Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Artifacts In Magnetic Resonance Imaging and Computed Tomography Caused By Dental Materials

BACKGROUND: Artifacts caused by dental restorations, such as dental crowns, dental fillings and orthodontic appliances, are a common problem in MRI and CT scans of the head and neck. The aim of this in-vitro study was to identify and evaluate the artifacts produced by different dental restoration materials in CT and MRI images. METHODS: Test samples of 44 materials (Metal and Non-Metal) commonly used in dental restorations were fabricated and embedded with reference specimens in gelatin moulds. MRI imaging of 1.5T and CT scan were performed on the samples and evaluated in two dimensions. Artifact size and distortions were measured using a digital image analysis software. RESULTS: In MRI, 13 out of 44 materials produced artifacts, while in CT 41 out of 44 materials showed artifacts. Artifacts produced in both MRI and CT images were categorized according to the size of the artifact. SIGNIFICANCE: Metal based restoration materials had strong influence on CT and less artifacts in MRI images. Rare earth elements such as Ytterbium trifluoride found in composites caused artifacts in both MRI and CT. Recognizing these findings would help dental materials manufacturers and developers to produce materials which can cause less artifacts in MRI and CT images

The Role of Maternal Depression on Treatment Outcome for Children with Externalizing Behavior Problems

Studies have shown that, on average, Parent Management Training combined with cognitive-behavioral therapy decreases children’s externalizing behavior, but some children do not improve through treatment. The current study aimed to examine the role of maternal depression in understanding this variability in treatment outcome. Children with externalizing behavioral problems and their parents were recruited from combined Parent Management Training and Cognitive-Behavioral programs in “real-world” clinical settings. At pre- and post treatment, maternal depression and children’s externalizing behavior were assessed. Results showed that treatment was less effective for children of depressed mothers compared to non-depressed mothers and that improvements in maternal depression were associated with improvements in children’s externalizing behavior. These findings suggest that treatment programs for children with externalizing problems may be able to improve outcomes if maternal depression is a target of intervention

The Role of Friends’ Disruptive Behavior in the Development of Children’s Tobacco Experimentation: Results from a Preventive Intervention Study

Having friends who engage in disruptive behavior in childhood may be a risk factor for childhood tobacco experimentation. This study tested the role of friends’ disruptive behavior as a mediator of the effects of a classroom based intervention on children’s tobacco experimentation. 433 Children (52% males) were randomly assigned to the Good Behavior Game (GBG) intervention, a universal preventive intervention targeting disruptive behavior, and facilitating positive prosocial peer interactions. Friends’ disruptive behavior was assessed from age 7–10 years. Participants’ experimentation with tobacco was assessed annually from age 10–13. Reduced rates in tobacco experimentation and friends’ disruptive behavior were found among GBG children, as compared to controls. Support for friends’ disruptive behavior as a mediator in the link between intervention status and tobacco experimentation was found. These results remained after controlling for friends’ and parental smoking status, and child ADHD symptoms. The results support the role of friends’ disruptive behavior in preadolescents’ tobacco experimentation

The Cytosolic Domain of Fis1 Binds and Reversibly Clusters Lipid Vesicles

Every lipid membrane fission event involves the association of two apposing bilayers, mediated by proteins that can promote membrane curvature, fusion and fission. We tested the hypothesis that Fis1, a tail-anchored protein involved in mitochondrial and peroxisomal fission, promotes changes in membrane structure. We found that the cytosolic domain of Fis1 alone binds lipid vesicles, which is enhanced upon protonation and increasing concentrations of anionic phospholipids. Fluorescence and circular dichroism data indicate that the cytosolic domain undergoes a membrane-induced conformational change that buries two tryptophan side chains upon membrane binding. Light scattering and electron microscopy data show that membrane binding promotes lipid vesicle clustering. Remarkably, this vesicle clustering is reversible and vesicles largely retain their original shape and size. This raises the possibility that the Fis1 cytosolic domain might act in membrane fission by promoting a reversible membrane association, a necessary step in membrane fission

Mechanisms Underlying the Confined Diffusion of Cholera Toxin B-Subunit in Intact Cell Membranes

Multivalent glycolipid binding toxins such as cholera toxin have the capacity to cluster glycolipids, a process thought to be important for their functional uptake into cells. In contrast to the highly dynamic properties of lipid probes and many lipid-anchored proteins, the B-subunit of cholera toxin (CTxB) diffuses extremely slowly when bound to its glycolipid receptor GM1 in the plasma membrane of living cells. In the current study, we used confocal FRAP to examine the origins of this slow diffusion of the CTxB/GM1 complex at the cell surface, relative to the behavior of a representative GPI-anchored protein, transmembrane protein, and fluorescent lipid analog. We show that the diffusion of CTxB is impeded by actin- and ATP-dependent processes, but is unaffected by caveolae. At physiological temperature, the diffusion of several cell surface markers is unchanged in the presence of CTxB, suggesting that binding of CTxB to membranes does not alter the organization of the plasma membrane in a way that influences the diffusion of other molecules. Furthermore, diffusion of the B-subunit of another glycolipid-binding toxin, Shiga toxin, is significantly faster than that of CTxB, indicating that the confined diffusion of CTxB is not a simple function of its ability to cluster glycolipids. By identifying underlying mechanisms that control CTxB dynamics at the cell surface, these findings help to delineate the fundamental properties of toxin-receptor complexes in intact cell membranes

Observations of Lyα\alpha Emitters at High Redshift

In this series of lectures, I review our observational understanding of high-$z$ Ly$\alpha$ emitters (LAEs) and relevant scientific topics. Since the discovery of LAEs in the late 1990s, more than ten (one) thousand(s) of LAEs have been identified photometrically (spectroscopically) at $z\sim 0$ to $z\sim 10$. These large samples of LAEs are useful to address two major astrophysical issues, galaxy formation and cosmic reionization. Statistical studies have revealed the general picture of LAEs' physical properties: young stellar populations, remarkable luminosity function evolutions, compact morphologies, highly ionized inter-stellar media (ISM) with low metal/dust contents, low masses of dark-matter halos. Typical LAEs represent low-mass high-$z$ galaxies, high-$z$ analogs of dwarf galaxies, some of which are thought to be candidates of population III galaxies. These observational studies have also pinpointed rare bright Ly$\alpha$ sources extended over $\sim 10-100$ kpc, dubbed Ly$\alpha$ blobs, whose physical origins are under debate. LAEs are used as probes of cosmic reionization history through the Ly$\alpha$ damping wing absorption given by the neutral hydrogen of the inter-galactic medium (IGM), which complement the cosmic microwave background radiation and 21cm observations. The low-mass and highly-ionized population of LAEs can be major sources of cosmic reionization. The budget of ionizing photons for cosmic reionization has been constrained, although there remain large observational uncertainties in the parameters. Beyond galaxy formation and cosmic reionization, several new usages of LAEs for science frontiers have been suggested such as the distribution of {\sc Hi} gas in the circum-galactic medium and filaments of large-scale structures. On-going programs and future telescope projects, such as JWST, ELTs, and SKA, will push the horizons of the science frontiers.Comment: Lecture notes for `Lyman-alpha as an Astrophysical and Cosmological Tool', Saas-Fee Advanced Course 46. Verhamme, A., North, P., Cantalupo, S., & Atek, H. (eds.) --- 147 pages, 103 figures. Abstract abridged. Link to the lecture program including the video recording and ppt files : https://obswww.unige.ch/Courses/saas-fee-2016/program.cg