Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Cognitive Information Processing

Contains reports on six research projects.National Institutes of Health (Grant 5 PO1 GM14940-03)National Institutes of Health (Grant 5 PO1 GM15006-03)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E)National Institutes of Health (Grant 5 TO1 GM01555-03

The Role of Factors Associated With Apoptosis in Assessing Periodontal Disease Status

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141031/1/jper1086-sup-0003.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/141031/2/jper1086-sup-0002.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/141031/3/jper1086.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/141031/4/jper1086-sup-0001.pd

Women’s health and well-being in low-income formal and informal neighbourhoods on the eve of the armed conflict in Aleppo

Objectives To explore how married women living in low-income formal and informal neighbourhoods in Aleppo, Syria, perceived the effects of neighbourhood on their health and well-being, and the relevance of these findings to future urban rebuilding policies post-conflict. Methods Semi-structured interviews were undertaken with eighteen married women living in informal or socioeconomically disadvantaged formal neighbourhoods in Aleppo in 2011, a year before the armed conflict caused massive destruction in all these neighbourhoods. Results Our findings suggest that the experience of neighbourhood social characteristics is even more critical to women’s sense of well-being than environmental conditions and physical infrastructure. Most prominent was the positive influence of social support on well-being. Conclusions The significance of this study lies, first, in its timing, before the widespread destruction of both formal and informal neighbourhoods in Aleppo and, second, and in its indication of the views of women who lived in marginalised communities on what neighbourhood characteristics mattered to them. Further research post-conflict needs to explore how decisions on urban rebuilding are made and their likely influence on health and well-being

Search for the Higgs boson in events with missing transverse energy and b quark jets produced in proton-antiproton collisions at s**(1/2)=1.96 TeV

We search for the standard model Higgs boson produced in association with an electroweak vector boson in events with no identified charged leptons, large imbalance in transverse momentum, and two jets where at least one contains a secondary vertex consistent with the decay of b hadrons. We use ~1 fb-1 integrated luminosity of proton-antiproton collisions at s**(1/2)=1.96 TeV recorded by the CDF II experiment at the Tevatron. We find 268 (16) single (double) b-tagged candidate events, where 248 +/- 43 (14.4 +/- 2.7) are expected from standard model background processes. We place 95% confidence level upper limits on the Higgs boson production cross section for several Higgs boson masses ranging from 110 GeV/c2 to 140 GeV/c2. For a mass of 115 GeV/c2 the observed (expected) limit is 20.4 (14.2) times the standard model prediction.Comment: 8 pages, 2 figures, submitted to Phys. Rev. Let

Observation and Mass Measurement of the Baryon Ξb−\Xi^-_b

We report the observation and measurement of the mass of the bottom, strange baryon $\Xi^-_b$ through the decay chain $\Xi^-_b \to J/\psi \Xi^-$, where $J/\psi \to \mu^+ \mu^-$, $\Xi^- \to \Lambda \pi^-$, and $\Lambda \to p \pi^-$. Evidence for observation is based on a signal whose probability of arising from the estimated background is 6.6 x 10^{-15}, or 7.7 Gaussian standard deviations. The $\Xi^-_b$ mass is measured to be $5792.9\pm 2.5$ (stat.) $\pm 1.7$ (syst.) MeV/$c^2$.Comment: Minor text changes for the second version. Accepted by Phys. Rev. Let

Polarizations of J/psi and psi(2S) Mesons Produced in ppbar Collisions at 1.96 TeV

We have measured the polarizations of \jpsi and \psiprime mesons as functions of their transverse momentum \pt when they are produced promptly in the rapidity range $|y|<0.6$ with \pt \geq 5 \pgev. The analysis is performed using a data sample with an integrated luminosity of about 800 \ipb collected by the CDF II detector. For both vector mesons, we find that the polarizations become increasingly longitudinal as \pt increases from 5 to 30 \pgev. These results are compared to the predictions of nonrelativistic quantum chromodynamics and other contemporary models. The effective polarizations of \jpsi and \psiprime mesons from $B$-hadron decays are also reported.Comment: 8 pages, 7 figures, published in Physical Review Letter

Search for Third Generation Vector Leptoquarks in p anti-p Collisions at sqrt(s) = 1.96 TeV

We describe a search for a third generation vector leptoquark (VLQ3) that decays to a b quark and tau lepton using the CDF II detector and 322 pb^(-1) of integrated luminosity from the Fermilab Tevatron. Vector leptoquarks have been proposed in many extensions of the standard model (SM). Observing a number of events in agreement with SM expectations, assuming Yang-Mills (minimal) couplings, we obtain the most stringent upper limit on the VLQ3 pair production cross section of 344 fb (493 fb) and lower limit on the VLQ3 mass of 317 GeV/c^2 (251 GeV/c^2) at 95% C.L.Comment: 7 pages, 2 figures, submitted to PR

Searches for Direct Pair Production of Supersymmetric Top and Supersymmetric Bottom Quarks in p-pbar Collisions at sqrt(s)=1.96 TeV

We search for direct pair production of supersymmetric top quarks and supersymmetric bottom quarks in proton-antiproton collisions at sqrt(s)=1.96 TeV, using 295 pb^-1 of data recorded by the Collider Detector at Fermilab (CDF II) experiment. The supersymmetric top (supersymmetric bottom) quarks are selected by reconstructing their decay into a charm (bottom) quark and a neutralino, which is assumed to be the lightest supersymmetric particle. The signature of such processes is two energetic heavy-flavor jets and missing transverse energy. The number of events that pass our selection for each search process is consistent with the expected standard model background. By comparing our results to the theoretical production cross sections of the supersymmetric top and supersymmetric bottom quarks in the minimal supersymmetric standard model, we exclude, at a 95% confidence level in the frame of that model, a supersymmetric top quark mass up to 132 GeV/c^2 for a neutralino mass of 48 GeV/c^2, and a supersymmetric bottom quark mass up to 193 GeV/c^2 for a neutralino mass of 40 GeV/c^2.Comment: 12 pages, 5 figures, submitted to Phys. Rev.