Semidefinite code bounds based on quadruple distances

Let $A(n,d)$ be the maximum number of $0,1$ words of length $n$, any two having Hamming distance at least $d$. We prove $A(20,8)=256$, which implies that the quadruply shortened Golay code is optimal. Moreover, we show $A(18,6)\leq 673$, $A(19,6)\leq 1237$, $A(20,6)\leq 2279$, $A(23,6)\leq 13674$, $A(19,8)\leq 135$, $A(25,8)\leq 5421$, $A(26,8)\leq 9275$, $A(21,10)\leq 47$, $A(22,10)\leq 84$, $A(24,10)\leq 268$, $A(25,10)\leq 466$, $A(26,10)\leq 836$, $A(27,10)\leq 1585$, $A(25,12)\leq 55$, and $A(26,12)\leq 96$. The method is based on the positive semidefiniteness of matrices derived from quadruples of words. This can be put as constraint in a semidefinite program, whose optimum value is an upper bound for $A(n,d)$. The order of the matrices involved is huge. However, the semidefinite program is highly symmetric, by which its feasible region can be restricted to the algebra of matrices invariant under this symmetry. By block diagonalizing this algebra, the order of the matrices will be reduced so as to make the program solvable with semidefinite programming software in the above range of values of $n$ and $d$.Comment: 15 page

The Lutz-Kelker bias in trigonometric parallaxes

The theoretical prediction that trigonometric parallaxes suffer from a statistical effect, has become topical again now that the results of the Hipparcos satellite have become available. This statistical effect, the so-called Lutz-Kelker bias, causes measured parallaxes to be too large. This has the implication that inferred distances, and hence inferred luminosities are too small. Published analytic calculations of the Lutz-Kelker bias indicate that the inferred luminosity of an object is, on average, 30% too small when the error in the parallax is only 17.5%. Yet, this bias has never been determined empirically. In this paper we investigate whether there is such a bias by comparing the best Hipparcos parallaxes which ground-based measurements. We find that there is indeed a large bias affecting parallaxes, with an average and scatter comparable to predictions. We propose a simple method to correct for the LK bias, and apply it successfully to a sub-sample of our stars. We then analyze the sample of 26 `best' Cepheids used by Feast & Catchpole (1997) to derive the zero-point of the fundamental mode pulsators and leads to a distance modulus to the Large Magellanic Cloud - based on Cepheid parallaxes- of 18.56 +/- 0.08, consistent with previous estimates.Comment: MNRAS Letters in press; 6 pages LaTeX, 6 ps figure

Reconstructing the Local Twist of Coronal Magnetic Fields and the Three-Dimensional Shape of the Field Lines from Coronal Loops in EUV and X-Ray Images

Non-linear force-free fields are the most general case of force-free fields, but the hardest to model as well. There are numerous methods of computing such fields by extrapolating vector magnetograms from the photosphere, but very few attempts have so far made quantitative use of coronal morphology. We present a method to make such quantitative use of X-Ray and EUV images of coronal loops. Each individual loop is fit to a field line of a linear force-free field, allowing the estimation of the field line's twist, three-dimensional geometry and the field strength along it. We assess the validity of such a reconstruction since the actual corona is probably not a linear force-free field and that the superposition of linear force-free fields is generally not itself a force-free field. To do so, we perform a series of tests on non-linear force-free fields, described in Low & Lou (1990). For model loops we project field lines onto the photosphere. We compare several results of the method with the original field, in particular the three-dimensional loop shapes, local twist (coronal alpha), distribution of twist in the model photosphere and strength of the magnetic field. We find that, (i) for these trial fields, the method reconstructs twist with mean absolute deviation of at most 15% of the range of photospheric twist, (ii) that heights of the loops are reconstructed with mean absolute deviation of at most 5% of the range of trial heights and (iii) that the magnitude of non-potential contribution to photospheric field is reconstructed with mean absolute deviation of at most 10% of the maximal value.Comment: submitted to Ap

Convective Dynamos and the Minimum X-ray Flux in Main Sequence Stars

The objective of this paper is to investigate whether a convective dynamo can account quantitatively for the observed lower limit of X-ray surface flux in solar-type main sequence stars. Our approach is to use 3D numerical simulations of a turbulent dynamo driven by convection to characterize the dynamic behavior, magnetic field strengths, and filling factors in a non-rotating stratified medium, and to predict these magnetic properties at the surface of cool stars. We use simple applications of stellar structure theory for the convective envelopes of main-sequence stars to scale our simulations to the outer layers of stars in the F0--M0 spectral range, which allows us to estimate the unsigned magnetic flux on the surface of non-rotating reference stars. With these estimates we use the recent results of \citet{Pevtsov03} to predict the level of X-ray emission from such a turbulent dynamo, and find that our results compare well with observed lower limits of surface X-ray flux. If we scale our predicted X-ray fluxes to \ion{Mg}{2} fluxes we also find good agreement with the observed lower limit of chromospheric emission in K dwarfs. This suggests that dynamo action from a convecting, non-rotating plasma is a viable alternative to acoustic heating models as an explanation for the basal emission level seen in chromospheric, transition region, and coronal diagnostics from late-type stars.Comment: ApJ, accepted, 30 pages with 7 figure

Mg II h + k emission lines as stellar activity indicators of main sequence F-K stars

The main purpose of this study is to use the IUE spectra in the analysis of magnetic activity of main sequence F-K stars. Combining IUE observations of MgII and optical spectroscopy of Ca II, the registry of ctivity of stars can be extended in time. We retrieved all the high-resolution spectra of F, G, and K main sequence stars observed by IUE (i.e. 1623 spectra of 259 F to K dwarf stars). We obtained the continuum surface flux near the Mg II h+k lines near 2800 \AA and the MgII line-core surface flux from the IUE spectra. We obtained a relation between the mean continuum flux near the MgII lines with the colour $B-V$ of the star. For a set of 117 nearly simultaneous observations of Mg II and Ca II fluxes of 21 F5 to K3 main sequence stars, we obtained a colour dependent relation between the Mount Wilson CaII S-index and the MgII emission line-core flux. As an application of this calibration, we computed the Mount Wilson index for all the dF to dK stars which have high resolution IUE spectra. For some of the most frequently observed main sequence stars, we analysed the Mount Wilson index S from the IUE spectra, together with the ones derived from visible spectra. We confirm the cyclic chromospheric activity of epsilon Eri (HD 22049) and beta Hydri (HD 2151), and we find a magnetic cycle in alpha Cen B (HD 128621). Complete abstract in the paper.Comment: 10 pages, accepted for publication in Astronomy and Astrophysic

Single machine scheduling with controllable processing times by submodular optimization

In scheduling with controllable processing times the actual processing time of each job is to be chosen from the interval between the smallest (compressed or fully crashed) value and the largest (decompressed or uncrashed) value. In the problems under consideration, the jobs are processed on a single machine and the quality of a schedule is measured by two functions: the maximum cost (that depends on job completion times) and the total compression cost. Our main model is bicriteria and is related to determining an optimal trade-off between these two objectives. Additionally, we consider a pair of associated single criterion problems, in which one of the objective functions is bounded while the other one is to be minimized. We reduce the bicriteria problem to a series of parametric linear programs defined over the intersection of a submodular polyhedron with a box. We demonstrate that the feasible region is represented by a so-called base polyhedron and the corresponding problem can be solved by the greedy algorithm that runs two orders of magnitude faster than known previously. For each of the associated single criterion problems, we develop algorithms that deliver the optimum faster than it can be deduced from a solution to the bicriteria problem

Quasi-periodic Fast-mode Wave Trains Within a Global EUV Wave and Sequential Transverse Oscillations Detected by SDO/AIA

We present the first unambiguous detection of quasi-periodic wave trains within the broad pulse of a global EUV wave (so-called "EIT wave") occurring on the limb. These wave trains, running ahead of the lateral CME front of 2-4 times slower, coherently travel to distances $>R_{sun}/2$ along the solar surface, with initial velocities up to 1400 km/s decelerating to ~650 km/s. The rapid expansion of the CME initiated at an elevated height of 110 Mm produces a strong downward and lateral compression, which may play an important role in driving the primary EUV wave and shaping its front forwardly inclined toward the solar surface. The waves have a dominant 2 min periodicity that matches the X-ray flare pulsations, suggesting a causal connection. The arrival of the leading EUV wave front at increasing distances produces an uninterrupted chain sequence of deflections and/or transverse (likely fast kink mode) oscillations of local structures, including a flux-rope coronal cavity and its embedded filament with delayed onsets consistent with the wave travel time at an elevated (by ~50%) velocity within it. This suggests that the EUV wave penetrates through a topological separatrix surface into the cavity, unexpected from CME caused magnetic reconfiguration. These observations, when taken together, provide compelling evidence of the fast-mode MHD wave nature of the {\it primary (outer) fast component} of a global EUV wave, running ahead of the {\it secondary (inner) slow} component of CME-caused restructuring.Comment: 17 pages, 12 figures; accepted by ApJ, April 24, 201

New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming

We give a new upper bound on the maximum size $A_q(n,d)$ of a code of word length $n$ and minimum Hamming distance at least $d$ over the alphabet of $q\geq 3$ letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in $n$ using semidefinite programming. For $q=3,4,5$ this gives several improved upper bounds for concrete values of $n$ and $d$. This work builds upon previous results of A. Schrijver [IEEE Trans. Inform. Theory 51 (2005), no. 8, 2859--2866] on the Terwilliger algebra of the binary Hamming schem