A relative approach to opinion formation

Formal models of opinion formation commonly represent an individual’s opinion by a value on a fixed opinion interval. We propose an alternative modeling method wherein interpretation is only provided to the relative positions of opinions vis-à-vis each other. This method is then considered in a similar setting as the discrete-time Altafini model (an extension of the well-known DeGroot model), but with more general influence weights. Even in a linear framework, the model can describe, in the long run, polarization, dynamics with a periodic pattern, and (modulus) consensus formation. In addition, in our alternative approach key characteristics of the opinion dynamic can be derived from real-valued square matrices of influence weights, which immediately allows one to transfer matrix theory insights to the field of opinion formation dynamics under more relaxed conditions than in the DeGroot or discrete-time Altafini models. A few specific themes are covered: (i) We demonstrate how stable patterns in relative opinion dynamics are identified which are hidden when opinions are considered in an absolute opinion framework. (ii) For the two-agent case, we provide an exhaustive closed-form description of the relative opinion model’s dynamic in the long run. (iii) We explore group dynamics analytically, in particular providing a non-trivial condition under which a subgroup’s asymptotic behavior carries over to the entire population

Hidden library: visualizing fragments of medieval manuscripts in early-modern bookbindings with mobile macro-XRF scanner

<p>This experiment demonstrates the large potential of macro-XRF imaging for the visualization of fragments of medieval manuscripts hidden in early-modern bookbindings. The invention of the printing press in the fifteenth century made manuscripts obsolete and bookbinders started recycling their strong parchment leaves to reinforce bindings of printed books. One in roughly every five early-modern books contains a fragment of a medieval manuscript hidden underneath the bookbinding. Systematically investigating these fragments will provide scholars with valuable information about transmission and variant readings of medieval texts. Four case studies were scanned with a Bruker M6 Jetstream mobile XRF scanner. We were able to visualize hidden texts underneath black paint, paper and parchment at such a high resolution that they could be read and dated. One of the findings was an early twelfth-century excerpt of a text by the Venerable Bede in a sixteenth-century bookbinding. In addition, we were able to separately visualize the lower and upper text of a famous palimpsest. The main limitation of the current set-up is the scanning time, which took anywhere between 6 and 66 h. In order to systematically employ macro-XRF for researching medieval fragments, the scanning time needs to be decreased. Nonetheless, this experiment shows that the macro-XRF technique is extremely suitable for visualizing fragments of medieval manuscripts in a non-destructive way in order to read, date and localize them.</p

Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions

We continue our study of nonperturbative superpotentials of four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, broken to N=1 due to a classical superpotential. In a previous paper, hep-th/0304061, we discussed how the low-energy quantum superpotential can be obtained by substituting the Lax matrix of the underlying integrable system directly into the classical superpotential. In this paper we prove algebraically that this recipe yields the correct factorization of the Seiberg-Witten curves, which is an important check of the conjecture. We will also give an independent proof using the algebraic-geometrical interpretation of the underlying integrable system.Comment: laTeX, 14 pages, uses AMSmat

Performance and structure of single-mode bosonic codes

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce new codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat/binomial/GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multi-qubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a new multi-qudit code.Comment: 34 pages, 11 figures, 4 tables. v3: published version. See related talk at https://absuploads.aps.org/presentation.cfm?pid=1351

Minimizing gravitational lensing contributions to the primordial bispectrum covariance

The next generation of ground-based cosmic microwave background (CMB) experiments aim to measure temperature and polarization fluctuations up to ℓmax≈5000 over half of the sky. Combined with Planck data on large scales, this will provide improved constraints on primordial non-Gaussianity. However, the impressive resolution of these experiments will come at a price. Besides signal confusion from galactic foregrounds, extragalactic foregrounds, and late-time gravitational effects, gravitational lensing will introduce large non-Gaussianity that can become the leading contribution to the bispectrum covariance through the connected four-point function. Here, we compute this effect analytically for the first time on the full sky for both temperature and polarization. We compare our analytical results with those obtained directly from map-based simulations of the CMB sky for several levels of instrumental noise. Of the standard shapes considered in the literature, the local shape is most affected, resulting in a 35% increase of the estimator standard deviation for an experiment such as the Simons Observatory (SO) and a 110% increase for a cosmic-variance limited experiment, including both temperature and polarization modes up to ℓmax=3800. Because of the nature of the lensing four-point function, the impact on other shapes is reduced while still non-negligible for the orthogonal shape. Two possible avenues to reduce the non-Gaussian contribution to the covariance are proposed: First by marginalizing over lensing contributions, such as the Integrated Sachs Wolfe (ISW)-lensing three-point function in temperature, and second by delensing the CMB. We show the latter method can remove almost all extra covariance, reducing the effect to below <5% for local bispectra. At the same time, delensing would remove signal biases from secondaries induced by lensing, such as ISW lensing. We aim to apply both techniques directly to the forthcoming SO data when searching for primordial non-Gaussianity

Comparison of a generic and a rhinitis-specific quality-of-life (QOL) instrument in patients with house dust mite allergy: Relationship between the SF-36 and rhinitis QOL questionnaire

Background: Generic and disease-specific quality-of-life (QOL) questionnaires are commonly used in subjects with allergic rhinitis (AR). AR, however, is closely associated with other disorders such as bronchial asthma and atopic dermatitis (AD). These co-morbid associations may have an effect on the inter-relation of generic and disease-specific QOL outcomes and the behaviour of this inter-relation in time. Objective: To unravel the inter-relationships between the outcome of a generic instrument (SF-36) and a disease-specific instrument (Rhinitis QOL Questionnaire (RQLQ)). Materials and methods: In the framework of a randomized clinical trial with respect to the efficacy of impermeable bedding covers in house dust mite (HDM) allergy, SF-36 and RQLQ were administered to 224 adults with AR and/or allergic asthma and/or AD at baseline and after 12 months of intervention. Regression analysis and canonical correlation were used to estimate overlap. Results: Overlap between SF-36 and RQLQ domains in terms of explained variance ranged from 6% to 56%. Canonical correlation yielded low coefficients (0.16-0.27). Moreover, both SF-36 and RQLQ s

Witnessing the birth of the red sequence: the physical scale and morphology of dust emission in hyper-luminous starbursts in the early Universe

We present high-spatial-resolution ($\sim 0.12''$ or $\approx 800 \, {\rm pc}$ at $z = 4.5$) ALMA $870\,\mu$m dust continuum observations of a sample of 44 ultrared dusty star-forming galaxies (DSFGs) selected from the H-ATLAS and HerMES far-infrared surveys because of their red colors from 250 to 500 $\mu$m: $S_{500} / S_{250} > 1.5$ and $S_{500} / S_{350} > 1.0$. With photometric redshifts in the range $z \sim 4$-6, our sample includes the most luminous starbursting systems in the early Universe known so far, with total obscured star-formation rates (SFRs) of up to $\sim 4,500 \, M_\odot \, {\rm yr}^{-1}$, as well as a population of lensed, less intrinsically luminous sources. The lower limit on the number of ultrared DSFGs at 870 $\mu$m (with flux densities measured from the ALMA maps and thus not affected by source confusion) derived in this work is in reasonable agreement with models of galaxy evolution, whereas there have been reports of conflicts at 500 $\mu$m (where flux densities are derived from SPIRE). Ultrared DSFGs have a variety of morphologies (from relatively extended disks with smooth radial profiles, to compact sources, both isolated and interacting) and an average size, $\theta_{\rm FWHM}$, of $1.46 \pm 0.41\, {\rm kpc}$, considerably smaller than the values reported in previous work for less-luminous DSFGs at lower redshifts. The size and the estimated gas-depletion times of our sources are compatible with their being the progenitors of the most massive, compact, red-and-dead galaxies at $z \sim 2$-3, and ultimately of local ultra-massive elliptical galaxies or massive galaxy clusters. We are witnessing the birth of the high-mass tail of the red sequence of galaxies.Comment: Submitted to ApJ. Comments welcom