Fixed point of multivalued mapping in uniform spaces

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.Comment: 5 page

Fast, Exact Bootstrap Principal Component Analysis for p>1 million

Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject ($p$) is much larger than the number of subjects ($n$), the challenge of calculating and storing the leading principal components from each bootstrap sample can be computationally infeasible. To address this, we outline methods for fast, exact calculation of bootstrap principal components, eigenvalues, and scores. Our methods leverage the fact that all bootstrap samples occupy the same $n$-dimensional subspace as the original sample. As a result, all bootstrap principal components are limited to the same $n$-dimensional subspace and can be efficiently represented by their low dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on the bootstrap distribution of these low dimensional coordinates, without calculating or storing the $p$-dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalogram (EEG) recordings ($p=900$, $n=392$), and to a dataset of brain magnetic resonance images (MRIs) ($p\approx$ 3 million, $n=352$). For the brain MRI dataset, our method allows for standard errors for the first 3 principal components based on 1000 bootstrap samples to be calculated on a standard laptop in 47 minutes, as opposed to approximately 4 days with standard methods.Comment: 25 pages, including 9 figures and link to R package. 2014-05-14 update: final formatting edits for journal submission, condensed figure

Taxonomy of the Crematogaster degeeri-species-assemblage in the Malagasy region (Hymenoptera: Formicidae)

We revise the species-level taxonomy of the Crematogaster (Crematogaster) degeerispecies-assemblage, a group of related ants occuring in Madagascar and the wider Malagasy region, and further provide an identification key to all species-groups of the genus Crematogaster in this region. Within the C. degeeri-assemblage, we recognize twelve species based upon morphological data from worker, queen and male ants, as well as genetic data from the barcode region of cytochrome oxidase I. Seven new species are described: Crematogaster alafara Blaimer sp. nov., C. bara Blaimer sp. nov., C. mafybe Blaimer sp. nov., C.maina Blaimer sp. nov., C. malahelo Blaimer sp. nov., C. masokely Blaimer sp. nov., C. ramamy Blaimer sp. nov. Crematogaster tricolor Gerstäcker, 1859 (stat. rev.) and C. dentata Dalla Torre, 1893 (stat. nov.) are raised to species level, and the following new synonymies are proposed: Crematogaster degeeri lunaris Santschi, 1928 as a synonym of C. degeeri Forel, 1886; Crematogaster sewelli improba Forel, 1907 and C. sewelli mauritiana Forel, 1907 as synonyms of C. dentata Dalla Torre, 1893, and C. pacifi ca Santschi, 1919 as a synonym of C. lobata Emery, 1895. Species descriptions, images, and distribution maps and identification keys based on worker ants, as well as on queen ants where available, are presented for all twelve species. In addition, we present a molecular gene tree for cytochrome oxidase I and summarize levels of sequence divergence within and between species of the C. degeeri-species-assemblage. Our findings are discussed in the light of previous work on Malagasy Crematogaster ants

Surface Acoustic Wave (saw) Cryogenic Liquid And Hydrogen Gas Sensors

This research was born from NASA Kennedy Space Center’s (KSC) need for passive, wireless and individually distinguishable cryogenic liquid and H2 gas sensors in various facilities. The risks of catastrophic accidents, associated with the storage and use of cryogenic fluids may be minimized by constant monitoring. Accidents involving the release of H2 gas or LH2 were responsible for 81% of total accidents in the aerospace industry. These problems may be mitigated by the implementation of a passive (or low-power), wireless, gas detection system, which continuously monitors multiple nodes and reports temperature and H2 gas presence. Passive, wireless, cryogenic liquid level and hydrogen (H2) gas sensors were developed on a platform technology called Orthogonal Frequency Coded (OFC) surface acoustic wave (SAW) radio frequency identification (RFID) tag sensors. The OFC-SAW was shown to be mechanically resistant to failure due to thermal shock from repeated cycles between room to liquid nitrogen temperature. This suggests that these tags are ideal for integration into cryogenic Dewar environments for the purposes of cryogenic liquid level detection. Three OFC-SAW H2 gas sensors were simultaneously wirelessly interrogated while being exposed to various flow rates of H2 gas. Rapid H2 detection was achieved for flow rates as low as 1ccm of a 2% H2, 98% N2 mixture. A novel method and theory to extract the electrical and mechanical properties of a semiconducting and high conductivity thin-film using SAW amplitude and velocity dispersion measurements were also developed. The SAW device was shown to be a useful tool in analysis and characterization of ultrathin and thin films and physical phenomena such as gas adsorption and desorption mechanisms

A Comprehensive Method of Estimating Electric Fields from Vector Magnetic Field and Doppler Measurements

Photospheric electric fields, estimated from sequences of vector magnetic field and Doppler measurements, can be used to estimate the flux of magnetic energy (the Poynting flux) into the corona and as time-dependent boundary conditions for dynamic models of the coronal magnetic field. We have modified and extended an existing method to estimate photospheric electric fields that combines a poloidal-toroidal (PTD) decomposition of the evolving magnetic field vector with Doppler and horizontal plasma velocities. Our current, more comprehensive method, which we dub the "{\bf P}TD-{\bf D}oppler-{\bf F}LCT {\bf I}deal" (PDFI) technique, can now incorporate Doppler velocities from non-normal viewing angles. It uses the \texttt{FISHPACK} software package to solve several two-dimensional Poisson equations, a faster and more robust approach than our previous implementations. Here, we describe systematic, quantitative tests of the accuracy and robustness of the PDFI technique using synthetic data from anelastic MHD (\texttt{ANMHD}) simulations, which have been used in similar tests in the past. We find that the PDFI method has less than $1$ error in the total Poynting flux and a $10$ error in the helicity flux rate at a normal viewing angle $(\theta=0$) and less than $25$ and $10$ errors respectively at large viewing angles ($\theta<60^\circ$). We compare our results with other inversion methods at zero viewing angle, and find that our method's estimates of the fluxes of magnetic energy and helicity are comparable to or more accurate than other methods. We also discuss the limitations of the PDFI method and its uncertainties.Comment: 56 pages, 10 figures, ApJ (in press

Shifting Global Climate Governance: Creating Long-Term Goals Through UNFCCC Article 2

I argue that the long-term risk of global climate change has been mischaracterized as an environmental issue, and therefore, solutions based solely on national emission targets will be ineffective. Thus, this paper argues for establishing long-term goals emphasizing both adaptation and clean energy to generate equitable and effective global climate policy that addresses this fundamental threat. This requires defining and operationalizing the overall objective contained in Article 2 of the United Nations Framework Convention on Climate Change. A second key aspect to operationalizing Article 2 is to understand those ‘particularly vulnerable’ as declared in the Article and in various climate agreements. Once operationalized, these long-term objectives can be achieved through approaches that emphasize the development of clean energy (and concomitant technology), and adaptation within vulnerable communities in their local context. It necessitates dropping formal mechanisms at the current core of the regime designed to regulate national emissions, and instead build the core of the regime around the ‘stabilization’ of both the climate system through clean energy and vulnerable people through effective adaptation

Renewable energy target scheme report of the expert panel

An examination of the operation, costs and benefits of the RET, including the economic, environmental and social impacts, the extent to which the objectives of the scheme are being met and the interaction of the RET with other Commonwealth and state and territory policies. Introduction The Review of the Renewable Energy Target (RET) scheme was jointly announced by the Hon Ian Macfarlane MP, the Minister for Industry, and the Hon Greg Hunt MP, the Minister for the Environment, on 17 February 2014. The Terms of Reference state that the review is to examine the operation, costs and benefits of the RET scheme including the economic, environmental and social impacts, the extent to which the objectives of the scheme are being met and the interaction of the RET with other Australian Government and state and territory government policies. The review is to provide advice on whether the objectives of the RET scheme are still appropriate and the range of options available for reducing its impact on electricity prices

Some results on the gamma function for negative integers

The Gamma function Γ (s)(-r) is defined by Γ (s)(-r) = N - lim ε→0 ∫ε ∞ t -r-1, ln s t e -t dt for r, s = 0, 1, 2, . . . , where N is the neutrix having domain N′ = {ε : 0 < ε < ∞} with negligible functions finite linear sums of the functions ε λ ln s-1 ε, ln s ε : λ < 0, s = 1, 2,. .. and all functions which converge to zero in the normal sense as CMMI9.-1.epsilon1 tends to zero. In the classical sense Gamma functions is not defined for the negative integer. In this study, it is proved that for r = 1, 2,..., where φ(r) = Σ r i=1 1/i. Further results are also proved

On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function

Lets F be a distribution in D' and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x)=F(x)*δn(x) for n=1, 2, … and {δn(x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ[(sinh x+)] exists and for s=0, 1, 2, … and r=1, 2, …, where M is the smallest integer greater than (s−r +1)/r and Further results are also proved