Families of spectral sets for Bernoulli convolutions

In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. For other cases, we exhibit maximal Fourier families that are not orthonormal bases.Comment: 25 pages, same result

Additive spectra of the 1/4 Cantor measure

In this paper, we add to the characterization of the Fourier spectra for Bernoulli convolution measures. These measures are supported on Cantor subsets of the line. We prove that performing an odd additive translation to half the canonical spectrum for the 1/4 Cantor measure always yields an alternate spectrum. We call this set an additive spectrum. The proof works by connecting the additive set to a spectrum formed by odd multiplicative scaling.Comment: 9 pages, 1 figur

Understanding the Elements of Executable Architectures Through a Multi-Dimensional Analysis Framework

The objective of this dissertation study is to conduct a holistic investigation into the elements of executable architectures. Current research in the field of Executable Architectures has provided valuable solution-specific demonstrations and has also shown the value derived from such an endeavor. However, a common theory underlying their applications has been missing. This dissertation develops and explores a method for holistically developing an Executable Architecture Specification (EAS), i.e., a meta-model containing both semantic and syntactic information, using a conceptual framework for guiding data coding, analysis, and validation. Utilization of this method resulted in the description of the elements of executable architecture in terms of a set of nine information interrogatives: an executable architecture information ontology. Once the detail-rich EAS was constructed with this ontology, it became possible to define the potential elements of executable architecture through an intermediate level meta-model. The intermediate level meta-model was further refined into an interrogative level meta-model using only the nine information interrogatives, at a very high level of abstraction

Is Leaving Work to Obtain Safety Good Cause to Leave Employment?—Providing Unemployment Insurance to Victims of Domestic Violence in Washington State

This paper focuses on the unemployment compensation statutes, administrative law decisions, and the case law of Washington state and proposes that domestic violence creates involuntary unemployment and should, therefore, be considered a compelling good cause situation for provision of unemployment compensation benefits. Title 50 of the Revised Code of Washington, which provides the structure and provisions of unemployment compensation eligibility, should be liberally construed by agency officials and courts or amended so as to provide unemployment compensation benefits to victims of domestic violence who leave work to obtain safety

Scaling by 5 on a 1/4-Cantor Measure

Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L^2(\mu), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB (\Gamma) is the original Jorgensen-Pedersen ONB for the Cantor measure (\mu) and the other ONB is is 5\Gamma. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.Comment: 34 page

Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks

Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance or similarity metric is, however, not trivial and can be highly dependent on the application at hand. In this work, we propose a novel metric learning method to evaluate distance between graphs that leverages the power of convolutional neural networks, while exploiting concepts from spectral graph theory to allow these operations on irregular graphs. We demonstrate the potential of our method in the field of connectomics, where neuronal pathways or functional connections between brain regions are commonly modelled as graphs. In this problem, the definition of an appropriate graph similarity function is critical to unveil patterns of disruptions associated with certain brain disorders. Experimental results on the ABIDE dataset show that our method can learn a graph similarity metric tailored for a clinical application, improving the performance of a simple k-nn classifier by 11.9% compared to a traditional distance metric.Comment: International Conference on Medical Image Computing and Computer-Assisted Interventions (MICCAI) 201

Atomic force microscopy shows that vaccinia topoisomerase IB generates filaments on DNA in a cooperative fashion

Type IB DNA topoisomerases cleave and rejoin one strand of the DNA duplex, allowing for the removal of supercoils generated during replication and transcription. In addition, electron microscopy of cellular and viral TopIB–DNA complexes has suggested that the enzyme promotes long-range DNA–DNA crossovers and synapses. Here, we have used the atomic force microscope to visualize and quantify the interaction between vaccinia topoisomerase IB (vTopIB) and DNA. vTopIB was found to form filaments on nicked-circular DNA by intramolecular synapsis of two segments of a single DNA molecule. Measuring the filament length as a function of protein concentration showed that synapsis is a highly cooperative process. At high protein:DNA ratios, synapses between distinct DNA molecules were observed, which led to the formation of large vTopIB-induced DNA clusters. These clusters were observed in the presence of Mg(2+), Ca(2+) or Mn(2+), suggesting that the formation of intermolecular vTopIB-mediated DNA synapsis is favored by screening of the DNA charge

The Beauty and Complexity of the Brunt Ice Shelf from MOA and ICESat

Beginning in February 2003, NASA's Ice, Cloud, and land Elevation Satellite (ICESat) has determined surface elevations from approx. 86degN to 86degS latitude. To date, altimetry data have been acquired in a series of observation periods in repeated track patterns using all three Geoscience Laser Altimeter System (GLAS) lasers. This paper will focus on ice shelf elevation data that were obtained in 2003 across the Brunt Ice Shelf and the Stancomb-Wills Ice Tongue. Integrating the altimetry with the recently available MODIS Mosaic of Antarctica (MOA), quantifies the relative accuracy and precision of the resulting ice shelf elevations. Furthermore, the elevation data was processed onto an elevation grid, by regional interpolation across the area s complex glacial features only. Ice thickness estimation from the altimetry of the floating ice is discussed. ICESat operates at 40Hz and its elevation data is obtained every 172m along track. These elevations have a relative accuracy of about 14cm based on the standard deviation of low-slope crossover differences and a precision of close to 2cm for the Laser 2a, Release 21, GLA12 data used here