Multi-black holes from nilpotent Lie algebra orbits

For N \ge 2 supergravities, BPS black hole solutions preserving four supersymmetries can be superposed linearly, leading to well defined solutions containing an arbitrary number of such BPS black holes at arbitrary positions. Being stationary, these solutions can be understood via associated non-linear sigma models over pseudo-Riemaniann spaces coupled to Euclidean gravity in three spatial dimensions. As the main result of this paper, we show that whenever this pseudo-Riemanniann space is an irreducible symmetric space G/H*, the most general solutions of this type can be entirely characterised and derived from the nilpotent orbits of the associated Lie algebra Lie(G). This technique also permits the explicit computation of non-supersymmetric extremal solutions which cannot be obtained by truncation to N=2 supergravity theories. For maximal supergravity, we not only recover the known BPS solutions depending on 32 independent harmonic functions, but in addition find a set of non-BPS solutions depending on 29 harmonic functions. While the BPS solutions can be understood within the appropriate N=2 truncation of N=8 supergravity, the general non-BPS solutions require the whole field content of the theory.Comment: Corrected version for publication, references adde

Mapping epilepsy-specific patient-reported outcome measures for children to a proposed core outcome set for childhood epilepsy

This is the final version. Available on open access from Elsevier via the DOI in this recordObjective: The objectives of the study were to (1) map questions in epilepsy-specific patient-reported outcome measures (PROMs) of children's health-related quality of life (HRQoL) to a proposed core outcome set (COS) for childhood epilepsy research and (2) gain insight into the acceptability of two leading candidate PROMs. Method: We identified 11 epilepsy-specific PROMs of children's HRQoL (17 questionnaire versions) in a previous systematic review. Each item from the PROMs was mapped to 38 discrete outcomes across 10 domains of the COS: seizures, sleep, social functioning, mental health, cognition, physical functioning, behavior, adverse events, family life, and global quality of life. We consulted with three children with epilepsy and six parents of children with epilepsy in Patient Public Involvement and Engagement (PPIE) work to gain an understanding of the acceptability of the two leading PROMs from our review of measurement properties: Quality of Life in Childhood Epilepsy (QOLCE-55) and Health-Related Quality of Life Measure for Children with Epilepsy (CHEQOL). Results: Social Functioning is covered by all PROMs except DISABKIDS and G-QOLCE and Mental Health is covered by all PROMs except G-QOLCE and Hague Restrictions in Childhood Epilepsy Scale (HARCES). Only two PROMs (Epilepsy and Learning Disability Quality of Life (ELDQOL) and Glasgow Epilepsy Outcome Scale (GEOS-YP)) have items that cover the Seizure domain. The QOLCE-55 includes items that cover the domains of Physical Functioning, Social Functioning, Behavior, Mental Health, and Cognition. The CHEQOL parent and child versions cover the same domains as QOLCE-55 except for Physical Functioning and Behavior, and the child version has one item that covers the discrete outcome of Overall Quality of Life and one item that covers the discrete outcome of Relationship with parents and siblings. The QOLCE-55 parent version was acceptable to the parents we consulted with, and CHEQOL parent and child versions were described as acceptable to our child and parent advisory panel members. Significance: Mapping items from existing epilepsy-specific PROMs for children is an important step in operationalizing our COS for childhood epilepsy research, alongside evaluation of their measurement properties. Two leading PROMS, QOLCE-55 and CHEQOL, cover a wide range of domains from our COS and would likely be used in conjunction with assessment tools selected for specific study objectives. The PPIE work provided practical insights into the administration and acceptability of candidate PROMs in appropriate context. We promote our COS as a framework for selecting outcomes and PROMs for future childhood epilepsy evaluative research.National Institute for Health Research (NIHR)Canadian Institutes of Health ResearchWaterloo FoundationCharles Sykes Epilepsy Research Trus

On all possible static spherically symmetric EYM solitons and black holes

We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein-Yang-Mills equations for any action of the rotation group (or SU(2)) by automorphisms of a principal bundle over space-time whose structure group is a compact semisimple Lie group G. These actions are characterized by a vector in the Cartan subalgebra of g and are called regular if the vector lies in the interior of a Weyl chamber. In the irregular cases (the majority for larger gauge groups) the boundary value problem that results for possible asymptotically flat soliton or black hole solutions is more complicated than in the previously discussed regular cases. In particular, there is no longer a gauge choice possible in general so that the Yang-Mills potential can be given by just real-valued functions. We prove the local existence of regular solutions near the singularities of the system at the center, the black hole horizon, and at infinity, establish the parameters that characterize these local solutions, and discuss the set of possible actions and the numerical methods necessary to search for global solutions. That some special global solutions exist is easily derived from the fact that su(2) is a subalgebra of any compact semisimple Lie algebra. But the set of less trivial global solutions remains to be explored.Comment: 26 pages, 2 figures, LaTeX, misprints corrected, 1 reference adde

Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

This paper is mainly a review of the multi--Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include master symmetries, recursion operators, higher Poisson brackets, invariants and group symmetries for the systems. In addition to the positive hierarchy we also consider the negative hierarchy which is crucial in establishing the bi--Hamiltonian structure for each particular simple Lie group. Finally, we include some results on point and Noether symmetries and an interesting connection with the exponents of simple Lie groups. The case of exceptional simple Lie groups is still an open problem.Comment: 65 pages, 67 reference

Global behavior of solutions to the static spherically symmetric EYM equations

The set of all possible spherically symmetric magnetic static Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge group $G$ was classified in two previous papers. Local analytic solutions near the center and a black hole horizon as well as those that are analytic and bounded near infinity were shown to exist. Some globally bounded solutions are also known to exist because they can be obtained by embedding solutions for the $G=SU(2)$ case which is well understood. Here we derive some asymptotic properties of an arbitrary global solution, namely one that exists locally near a radial value $r_{0}$, has positive mass $m(r)$ at $r_{0}$ and develops no horizon for all $r>r_{0}$. The set of asymptotic values of the Yang-Mills potential (in a suitable well defined gauge) is shown to be finite in the so-called regular case, but may form a more complicated real variety for models obtained from irregular rotation group actions.Comment: 43 page

Gene co-expression networks shed light into diseases of brain iron accumulation

Aberrant brain iron deposition is observed in both common and rare neurodegenerative disorders, including those categorized as Neurodegeneration with Brain Iron Accumulation (NBIA), which are characterized by focal iron accumulation in the basal ganglia. Two NBIA genes are directly involved in iron metabolism, but whether other NBIA-related genes also regulate iron homeostasis in the human brain, and whether aberrant iron deposition contributes to neurodegenerative processes remains largely unknown. This study aims to expand our understanding of these iron overload diseases and identify relationships between known NBIA genes and their main interacting partners by using a systems biology approach. We used whole-transcriptome gene expression data from human brain samples originating from 101 neuropathologically normal individuals (10 brain regions) to generate weighted gene co-expression networks and cluster the 10 known NBIA genes in an unsupervised manner. We investigated NBIA-enriched networks for relevant cell types and pathways, and whether they are disrupted by iron loading in NBIA diseased tissue and in an in vivo mouse model. We identified two basal ganglia gene co-expression modules significantly enriched for NBIA genes, which resemble neuronal and oligodendrocytic signatures. These NBIA gene networks are enriched for iron-related genes, and implicate synapse and lipid metabolism related pathways. Our data also indicates that these networks are disrupted by excessive brain iron loading. We identified multiple cell types in the origin of NBIA disorders. We also found unforeseen links between NBIA networks and iron-related processes, and demonstrate convergent pathways connecting NBIAs and phenotypically overlapping diseases. Our results are of further relevance for these diseases by providing candidates for new causative genes and possible points for therapeutic intervention

Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist around the defect. This class is a natural generalisation of the defects of the 6d theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the 4d central charges a and c, and to the flavour central charge k.Comment: 57 pages, LaTeX2

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde