Consensus in non-commutative spaces

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

Statistics of reaction progress variable and mixture fraction gradients from DNS of turbulent partially premixed flames

Statistically planar turbulent partially premixed flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios = 0.7 and 1.0 using three-dimensional, simplified chemistry-based direct numerical simulations (DNS). The simulation parameters are chosen such that the flames represent the thin reaction zones regime combustion. A random bimodal distribution of equivalence ratio is introduced in the unburned gas ahead of the flame to account for the mixture inhomogeneity. The results suggest that the probability density functions (PDFs) of the mixture fraction gradient magnitude |Δξ| (i.e., P(|Δξ|)) can be reasonably approximated using a log-normal distribution. However, this presumed PDF distribution captures only the qualitative nature of the PDF of the reaction progress variable gradient magnitude |Δc| (i.e., P(|Δc|)). It has been found that a bivariate log-normal distribution does not sufficiently capture the quantitative behavior of the joint PDF of |Δξ| and |Δc| (i.e., P(|Δξ|, |Δc|)), and the agreement with the DNS data has been found to be poor in certain regions of the flame brush, particularly toward the burned gas side of the flame brush. Moreover, the variables |Δξ| and |Δc| show appreciable correlation toward the burned gas side of the flame brush. These findings are corroborated further using a DNS data of a lifted jet flame to study the flame geometry dependence of these statistics. © 2013 Copyright Taylor and Francis Group, LLC.

Stiffness of clays and silts: Normalizing shear modulus and shear strain

An analysis is presented of a database of 67 tests on 21 clays and silts of undrained shear stress-strain data of fine-grained soils. Normalizations of secant G in terms of initial mean effective stress p9 (i.e., G=p9 versus log g) or undrained shear strength cu (i.e., G=cu versus log g) are shown to be much less successful in reducing the scatter between different clays than the approach that uses the maximum shear modulus,Gmax, a technique still not universally adopted by geotechnical researchers and constitutive modelers. Analysis of semiempirical expressions forGmax is presented and a simple expression that uses only a void-ratio function and a confining-stress function is proposed. This is shown to be superior to a Hardin-style equation, and the void ratio function is demonstrated as an alternative to an overconsolidation ratio (OCR) function. To derive correlations that offer reliable estimates of secant stiffness at any required magnitude of working strain, secant shear modulus G is normalized with respect to its small-strain value Gmax, and shear strain g is normalized with respect to a reference strain gref at which this stiffness has halved. The data are corrected to two standard strain rates to reduce the discrepancy between data obtained from static and cyclic testing. The reference strain gref is approximated as a function of the plasticity index.Aunique normalized shear modulus reduction curve in the shape of a modified hyperbola is fitted to all the available data up to shear strains of the order of 1%. As a result, good estimates can be made of the modulus reduction G/Gmax ±30% across all strain levels in approximately 90% of the cases studied. New design charts are proposed to update the commonly used design curves. © 2013 American Society of Civil Engineers.

FACTORS INFLUENCING CHLOROPHYLL A CONCENTRATION IN THE YANGTZE-CONNECTED LAKES

To determine the environmental factors influencing C, phytoplankton chlorophyll a (Ch1 a), field investigations 4 were conducted in three river-connected lakes (Dongting Lake, Poyang Lake and Shijiu Lake) of the Yangtze floodplain in 2004. Results showed that the average Chi a concentration in these lakes ranged from 2.98 to 3.65 mg m(-3). The major factors influencing Chl a in lentic and lotic regions were total phosphorus (TP) and water velocity (U), respectively. Multiple relationships including total nitrogen (log(10)TN) and water depth (log(10)Z) were established. Further analyses found that the absolute Chi a and slope of log(10)Chl a=f (log(10)TP) in the river-connected lakes were obviously lower than those in the river-isolated lakes. This suggests the river-lake connectivity can significantly modify relationship between TP and chlorophyll a concentration.

Efficient decoding with generative score-spaces using the expectation semiring

State-of-the-art speech recognisers are usually based on hidden Markov models (HMMs). They model a hidden symbol sequence with a Markov process, with the observations independent given that sequence. These assumptions yield efficient algorithms, but limit the power of the model. An alternative model that allows a wide range of features, including word- and phone-level features, is a log-linear model. To handle, for example, word-level variable-length features, the original feature vectors must be segmented into words. Thus, decoding must find the optimal combination of segmentation of the utterance into words and word sequence. Features must therefore be extracted for each possible segment of audio. For many types of features, this becomes slow. In this paper, long-span features are derived from the likelihoods of word HMMs. Derivatives of the log-likelihoods, which break the Markov assumption, are appended. Previously, decoding with this model took cubic time in the length of the sequence, and longer for higher-order derivatives. This paper shows how to decode in quadratic time. © 2013 IEEE.

"Plateau"-related summary statistics are uninformative for comparing working memory models.

Performance on visual working memory tasks decreases as more items need to be remembered. Over the past decade, a debate has unfolded between proponents of slot models and slotless models of this phenomenon (Ma, Husain, Bays (Nature Neuroscience 17, 347-356, 2014). Zhang and Luck (Nature 453, (7192), 233-235, 2008) and Anderson, Vogel, and Awh (Attention, Perception, Psychophys 74, (5), 891-910, 2011) noticed that as more items need to be remembered, "memory noise" seems to first increase and then reach a "stable plateau." They argued that three summary statistics characterizing this plateau are consistent with slot models, but not with slotless models. Here, we assess the validity of their methods. We generated synthetic data both from a leading slot model and from a recent slotless model and quantified model evidence using log Bayes factors. We found that the summary statistics provided at most 0.15 % of the expected model evidence in the raw data. In a model recovery analysis, a total of more than a million trials were required to achieve 99 % correct recovery when models were compared on the basis of summary statistics, whereas fewer than 1,000 trials were sufficient when raw data were used. Therefore, at realistic numbers of trials, plateau-related summary statistics are highly unreliable for model comparison. Applying the same analyses to subject data from Anderson et al. (Attention, Perception, Psychophys 74, (5), 891-910, 2011), we found that the evidence in the summary statistics was at most 0.12 % of the evidence in the raw data and far too weak to warrant any conclusions. The evidence in the raw data, in fact, strongly favored the slotless model. These findings call into question claims about working memory that are based on summary statistics.

Respiratory pattern of captive Yangtze finless porpoises (Neophocaena phocaenoides asiaeorientalis)

Cetacean respiration usually happen in bouts. The most widely applied quantitative method used to analyze the structure of these bouts is the log(e)-survivorship analysis, based on the assumption that the respiratory intervals are distributed as negative exponentials. However, for the data collected from three captive Yangtze finless porpoises (Neophocaena phocaenoides asiaeorientalis), we failed to obtain a convergent result with the application of log,survivorship analysis. However, the two-Gaussian model, which was recently proposed to analyze the feeding behavior of cows, was successfully fitted to the data. According to the fitting results, the overall respiratory pattern of the captive Yangtze finless porpoises can be described as a dive with a mean duration of around 30-40 s, followed by two or three ventilations with a mean interval of approximately 9 s. The average intra-bout intervals during both active and inactive periods are constant at 7.7-9.9 s for all individuals. However, when shifting from active to inactive states, the adult male and female decrease their mean numbers of respirations per bout and average length of inter-bout respiratory intervals, while the estimates of both parameters increase for the juvenile female. It was pointed out that the two-Gaussian model might be more adequate for cetacean respiratory-bout structure analyses than the log(e)-survivorship technique.

Nonconstant quality of auditory filters in the porpoises, Phocoena phocoena and Neophocaena phocaenoides (Cetacea, Phocoenidae)

Simultaneous tone-tone masking in conjunction with the envelope-following response (EFR) recording was used to obtain tuning curves in porpoises Phocoena phocoena and Neophocaena phocaenoides asiaeorientalis. The EFR was evoked by amplitude-modulated probes with a modulation rate of 1000 Hz and carrier frequencies from 22.5 to 140 kHz. Equivalent rectangular quality Q(ERB) of the obtained tuning curves varied from 8.3-8.6 at lower (22.5-32 kHz) probe frequencies to 44.8-47.4 at high (128-140 kHz) frequencies. The QERB dependence on probe frequency could be approximated by regression lines with a slope of 0.83 to 0.86 in log-log scale., which corresponded to almost frequency-proportional quality and almost constant bandwidth of 34 kHz. Thus, the frequency representation in the porpoise auditory system is much closer to a constant-bandwidth rather that to a constant-quality manner. (c) 2006 Acoustical Society of America.

Microcalorimetry as a possible tool for phylogenetic studies of Tetrahymena

Using isothermal microcalorimetry, the growth power-time curves of three strains of Tetrahymena were determined at 28 degrees C. Their Euclidean distances and cluster analysis diagram were obtained by using two thermokinetic parameters (r and Q(log)), which showed that T. thermophila BF1 and T. thermophila BF5 had a closer relationship. Compared with the single molecular biomarker (ITS1) method, microcalorimetry wasmaybe a simpler, more sensitive andmore economic technique in the phylogenetic studies of Tetrahymena species.

Quantitative structure-property relationships for octanol-air partition coefficients of polychlorinated naphthalenes, chlorobenzenes and p,p '-DDT

The octanol-air partition coefficient (K-OA) is a key descriptor of chemicals partitioning between the atmosphere and environmental organic phases. Quantitative structure-property relationships (QSPR) are necessary to model and predict KOA from molecular structures. Based on 12 quantum chemical descriptors computed by the PM3 Hamiltonian, using partial least squares (PLS) analysis, a QSPR model for logarithms of K-OA to base 10 (log K-OA) for polychlorinated naphthalenes (PCNs), chlorobenzenes and p,p'-DDT was obtained. The cross-validated Q(cum)(2) value of the model is 0.973, indicating a good predictive ability of the model. The main factors governing log K-OA of the PCNs, chlorobenzenes, and p,p'-DDT are, in order of decreasing importance, molecular size and molecular ability of donating/accepting electrons to participate in intermolecular interactions. The intermolecular dispersive interactions play a leading role in governing log K-OA. The more chlorines in PCN and chlorobenzene molecules, the greater the log K-OA values. Increasing E-LUMO (the energy of the lowest unoccupied molecular orbital) of the molecules leads to decreasing log K-OA values, implying possible intermolecular interactions between the molecules under study and octanol molecules. (C) 2002 Elsevier Science Ltd. All rights reserved.

Water solubility enhancement of phthalates by cetyltrimethylammonium bromide and beta-cyclodextrin

Water solubility enhancements of six phthalates (five aliphatic phthalates and one phenyl phthalate) by cetyltrimethylammonium bromide (CTAB) and beta-cyclodextrin (beta-CD) were studied at 25 degreesC. The solubilities of these plithalates are remarkably enhanced by CTAB solutions above the critical micelle concentration (cmc). Only marginal enhancement of phthalate solubility was observed in solutions containing CTAB below its cmc and beta-CD at low concentrations (less than 5 mM). The solubility enhancements of the plithalates are proportional to the added amount of CTAB and beta-CD. Partition coefficients of the plithalates between monomeric CTAB surfactant and water (K-MN) and between CTAB micelle and water K-MC) were estimated from the experimental data. The mechanisms of solubility enhancements by CTAB and beta-CD were discussed. A log-linear equation was proposed and evaluated for the solubilization by CTAB below cmc, while the previously proposed linear partitioning model was questioned. The structures of the complexes formed between plithalates and beta-CD were proposed, and the formation constants were estimated. The values of log K-MC, log K-MN, and log Kbeta-CD of the plithalates were found to correlate linearly with the log K-OW of plithalates, with the exception of the solid phenyl phthalate.

Quantitative structure-property relationships for octanol-air partition coefficients of polychlorinated biphenyls

Based on nine quantum chemical descriptors computed by PM3 Hamiltonian, using partial least squares analysis, a significant quantitative structure-property relationship for the logarithm of octanol-air partition coefficients (log K-OA) of polychlorinated biphenyls (PCBs) was obtained. The cross-validated Q(cum)(2) value of the model is 0.962, indicating a good predictive ability. The intermolecular dispersive interactions and thus the size of the PCB molecules play a key role in governing log K-OA. The greater the size of PCB molecules, the greater the log K-OA values. Increasing E-LUMO (the energy of the lowest unoccupied molecular orbital) values of the PCBs leads to decreasing log K-OA values, indicating possible interactions between PCB and octanol molecules. Increasing Q(Cl)(+) (the most positive net atomic charges on a chlorine atom) and Q(C)(-) (the largest negative net atomic charge on a carbon atom) values of PCBs results in decreasing log K-OA values, implying possible intermolecular electrostatic interactions between octanol and PCB molecules. (C) 2002 Elsevier Science Ltd. All rights reserved.

Quantitative structure-property relationships (QSPRs) on direct photolysis of PCDDs

By the use of partial least squares (PLS) method and 27 quantum chemical descriptors computed by PM3 Hamiltonian, a statistically significant QSPR were obtained for direct photolysis quantum yields (Y) of selected Polychlorinated dibenzo-p-dioxins (PCDDs). The QSPR can be used for prediction. The direct photolysis quantum yields of the PCDDs are dependent on the number of chlorine atoms bonded with the parent structures, the character of the carbon-oxygen bonds, and molecular polarity. Increasing bulkness and polarity of PCDDs lead to decrease of log Y values. Increasing the frontier molecular orbital energies (E-lumo and E-homo) and heat of formation (HOF) values leads to increase of log Y values. (C) 2001 Elsevier Science Ltd. All rights reserved.