Variational analysis of ablation for variable properties

"Work was performed as part of a Cornell Aeronautical Laboratory Internal Research Project."

Convergence analysis of a discrete-time single-unit gradient ICA algorithm

We revisit the one-unit gradient ICA algorithm derived from the kurtosis function. By carefully studying properties of the stationary points of the discrete-time one-unit gradient ICA algorithm, with suitable condition on the learning rate, convergence can be proved. The condition on the learning rate helps alleviate the guesswork that accompanies the problem of choosing suitable learning rate in practical computation. These results may be useful to extract independent source signals on-line.

Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Independent detectors for expansion and rotation, and for orthogonal components of deformation

It is well known that optic flow - the smooth transformation of the retinal image experienced by a moving observer - contains valuable information about the three-dimensional layout of the environment. From psychophysical and neurophysiological experiments, specialised mechanisms responsive to components of optic flow (sometimes called complex motion) such as expansion and rotation have been inferred. However, it remains unclear (a) whether the visual system has mechanisms for processing the component of deformation and (b) whether there are multiple mechanisms that function independently from each other. Here, we investigate these issues using random-dot patterns and a forced-choice subthreshold summation technique. In experiment 1, we manipulated the size of a test region that was permitted to contain signal and found substantial spatial summation for signal components of translation, expansion, rotation, and deformation embedded in noise. In experiment 2, little or no summation was found for the superposition of orthogonal pairs of complex motion patterns (eg expansion and rotation), consistent with probability summation between pairs of independent detectors. Our results suggest that optic-flow components are detected by mechanisms that are specialised for particular patterns of complex motion.

Statnote 5: Is one set of data more variable than another?

There may be circumstances where it is necessary for microbiologists to compare variances rather than means, e,g., in analysing data from experiments to determine whether a particular treatment alters the degree of variability or testing the assumption of homogeneity of variance prior to other statistical tests. All of the tests described in this Statnote have their limitations. Bartlett’s test may be too sensitive but Levene’s and the Brown-Forsythe tests also have problems. We would recommend the use of the variance-ratio test to compare two variances and the careful application of Bartlett’s test if there are more than two groups. Considering that these tests are not particularly robust, it should be remembered that the homogeneity of variance assumption is usually the least important of those considered when carrying out an ANOVA. If there is concern about this assumption and especially if the other assumptions of the analysis are also not likely to be met, e.g., lack of normality or non additivity of treatment effects then it may be better either to transform the data or to carry out a non-parametric test on the data.

Phase discrimination and simultaneous frequency conversion of the orthogonal components of an optical signal by four-wave mixing in an SOA

Simultaneous conversion of the two orthogonal phase components of an optical input to different output frequencies has been demonstrated by simulation and experiment. A single stage of four-wave mixing between the input signal and four pumps derived from a frequency comb was employed. The nonlinear device was a semiconductor optical amplifier, which provided overall signal gain and sufficient contrast for phase sensitive signal processing. The decomposition of a quadrature phase-shift keyed signal into a pair of binary phase-shift keyed outputs at different frequencies was also demonstrated by simulation.

Polynomials of Pellian Type and Continued Fractions

We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued fraction ex- pansion of √fk (X) is related to that of √C, where √fk (X) = ak*X^2 +bk*X + C. This continues work in [1]–[4].

Method for Analytical Representation of the Maximum Inaccuracies of Indirectly Measurable Variable

Let us have an indirectly measurable variable which is a function of directly measurable variables. In this survey we present the introduced by us method for analytical representation of its maximum absolute and relative inaccuracy as functions, respectively, of the maximum absolute and of the relative inaccuracies of the directly measurable variables. Our new approach consists of assuming for fixed variables the statistical mean values of the absolute values of the coefficients of influence, respectively, of the absolute and relative inaccuracies of the directly measurable variables in order to determine the analytical form of the maximum absolute and relative inaccuracies of an indirectly measurable variable. Moreover, we give a method for determining the numerical values of the maximum absolute and relative inaccuracies. We define a sample plane of the ideal perfectly accurate experiment and using it we give a universal numerical characteristic – a dimensionless scale for determining the quality (accuracy) of the experiment.

Analysis of extended range variable gain hybrid Raman-EDFAs in systems using Nyquist-WDM 100/200G PM-QPSK/16QAM

We use the GN-model to assess Nyquist-WDM 100/200Gbit/s PM-QPSK/16QAM signal reach on low loss, large core area fibre using extended range, variable gain hybrid Raman-EDFAs. 5000/1500km transmission is possible over a wide range of amplifier spans. © OSA 2014.

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Preferences of Hungarian consumers for quality, access and price attributes of health care services — result of a discrete choice experiment

In 2010, a household survey was carried out in Hungary among 1037 respondents to study consumer preferences and willingness to pay for health care services. In this paper, we use the data from the discrete choice experiments included in the survey, to elicit the preferences of health care consumers about the choice of health care providers. Regression analysis is used to estimate the effect of the improvement of service attributes (quality, access, and price) on patients’ choice, as well as the differences among the socio-demographic groups. We also estimate the marginal willingness to pay for the improvement in attribute levels by calculating marginal rates of substitution. The results show that respondents from a village or the capital, with low education and bad health status are more driven by the changes in the price attribute when choosing between health care providers. Respondents value the good skills and reputation of the physician and the attitude of the personnel most, followed by modern equipment and maintenance of the office/hospital. Access attributes (travelling and waiting time) are less important. The method of discrete choice experiment is useful to reveal patients’ preferences, and might support the development of an evidence-based and sustainable health policy on patient payments.

Combination of 16S rRNA variable regions provides a detailed analysis of bacterial community dynamics in the lungs of cystic fibrosis patients

Chronic bronchopulmonary bacterial infections remain the most common cause of morbidity and mortality among patients with cystic fibrosis (CF). Recent community sequencing work has now shown that the bacterial community in the CF lung is polymicrobial. Identifying bacteria in the CF lung through sequencing can be costly and is not practical for many laboratories. Molecular techniques such as terminal restriction fragment length polymorphism or amplicon length heterogeneity-polymerase chain reaction (LH-PCR) can provide many laboratories with the ability to study CF bacterial communities without costly sequencing. The aim of this study was to determine if the use of LH-PCR with multiple hypervariable regions of the 16S rRNA gene could be used to identify organisms found in sputum DNA. This work also determined if LH-PCR could be used to observe the dynamics of lung infections over a period of time. Nineteen samples were analysed with the V1 and the V1_V2 region of the 16S rRNA gene. Based on the amplicon size present in the V1_V2 region, Pseudomonas aeruginosa was confirmed to be in all 19 samples obtained from the patients. The V1 region provided a higher power of discrimination between bacterial profiles of patients. Both regions were able to identify trends in the bacterial population over a period of time. LH profiles showed that the CF lung community is dynamic and that changes in the community may in part be driven by the patient's antibiotic treatment. LH-PCR is a tool that is well suited for studying bacterial communities and their dynamics.

Dissolution of a spatially variable DNAPL (dense non aqueous phase liquid) source

Dissolution of non-aqueous phase liquids (NAPLs) or gases into groundwater is a key process, both for contamination problems originating from organic liquid sources, and for dissolution trapping in geological storage of CO2. Dissolution in natural systems typically will involve both high and low NAPL saturations and a wide range of pore water flow velocities within the same source zone for dissolution to groundwater. To correctly predict dissolution in such complex systems and as the NAPL saturations change over time, models must be capable of predicting dissolution under a range of saturations and flow conditions. To provide data to test and validate such models, an experiment was conducted in a two-dimensional sand tank, where the dissolution of a spatially variable, 5x5 cm**2 DNAPL tetrachloroethene source was carefully measured using x-ray attenuation techniques at a resolution of 0.2x0.2 cm**2. By continuously measuring the NAPL saturations, the temporal evolution of DNAPL mass loss by dissolution to groundwater could be measured at each pixel. Next, a general dissolution and solute transport code was written and several published rate-limited (RL) dissolution models and a local equilibrium (LE) approach were tested against the experimental data. It was found that none of the models could adequately predict the observed dissolution pattern, particularly in the zones of higher NAPL saturation. Combining these models with a model for NAPL pool dissolution produced qualitatively better agreement with experimental data, but the total matching error was not significantly improved. A sensitivity study of commonly used fitting parameters further showed that several combinations of these parameters could produce equally good fits to the experimental observations. The results indicate that common empirical model formulations for RL dissolution may be inadequate in complex, variable saturation NAPL source zones, and that further model developments and testing is desirable.