On-line construction of position heaps

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it considers the suffixes ordered from left to right. Our construction is based on classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees [Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into the augmented position heap that allows for a linear-time string matching algorithm [Ehrenfeucht et al, 2011].Comment: to appear in Journal of Discrete Algorithm

Morphological and molecular diversity among cassava genotypes.

The objective of this work was to characterize morphologically and molecularly the genetic diversity of cassava accessions, collected from different regions in Brazil. A descriptive analysis was made for 12 morphological traits in 419 accessions. Data was transformed into binary data for cluster analysis and analysis of molecular variance. A higher proportion of white or cream (71%) root cortex color was found, while flesh colors were predominantly white (49%) and cream (42%). Four accession groups were classified by the cluster analysis, but they were not grouped according to their origin, which indicates that diversity is not structured in space. The variation was greater within regions (95.6%). Sixty genotypes were also evaluated using 14 polymorphic microsatellite markers. Molecular results corroborated the morphological ones, showing the same random distribution of genotypes, with no grouping according to origin. Diversity indices were high for each region, and a greater diversity was found within regions, with: a mean number of alleles per locus of 3.530; observed and expected heterozygosity of 0.499 and 0.642, respectively; and Shannon index of 1.03. The absence of spatial structure among cassava genotypes according to their origins shows the anthropic influence in the distribution and movement of germplasm, both within and among regions.Título em português: Diversidade morfológica e molecular entre genótipos de mandioca

Structural and molecular characteristics of axons in the long head of the biceps tendon

The innervation of the long head of the biceps tendon (LHBT) is not sufficiently documented. This is a drawback since pathologies of the LHBT are a major source of shoulder pain. Thus, the study aimed to characterize structurally and molecularly nervous elements of the LHBT. The proximal part of 11 LHBTs was harvested intraoperatively. There were 8 female and 3 male specimens. Age ranged from 66 to 86 years. For structural analyses, nervous elements were viewed in the transmission electron microscope. For molecular characterization, we used general neuronal markers including antibodies against neurofilament and protein gene product 9.5 (PGP9.5) as well as specific neuronal markers including antibodies against myelin basic protein (MBP), calcitonin gene-related product (CGRP), substance P (SP), tyrosine hydroxylase (TH), and growth-associated protein 43 (GAP43). Anti-neurofilament and anti-PGP9.5 visualized the overall innervation. Anti-MBP visualized myelination, anti-CGRP and anti-SP nociceptive fibers, anti-TH sympathetic nerve fibers, and anti-GAP43 nerve fibers during development and regeneration. Immunolabeled sections were analyzed in the confocal laser scanning microscope. We show that the LHBT contains unmyelinated as well as myelinated nerve fibers which group in nerve fascicles and follow blood vessels. Manny myelinated and unmyelinated axons exhibit molecular features of nociceptive nerve fibers. Another subpopulation of unmyelinated axons exhibits molecular characteristics of sympathetic nerve fibers. Unmyelinated sympathetic fibers and unmyelinated nociceptive fibers express proteins that are found during development and regeneration. Present findings support the hypothesis that ingrowth of nociceptive fibers are the source of chronic tendon pain

Single-qubit unitary gates by graph scattering

We consider the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to $n=9$ vertices for which the scattering implements a single-qubit gate. As $n$ increases, the number of new unitary operations increases exponentially, and for $n>6$ the majority correspond to rotations about axes distributed roughly uniformly across the Bloch sphere. Rotations by both rational and irrational multiples of $\pi$ are found.Comment: 8 pages, 7 figure

Improved Bounds on Quantum Learning Algorithms

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum black-box queries which are required to exactly identify an unknown function from C is $O(\frac{\log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$, where $\hat{\gamma}^{C}$ is a combinatorial parameter of the class C. We essentially resolve this conjecture in the affirmative by giving a quantum algorithm that, for any class C, identifies any unknown function from C using $O(\frac{\log |C| \log \log |C|}{\sqrt{{\hat{\gamma}}^{C}}})$ quantum black-box queries. We consider a range of natural problems intermediate between the exact learning problem (in which the learner must obtain all bits of information about the black-box function) and the usual problem of computing a predicate (in which the learner must obtain only one bit of information about the black-box function). We give positive and negative results on when the quantum and classical query complexities of these intermediate problems are polynomially related to each other. Finally, we improve the known lower bounds on the number of quantum examples (as opposed to quantum black-box queries) required for $(\epsilon,\delta)$-PAC learning any concept class of Vapnik-Chervonenkis dimension d over the domain $\{0,1\}^n$ from $\Omega(\frac{d}{n})$ to $\Omega(\frac{1}{\epsilon}\log \frac{1}{\delta}+d+\frac{\sqrt{d}}{\epsilon})$. This new lower bound comes closer to matching known upper bounds for classical PAC learning.Comment: Minor corrections. 18 pages. To appear in Quantum Information Processing. Requires: algorithm.sty, algorithmic.sty to buil