin we identified two subdomains interacting with F-actin, one located in R11 and a neighbouring region in R12 and another one in R15, while a single lipid binding domain was identified at the C-terminal end of R12. Relative orientations of the dystrophin central domain with F-actin and a membrane model were obtained from docking simulation under experimental constraints. SAXS-based models were then built for an extended central subdomain from R4 to R19, including ABD2. Overall results are compatible with a potential F-actin/dystrophin/membrane lipids ternary complex. Our description of this selected part of the dystrophin associated complex bridging muscle cell membrane and cytoskeleton opens the way to a better understanding of how cell muscle scaffolding is maintained through this essential protein

Planck pre-launch status: calibration of the Low Frequency Instrument flight model radiometers

The Low Frequency Instrument (LFI) on-board the ESA Planck satellite carries eleven radiometer subsystems, called Radiometer Chain Assemblies (RCAs), each composed of a pair of pseudo-correlation receivers. We describe the on-ground calibration campaign performed to qualify the flight model RCAs and to measure their pre-launch performances. Each RCA was calibrated in a dedicated flight-like cryogenic environment with the radiometer front-end cooled to 20K and the back-end at 300K, and with an external input load cooled to 4K. A matched load simulating a blackbody at different temperatures was placed in front of the sky horn to derive basic radiometer properties such as noise temperature, gain, and noise performance, e.g. 1/f noise. The spectral response of each detector was measured as was their susceptibility to thermal variation. All eleven LFI RCAs were calibrated. Instrumental parameters measured in these tests, such as noise temperature, bandwidth, radiometer isolation, and linearity, provide essential inputs to the Planck-LFI data analysis.Comment: 15 pages, 18 figures. Accepted for publication in Astronomy and Astrophysic

Planck pre-launch status: Low Frequency Instrument calibration and expected scientific performance

We give the calibration and scientific performance parameters of the Planck Low Frequency Instrument (LFI) measured during the ground cryogenic test campaign. These parameters characterise the instrument response and constitute our best pre-launch knowledge of the LFI scientific performance. The LFI shows excellent $1/f$ stability and rejection of instrumental systematic effects; measured noise performance shows that LFI is the most sensitive instrument of its kind. The set of measured calibration parameters will be updated during flight operations through the end of the mission.Comment: Accepted for publications in Astronomy and Astrophysics. Astronomy & Astrophysics, 2010 (acceptance date: 12 Jan 2010

The impacts of environmental warming on Odonata: a review

Climate change brings with it unprecedented rates of increase in environmental temperature, which will have major consequences for the earth's flora and fauna. The Odonata represent a taxon that has many strong links to this abiotic factor due to its tropical evolutionary history and adaptations to temperate climates. Temperature is known to affect odonate physiology including life-history traits such as developmental rate, phenology and seasonal regulation as well as immune function and the production of pigment for thermoregulation. A range of behaviours are likely to be affected which will, in turn, influence other parts of the aquatic ecosystem, primarily through trophic interactions. Temperature may influence changes in geographical distributions, through a shifting of species' fundamental niches, changes in the distribution of suitable habitat and variation in the dispersal ability of species. Finally, such a rapid change in the environment results in a strong selective pressure towards adaptation to cope and the inevitable loss of some populations and, potentially, species. Where data are lacking for odonates, studies on other invertebrate groups will be considered. Finally, directions for research are suggested, particularly laboratory studies that investigate underlying causes of climate-driven macroecological patterns

Long-Term Conditioning to Elevated pCO2 and Warming Influences the Fatty and Amino Acid Composition of the Diatom Cylindrotheca fusiformis

The unabated rise in anthropogenic CO2 emissions is predicted to strongly influence the ocean's environment, increasing the mean sea-surface temperature by 4°C and causing a pH decline of 0.3 units by the year 2100. These changes are likely to affect the nutritional value of marine food sources since temperature and CO2 can influence the fatty (FA) and amino acid (AA) composition of marine primary producers. Here, essential amino (EA) and polyunsaturated fatty (PUFA) acids are of particular importance due to their nutritional value to higher trophic levels. In order to determine the interactive effects of CO2 and temperature on the nutritional quality of a primary producer, we analyzed the relative PUFA and EA composition of the diatom Cylindrotheca fusiformis cultured under a factorial matrix of 2 temperatures (14 and 19°C) and 3 partial pressures of CO2 (180, 380, 750 μatm) for >250 generations. Our results show a decay of ∼3% and ∼6% in PUFA and EA content in algae kept at a pCO2 of 750 μatm (high) compared to the 380 μatm (intermediate) CO2 treatments at 14°C. Cultures kept at 19°C displayed a ∼3% lower PUFA content under high compared to intermediate pCO2, while EA did not show differences between treatments. Algae grown at a pCO2 of 180 μatm (low) had a lower PUFA and AA content in relation to those at intermediate and high CO2 levels at 14°C, but there were no differences in EA at 19°C for any CO2 treatment. This study is the first to report adverse effects of warming and acidification on the EA of a primary producer, and corroborates previous observations of negative effects of these stressors on PUFA. Considering that only ∼20% of essential biomolecules such as PUFA (and possibly EA) are incorporated into new biomass at the next trophic level, thepotential impacts of adverse effects of ocean warming and acidification at the base of the food web may be amplified towards higher trophic levels, which rely on them as source of essential biomolecules