Average number of flips in pancake sorting

We are given a stack of pancakes of different sizes and the only allowed operation is to take several pancakes from top and flip them. The unburnt version requires the pancakes to be sorted by their sizes at the end, while in the burnt version they additionally need to be oriented burnt-side down. We present an algorithm with the average number of flips, needed to sort a stack of n burnt pancakes, equal to 7n/4+O(1) and a randomized algorithm for the unburnt version with at most 17n/12+O(1) flips on average. In addition, we show that in the burnt version, the average number of flips of any algorithm is at least n+\Omega(n/log n) and conjecture that some algorithm can reach n+\Theta(n/log n). We also slightly increase the lower bound on g(n), the minimum number of flips needed to sort the worst stack of n burnt pancakes. This bound, together with the upper bound found by Heydari and Sudborough in 1997, gives the exact number of flips to sort the previously conjectured worst stack -I_n for n=3 mod 4 and n>=15. Finally we present exact values of f(n) up to n=19 and of g(n) up to n=17 and disprove a conjecture of Cohen and Blum by showing that the burnt stack -I_{15} is not the worst one for n=15.Comment: 21 pages, new computational results for unburnt pancakes (up to n=19

Outcomes of a marketing knowledge intervention using a metaphoric story-line approach: a mixed-methods study of 5 Israeli SMEs.

The purpose of this mixed-methods research is to determine the effectiveness of the Kingdom Marketing (KM) intervention for improving Israeli SME marketing knowledge among managers and employees of Israeli small and medium-sized business. The secondary objective of the study was to portray the process of change in participating organisations. The newly developed KM intervention programme was designed to enhance Israeli SMEs’ marketing knowledge and marketing strategy, imparting new marketing skills and allowing SMEs to operate with better marketing knowledge. The intervention uses a metaphoric story-line approach to teach participants in mediator-led sessions to understand and use important marketing concepts, such as the difference between sales and marketing. Although the intervention has been used in business settings, it has not yet been empirically validated using rigorous methods. This study was conducted using a mixed methods paradigm with an embedded experimental design. Five Israeli based SMEs were recruited to take part in the training programme. The research consisted of three phases. In Phase 1, I administered a preintervention evaluation to measure five variables: awareness of marketing processes, mistaken marketing attitudes, incorrect marketing process beliefs, organisational marketing skills, and marketing need awareness. Participants were also interviewed during Phase 1. In Phase 2, I administered the KM intervention and collected qualitative data in the form of daily open-ended feedback and a researcher diary. In Phase 3, I administered a postintervention evaluation to assess change in the five quantitative variables, and I conducted a second round of interviews. The findings indicated that the KM intervention programme (a) increased awareness of marketing processes, (b) reduced mistaken marketing attitudes, (c) reduced incorrect marketing process believes, and (d) increased marketing need awareness. However, the intervention had no significant effect on organisational marketing skills. Qualitative analysis confirmed that, although the KM intervention empowered participants with marketing knowledge and skills, it did not result in broad organisational changes. I conclude that the KM intervention programme is valid and worthy of wider use for promoting the survival of SME businesses through marketing knowledge and skill improvement. However, the intervention should be used in conjunction with internal efforts to translate increased knowledge into lasting organisational change.N/

The Frequency of Carbon Stars Among Extremely Metal-Poor Stars

We demonstrate that there are systematic scale errors in the [Fe/H] values determined by the Hamburg/ESO Survey (and by inference by the HK Survey in the past) for certain extremely metal poor highly C-enhanced giants. The consequences of these scale errors are that a) the fraction of carbon stars at extremely low metallicities has been overestimated in several papers in the recent literature b) the number of extremely metal poor stars known is somewhat lower than has been quoted in the recent literature c) the yield for extremely metal poor stars by the HES Survey is somewhat lower than is stated in the recent literature. A preliminary estimate for the frequency of Carbon stars among the giants in the HES sample with -4 < [Fe/H] < -2.0 dex is 7.4 +-2.9%; adding an estimate for the C-enhanced giants with [C/Fe] > 1.0 dex without detectable C2 bands raises the fraction to 14 +-4$%. We rely on the results of an extensive set of homogeneous detailed abundance analyses of stars expected to have [Fe/H] < -3.0 dex selected from the HES to establish these claims. We have found that the Fe-metallicity of the cooler (Teff < 5200K) C-stars as derived from spectra taken with HIRES at Keck are a factor of ~10 higher than those obtained via the algorithm used by the HES project to analyze the moderate resolution follow-up spectra, which is identical to that used until very recently by the HK Survey. This error in Fe-abundance estimate for C-stars arises from a lowering of the emitted flux in the continuum bandpasses of the KP (3933 A line of CaII) and particularly the HP2 (Hdelta) indices used to estimate [Fe/H] due to absorption from strong molecular bands.Comment: Accepted to the ApJL after a very lengthly duel with the 3 simultaneous referee

Polynomial-time sortable stacks of burnt pancakes

Pancake flipping, a famous open problem in computer science, can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible. In that context, a prefix reversal of length k reverses the order of the first k elements of the permutation. The burnt variant of pancake flipping involves permutations of signed integers, and reversals in that case not only reverse the order of elements but also invert their signs. Although three decades have now passed since the first works on these problems, neither their computational complexity nor the maximal number of prefix reversals needed to sort a permutation is yet known. In this work, we prove a new lower bound for sorting burnt pancakes, and show that an important class of permutations, known as "simple permutations", can be optimally sorted in polynomial time.Comment: Accepted pending minor revisio

Hermitian vector fields and special phase functions

We start by analysing the Lie algebra of Hermitian vector fields of a Hermitian line bundle. Then, we specify the base space of the above bundle by considering a Galilei, or an Einstein spacetime. Namely, in the first case, we consider, a fibred manifold over absolute time equipped with a spacelike Riemannian metric, a spacetime connection (preserving the time fibring and the spacelike metric) and an electromagnetic field. In the second case, we consider a spacetime equipped with a Lorentzian metric and an electromagnetic field. In both cases, we exhibit a natural Lie algebra of special phase functions and show that the Lie algebra of Hermitian vector fields turns out to be naturally isomorphic to the Lie algebra of special phase functions. Eventually, we compare the Galilei and Einstein cases

Experimental study on the structure and stability of a double-diffusive interface in a laterally heated enclosure

Experiments are carried out to investigate the structure of a double diffusive interface separating two layers in a laterally heated enclosure. The main goal of this work is to study the structure of the interface and some of its instability characteristics. The velocity field at the vicinity of the interface is measured by a PIV system. Vertical concentration and temperature profiles are measured using a micro-scale conductivity/temperature instrument and the flow is visualized using the schlieren technique. Analysis of mean horizontal velocity profiles, obtained at different times during the experiment, illustrates the increasing tilt of the interface with time. Spectral analyses of velocity perturbations under unstable and stable conditions confirm the existence of the coherent vortices observed by the schlieren technique. The vortices above and below the interface are associated with different dominant frequencies due to the asymmetric character of the flow. Measurements show that the vortices are generated outside the region of the stabilizing concentration profile by a mechanism, which is essentially thermal and similar to Rayleigh-Bénard instability with weak shear

The Frequency of Carbon Rich Stars Among Extremely Metal Poor Stars

We demonstrate that there are systematic scale errors in the [Fe/H] values determined by the Hamburg/ESO Survey (and by the HK Survey by inference) for certain extremely metal poor (EMP) highly C-enhanced giants. The consequences of these scale errors are that a) the fraction of carbon stars at extremely low metallicities has been substantially overestimated in several papers in the recent literature b) the number of EMP stars known is somewhat lower than has been quoted in the recent literature c) the yield for EMP stars by the HK and the HES Survey is somewhat lower than is stated in the recent literature. A preliminary estimate for the frequency of Carbon stars among the giants in the HES sample with -4 < [Fe/H] < -2.0 dex is 7.4 \pm 2.9%, and for C-rich giants with [C/Fe] > +1.0 dex is 14.4 \pm 4%. Here we present the key results of detailed abundance analyses of 14 C-stars selected from the HES as candidate EMP stars, of ~50 such stars analyzed. About 80% of such C-stars show highly enhanced Ba as well, with C enhanced by a factor of about 100, and [Ba/C] roughly Solar. These stars often show prominent lead lines, The remaining 20% of the C-stars do not show an enhancemement of the s-process neutron capture elements around the Ba peak. They tend to be the most metal-poor stars studied. We suggest that all these EMP C-stars are the remnants of the secondary in a mass transfer binary system where the former primary was an AGB star, which transferred substantial mass at that evolutionary stage. (published abstract will be shorter due to space limitations)Comment: Submitted to the proceedings of the IAU Symposium 228, From Lithium to Uranium: Elemental Tracers of Early Cosmic Evolution (Paris, 23--27 May 2005), Cambridge University Press, ed: Vanessa Hill, Patrick Francois & Francesca Prima

Splitting full matrix algebras over algebraic number fields

Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. (An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.) As a consequence, we obtain a polynomial time ff-algorithm to compute isomorphisms of central simple algebras of bounded degree over K.Comment: 15 pages; Theorem 2 and Lemma 8 correcte

Carbon Stars in the Hamburg/ESO Survey: Abundances

We have carried out a detailed abundance analysis for a sample of 16 carbon stars found among candidate extremely metal-poor (EMP) stars from the Hamburg/ESO Survey. We find that the Fe-metallicities for the cooler C-stars (Teff ~ 5100K) have been underestimated by a factor of ~10 by the standard HES survey tools. The results presented here provided crucial supporting data used by Cohen et al (2006) to derive the frequency of C-stars among EMP stars. C-enhancement in these EMP C-stars appears to be independent of Fe-metallicity and approximately constant at ~1/5 the solar C/H. The mostly low C12/C13 ratios (~4) and the high N abundances in many of these stars suggest that material which has been through proton burning via the CN cycle comprises most of the stellar envelope. C-enhancement is associated with strong enrichment of heavy nuclei beyond the Fe-peak for 12 of the 16 stars. The remaining C-stars from the HES, which tend to be the most Fe-metal poor, show no evidence for enhancement of the heavy elements. Very high enhancements of lead are detected in some of the C-stars with highly enhanced Ba. (We show that) the s-process is responsible for the enhancement of the heavy elements for the majority of the C-stars in our sample. We suggest that both the s-process rich and Ba-normal C-stars result from phenomena associated with mass transfer in binary systems. This leads directly to the progression from C-stars to CH stars and then to Ba stars as the Fe-metallicity increases. (abridged and slightly edited to shorten)Comment: AJ, in press, submitted 13 Dec, 2005, accepted 21 March 200

Competition as rational action : why young children cannot appreciate competitive games

Understanding rational actions requires perspective taking both with respect to means and with respect to objectives. This study addresses the question of whether the two kinds of perspective taking develop simultaneously or in sequence. It is argued that evidence from competitive behavior is best suited for settling this issue. A total of 71 kindergarten children between 3 and 5 years of age participated in a competitive game of dice and were tested on two traditional false belief stories as well as on several control tasks (verbal intelligence, inhibitory control, and working memory). The frequency of competitive poaching moves in the game correlated with correct predictions of mistaken actions in the false belief task. Hierarchical linear regression after controlling for age and control variables showed that false belief understanding significantly predicted the amount of poaching moves. The results speak for an interrelated development of the capacity for “instrumental” and “telic” perspective taking. They are discussed in the light of teleology as opposed to theory use and simulation