The Heider balance - a continuous approach

The Heider balance (HB) is investigated in a fully connected graph of $N$ nodes. The links are described by a real symmetric array r(i,j), i,j=1,...,N. In a social group, nodes represent group members and links represent relations between them, positive (friendly) or negative (hostile). At the balanced state, r(i,j)r(j,k)r(k,i)>0 for all the triads (i,j,k). As follows from the structure theorem of Cartwright and Harary, at this state the group is divided into two subgroups, with friendly internal relations and hostile relations between the subgroups. Here the system dynamics is proposed to be determined by a set of differential equations. The form of equations guarantees that once HB is reached, it persists. Also, for N=3 the dynamics reproduces properly the tendency of the system to the balanced state. The equations are solved numerically. Initially, r(i,j) are random numbers distributed around zero with a symmetric uniform distribution of unit width. Calculations up to N=500 show that HB is always reached. Time to get the balanced state varies with the system size N as N^{-1/2}. The spectrum of relations, initially narrow, gets very wide near HB. This means that the relations are strongly polarized. In our calculations, the relations are limited to a given range around zero. With this limitation, our results can be helpful in an interpretation of somestatistical data.Comment: 9 pages, 4 figures. Int. J. Mod. Phys. C (2005), in prin

First Results from SPARO: Evidence for Large-Scale Toroidal Magnetic Fields in the Galactic Center

We have observed the linear polarization of 450 micron continuum emission from the Galactic center, using a new polarimetric detector system that is operated on a 2 m telescope at the South Pole. The resulting polarization map extends ~ 170 pc along the Galactic plane and ~ 30 pc in Galactic latitude, and thus covers a significant fraction of the central molecular zone. Our map shows that this region is permeated by large-scale toroidal magnetic fields. We consider our results together with radio observations that show evidence for poloidal fields in the Galactic center, and with Faraday rotation observations. We compare all of these observations with the predictions of a magnetodynamic model for the Galactic center that was proposed in order to explain the Galactic Center Radio Lobe as a magnetically driven gas outflow. We conclude that the observations are basically consistent with the model.Comment: 11 pages, 2 figures, 1 table, submitted to ApJ Let

A Joint Sunyaev-Zel'dovich Effect and X-ray Analysis of Abell 3667

We present a 40GHz (7.5 mm) raster scan image of a 3.6x2 degree region centered on the low redshift (z=0.055) cluster of galaxies Abell 3667. The cluster was observed during the Antarctic winter of 1999 using the Corona instrument (15.7' FWHM beam) on the Viper Telescope at the South Pole. The Corona image of A3667 is one of the first direct (i.e. rather than interferometer) thermal Sunyaev-Zel'dovich effect images of a low redshift cluster. The brightness temperature decrement at the X-ray centroid (20h 12m 28.9s, -56 49 51 J2000) was measured to be $\Delta T_{\rm CMB}=-154\mu K$. We have used the 40GHz map of A3667 in conjunction with a deep ROSAT PSPC (X-ray) image of the cluster, to make a measurement of the Hubble Constant. We find $H_0 = 64^{+96}_{-30}$ km s$^{-1}$ Mpc$^{-1}$ (68% confidence interval). Our $H_0$ calculation assumes that the cluster can be described using an isothermal, tri-axial ellipsoidal, $\beta$-model and includes several new analysis techniques including an automated method to remove point sources from X-ray images with variable point spread functions, and an efficient method for determining the errors in multi-parameter maximum likelihood analyzes. The large errors on the $H_0$ measurement are primarily due to the statistical noise in the Corona image. We plan to increase the precision of our measurement by including additional clusters in our analysis and by increasing the sensitivity of the Viper SZE maps.Comment: 15 pages, 4 figures, submitted to ApJ (count rate units corrected in Table 1 and Figure 4

Anisotropy in the Cosmic Microwave Background at Degree Angular Scales: Python V Results

Observations of the microwave sky using the Python telescope in its fifth season of operation at the Amundsen-Scott South Pole Station in Antarctica are presented. The system consists of a 0.75 m off-axis telescope instrumented with a HEMT amplifier-based radiometer having continuum sensitivity from 37-45 GHz in two frequency bands. With a 0.91 deg x 1.02 deg beam the instrument fully sampled 598 deg^2 of sky, including fields measured during the previous four seasons of Python observations. Interpreting the observed fluctuations as anisotropy in the cosmic microwave background, we place constraints on the angular power spectrum of fluctuations in eight multipole bands up to l ~ 260. The observed spectrum is consistent with both the COBE experiment and previous Python results. There is no significant contamination from known foregrounds. The results show a discernible rise in the angular power spectrum from large (l ~ 40) to small (l ~ 200) angular scales. The shape of the observed power spectrum is not a simple linear rise but has a sharply increasing slope starting at l ~ 150.Comment: 5 page

Performance of PCA3 and TMPRSS2:ERG urinary biomarkers in prediction of biopsy outcome in the Canary Prostate Active Surveillance Study (PASS).

BackgroundFor men on active surveillance for prostate cancer, biomarkers may improve prediction of reclassification to higher grade or volume cancer. This study examined the association of urinary PCA3 and TMPRSS2:ERG (T2:ERG) with biopsy-based reclassification.MethodsUrine was collected at baseline, 6, 12, and 24 months in the multi-institutional Canary Prostate Active Surveillance Study (PASS), and PCA3 and T2:ERG levels were quantitated. Reclassification was an increase in Gleason score or ratio of biopsy cores with cancer to ≥34%. The association of biomarker scores, adjusted for common clinical variables, with short- and long-term reclassification was evaluated. Discriminatory capacity of models with clinical variables alone or with biomarkers was assessed using receiver operating characteristic (ROC) curves and decision curve analysis (DCA).ResultsSeven hundred and eighty-two men contributed 2069 urine specimens. After adjusting for PSA, prostate size, and ratio of biopsy cores with cancer, PCA3 but not T2:ERG was associated with short-term reclassification at the first surveillance biopsy (OR = 1.3; 95% CI 1.0-1.7, p = 0.02). The addition of PCA3 to a model with clinical variables improved area under the curve from 0.743 to 0.753 and increased net benefit minimally. After adjusting for clinical variables, neither marker nor marker kinetics was associated with time to reclassification in subsequent biopsies.ConclusionsPCA3 but not T2:ERG was associated with cancer reclassification in the first surveillance biopsy but has negligible improvement over clinical variables alone in ROC or DCA analyses. Neither marker was associated with reclassification in subsequent biopsies

ACBAR: The Arcminute Cosmology Bolometer Array Receiver

We describe the Arcminute Cosmology Bolometer Array Receiver (ACBAR); a multifrequency millimeter-wave receiver designed for observations of the Cosmic Microwave Background (CMB) and the Sunyaev-Zel'dovich effect in clusters of galaxies. The ACBAR focal plane consists of a 16-pixel, background-limited, 240 mK bolometer array that can be configured to observe simultaneously at 150, 220, 280, and 350 GHz. With 4-5' FWHM Gaussian beam sizes and a 3 degree azimuth chop, ACBAR is sensitive to a wide range of angular scales. ACBAR was installed on the 2 m Viper telescope at the South Pole in January 2001. We describe the design of the instrument and its performance during the 2001 and 2002 observing seasons.Comment: 59 pages, 16 figures -- updated to reflect version published in ApJ