On Optimal Frame Conditioners

A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity. In this paper we reformulate the scalability problem as a convex optimization question. In particular, we present examples of various formulations of the problem along with numerical results obtained by using our methods on randomly generated frames.Comment: 11 page

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult

Nanostructures from self-assembling triazine tertiary amine N-oxide amphiphiles

A new set of amphiphilic tertiary amine N-oxides has been prepared and their self-assembly properties observed in aqueous solution by tensiometry, dynamic and static light scattering. X-ray crystallographic analysis of parent amines and sulfoxide congeners indicates the formation of hydrogen bonded dimers as the primary assembly unit for formation of vesicles in preference to the compact micelles typical of lauryl dimethylamine N-oxide (LDAO). 6-Benzyloxy-N,N'-bis(5-diethylaminopentylamine oxide)[1,3,5]triazine-2,4-diamine forms a 1 μm vesicle observed to entrap fluorescein. The [1,3,5]triazine core thus allows variation of the new self-assembled structures from nano- to micrometre length scales

Molecular characterization, expression and localization of a peroxiredoxin from the sheep scab mite, Psoroptes ovis

The sheep scab mite, Psoroptes ovis, induces an intensely pruritic exudative dermatitis which is responsible for restlessness, loss of appetite and weight loss. Within the first 24 h of infection, there is a rapid inflammatory influx of eosinophils and apoptosis of the keratinocytes at the site of infection. The former cell type is capable of a sustained respiratory burst, toxic products of which may directly damage the mite and also contribute to lesion formation. Analysis of a P. ovis expressed sequence tag (EST) database identified a number of antioxidant enzyme-encoding sequences, including peroxiredoxin (thioredoxin peroxidase EC 1.11.1.15), all of which may help the mite endure the potentially toxic skin environment. A full length sequence encoding Po-TPx, a protein of 206 amino acids which showed high homology to a peroxiredoxin from the salivary gland of the tick Ixodes scapularis, was amplified from P. ovis cDNA. Recombinant Po-TPx was expressed in bacteria and antiserum to this protein was used to localize native Po-TPx in mite sections. Peroxiredoxin was localized, amongst other sites, to a subpharyngeal region in mite sections. The recombinant protein was recognized by sera from sheep infested with the mite suggesting that it may be secreted or excreted by the mite and interact with the host immune response

When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥Δ, where Δ denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size <Δ are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than Δ; and (b) damp any disturbances having a scale of size smaller than Δ initially. From this we deduce that the eddy viscosity νe has to depend on the invariants q = ½tr(S^2) and r =−⅓tr(S^3) of the (filtered) strain rate tensor S. The simplest model is then given by νe = 3/2(Δ/π)^2|r|/q. This model is successfully tested for a turbulent channel flow (Reτ = 590).

Xenopus: An ideal system for chemical genetics

Chemical genetics, or chemical biology, has become an increasingly powerful method for studying biological processes. The main objective of chemical genetics is the identification and use of small molecules that act directly on proteins, allowing rapid and reversible control of activity. These compounds are extremely powerful tools for researchers, particularly in biological systems that are not amenable to genetic methods. In addition, identification of small molecule interactions is an important step in the drug discovery process. Increasingly, the African frog Xenopus is being used for chemical genetic approaches. Here, we highlight the advantages of Xenopus as a first-line in vivo model for chemical screening as well as for testing reverse engineering approaches. genesis 50:207–218, 2012. © 2012 Wiley Periodicals, Inc

Two-dimensional nanovaristors at grain boundaries account for memristive switching in polycrystalline BiFeO3

Memristive switching in polycrystalline materials is widely attributed to the formation and rupture of conducting filaments, believed to be mediated by oxygen-vacancy redistribution. The underlying atomic-scale processes are still unknown, however, which limits device modeling and design. Here we combine experimental data with multi-scale calculations to elucidate the entire atomic-scale cycle in undoped polycrystalline BiFeO3. Conductive atomic force microscopy reveals that the grain boundaries behave like two-dimensional nanovaristors while, on the return part of the cycle, the decreasing current is through the grains. Using density-functional-theory and Monte-Carlo calculations we deduce the atomic-scale mechanism of the observed phenomena. Oxygen vacancies in non-equilibrium concentrations are initially distributed relatively uniformly, but they are swept into the grain boundaries by an increasing voltage. A critical voltage, the SET voltage, then eliminates the barrier for hopping conduction through vacancy energy levels in grain boundaries. On the return part of the cycle, the grain boundaries are again non-conductive, but the grains show nonzero conductivity by virtue of remote doping by oxygen vacancies. The RESET voltage amounts to a heat pulse that redistributes the vacancies. The realization that nanovaristors are at the heart of memristive switching in polycrystalline materials may open possibilities for novel devices and circuits

Characterizing cometary electrons with kappa distributions

The Rosetta spacecraft has escorted comet 67P/Churyumov-Gerasimenko since 6 August 2014 and has offered an unprecedented opportunity to study plasma physics in the coma. We have used this opportunity to make the fi rst characterization of cometary electrons with kappa distributions. Two three-dimensional kappa functions were fi t to the observations, which we interpret as two populations of dense and warm (density=10cm 3 , temperature=2×10 5 K, invariant kappa index=10 > 1000), and rare fi ed and hot (density=0.005cm 3 , temperature=5×10 5 K, invariant kappa index=1 – 10) electrons. We fi t the observations on 30 October 2014 when Rosetta was 20km from 67P, and 3AU from the Sun. We repeated the analysis on 15 August 2015 when Rosetta was 300km from the comet and 1.3AU from the Sun. Comparing the measurements on both days gives the fi rst comparison of the cometary electron environment between a nearly inactive comet far from the Sun and an active comet near perihelion. We fi nd that the warm population density increased by a factor of 3, while the temperature cooled by a factor of 2, and the invariant kappa index was unaffected. We fi nd that the hot population density increased by a factor of 10, while the temperature and invariant kappa index were unchanged. We conclude that the hot population is likely the solar wind halo electrons in the coma. The warm population is likely of cometary origin, but its mechanism for production is not known

A multifaceted study of stigma/style cysteine-rich adhesin (SCA)-like Arabidopsis lipid transfer proteins (LTPs) suggests diversified roles for these LTPs in plant growth and reproduction

Lily stigma/style cysteine-rich adhesin (SCA), a plant lipid transfer protein (LTP) which is secreted into the extracellular matrix, functions in pollen tube guidance in fertilization. A gain-of-function mutant (ltp5-1) for Arabidopsis LTP5, an SCA-like molecule, was recently shown to display defects in sexual reproduction. In the current study, it is reported that ltp5-1 plants have dwarfed primary shoots, delayed hypocotyl elongation, various abnormal tissue fusions, and display multibranching. These mutant phenotypes in vegetative growth are recessive. No abnormality was found in ltp5-1/+ plants. In a phylogenetic analysis of plant LTPs, SCA-like Arabidopsis LTPs were classified with conventional plant LTPs. Homology modelling-based electrostatic similarity index (ESI) clustering was used to show diversity in spatial distributions of electrostatic potentials of SCA-like LTPs, suggestive of their various roles in interaction in the extracellular matrix space. β-Glucuronidase (GUS) analysis showed that SCA-like Arabidopsis LTP genes are diversely present in various tissues. LTP4 was found specifically in the guard cells and LTP6 in trichomes as well as in other tissues. LTP1 levels were specifically abundant in the stigma, and both LTP3 and LTP6 in the ovules. LTP2 and LTP4 gene levels were up-regulated in whole seedlings with 20% polyethylene glycol (PEG) and 300 mM NaCl treatments, respectively. LTP5 was up-regulated in the hypocotyl with 3 d dark growth conditions. LTP6 was specifically expressed in the tip of the cotyledon under drought stress conditions. The results suggest that SCA-like Arabidopsis LTPs are multifunctional, with diversified roles in plant growth and reproduction

Systematizing Confidence in Open Research and Evidence (SCORE)

Assessing the credibility of research claims is a central, continuous, and laborious part of the scientific process. Credibility assessment strategies range from expert judgment to aggregating existing evidence to systematic replication efforts. Such assessments can require substantial time and effort. Research progress could be accelerated if there were rapid, scalable, accurate credibility indicators to guide attention and resource allocation for further assessment. The SCORE program is creating and validating algorithms to provide confidence scores for research claims at scale. To investigate the viability of scalable tools, teams are creating: a database of claims from papers in the social and behavioral sciences; expert and machine generated estimates of credibility; and, evidence of reproducibility, robustness, and replicability to validate the estimates. Beyond the primary research objective, the data and artifacts generated from this program will be openly shared and provide an unprecedented opportunity to examine research credibility and evidence