Comeback from Failure

John 21:1-2

Efficient digital-to-analog encoding

An important issue in analog circuit design is the problem of digital-to-analog conversion, i.e., the encoding of Boolean variables into a single analog value which contains enough information to reconstruct the values of the Boolean variables. A natural question is: what is the complexity of implementing the digital-to-analog encoding function? That question was answered by Wegener (see Inform. Processing Lett., vol.60, no.1, p.49-52, 1995), who proved matching lower and upper bounds on the size of the circuit for the encoding function. In particular, it was proven that [(3n-1)/2] 2-input arithmetic gates are necessary and sufficient for implementing the encoding function of n Boolean variables. However, the proof of the upper bound is not constructive. In this paper, we present an explicit construction of a digital-to-analog encoder that is optimal in the number of 2-input arithmetic gates. In addition, we present an efficient analog-to-digital decoding algorithm. Namely, given the encoded analog value, our decoding algorithm reconstructs the original Boolean values. Our construction is suboptimal in that it uses constants of maximum size n log n bits; the nonconstructive proof uses constants of maximum size 2n+[log n] bits

Modeling the chemical evolution of Omega Centauri using three-dimensional hydrodynamical simulations

We present a hydrodynamical and chemical model for the globular cluster Omega Cen, under the assumption that it is the remnant of an ancient dwarf spheroidal galaxy (dSph), the bulk of which was disrupted and accreted by our Galaxy ~10 Gyr ago. We highlight the very different roles played by Type II and Type Ia supernovae (SNe) in the chemical enrichment of the inner regions of the putative parent dSph. While the SNe II pollute the interstellar medium rather uniformly, the SNe Ia ejecta may remain confined inside dense pockets of gas as long as succesive SNe II explosions spread them out. Stars forming in such pockets have lower alpha-to-iron ratios than the stars forming elsewhere. Owing to the inhomogeneous pollution by SNe Ia, the metal distribution of the stars in the central region differs substantially from that of the main population of the dwarf galaxy, and resembles that observed in Omega Cen. This inhomogeneous mixing is also responsible for a radial segregation of iron-rich stars with depleted [alpha/Fe] ratios, as observed in some dSphs. Assuming a star formation history of ~1.5 Gyr, our model succeeds in reproducing both the iron and calcium distributions observed in Omega Cen and the main features observed in the empirical alpha/Fe versus Fe/H plane. Finally, our model reproduces the overall spread of the color-magnitude diagram, but fails in reproducing the morphology of the SGB-a and the double morphology of the main sequence. However, the inhomogeneous pollution reduces (but does not eliminate) the need for a significantly enhanced helium abundance to explain the anomalous position of the blue main sequence. Further models taking into account the dynamical interaction of the parent dwarf galaxy with the Milky Way and the effect of AGB pollution will be required.Comment: 15 pages, 13 figures. MNRAS accepte

Corporate Real Estate Management in the Retail Sector: Investigation of Current Strategy and Structure

Retail organizations are often cited as being at the forefront of corporate real estate management. This research found that the retail sector is characterized by diversity both in terms of the degree to which organizations are vertically integrated and in terms of the range of modes of retailing they engage in. This in turn led to diverse real estate portfolios. However, regardless of this diversity, the over riding strategy was focused on supporting the core activity. This study provides a snapshot of current practice however it also uncovers the need for a greater understanding of the diversity in practice.

Colour analysis of degraded parchment

Multispectral imaging was employed to collect data on the degradation of an 18th century parchment by a series of physical and chemical treatments. Each sample was photographed before and after treatment by a monochrome digital camera with 21 narrow-band filters. A template-matching technique was used to detect the circular holes in each sample and a four-point projective transform to register the 21 images. Colour accuracy was verified by comparison of reconstructed spectra with measurements by spectrophotometer

All for One and One for All! Disparity Between Overall Crew’s and Individual Rowers’ Pacing Strategies During Rowing

Purpose: This study examined individual contributions to overall pacing strategy during 2- and 5-km rowing trials in a cox-less-4 boat. Methods: A crew of 4 male rowers performed maximal-effort on-water trials over 2 and 5 km, and power output during every individual stroke was measured for each crew member. Mean overall boat and individual rower stroke power were calculated for each 25% epoch (25% of total strokes taken), and power for each individual epoch was calculated as a percentage of mean power maintained over the entire distance. The coefficient of variation was used to determine stroke-to-stroke and epoch-to-epoch variability for individual rowers and the overall boat. Results: In both trials, the overall pacing strategy consisted of a high power output in the initial 25% that decreased in the middle 50% and increased again in the final 25%. However, individual rower data indicate wide variation in individual power profiles that did not always mimic the overall boat profile. Conclusions: This study demonstrates that overall boat power profiles during 2- and 5-km rowing trials are similar to velocity profiles previously reported for individual ergometry and on-water racing events. However, this over-all profile is achieved despite considerable variation in individual rower profiles. Further research is warranted to determine the mechanisms through which individual contributions to overall pacing strategy are regulated and the effectiveness or oth-erwise of seemingly disparate individual strategies on overall performance

Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings

By using a semi-analytical dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E, {\bf 70}, 066107 (2004)], we have studied the synchronization of stochastic, small-world (SW) networks of FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity between results for {\it diffusive} and {\it sigmoid} couplings have been discussed. It has been shown that with introducing the weak heterogeneity to regular networks, the synchronization may be slightly increased for diffusive couplings, while it is decreased for sigmoid couplings. This increase in the synchronization for diffusive couplings is shown to be due to their local, negative feedback contributions, but not due to the shorten average distance in SW networks. Synchronization of SW networks depends not only on their structure but also on the type of couplings.Comment: 17 pages, 8 figures, accepted in Phys. Rev. E with some change