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

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

Nonperturbative Superpotentials and Compactification to Three Dimensions

We consider four-dimensional N=2 supersymmetric gauge theories with gauge group U(N) on R^3 x S^1, in the presence of a classical superpotential. The low-energy quantum superpotential is obtained by simply replacing the adjoint scalar superfield in the classical superpotential by the Lax matrix of the integrable system that underlies the 4d field theory. We verify in a number of examples that the vacuum structure obtained in this way matches precisely that in 4d, although the degrees of freedom that appear are quite distinct. Several features of 4d field theories, such as the possibility of lifting vacua from U(N) to U(tN), become particularly simple in this framework. It turns out that supersymmetric vacua give rise to a reduction of the integrable system which contains information about the field theory but also about the Dijkgraaf-Vafa matrix model. The relation between the matrix model and the quantum superpotential on R^3 x S^1 appears to involve a novel kind of mirror symmetry.Comment: LaTeX, 45 pages, uses AmsMath, minor correction, reference adde