Independence property and hyperbolic groups

We prove that existentially closed $CSA$-groups have the independence property. This is done by showing that there exist words having the independence property relatively to the class of torsion-free hyperbolic groups.Comment: v3: 10 pages (11pt), a few typos corrected, minor rearrangements (e.g. Fact 2.3 and Lemma 2.5); v2: 8 pages (10pt), a false statement in the proof of Fact 2.4 is replaced with a true one; v1: 8 page

A Classification of Infographics

Classifications are useful for describing existing phenomena and guiding further investigation. Several classifications of diagrams have been proposed, typically based on analytical rather than empirical methodologies. A notable exception is the work of Lohse and his colleagues, published in Communications of the ACM in December 1994. The classification of diagrams that Lohse proposed was derived from bottom-up grouping data collected from sixteen participants and based on 60 diagrams. Mean values on ten Likert-scales were used to predict diagram class. We follow a similar methodology to Lohse, using real-world infographics (i.e. embellished data charts) as our stimuli. We propose a structural classification of infographics, and determine whether infographics class can be predicted from values on Likert scales

Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid

New Dual Conformally Invariant Off-Shell Integrals

Evidence has recently emerged for a hidden symmetry of scattering amplitudes in N=4 super Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong coupling the symmetry has been shown to have a natural interpretation in terms of a T-dualized AdS_5. In this paper we study dual conformally invariant off-shell four-point Feynman diagrams. We classify all such diagrams through four loops and evaluate 10 new off-shell integrals in terms of Mellin-Barnes representations, also finding explicit expressions for their infrared singularities.Comment: 21 pages, 9 figure

Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions

We consider a class of quantum lattice models in $1+1$ dimensions represented as local quantum circuits that enjoy a particular "dual-unitarity" property. In essence, this property ensures that both the evolution "in time" and that "in space" are given in terms of unitary transfer matrices. We show that for this class of circuits, generically non-integrable, one can compute explicitly all dynamical correlations of local observables. Our result is exact, non-pertubative, and holds for any dimension $d$ of the local Hilbert space. In the minimal case of qubits ($d = 2$) we also present a classification of all dual-unitary circuits which allows us to single out a number of distinct classes for the behaviour of the dynamical correlations. We find "non-interacting" classes, where all correlations are preserved, the ergodic and mixing one, where all correlations decay, and, interestingly, also classes that are are both interacting and non-ergodic.Comment: 6+5 pages, no figures; v2 minor changes; v3 as appears in Phys. Rev. Let