Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

Functional source separation applied to induced visual gamma activity

Objective of this work was to explore the performance of a recently introduced source extraction method, FSS (Functional Source Separation), in recovering induced oscillatory change responses from extra-cephalic magnetoencephalographic (MEG) signals. Unlike algorithms used to solve the inverse problem, FSS does not make any assumption about the underlying biophysical source model; instead, it makes use of task-related features (functional constraints) to estimate source/s of interest. FSS was compared with blind source separation (BSS) approaches such as Principal and Independent Component Analysis, PCA and ICA, which are not subject to any explicit forward solution or functional constraint, but require source uncorrelatedness (PCA), or independence (ICA). A visual MEG experiment with signals recorded from six subjects viewing a set of static horizontal black/white square-wave grating patterns at different spatial frequencies was analyzed. The beamforming technique Synthetic Aperture Magnetometry (SAM) was applied to localize task-related sources; obtained spatial filters were used to automatically select BSS and FSS components in the spatial area of interest. Source spectral properties were investigated by using Morlet-wavelet time-frequency representations and significant task-induced changes were evaluated by means of a resampling technique; the resulting spectral behaviours in the gamma frequency band of interest (20-70 Hz), as well as the spatial frequency-dependent gamma reactivity, were quantified and compared among methods. Among the tested approaches, only FSS was able to estimate the expected sustained gamma activity enhancement in primary visual cortex, throughout the whole duration of the stimulus presentation for all subjects, and to obtain sources comparable to invasively recorded data.

The use of context in the classification of urban aerial imagery

Urban regions present some of the most challenging areas for the remote sensing community. Many different types of land cover have similar spectral responses, making them difficult to distinguish from one another. Traditional per-pixel classification techniques suffer particularly badly because they only use these spectral properties to determine a class, and no other properties of the image, such as context. This project presents the results of the classification of a deeply urban area of Dudley, West Midlands, using 4 methods: Supervised Maximum Likelihood, SMAP, ECHO and Unsupervised Maximum Likelihood. An accuracy assessment method is then developed to allow a fair representation of each procedure and a direct comparison between them. Subsequently, a classification procedure is developed that makes use of the context in the image, though a per-polygon classification. The imagery is broken up into a series of polygons extracted from the Marr-Hildreth zero-crossing edge detector. These polygons are then refined using a region-growing algorithm, and then classified according to the mean class of the fine polygons. The imagery produced by this technique is shown to be of better quality and of a higher accuracy than that of other conventional methods. Further refinements are suggested and examined to improve the aesthetic appearance of the imagery. Finally a comparison with the results produced from a previous study of the James Bridge catchment, in Darleston, West Midlands, is made, showing that the Polygon classified ATM imagery performs significantly better than the Maximum Likelihood classified videography used in the initial study, despite the presence of geometric correction errors.

The application of remote sensing to water resources

Techniques are developed for the visual interpretation of drainage features from satellite imagery. The process of interpretation is formalised by the introduction of objective criteria. Problems of assessing the accuracy of maps are recognized, and a method is developed for quantifying the correctness of an interpretation, in which the more important features are given an appropriate weight. A study was made of imagery from a variety of landscapes in Britain and overseas, from which maps of drainage networks were drawn. The accuracy of the mapping was assessed in absolute terms, and also in relation to the geomorphic parameters used in hydrologic models. Results are presented relating the accuracy of interpretation to image quality, subjectivity and the effects of topography. It is concluded that the visual interpretation of satellite imagery gives maps of sufficient accuracy for the preliminary assessment of water resources, and for the estimation of geomorphic parameters. An examination is made of the use of remotely sensed data in hydrologic models. It is proposed that the spectral properties of a scene are holistic, and are therefore more efficient than conventional catchment characteristics. Key hydrologic parameters were identified, and were estimated from streamflow records. The correlation between hydrologic variables and spectral characteristics was examined, and regression models for streamflow were developed, based solely on spectral data. Regression models were also developed using conventional catchment characteristics, whose values were estimated using satellite imagery. It was concluded that models based primarily on variables derived from remotely sensed data give results which are as good as, or better than, models using conventional map data. The holistic properties of remotely sensed data are realised only in undeveloped areas. In developed areas an assessment of current land-use is a more useful indication of hydrologic response.

NLSE-based model of a random distributed feedback fiber laser

In this work we propose a NLSE-based model of power and spectral properties of the random distributed feedback (DFB) fiber laser. The model is based on coupled set of non-linear Schrödinger equations for pump and Stokes waves with the distributed feedback due to Rayleigh scattering. The model considers random backscattering via its average strength, i.e. we assume that the feedback is incoherent. In addition, this allows us to speed up simulations sufficiently (up to several orders of magnitude). We found that the model of the incoherent feedback predicts the smooth and narrow (comparing with the gain spectral profile) generation spectrum in the random DFB fiber laser. The model allows one to optimize the random laser generation spectrum width varying the dispersion and nonlinearity values: we found, that the high dispersion and low nonlinearity results in narrower spectrum that could be interpreted as four-wave mixing between different spectral components in the quasi-mode-less spectrum of the random laser under study could play an important role in the spectrum formation. Note that the physical mechanism of the random DFB fiber laser formation and broadening is not identified yet. We investigate temporal and statistical properties of the random DFB fiber laser dynamics. Interestingly, we found that the intensity statistics is not Gaussian. The intensity auto-correlation function also reveals that correlations do exist. The possibility to optimize the system parameters to enhance the observed intrinsic spectral correlations to further potentially achieved pulsed (mode-locked) operation of the mode-less random distributed feedback fiber laser is discussed.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

On the 3-Wave Equations with Constant Boundary Conditions

2010 Mathematics Subject Classification: 37K40, 35Q15, 35Q51, 37K15.

Riccati Representation for Elements in H^(-1) and Its Applications

2002 Mathematics Subject Classification: 35L05, 34L15, 35D05, 35Q53

NLSE-based modelling of a random distributed feedback fiber laser

Random distributed feedback (DFB) fiber lasers have attracted a great attention since first demonstration [1]. Despite big advance in practical laser systems, random DFB fiber laser spectral properties are far away to be understood or even numerically modelled. Up to date, only generation power could be calculated and optimized numerically [1,2] or analytically [3] within the power balance model. However, spectral and statistical properties of random DFB fiber laser can not be found in this way. Here we present first numerical modelling of the random DFB fiber laser, including its spectral and statistical properties, using NLSE-based model. © 2013 IEEE.

Narrow-band radiation in the random distributed feedback fiber laser

Narrow-band generation is achieved in random distributed feedback (RDFB) fiber laser by using narrow-band filters in the center of a distributed cavity. The resulting line-width of ∼0.1 nm is 10 times less than line-width in classical random distributed feedback fiber laser. Spectral properties can be optimized further. © 2012 OSA.

Tailoring heme -thiolate proteins into efficient biocatalysts with high specificity and selectivity

Cytochrome P450 monooxygenases, one of the most important classes of heme-thiolate proteins, have attracted considerable interest in the biochemical community because of its catalytic versatility, substrate diversity and great number in the superfamily. Although P450s are capable of catalyzing numerous difficult oxidation reactions, the relatively low stability, low turnover rates and the need of electron-donating cofactors have limited their practical biotechnological and pharmaceutical applications as isolated enzymes. The goal of this study is to tailor such heme-thiolate proteins into efficient biocatalysts with high specificity and selectivity by protein engineering and to better understand the structure-function relationship in cytochromes P450. In the effort to engineer P450cam, the prototype member of the P450 superfamily, into an efficient peroxygenase that utilizes hydrogen peroxide via the “peroxide-shunt” pathway, site-directed mutagenesis has been used to elucidate the critical roles of hydrophobic residues in the active site. Various biophysical, biochemical and spectroscopic techniques have been utilized to investigate the wild-type and mutant proteins. Three important P450cam variants were obtained showing distinct structural and functional features. In P450camV247H mutant, which exhibited almost identical spectral properties with the wild-type, it is demonstrated that a single amino acid switch turned the monooxygenase into an efficient preoxidase by increasing the peroxidase activity nearly one thousand folds. In order to tune the distal pocket of P450cam with polar residues, Leu 246 was replaced with a basic residue, lysine, resulting in a mutant with spectral features identical to P420, the inactive species of P450. But this inactive-species-like mutant showed catalytic activities without the facilitation of any cofactors. By substituting Gly 248 with a histidine, a novel Cys-Fe-His ligation set was obtained in P450cam which represented the very rare case of His ligation in heme-thiolate proteins. In addition to serving as a convenient model for hemoprotein structural studies, the G248H mutant also provided evidence about the nature of the axial ligand in cytochrome P420 and other engineered hemoproteins with thiolate ligations. Furthermore, attempts have been made to replace the proximal ligand in sperm whale myoglobin to construct a heme-thiolate protein model by mimicking the protein environment of cytochrome P450cam and chloroperoxidase.

Tailoring Heme-Thiolate Proteins into Efficient Biocatalysts with High Specificity and Selectivity

Cytochrome P450 monooxygenases, one of the most important classes of heme-thiolate proteins, have attracted considerable interest in the biochemical community because of its catalytic versatility, substrate diversity and great number in the superfamily. Although P450s are capable of catalyzing numerous difficult oxidation reactions, the relatively low stability, low turnover rates and the need of electron-donating cofactors have limited their practical biotechnological and pharmaceutical applications as isolated enzymes. The goal of this study is to tailor such heme-thiolate proteins into efficient biocatalysts with high specificity and selectivity by protein engineering and to better understand the structure-function relationship in cytochromes P450. In the effort to engineer P450cam, the prototype member of the P450 superfamily, into an efficient peroxygenase that utilizes hydrogen peroxide via the “peroxide-shunt” pathway, site-directed mutagenesis has been used to elucidate the critical roles of hydrophobic residues in the active site. Various biophysical, biochemical and spectroscopic techniques have been utilized to investigate the wild-type and mutant proteins. Three important P450cam variants were obtained showing distinct structural and functional features. In P450camV247H mutant, which exhibited almost identical spectral properties with the wild-type, it is demonstrated that a single amino acid switch turned the monooxygenase into an efficient preoxidase by increasing the peroxidase activity nearly one thousand folds. In order to tune the distal pocket of P450cam with polar residues, Leu 246 was replaced with a basic residue, lysine, resulting in a mutant with spectral features identical to P420, the inactive species of P450. But this inactive-species-like mutant showed catalytic activities without the facilitation of any cofactors. By substituting Gly 248 with a histidine, a novel Cys-Fe-His ligation set was obtained in P450cam which represented the very rare case of His ligation in heme-thiolate proteins. In addition to serving as a convenient model for hemoprotein structural studies, the G248H mutant also provided evidence about the nature of the axial ligand in cytochrome P420 and other engineered hemoproteins with thiolate ligations. Furthermore, attempts have been made to replace the proximal ligand in sperm whale myoglobin to construct a heme-thiolate protein model by mimicking the protein environment of cytochrome P450cam and chloroperoxidase.

An X-ray study of the SNR G344.7-0.1 and the central object CXOU J170357.8-414302

Aims. We report results of an X-ray study of the supernova remnant (SNR) G344.7-0.1 and the point-like X-ray source located at the geometrical center of the SNR radio structure. Methods. The morphology and spectral properties of the remnant and the central X-ray point-like source were studied using data from the XMM-Newton and Chandra satellites. Archival radio data and infrared Spitzer observations at 8 and 24 mu m were used to compare and study its multi-band properties at different wavelengths. Results. The XMM-Newton and Chandra observations reveal that the overall X-ray emission of G344.7-0.1 is extended and correlates very well with regions of bright radio and infrared emission. The X-ray spectrum is dominated by prominent atomic emission lines. These characteristics suggest that the X-ray emission originated in a thin thermal plasma, whose radiation is represented well by a plane-parallel shock plasma model (PSHOCK). Our study favors the scenario in which G344.7-0.1 is a 6 x 10^3 year old SNR expanding in a medium with a high density gradient and is most likely encountering a molecular cloud on the western side. In addition, we report the discovery of a soft point-like X-ray source located at the geometrical center of the radio SNR structure. The object presents some characteristics of the so-called compact central objects (CCO). However, its neutral hydrogen absorption column (N_H) is inconsistent with that of the SNR. Coincident with the position of the source, we found infrared and optical objects with typical early-K star characteristics. The X-ray source may be a foreground star or the CCO associated with the SNR. If this latter possibility were confirmed, the point-like source would be the farthest CCO detected so far and the eighth member of the new population of isolated and weakly magnetized neutron stars.

Mid-infrared spectroscopy of lensed galaxies at 1 < z < 3: The nature of sources near the MIPS confusion limit

We present Spitzer IRS mid-infrared spectra for 15 gravitationally lensed, 24 μm-selected galaxies, and combine the results with four additional very faint galaxies with IRS spectra in the literature. The median intrinsic 24 μm flux density of the sample is 130 μJy, enabling a systematic survey of the spectral properties of the very faint 24 μm sources that dominate the number counts of Spitzer cosmological surveys. Six of the 19 galaxy spectra (32%) show the strong mid-IR continuua expected of AGNs; X-ray detections confirm the presence of AGNs in three of these cases, and reveal AGNs in two other galaxies. These results suggest that nuclear accretion may contribute more flux to faint 24 μm-selected samples than previously assumed. Almost all the spectra show some aromatic (PAH) emission features; the measured aromatic flux ratios do not show evolution from z = 0. In particular, the high signal-to-noise mid-IR spectrum of SMM J163554.2+661225 agrees remarkably well with low-redshift, lower luminosity templates. We compare the rest-frame 8 μm and total infrared luminosities of star-forming galaxies, and find that the behavior of this ratio with total IR luminosity has evolved modestly from z = 2 to z = 0. Since the high aromatic-to-continuum flux ratios in these galaxies rule out a dominant contribution by AGNs, this finding implies systematic evolution in the structure and/or metallicity of infrared sources with redshift. It also has implications for the estimates of star-forming rates inferred from 24 μm measurements, in the sense that at z ~ 2, a given observed frame 24 μm luminosity corresponds to a lower bolometric luminosity than would be inferred from low-redshift templates of similar luminosity at the corresponding rest wavelength.

Absolutely Continuous Spectrum for Parabolic Flows/Maps

This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive spectral results for skew products over translations and Furstenberg transformations.