Unitary Representations of Lie Groups with Reflection Symmetry

We consider the following class of unitary representations $\pi$ of some (real) Lie group $G$ which has a matched pair of symmetries described as follows: (i) Suppose $G$ has a period-2 automorphism $\tau$, and that the Hilbert space $\mathbf{H} (\pi)$ carries a unitary operator $J$ such that $J\pi =(\pi \circ \tau)J$ (i.e., selfsimilarity). (ii) An added symmetry is implied if $\mathbf{H} (\pi)$ further contains a closed subspace $\mathbf{K}_0$ having a certain order-covariance property, and satisfying the $\mathbf{K}_0$-restricted positivity: $\ge 0$, $\forall v\in \mathbf{K}_0$, where $$ is the inner product in $\mathbf{H} (\pi)$. From (i)--(ii), we get an induced dual representation of an associated dual group $G^c$. All three properties, selfsimilarity, order-covariance, and positivity, are satisfied in a natural context when $G$ is semisimple and hermitean; but when $G$ is the $(ax+b)$-group, or the Heisenberg group, positivity is incompatible with the other two axioms for the infinite-dimensional irreducible representations. We describe a class of $G$, containing the latter two, which admits a classification of the possible spaces $\mathbf{K}_0 \subset \mathbf{H} (\pi)$ satisfying the axioms of selfsimilarity and order-covariance.Comment: 49 pages, LaTeX article style, 11pt size optio

Coarse-Graining and Renormalization Group in the Einstein Universe

The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes is constructed in a nonflat background and explicitly computed within the loop-expansion approximation for an Einstein universe. The curvature turns out to be dominant in setting the crossover scale from a double-peak and a symmetric distribution of the block variables. The evolution of all the coupling constants generated by the blocking procedure is examined: the renormalized trajectories agree with the standard perturbative results for the relevant vertices near the ultraviolet fixed point, but new effective interactions between gravity and matter are present. The flow of the conformal coupling constant is therefore analyzed in the improved scheme and the infrared fixed point is reached for arbitrary values of the renormalized parameters.Comment: 18 pages, REVTex, two uuencoded figures. (to appear in Phys. Rev. D15, July) Transmission errors have been correcte

Mass equidistribution of Hilbert modular eigenforms

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for

Search for the Rare Decay KL --> pi0 ee

The KTeV/E799 experiment at Fermilab has searched for the rare kaon decay KL--> pi0ee. This mode is expected to have a significant CP violating component. The measurement of its branching ratio could support the Standard Model or could indicate the existence of new physics. This letter reports new results from the 1999-2000 data set. One event is observed with an expected background at 0.99 +/- 0.35 events. We set a limit on the branching ratio of 3.5 x 10^(-10) at the 90% confidence level. Combining the results with the dataset taken in 1997 yields the final KTeV result: BR(KL --> pi0 ee) < 2.8 x 10^(-10) at 90% CL.Comment: 4 pages, three figure

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Magnetic Field Amplification in Galaxy Clusters and its Simulation

We review the present theoretical and numerical understanding of magnetic field amplification in cosmic large-scale structure, on length scales of galaxy clusters and beyond. Structure formation drives compression and turbulence, which amplify tiny magnetic seed fields to the microGauss values that are observed in the intracluster medium. This process is intimately connected to the properties of turbulence and the microphysics of the intra-cluster medium. Additional roles are played by merger induced shocks that sweep through the intra-cluster medium and motions induced by sloshing cool cores. The accurate simulation of magnetic field amplification in clusters still poses a serious challenge for simulations of cosmological structure formation. We review the current literature on cosmological simulations that include magnetic fields and outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure

New games, new rules: big data and the changing context of strategy

Big data and the mechanisms by which it is produced and disseminated introduce important changes in the ways information is generated and made relevant for organizations. Big data often represents miscellaneous records of the whereabouts of large and shifting online crowds. It is frequently agnostic, in the sense of being produced for generic purposes or purposes different from those sought by big data crunching. It is based on varying formats and modes of communication (e.g., texts, image and sound), raising severe problems of semiotic translation and meaning compatibility. Crucially, the usefulness of big data rests on their steady updatability, a condition that reduces the time span within which this data is useful or relevant. Jointly, these attributes challenge established rules of strategy making as these are manifested in the canons of procuring structured information of lasting value that addresses specific and long-term organizational objectives. The developments underlying big data thus seem to carry important implications for strategy making, and the data and information practices with which strategy has been associated. We conclude by placing the understanding of these changes within the wider social and institutional context of longstanding data practices and the significance they carry for management and organizations

Female genital tract shedding of HIV-1 is rare in women with suppressed HIV-1 in plasma

Objective: Determine the frequency of genital HIV-1 shedding in a large cohort of women on long-term suppressive antiretroviral therapy (ART) and its association with mucosal inflammation.Design:We measured levels of HIV-1 RNA and inflammation biomarkers in cervicovaginal lavage (CVL) from HIV-seropositive women enrolled in the Women's Interagency HIV Study (WIHS).Methods:HIV-1 was quantified (Abbott RealTime HIV-1 assay) from CVL samples of 332 WIHS participants with and without clinical evidence of genital inflammation at the time of CVL collection; participants had suppressed plasma viral load (PVL; limit of quantitation less than 20-4000copies/ml depending on year of collection) for a median of 7.1 years [interquartile range (IQR) 3.4-9.8, Group 1] or for a median of 1.0 years (IQR=0.5-1.0, Group 2). Twenty-two biomarkers of inflammation were measured in CVL to compare with clinical markers.Results:HIV-1 was detected in 47% of 38 pre-ART CVL samples (median 668copies/ml) and detection in CVL was associated with higher pre-ART PVL. HIV-1 was detected in only 1 of 38 CVL samples from these women on suppressive antiretroviral therapy for 1 year. No HIV-1 RNA was detected in 294 CVL samples from a cross-sectional set of women with suppressed PVL for a median of 7 years. Clinical inflammation markers were correlated with inflammatory biomarkers in CVL specimens, although genital inflammation was not associated with measurable genital HIV-1 shedding in these WIHS participants on ART.Conclusion:ART that suppresses HIV-1 in the plasma of women also prevents genital tract HIV-1 shedding, even in the presence of genital tract inflammation. Copyright © 2019 The Author(s)

Review Section : Nature/Nurture Revisited I

Biologically oriented approaches to the study of human conflict have thus far been limited largely to the study of aggression. A sample of the literature on this topic is reviewed, drawing upon four major approaches: comparative psychology, ethology (including some popularized accounts), evolutionary-based theories, and several areas of human physiology. More sophisticated relationships between so-called "innate" and "acquired" determinants of behavior are discussed, along with the proper relevance of animal behavior studies for human behavior. Unless contained in a comprehensive theory which includes social and psychological variables, biolog ically oriented theories (although often valid within their domain) offer at best severely limited and at worst highly misleading explanations of complex social conflicts. The review concludes with a list of several positive contributions of these biological approaches and suggests that social scientists must become more knowledgeable about them.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68270/2/10.1177_002200277401800206.pd