Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

The Critical Exponent is Computable for Automatic Sequences

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Towards the implementation of a sustainable cold chain for the livestock value chain in Bangladesh

The cold chain is essential for food quality and safety. Good management of the postharvest cold chain can reduce food losses. The International Institute of Refrigeration (IIR) estimated that the lack of a cold chain causes significant global food losses of up to 20% of the global food supply (IIR, 2009). Besides economic and health considerations, the environmental sustainability of the food cold supply chain should be considered to prevent further increases in emissions that could potentially increase global warming. This paper presents an assessment of the livestock cold chain related gaps in Bangladesh which is one of the initiative within the World Bank LDDP (Livestock and Dairy Development Project) project (LDDP, P161246). Information on technological and non-technological issues which can be tackled are presented. Practical recommendations to develop the cold chain in Bangladesh for milk and meat are provided

Multifractal eigenstates of quantum chaos and the Thue-Morse sequence

We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasi-periodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to Thue-Morse sequence, and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.Comment: Substantially modified from the original, worth a second download. To appear in Phys. Rev. E as a Rapid Communicatio

Shuffling cards, factoring numbers, and the quantum baker's map

It is pointed out that an exactly solvable permutation operator, viewed as the quantization of cyclic shifts, is useful in constructing a basis in which to study the quantum baker's map, a paradigm system of quantum chaos. In the basis of this operator the eigenfunctions of the quantum baker's map are compressed by factors of around five or more. We show explicitly its connection to an operator that is closely related to the usual quantum baker's map. This permutation operator has interesting connections to the art of shuffling cards as well as to the quantum factoring algorithm of Shor via the quantum order finding one. Hence we point out that this well-known quantum algorithm makes crucial use of a quantum chaotic operator, or at least one that is close to the quantization of the left-shift, a closeness that we also explore quantitatively.Comment: 12 pgs. Substantially elaborated version, including a new route to the quantum bakers map. To appear in J. Phys.

Quantum chaos in the spectrum of operators used in Shor's algorithm

We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the eigenangles as well as the distribution of the eigenvector components follow the CUE ensemble of random matrices, of relevance to quantized chaotic systems that violate time-reversal symmetry. However, as the algorithm tracks the evolution of a single state, it is possible to employ other operators, in particular it is possible that the generic quantum chaos found above becomes of a nongeneric kind such as is found in the quantum cat maps, and in toy models of the quantum bakers map.Comment: Title and paper modified to include interesting additional possibilities. Principal results unaffected. Accepted for publication in Phys. Rev. E as Rapid Com

Investigation of genetic variability related to the in vitro floral hermaphrodism induction in Date palm (Phoenix dactylifera L.)

This paper reports on a molecular analysis study conducted on Date palm flowers from the Deglet Nour cultivar to investigate putative genetic variability related to the in vitro floral hermaphrodism induction. Natural male and female as well as hermaphrodite ones that were produced in vitro through the hormonal treatment of female flowers were submitted to ISSR-PCR analysis. Microsatellite based amplification (ISSR) was applied on genomic DNA from inflorescences taken at different periods of hormonal treatment corresponding to the various deviation stages to search for putative variations that may have occurred on the initial genome due to the application of plant growth regulators. Several amplification bands were purified, cloned, and sequenced. The results revealed that hormonal treatment entailed no detectable genetic variation in the treated Date palm flowers. Two of the selected and ISSR-PCR amplified DNA fragments showed however, possible links with flowering regulation. The findings indicate that these sequences are potential candidate gene markers that may enhance our understanding of flower development and sex identification in this species.Key words: Date palm, female inflorescences, hermaphrodite flowers, in vitro culture, ISSR, sex identification

Resveratrol Reverses Endothelial Colony-Forming Cell Dysfunction in Adulthood in a Rat Model of Intrauterine Growth Restriction.

Individuals born after intrauterine growth restriction (IUGR) are at risk of developing cardiovascular diseases (CVDs). Endothelial dysfunction plays a role in the pathogenesis of CVDs; and endothelial colony-forming cells (ECFCs) have been identified as key factors in endothelial repair. In a rat model of IUGR induced by a maternal low-protein diet, we observed an altered functionality of ECFCs in 6-month-old males, which was associated with arterial hypertension related to oxidative stress and stress-induced premature senescence (SIPS). Resveratrol (R), a polyphenol compound, was found to improve cardiovascular function. In this study, we investigated whether resveratrol could reverse ECFC dysfunctions in the IUGR group. ECFCs were isolated from IUGR and control (CTRL) males and were treated with R (1 μM) or dimethylsulfoxide (DMSO) for 48 h. In the IUGR-ECFCs, R increased proliferation (5'-bromo-2'-deoxyuridine (BrdU) incorporation, p < 0.001) and improved capillary-like outgrowth sprout formation (in Matrigel), nitric oxide (NO) production (fluorescent dye, p < 0.01), and endothelial nitric oxide synthase (eNOS) expression (immunofluorescence, p < 0.001). In addition, R decreased oxidative stress with reduced superoxide anion production (fluorescent dye, p < 0.001); increased Cu/Zn superoxide dismutase expression (Western blot, p < 0.05); and reversed SIPS with decreased beta-galactosidase activity (p < 0.001), and decreased p16 <sup>ink4a</sup> (p < 0.05) and increased Sirtuin-1 (p < 0.05) expressions (Western blot). No effects of R were observed in the CTRL-ECFCs. These results suggest that R reverses long-term ECFC dysfunctions related to IUGR