Thurston equivalence of topological polynomials

We answer Hubbard's question on determining the Thurston equivalence class of ``twisted rabbits'', i.e. images of the ``rabbit'' polynomial under n-th powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions.Comment: 40 pages, lots of figure

Two Dimensional QCD as a String Theory

I explore the possibility of finding an equivalent string representation of two dimensional QCD. I develop the large N expansion of the ${\rm QCD_2}$ partition function on an arbitrary two dimensional Euclidean manifold. If this is related to a two-dimensional string theory then many of the coefficients of the ${1\over N}$ expansion must vanish. This is shown to be true to all orders, giving strong evidence for the existence of a string representation.Comment: 24 page

Artificial Interpretation: An investigation into the feasibility of archaeologically focused seismic interpretation via machine learning

YesThe value of artificial intelligence and machine learning applications for use in heritage research is increasingly appreciated. In specific areas, notably remote sensing, datasets have increased in extent and resolution to the point that manual interpretation is problematic and the availability of skilled interpreters to undertake such work is limited. Interpretation of the geophysical datasets associated with prehistoric submerged landscapes is particularly challenging. Following the Last Glacial Maximum, sea levels rose by 120 m globally, and vast, habitable landscapes were lost to the sea. These landscapes were inaccessible until extensive remote sensing datasets were provided by the offshore energy sector. In this paper, we provide the results of a research programme centred on AI applications using data from the southern North Sea. Here, an area of c. 188,000 km2 of habitable terrestrial land was inundated between c. 20,000 BP and 7000 BP, along with the cultural heritage it contained. As part of this project, machine learning tools were applied to detect and interpret features with potential archaeological significance from shallow seismic data. The output provides a proof-of-concept model demonstrating verifiable results and the potential for a further, more complex, leveraging of AI interpretation for the study of submarine palaeolandscapes

Virtually abelian K\"ahler and projective groups

We characterise the virtually abelian groups which are fundamental groups of compact K\"ahler manifolds and of smooth projective varieties. We show that a virtually abelian group is K\"ahler if and only if it is projective. In particular, this allows to describe the K\"ahler condition for such groups in terms of integral symplectic representations

A multi-vendor, multi-center study on reproducibility and comparability of fast strain-encoded cardiovascular magnetic resonance imaging

Myocardial strain is a convenient parameter to quantify left ventricular (LV) function. Fast strain-encoding (fSENC) enables the acquisition of cardiovascular magnetic resonance images for strain-measurement within a few heartbeats during free-breathing. It is necessary to analyze inter-vendor agreement of techniques to determine strain, such as fSENC, in order to compare existing studies and plan multi-center studies. Therefore, the aim of this study was to investigate inter-vendor agreement and test-retest reproducibility of fSENC for three major MRI-vendors. fSENC-images were acquired three times in the same group of 15 healthy volunteers using 3 Tesla scanners from three different vendors: at the German Heart Institute Berlin, the Charité University Medicine Berlin-Campus Buch and the Theresien-Hospital Mannheim. Volunteers were scanned using the same imaging protocol composed of two fSENC-acquisitions, a 15-min break and another two fSENC-acquisitions. LV global longitudinal and circumferential strain (GLS, GCS) were analyzed by a trained observer (Myostrain 5.0, Myocardial Solutions) and for nine volunteers repeatedly by another observer. Inter-vendor agreement was determined using Bland-Altman analysis. Test-retest reproducibility and intra- and inter-observer reproducibility were analyzed using intraclass correlation coefficient (ICC) and coefficients of variation (CoV). Inter-vendor agreement between all three sites was good for GLS and GCS, with biases of 0.01-1.88%. Test-retest reproducibility of scans before and after the break was high, shown by ICC- and CoV values of 0.63-0.97 and 3-9% for GLS and 0.69-0.82 and 4-7% for GCS, respectively. Intra- and inter-observer reproducibility were excellent for both parameters (ICC of 0.77-0.99, CoV of 2-5%). This trial demonstrates good inter-vendor agreement and test-retest reproducibility of GLS and GCS measurements, acquired at three different scanners from three different vendors using fSENC. The results indicate that it is necessary to account for a possible bias (< 2%) when comparing strain measurements of different scanners. Technical differences between scanners, which impact inter-vendor agreement, should be further analyzed and minimized.DRKS Registration Number: 00013253. Universal Trial Number (UTN): U1111-1207-5874

Commutative association schemes

Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of inception, the concept has proved useful in the study of group actions, in algebraic graph theory, in algebraic coding theory, and in areas as far afield as knot theory and numerical integration. This branch of the theory, viewed in this collection of surveys as the "commutative case," has seen significant activity in the last few decades. The goal of the present survey is to discuss the most important new developments in several directions, including Gelfand pairs, cometric association schemes, Delsarte Theory, spin models and the semidefinite programming technique. The narrative follows a thread through this list of topics, this being the contrast between combinatorial symmetry and group-theoretic symmetry, culminating in Schrijver's SDP bound for binary codes (based on group actions) and its connection to the Terwilliger algebra (based on combinatorial symmetry). We propose this new role of the Terwilliger algebra in Delsarte Theory as a central topic for future work.Comment: 36 page

Local chromatic number of quadrangulations of surfaces

The local chromatic number of a graph G, as introduced in [4], is the minimum integer k such that G admits a proper coloring (with an arbitrary number of colors) in which the neighborhood of each vertex uses less than k colors. In [17] a connection of the local chromatic number to topological properties of (a box complex of) the graph was established and in [18] it was shown that a topological condition implying the usual chromatic number being at least four has the stronger consequence that the local chromatic number is also at least four. As a consequence one obtains a generalization of the following theorem of Youngs [19]: If a quadrangulation of the projective plane is not bipartite it has chromatic number four. The generalization states that in this case the local chromatic number is also four. Both papers [1] and [13] generalize Youngs’ result to arbitrary non-orientable surfaces replacing the condition of the graph being not bipartite by a more technical condition of an odd quadrangulation. This paper investigates when these general results are true for the local chromatic number instead of the chromatic number. Surprisingly, we find out that (unlike in the case of the chromatic number) this depends on the genus of the surface. For the non-orientable surfaces of genus at most four, the local chromatic number of any odd quadrangulation is at least four, but this is not true for non-orientable surfaces of genus 5 or higher. We also prove that face subdivisions of odd quadrangulations and Fisk triangulations of arbitrary surfaces exhibit the same behavior for the local chromatic number as they do for the usual chromatic number