Autoequivalences of tensor categories attached to quantum groups at roots of 11

We compute the group of braided tensor autoequivalences and the Brauer-Picard group of the representation category of the small quantum group $\mathfrak{u}_q(\mathfrak{g})$, where $q$ is a root of unity.Comment: 29 pages, late

On the structure of the Witt group of braided fusion categories

We analyze the structure of the Witt group W of braided fusion categories introduced in the previous paper arXiv:1009.2117v2. We define a "super" version of the categorical Witt group, namely, the group sW of slightly degenerate braided fusion categories. We prove that sW is a direct sum of the classical part, an elementary Abelian 2-group, and a free Abelian group. Furthermore, we show that the kernel of the canonical homomorphism S: W --> sW is generated by Ising categories and is isomorphic to Z/16Z. Finally, we give a complete description of etale algebras in tensor products of braided fusion categories.Comment: 27 page

Einstein--Yang--Mills strings

We present globally regular vortex-type solutions for a pure SU(2) Yang-Mills field coupled to gravity in 3+1 dimensions. These gravitating vortices are static, cylindrically symmetric and purely magnetic, and they support a non-zero chromo-magnetic flux through their cross section. In addition, they carry a constant non-Abelian current, and so in some sense they are analogs of the superconducting cosmic strings. They have a compact central core dominated by a longitudinal magnetic field and endowed with an approximately Melvin geometry. This magnetic field component gets color screened in the exterior part of the core, outside of which the fields approach exponentially fast those of the electrovacuum Bonnor solutions with a circular magnetic field. In the far field zone the solutions are not asymptotically flat but tend to vacuum Kasner metrics.Comment: 9 pages, 3 figure

A flux-corrected RBF-FD method for convection dominated problems in domains and on manifolds

In this article we introduce a FCT stabilized Radial Basis Function (RBF)-Finite Difference (FD) method for the numerical solution of convection dominated problems. The proposed algorithm is designed to maintain mass conservation and to guarantee positivity of the solution for an almost random placement of scattered data nodes. The method can be applicable both for problems defined in a domain or if equipped with level set techniques, on a stationary manifold. We demonstrate the numerical behavior of the method by performing numerical tests for the solid-body rotation benchmark in a unit square and for a transport problem along a curve implicitly prescribed by a level set function. Extension of the proposed method to higher dimensions is straightforward and easily realizable

Cylindrically symmetric solitons in Einstein-Yang-Mills theory

Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal $B_\phi$ and the longitudinal $B_z$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on the parameters, the solution looks like a straight string or a pair of straight and circular strings. The existence of such non-linear superposition of two strings becomes possible due to self-interaction terms in the Yang-Mills action which suppress contribution of the circular string near the polar axis.Comment: 21 pages, 11 figure

Faster than Neutral Evolution of Constrained Sequences: The Complex Interplay of Mutational Biases and Weak Selection

Comparative genomics has become widely accepted as the major framework for the ascertainment of functionally important regions in genomes. The underlying paradigm of this approach is that most of the functional regions are assumed to be under selective constraint, which in turn reduces the rate of evolution relative to neutrality. This assumption allows detection of functional regions through sequence conservation. However, constraint does not always lead to sequence conservation. When purifying selection is weak and mutation is biased, constrained regions can even evolve faster than neutral sequences and thus can appear to be under positive selection. Moreover, conservation estimates depend also on the orientation of selection relative to mutational biases and can vary over time. In the light of recent data of the ubiquity of mutational biases and weak selective forces, these effects should reduce the power of conservation analyses to define functional regions using comparative genomics data. We argue that the estimation of true mutational biases and the use of explicit evolutionary models are essential to improve methods inferring the action of natural selection and functionality in genome sequences

Global Education Monitoring Report 2023: Technology in education: A tool on whose terms?

The adoption of digital technology has resulted in many changes in education and learning, yet it is debatable whether technology has transformed education as many claim. The application of digital technology varies by community and socioeconomic level, by teacher willingness and preparedness, by education level and by country income. Except in the most technologically advanced countries, computers and devices are not used in classrooms on a large scale. Moreover, evidence is mixed on its impact. The short- and long-term costs of using digital technology appear to be significantly underestimated. The most disadvantaged are typically denied the opportunity to benefit. In asking ‘A tool on whose terms?’, the Report shows that regulations for technology set outside of the education sector will not necessarily address education’s needs. It is released along with a #TechOnOurTerms campaign, calling for decisions about technology in education to prioritize learner needs after assessment of whether its application would be appropriate, equitable, evidence-based and sustainable. It provides a compass for policy makers to use when making these decisions. Those in decision-making positions are asked to look down at where they are, to see if technology is appropriate for their context, and learning needs. They are asked to look back at those left behind, to make sure they are focusing on the marginalized. They are reminded to look up at whether they have evidence on impact and enough information on the full cost needed to make informed decisions. And, finally they are asked to look forwards, to make sure their plans fit their vision for sustainable development. The report underscores the importance of learning to live both with and without digital technology; to take what is needed from an abundance of information but ignore what is not necessary; to let technology support, but never supplant, the human connection on which teaching and learning are based. The focus should be on learning outcomes, not digital inputs. To help improve learning, digital technology should be not a substitute for but a complement to face-to-face interaction with teachers. Supporting the sixth Global Education Monitoring Report is a new series of country profiles on PEER, a policy dialogue resource describing policies and regulations related to technology in the world’s education systems