The Rényi Redundancy of Generalized Huffman Codes

Huffman's algorithm gives optimal codes, as measured by average codeword length, and the redundancy can be measured as the difference between the average codeword length and Shannon's entropy. If the objective function is replaced by an exponentially weighted average, then a simple modification of Huffman's algorithm gives optimal codes. The redundancy can now be measured as the difference between this new average and A. Renyi's (1961) generalization of Shannon's entropy. By decreasing some of the codeword lengths in a Shannon code, the upper bound on the redundancy given in the standard proof of the noiseless source coding theorem is improved. The lower bound is improved by randomizing between codeword lengths, allowing linear programming techniques to be used on an integer programming problem. These bounds are shown to be asymptotically equal. The results are generalized to the Renyi case and are related to R.G. Gallager's (1978) bound on the redundancy of Huffman codes

Orbiter windward surface entry Heating: Post-orbital flight test program update

Correlations of orbiter windward surface entry heating data from the first five flights are presented with emphasis on boundary layer transition and the effects of catalytic recombination. Results show that a single roughness boundary layer transition correlation developed for spherical element trips works well for the orbiter tile system. Also, an engineering approach for predicting heating in nonequilibrium flow conditions shows good agreement with the flight test data in the time period of significant heating. The results of these correlations, when used to predict orbiter heating for a high cross mission, indicate that the thermal protection system on the windward surface will perform successfully in such a mission

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

Low-energy electron scattering from methanol and ethanol

Measured and calculated differential cross sections for elastic (rotationally unresolved) electron scattering from two primary alcohols, methanol (CH3OH) and ethanol (C2H5OH), are reported. The measurements are obtained using the relative flow method with helium as the standard gas and a thin aperture as the collimating target gas source. The relative flow method is applied without the restriction imposed by the relative flow pressure conditions on helium and the unknown gas. The experimental data were taken at incident electron energies of 1, 2, 5, 10, 15, 20, 30, 50, and 100 eV and for scattering angles of 5°–130°. There are no previous reports of experimental electron scattering differential cross sections for CH3OH and C2H5OH in the literature. The calculated differential cross sections are obtained using two different implementations of the Schwinger multichannel method, one that takes all electrons into account and is adapted for parallel computers, and another that uses pseudopotentials and considers only the valence electrons. Comparison between theory and experiment shows that theory is able to describe low-energy electron scattering from these polyatomic targets quite well

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

Redefining smoking relapse as recovered social identity – secondary qualitative analysis of relapse narratives

Although many people in the general population manage to quit smoking, relapse is common. Theory underpinning the determinants of smoking relapse is under-developed. This article aims to specify theoretical insight into the process of relapse to smoking, to underpin effective intervention development. Secondary qualitative analysis of extended narratives of smoking relapse (n=23) were inductively coded within our conceptual framework of a socially situated narrative theoretical approach to identity. Smoking relapse is conceptualised as a situated rational response to a ‘disruption’ in individual narrative identity formation, and an attempt to recover a lost social identity. Emotional reactions to relapse, such as pleasure, but also guilt and shame, support this assertion by demonstrating the ambivalence of re-engaging in a behaviour that is situated and rational in terms of individual identity formation, yet ostracised and stigmatised by wider culture

Determining Principal Component Cardinality through the Principle of Minimum Description Length

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives objective compression-based criteria for model selection, but it is difficult to analytically applyits modern definition - NML (Normalized Maximum Likelihood) - to theproblem of PCA. This work shows a general reduction of NML prob-lems to lower-dimension problems. Applying this reduction, it boundsthe NML of PCA, by terms of the NML of linear regression, which areknown.Comment: LOD 201