950 resultados para Gaussian random fields
Resumo:
Anisotropic gaussian beams are obtained as exact solutions to the parabolic wave equation. These beams have a quadratic phase front whose principal radii of curvature are non-degenerate everywhere. It is shown that, for the lowest order beams, there exists a plane normal to the beam axis where the intensity distribution is rotationally symmetric about the beam axis. A possible application of these beams as normal modes of laser cavities with astigmatic mirrors is noted.
Resumo:
Through an analysis using the transfer function of a pinhole camera, the multiple imaging characteristics of photographic diffusers described by Grover and Tremblay [Appl. Opt.21,4500(1982)] is studied. It is found that only one pinhole diameter satisfies the optimum imaging condition for best contrast transfer at any desired spatial frequency. A simple method of generating random pinhole arrays with a controlled pinhole diameter is described. These pinhole arrays are later used to generate high frequency sinusoidal gratings from a coarse grid. The contrast in the final gratings is found to be reasonably high.
Resumo:
It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.
Resumo:
Pseudo-marginal methods such as the grouped independence Metropolis-Hastings (GIMH) and Markov chain within Metropolis (MCWM) algorithms have been introduced in the literature as an approach to perform Bayesian inference in latent variable models. These methods replace intractable likelihood calculations with unbiased estimates within Markov chain Monte Carlo algorithms. The GIMH method has the posterior of interest as its limiting distribution, but suffers from poor mixing if it is too computationally intensive to obtain high-precision likelihood estimates. The MCWM algorithm has better mixing properties, but less theoretical support. In this paper we propose to use Gaussian processes (GP) to accelerate the GIMH method, whilst using a short pilot run of MCWM to train the GP. Our new method, GP-GIMH, is illustrated on simulated data from a stochastic volatility and a gene network model.
Resumo:
The host-guest technique has been applied to the determination of the helix-coil stability constants of two naturally occurring amino acids, L-alanine and L-leucine, in a nonaqueous solvent system. Random copolymers containing L-alanine and L-leucine, respectively, as guest residues and -benzyl-L-glutamate as the host residue were synthesized. The polymers were fractionated and characterized for their amino acid content, molecular weight, and helix-coil transition behavior in a dichloroacetic acid (DCA)-1,2-dichloroethane (DCE) mixture. Two types of helix-coil transitions were carried out on the copolymers: solvent-induced transitions in DCA-DCE mixtures at 25°C and thermally induced transitions in a 82:18 (wt %) DCA-DCE mixture. The thermally induced transitions were analyzed by statistical mechanical methods to determine the Zimm-Bragg parameters, and s, of the guest residues. The experimental data indicate that, in the nonaqueous solvent, the L-alanine residue stabilizes the -helical conformation more than the L-leucine residue does. This is in contrast to their behavior in aqueous solution, where the reverse is true. The implications of this finding for the analysis of helical structures in globular proteins are discussed.
Resumo:
This paper considers the applicability of the least mean fourth (LM F) power gradient adaptation criteria with 'advantage' for signals associated with gaussian noise, the associated noise power estimate not being known. The proposed method, as an adaptive spectral estimator, is found to provide superior performance than the least mean square (LMS) adaptation for the same (or even lower) speed of convergence for signals having sufficiently high signal-to-gaussian noise ratio. The results include comparison of the performance of the LMS-tapped delay line, LMF-tapped delay line, LMS-lattice and LMF-lattice algorithms, with the Burg's block data method as reference. The signals, like sinusoids with noise and stochastic signals like EEG, are considered in this study.
Resumo:
Gaussian processes (GPs) are promising Bayesian methods for classification and regression problems. Design of a GP classifier and making predictions using it is, however, computationally demanding, especially when the training set size is large. Sparse GP classifiers are known to overcome this limitation. In this letter, we propose and study a validation-based method for sparse GP classifier design. The proposed method uses a negative log predictive (NLP) loss measure, which is easy to compute for GP models. We use this measure for both basis vector selection and hyperparameter adaptation. The experimental results on several real-world benchmark data sets show better orcomparable generalization performance over existing methods.
Resumo:
Values of Ko, Flory constant related to unperturbed dimensions, are evaluated for methyl methacrylate-acrylonitrile random copolymers using Flory-Fox, Kurata-Stockmayer and Inagaki-Ptitsyn methods and compared with the Ko values obtained by Stockmayer-Fixman method. Ko values are seen to be less in solvents which have large a (Mark-Houwink exponent) values. A correlation between Ko and a is developed to arrive at a more reliable estimate of Ko for this copolymer system.
Resumo:
Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.
Resumo:
This study addresses four issues concerning technological product innovations. First, the nature of the very early phases or "embryonic stages" of technological innovation is addressed. Second, this study analyzes why and by what means people initiate innovation processes outside the technological community and the field of expertise of the established industry. In other words, this study addresses the initiation of innovation that occurs without the expertise of established organizations, such as technology firms, professional societies and research institutes operating in the technological field under consideration. Third, the significance of interorganizational learning processes for technological innovation is dealt with. Fourth, this consideration is supplemented by considering how network collaboration and learning change when formalized product development work and the commercialization of innovation advance. These issues are addressed through the empirical analysis of the following three product innovations: Benecol margarine, the Nordic Mobile Telephone system (NMT) and the ProWellness Diabetes Management System (PDMS). This study utilizes the theoretical insights of cultural-historical activity theory on the development of human activities and learning. Activity-theoretical conceptualizations are used in the critical assessment and advancement of the concept of networks of learning. This concept was originally proposed by the research group of organizational scientist Walter Powell. A network of learning refers to the interorganizational collaboration that pools resources, ideas and know-how without market-based or hierarchical relations. The concept of an activity system is used in defining the nodes of the networks of learning. Network collaboration and learning are analyzed with regard to the shared object of development work. According to this study, enduring dilemmas and tensions in activity explain the participants' motives for carrying out actions that lead to novel product concepts in the early phases of technological innovation. These actions comprise the initiation of development work outside the relevant fields of expertise and collaboration and learning across fields of expertise in the absence of market-based or hierarchical relations. These networks of learning are fragile and impermanent. This study suggests that the significance of networks of learning across fields of expertise becomes more and more crucial for innovation activities.
Resumo:
Based on morphological features alone, there is considerable difficulty in identifying the 5 most economically damaging weed species of Sporobolus [viz. S. pyramidalis P. Beauv., S. natalensis (Steud.) Dur and Schinz, S. fertilis (Steud.) Clayton, S. africanus (Poir.) Robyns and Tourney, and S. jacquemontii Kunth.] found in Australia. A polymerase chain reaction (PCR)-based random amplified polymorphic DNA (RAPD) technique was used to create a series of genetic markers that could positively identify the 5 major weeds from the other less damaging weedy and native Sporobolus species. In the initial RAPD profiling experiment, using arbitrarily selected primers and involving 12 species of Sporobolus, 12 genetic markers were found that, when used in combination, could consistently identify the 5 weedy species from all others. Of these 12 markers, the most diagnostic were UBC51490 for S. pyramidalis and S. natalensis; UBC43310.2000.2100 for S. fertilis and S. africanus; and ORA20850 and UBC43470 for S. jacquemontii. Species-specific markers could be found only for S. jacquemontii. In an effort to understand why there was difficulty in obtaining species-specific markers for some of the weedy species, a RAPD data matrix was created using 40 RAPD products. These 40 products amplified by 6 random primers from 45 individuals belonging to 12 species, were then subjected to numerical taxonomy and multivariate system (NTSYS pc version 1.70) analysis. The RAPD similarity matrix generated from the analysis indicated that S. pyramidalis was genetically more similar to S. natalensis than to other species of the 'S. indicus complex'. Similarly, S. jacquemontii was more similar to S. pyramidalis, and S. fertilis was more similar to S. africanus than to other species of the complex. Sporobolus pyramidalis, S. jacquemontii, S. africanus, and S. creber exhibited a low within-species genetic diversity, whereas high genetic diversity was observed within S. natalensis, S. fertilis, S. sessilis, S. elongates, and S. laxus. Cluster analysis placed all of the introduced species (major and minor weedy species) into one major cluster, with S. pyramidalis and S. natalensis in one distinct subcluster and S. fertilis and S. africanus in another. The native species formed separate clusters in the phenograms. The close genetic similarity of S. pyramidalis to S. natalensis, and S. fertilis to S. africanus may explain the difficulty in obtaining RAPD species-specific markers. The importance of these results will be within the Australian dairy and beef industries and will aid in the development of integrated management strategy for these weeds.
Resumo:
Studies on the dilute solution properties of methylmethacrylate-acrylonitrile random copolymers of three different compositions, 0.236, 0.5 and 0.74 mole fraction (m.f.) of acrylonitrile (AN) designated as MAa, MAb and MAc, respectively, have been made in good solvents and theta solvents. MAa has been studied in benzene (Bz) and ethylacetate (EAc). MAb in acetonitrile (MeCN), dimethyl sulphoxide (DMSO) and a binary solvent mixture of Bz and dimentyl formamide (DMF) in the volume ratio 6.5:1 designated as BM1 and MAc in MeCN, DMSO and Bz + DMF in the volume ratio 1.667:1 designated as BM2. The Mark-Houwink exponent ‘a’ reveals that Bz is a theta solvent for MAa at 20°C. For MAb and MAc, BM1 and BM2, respectively have ‘a’ values of 0.5 at all three temperatures studied (30°, 40° and 50°C). It is not clear whether they represent theta states or preferential adsorption plays a role complicating the behaviour in solution. The values of A2 are very low in MeCN considering that it is a very good solvent for the copolymer, ‘a’ values for MAb and MAc being 0.75 and 0.7, respectively.
Resumo:
It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.