Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

The first polarimetric signatures of infrared jets in X-ray binaries

We present near-infrared linear spectropolarimetry of a sample of persistent X-ray binaries, Sco X-1, Cyg X-2, and GRS 1915+105. The slopes of the spectra are shallower than what is expected from a standard steady state accretion disk, and can be explained if the near-infrared flux contains a contribution from an optically thin jet. For the neutron star systems, Sco X-1 and Cyg X-2, the polarization levels at 2.4 mu m are 1.3% +/- 0.10% and 5.4% +/- 0.7%, respectively, which is greater than the polarization level at 1.65 mu m. This cannot be explained by interstellar polarization or electron scattering in the anisotropic environment of the accretion flow. We propose that the most likely explanation is that this is the polarimetric signature of synchrotron emission arising from close to the base of the jets in these systems. In the black hole system GRS 1915+105 the observed polarization, although high (5.0% +/- 1.2% at 2.4 mu m), may be consistent with interstellar polarization. For Sco X-1 the position angle of the radio jet on the sky is approximately perpendicular to the near-infrared position angle (electric vector), suggesting that the magnetic field is aligned with the jet. These observations may be a first step toward probing the ordering, alignment, and variability of the outflow magnetic field in a region closer to the central accreting object than is observed in the radio band.

sscMap: An extensible Java application for connecting small-molecule drugs using gene-expression signatures

Background
Connectivity mapping is a process to recognize novel pharmacological and toxicological properties in small molecules by comparing their gene expression signatures with others in a database. A simple and robust method for connectivity mapping with increased specificity and sensitivity was recently developed, and its utility demonstrated using experimentally derived gene signatures.

Results
This paper introduces sscMap (statistically significant connections' map), a Java application designed to undertake connectivity mapping tasks using the recently published method. The software is bundled with a default collection of reference gene-expression profiles based on the publicly available dataset from the Broad Institute Connectivity Map 02, which includes data from over 7000 Affymetrix microarrays, for over 1000 small-molecule compounds, and 6100 treatment instances in 5 human cell lines. In addition, the application allows users to add their custom collections of reference profiles and is applicable to a wide range of other 'omics technologies.

Conclusion
The utility of sscMap is two fold. First, it serves to make statistically significant connections between a user-supplied gene signature and the 6100 core reference profiles based on the Broad Institute expanded dataset. Second, it allows users to apply the same improved method to custom-built reference profiles which can be added to the database for future referencing. The software can be freely downloaded from http://purl.oclc.org/NET/sscMap

A simple and robust method for connecting small-molecule drugs using gene-expression signatures

Background

Interaction of a drug or chemical with a biological system can result in a gene-expression profile or signature characteristic of the event. Using a suitably robust algorithm these signatures can potentially be used to connect molecules with similar pharmacological or toxicological properties by gene expression profile. Lamb et al first proposed the Connectivity Map [Lamb et al (2006), Science 313, 1929–1935] to make successful connections among small molecules, genes, and diseases using genomic signatures.

Results

Here we have built on the principles of the Connectivity Map to present a simpler and more robust method for the construction of reference gene-expression profiles and for the connection scoring scheme, which importantly allows the valuation of statistical significance of all the connections observed. We tested the new method with two randomly generated gene signatures and three experimentally derived gene signatures (for HDAC inhibitors, estrogens, and immunosuppressive drugs, respectively). Our testing with this method indicates that it achieves a higher level of specificity and sensitivity and so advances the original method.

Conclusion

The method presented here not only offers more principled statistical procedures for testing connections, but more importantly it provides effective safeguard against false connections at the same time achieving increased sensitivity. With its robust performance, the method has potential use in the drug development pipeline for the early recognition of pharmacological and toxicological properties in chemicals and new drug candidates, and also more broadly in other 'omics sciences.

Polarimetric signatures of infrared jets in X-ray binaries

We present near-infrared linear spectropolarimetry of a sample of persistent X-ray binaries, Sco X-1, Cyg X-2 and GRS 1915+105. For Sco X-1 and Cyg X-2, the polarization levels at 2.4 µm are 1.3+/-0.10% and 5.4+/-0.7%, respectively, which is greater than the polarization level at 1.65 µm. This cannot be explained by interstellar polarization or electron scattering in the anisotropic environment of the accretion flow. We propose that the most likely explanation is that this is the polarimetric signature of synchrotron emission arising from close to the base of the jet. For Sco X-1 the position angle of the radio jet on the sky is approximately perpendicular to the near-infrared position angle (electric vector), suggesting that the magnetic field is aligned with the jet. These observations may be a first step towards probing the ordering, alignment, and variability of the outflow magnetic field, in a region closer to the central accreting object than is observed in the radio band.

Spectral induced polarization signatures of abiotic FeS precipitation

In recent years, geophysical methods have been shown to be sensitive to microbial-induced mineralization processes. The spectral induced-polarization (SIP) method appears to be very promising for monitoring mineralization and microbial processes. With this work, we study the links of mineralization and SIP signals, in the absence of microbial activity. We recorded the SIP response during abiotic FeS precipitation. We show that the SIP signals are diagnostic of FeS mineralization and can be differentiated from SIP signals from biomineralization processes. More specifically, the imaginary conductivity shows almost linear dependence on the amount of FeS precipitating out of solution, above the threshold value 0.006 gr under our experimental conditions. This research has direct implications for the use of the SIP method as a monitoring and decision-making tool for sustainable remediation of metals in contaminated soils and groundwater.

Self-potential signatures associated with an injection experiment at an in situ biological permeable reactive barrier

Strategies available to evaluate the performance of in situ permeable reactive barriers are currently not well developed and often rely on fluid and media sampling directly from the permeable reactive barrier (PRB). Here, we investigate the utility of the self-potential (SP) method as a technique to monitor in situ PRB performance. Our field study was conducted at in situ biological PRB in Portadown, Northern Ireland, UK, which was emplaced to assist in the remediation of groundwater contamination (e.g., hydrocarbons, ammonia) that resulted from the operations and waste disposal practices of a former gasworks. Borehole SP measurements were collected during the injection of contaminant groundwater slugs in an attempt to monitor/detect the response of the microbial activity associated with the breakdown of the added contaminants into the PRB. In addition, an uncontaminated groundwater slug was injected into a different portion of the PRB as a ‘control’ and SP measurements were collected for comparison to the SP response of the contaminant slugs. The results of the SP signals due to the contaminant injections show that the magnitude of the response was relatively small (<10 mV) yet showed a consistent decrease during both contaminant injections. The net decrease in SP recorded during the contaminant injections slowly rebounded to near background values through ~44 hours post-injection. The SP response during the uncontaminated injection showed a slight, albeit negligible (within the margin of error), 1 mV increase in the measured SP signals, in contrast to the contaminant injections. The results of the SP signals recorded from the uncontaminated groundwater injection also persisted through a period of ~47 hours after injection but show a net increase in SP relative to pre-injection values. Based on the difference in SP response between the contaminated and uncontaminated injections, we suggest that the responses are likely to be the result of differences in the chemistry of the injection types (contaminated versus uncontaminated) and in situ groundwater. We argue that the SP signals associated with the contaminated injections are dominated by diffusion (electrochemical) potential, possibly enhanced by a microbial effect. While the results of our investigation show a consistent SP response associated with the contaminant injections that is dominated by diffusional effects, further studies are required in order to better understand the effect of microbial activity on SP signals and the potential utility for the SP method to detect/monitor changes that may be indicative of biological PRB performance.

Evaluating signatures of glacial refugia for North Atlantic benthic marine taxa

A goal of phylogeography is to relate patterns of genetic differentiation to potential historical geographic isolating events. Quaternary glaciations, particularly the one culminating in the Last Glacial Maximum ~21 ka (thousands of years ago), greatly affected the distributions and population sizes of temperate marine species as their ranges retreated southward to escape ice sheets. Traditional genetic models of glacial refugia and routes of recolonization include these predictions: low genetic diversity in formerly glaciated areas, with a small number of alleles/haplotypes dominating disproportionately large areas, and high diversity including "private" alleles in glacial refugia. In the Northern Hemisphere, low diversity in the north and high diversity in the south are expected. This simple model does not account for the possibility of populations surviving in relatively small northern periglacial refugia. If these periglacial populations experienced extreme bottlenecks, they could have the low genetic diversity expected in recolonized areas with no refugia, but should have more endemic diversity (private alleles) than recently recolonized areas. This review examines evidence of putative glacial refugia for eight benthic marine taxa in the temperate North Atlantic. All data sets were reanalyzed to allow direct comparisons between geographic patterns of genetic diversity and distribution of particular clades and haplotypes including private alleles. We contend that for marine organisms the genetic signatures of northern periglacial and southern refugia can be distinguished from one another. There is evidence for several periglacial refugia in northern latitudes, giving credence to recent climatic reconstructions with less extensive glaciation.

A topological algorithm for identification of structural domains of proteins

Background: Identification of the structural domains of proteins is important for our understanding of the organizational principles and mechanisms of protein folding, and for insights into protein function and evolution. Algorithmic methods of dissecting protein of known structure into domains developed so far are based on an examination of multiple geometrical, physical and topological features. Successful as many of these approaches are, they employ a lot of heuristics, and it is not clear whether they illuminate any deep underlying principles of protein domain organization. Other well-performing domain dissection methods rely on comparative sequence analysis. These methods are applicable to sequences with known and unknown structure alike, and their success highlights a fundamental principle of protein modularity, but this does not directly improve our understanding of protein spatial structure.