Disconnection in the Alexandroff duplicate

[EN] It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of van Douwen is significant. In a slightly different direction we also characterize when the Alexandroff duplicate of a space is a P-space as well as when it is an almost P-space.Bhattacharjee, P.; Knox, ML.; Mcgovern, WW. (2021). Disconnection in the Alexandroff duplicate. Applied General Topology. 22(2):331-344. https://doi.org/10.4995/agt.2021.14602OJS331344222P. Alexandrov and P. Urysohn, Memoire sur les espaces topologiques compacts, Verh. Akad. Wetensch. Amsterdam, 14 (1929), 1-96.K. Almontashery and L. Kalantan, Results about the Alexandroff duplicate space, Appl. Gen. Topol. 17, no. 2 (2016), 117-122. https://doi.org/10.4995/agt.2016.4521A. V. Arkhangel'skii, Topological Function Spaces, Mathematics and Its Applications, 78, Springer, Netherlands, 1992. https://doi.org/10.1007/978-94-011-2598-7G. Bezhanishvili, N. Bezhanishvili, J. Lucero-Bryan and J. van Mill, S4.3 and hereditarily extremally disconnected spaces, Georgian Mathematical Journal 22, no. 4 (2015), 469-475. https://doi.org/10.1515/gmj-2015-0041A. Caserta and S. Watson, The Alexandroff duplicate and its subspaces, Appl. Gen. Topol. 8, no. 2 (2007), 187-205. https://doi.org/10.4995/agt.2007.1880R. Engelking, On functions defined on Cartesian products, Fund. Math. 59 (1966), 221-231. https://doi.org/10.4064/fm-59-2-221-231L. Gillman and M. Jerison, Rings of Continuous Functions, Graduate Texts in Mathametics, vol. 43, Springer Verlag, Berlin-Heidelberg-New York, 1976.E. van Douwen, Applications of maximal topologies, Topology Appl. 51 (1993), 125-139. https://doi.org/10.1016/0166-8641(93)90145-4J. van Mill, Weak P-points in Čech-Stone compactifications, Trans. Amer. Math. Soc. 273 (1982), 657-678. https://doi.org/10.2307/1999934J. L. Verner, Lonely points revisited, Comment. Math. Univ. Carolin. 54, no. 1 (2013), 105-110

The classical ring of quotients of Cc(X)C_c(X)

[EN] We construct the classical ring of quotients of the algebra of continuous real-valued functions with countable range. Our construction is a slight modification of the construction given in [M. Ghadermazi, O.A.S. Karamzadeh, and M. Namdari, On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova, to appear]. Dowker's example shows that the two constructions can be different.Bhattacharjee, P.; Knox, ML.; Mcgovern, WW. (2014). The classical ring of quotients of $C_c(X)$. Applied General Topology. 15(2):147-154. doi:http://dx.doi.org/10.4995/agt.2014.3181.SWORD147154152Hager, A. W., Kimber, C. M., & McGovern, W. W. (2005). Unique a-closure for some ℓ-groups of rational valued functions. Czechoslovak Mathematical Journal, 55(2), 409-421. doi:10.1007/s10587-005-0031-zHenriksen, M., & Woods, R. G. (2004). Cozero complemented spaces; when the space of minimal prime ideals of a C(X) is compact. Topology and its Applications, 141(1-3), 147-170. doi:10.1016/j.topol.2003.12.004Knox, M. L., & McGovern, W. W. (2008). Rigid extensions of ℓ-groups of continuous functions. Czechoslovak Mathematical Journal, 58(4), 993-1014. doi:10.1007/s10587-008-0064-1R. Levy and M. D. Rice, Normal $P$-spaces and the $G_delta$-topology, Colloq. Math. 44, no. 2 (1981), 227-240.Levy, R., & Shapiro, J. (2005). Rings of quotients of rings of functions. Topology and its Applications, 146-147, 253-265. doi:10.1016/j.topol.2003.03.003A. Mysior, Two easy examples of zero-dimensional spaces, Proc. Amer. Math. Soc. 92, no. 4 (1984), 615-617.Porter, J. R., & Woods, R. G. (1988). Extensions and Absolutes of Hausdorff Spaces. doi:10.1007/978-1-4612-3712-9Rudin, W. (1957). Continuous functions on compact spaces without perfect subsets. Proceedings of the American Mathematical Society, 8(1), 39-39. doi:10.1090/s0002-9939-1957-0085475-

MSSM Baryogenesis and Electric Dipole Moments: An Update on the Phenomenology

We explore the implications of electroweak baryogenesis for future searches for permanent electric dipole moments in the context of the minimal supersymmetric extension of the Standard Model (MSSM). From a cosmological standpoint, we point out that regions of parameter space that over-produce relic lightest supersymmetric particles can be salvaged only by assuming a dilution of the particle relic density that makes it compatible with the dark matter density: this dilution must occur after dark matter freeze-out, which ordinarily takes place after electroweak baryogenesis, implying the same degree of dilution for the generated baryon number density as well. We expand on previous studies on the viable MSSM regions for baryogenesis, exploring for the first time an orthogonal slice of the relevant parameter space, namely the (tan\beta, m_A) plane, and the case of non-universal relative gaugino-higgsino CP violating phases. The main result of our study is that in all cases lower limits on the size of the electric dipole moments exist, and are typically on the same order, or above, the expected sensitivity of the next generation of experimental searches, implying that MSSM electroweak baryogenesis will be soon conclusively tested.Comment: 23 pages, 10 figures, matches version published in JHE

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

Detection of Murine Leukemia Virus or Mouse DNA in Commercial RT-PCR Reagents and Human DNAs

The xenotropic murine leukemia virus (MLV)-related viruses (XMRV) have been reported in persons with prostate cancer, chronic fatigue syndrome, and less frequently in blood donors. Polytropic MLVs have also been described in persons with CFS and blood donors. However, many studies have failed to confirm these findings, raising the possibility of contamination as a source of the positive results. One PCR reagent, Platinum Taq polymerase (pol) has been reported to contain mouse DNA that produces false-positive MLV PCR results. We report here the finding of a large number of PCR reagents that have low levels of MLV sequences. We found that recombinant reverse-transcriptase (RT) enzymes from six companies derived from either MLV or avian myeloblastosis virus contained MLV pol DNA sequences but not gag or mouse DNA sequences. Sequence and phylogenetic analysis showed high relatedness to Moloney MLV, suggesting residual contamination with an RT-containing plasmid. In addition, we identified contamination with mouse DNA and a variety of MLV sequences in commercially available human DNAs from leukocytes, brain tissues, and cell lines. These results identify new sources of MLV contamination and highlight the importance of careful pre-screening of commercial specimens and diagnostic reagents to avoid false-positive MLV PCR results

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

No Evidence of Murine Leukemia Virus-Related Viruses in Live Attenuated Human Vaccines

The association of xenotropic murine leukemia virus (MLV)-related virus (XMRV) in prostate cancer and chronic fatigue syndrome reported in previous studies remains controversial as these results have been questioned by recent data. Nonetheless, concerns have been raised regarding contamination of human vaccines as a possible source of introduction of XMRV and MLV into human populations. To address this possibility, we tested eight live attenuated human vaccines using generic PCR for XMRV and MLV sequences. Viral metagenomics using deep sequencing was also done to identify the possibility of other adventitious agents.All eight live attenuated vaccines, including Japanese encephalitis virus (JEV) (SA-14-14-2), varicella (Varivax), measles, mumps, and rubella (MMR-II), measles (Attenuvax), rubella (Meruvax-II), rotavirus (Rotateq and Rotarix), and yellow fever virus were negative for XMRV and highly related MLV sequences. However, residual hamster DNA, but not RNA, containing novel endogenous gammaretrovirus sequences was detected in the JEV vaccine using PCR. Metagenomics analysis did not detect any adventitious viral sequences of public health concern. Intracisternal A particle sequences closest to those present in Syrian hamsters and not mice were also detected in the JEV SA-14-14-2 vaccine. Combined, these results are consistent with the production of the JEV vaccine in Syrian hamster cells.We found no evidence of XMRV and MLV in eight live attenuated human vaccines further supporting the safety of these vaccines. Our findings suggest that vaccines are an unlikely source of XMRV and MLV exposure in humans and are consistent with the mounting evidence on the absence of these viruses in humans

Standardized ultrasound evaluation of carotid stenosis for clinical trials: University of Washington Ultrasound Reading Center

<p>Abstract</p> <p>Introduction</p> <p>Serial monitoring of patients participating in clinical trials of carotid artery therapy requires noninvasive precision methods that are inexpensive, safe and widely available. Noninvasive ultrasonic duplex Doppler velocimetry provides a precision method that can be used for recruitment qualification, pre-treatment classification and post treatment surveillance for remodeling and restenosis. The University of Washington Ultrasound Reading Center (UWURC) provides a uniform examination protocol and interpretation of duplex Doppler velocity measurements.</p> <p>Methods</p> <p>Doppler waveforms from 6 locations along the common carotid and internal carotid artery path to the brain plus the external carotid and vertebral arteries on each side using a Doppler examination angle of 60 degrees are evaluated. The UWURC verifies all measurements against the images and waveforms for the database, which includes pre-procedure, post-procedure and annual follow-up examinations. Doppler angle alignment errors greater than 3 degrees and Doppler velocity measurement errors greater than 0.05 m/s are corrected.</p> <p>Results</p> <p>Angle adjusted Doppler velocity measurements produce higher values when higher Doppler examination angles are used. The definition of peak systolic velocity varies between examiners when spectral broadening due to turbulence is present. Examples of measurements are shown.</p> <p>Discussion</p> <p>Although ultrasonic duplex Doppler methods are widely used in carotid artery diagnosis, there is disagreement about how the examinations should be performed and how the results should be validated. In clinical trails, a centralized reading center can unify the methods. Because the goals of research examinations are different from those of clinical examinations, screening and diagnostic clinical examinations may require fewer velocity measurements.</p

Multiple Sources of Contamination in Samples from Patients Reported to Have XMRV Infection

Xenotropic murine leukemia virus (MLV)-related retrovirus (XMRV) was reported to be associated with prostate cancer by Urisman, et al. in 2006 and chronic fatigue syndrome (CFS) by Lombardi, et al. in 2009. To investigate this association, we independently evaluated plasma samples from 4 patients with CFS reported by Lombardi, et al. to have XMRV infection and from 5 healthy controls reported to be XMRV uninfected. We also analyzed viral sequences obtained from supernatants of cell cultures found to contain XMRV after coculture with 9 clinical samples from 8 patients. A qPCR assay capable of distinguishing XMRV from endogenous MLVs showed that the viral sequences detected in the CFS patient plasma behaved like endogenous MLVs and not XMRV. Single-genome sequences (N = 89) from CFS patient plasma were indistinguishable from endogenous MLVs found in the mouse genome that are distinct from XMRV. By contrast, XMRV sequences were detected by qPCR in 2 of the 5 plasma samples from healthy controls (sequencing of the qPCR product confirmed XMRV not MLV). Single-genome sequences (N = 234) from the 9 culture supernatants reportedly positive for XMRV were indistinguishable from XMRV sequences obtained from 22Rv1 and XMRV-contaminated 293T cell-lines. These results indicate that MLV DNA detected in the plasma samples from CFS patients evaluated in this study was from contaminating mouse genomic DNA and that XMRV detected in plasma samples from healthy controls and in cultures of patient samples was due to cross-contamination with XMRV (virus or nucleic acid)