Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the computation depends only on a one-dimensional ray in the Kahler moduli space, it can probe slope-stability regardless of the size of h^{1,1}. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kahler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, an efficient numerical check is proposed for determining whether or not a vector bundle is slope-stable without computing its full connection.Comment: 38 pages, 10 figure

Quiver Structure of Heterotic Moduli

We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli space using the Reineke formula, we can learn about such useful concepts as Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.Comment: 38 pages, 5 figures, 1 tabl

The relationship between regional pain with or without neuropathic symptoms and chronic widespread pain.

This study was performed to test whether the risk of developing chronic widespread pain (CWP) in those with regional pain was augmented in those with symptoms of neuropathic pain (NP). Persons free of CWP completed the Douleur Neuropathique 4 (scores ≥3 indicating NP); demographics; Hospital Anxiety and Depression scale; Pittsburgh Sleep Quality Index; and pain medications. Participants were classified as having no pain, regional pain with no symptoms of NP (NP-), or regional pain with symptoms of NP (NP). At the 12-month follow-up, participants with CWP were identified. Logistic regression estimated the odds ratio, with 95% confidence intervals, of CWP in the NP- and NP groups compared with no pain, and NP compared with NP-. Partial population attributable risks estimated the proportion of CWP attributable to baseline NP- or NP exposure. One thousand one hundred sixty-two participants completed the baseline DN4 and provided pain data at follow-up: 523 (45.0%) had no baseline pain, 562 (48.4%) NP-, and 77 (6.6%) NP. One hundred fifty-three (13.2%) had CWP at 12 months: 19 (3.6%) no pain, 108 (19.2%) NP-, and 26 (33.8%) NP. NP- (2.9 [1.9-4.3]) and NP (2.1 [1.1-4.0]) predicted CWP after adjusting for demographics, Hospital Anxiety and Depression scale, Pittsburgh Sleep Quality Index, and medications. The partial population attributable risk was 41.3% (25.2-54.0) for NP- and 6.0% (0.1-11.6) for NP. The NP group were not more likely to develop CWP when compared directly with NP- (1.5 [0.8-2.8]). Neuropathic pain was relatively rare and predicted a small number of new-onset CWP cases. Using these estimates, treatments targeting NP would at best prevent 6% of CWP cases

Experiments on Multidimensional Solitons

This article presents an overview of experimental efforts in recent years related to multidimensional solitons in Bose-Einstein condensates. We discuss the techniques used to generate and observe multidimensional nonlinear waves in Bose-Einstein condensates with repulsive interactions. We further summarize observations of planar soliton fronts undergoing the snake instability, the formation of vortex rings, and the emergence of hybrid structures.Comment: review paper, to appear as Chapter 5b in "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer-Verlag

Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in version 2

Yukawa Textures From Heterotic Stability Walls

A holomorphic vector bundle on a Calabi-Yau threefold, X, with h^{1,1}(X)>1 can have regions of its Kahler cone where it is slope-stable, that is, where the four-dimensional theory is N=1 supersymmetric, bounded by "walls of stability". On these walls the bundle becomes poly-stable, decomposing into a direct sum, and the low energy gauge group is enhanced by at least one anomalous U(1) gauge factor. In this paper, we show that these additional symmetries can strongly constrain the superpotential in the stable region, leading to non-trivial textures of Yukawa interactions and restrictions on allowed masses for vector-like pairs of matter multiplets. The Yukawa textures exhibit a hierarchy; large couplings arise on the stability wall and some suppressed interactions "grow back" off the wall, where the extended U(1) symmetries are spontaneously broken. A number of explicit examples are presented involving both one and two stability walls, with different decompositions of the bundle structure group. A three family standard-like model with no vector-like pairs is given as an example of a class of SU(4) bundles that has a naturally heavy third quark/lepton family. Finally, we present the complete set of Yukawa textures that can arise for any holomorphic bundle with one stability wall where the structure group breaks into two factors.Comment: 53 pages, 4 figures and 13 table

Integrated Flight and Propulsion Control for Novel Rotorcraft

Distributed Electric Propulsion (DEP) has increased the design space for aerospace vehicles, especially those categorized as eVTOL (Electric Vertical Take-Off and Landing). This new class of vehicles not only looks different from the typical airplane or helicopter, but functions differently as well. A robust understanding of how the vehicle is controlled in both nominal and off-nominal modes will frame the approach to certification for private and commercial VTOL aircraft. Embry-Riddle Aeronautical University’s Eagle Flight Research Center (EFRC) is researching how the various methods of DEP thrust control apply to larger eVTOL vehicle operation. Researchers will utilize a mixture of flight dynamic simulation and physical testing in collaboration with FAA experts in rotorcraft handling qualities certification. Outcomes of the research include the characterization of various DEP thrust and moment control methods and how this maps to certifiable vehicle-level attributes like handling qualities in nominal and degraded flight modes. A prototype will be built and tested showing the ability of a quad-rotor vehicle to continue flight after the loss of thrust by failure of one rotor. It is anticipated that a better understanding of the DEP units will help inform the process of certification for the emerging market of urban air mobility vehicles. The data obtained from testing will be utilized to define the possible performance parameters, which will aid in developing appropriate means of compliance for advanced fly-by-wire N-rotor eVTOL vehicles

Signal transducer and activator of transcription 2 deficiency is a novel disorder of mitochondrial fission

Defects of mitochondrial dynamics are emerging causes of neurological disease. In two children presenting with severe neurological deterioration following viral infection we identified a novel homozygous STAT2 mutation, c.1836C4A (p.Cys612Ter), using whole exome sequencing. In muscle and fibroblasts from these patients, and a third unrelated STAT2-deficient patient, we observed extremely elongated mitochondria. Western blot analysis revealed absence of the STAT2 protein and that the mitochondrial fission protein DRP1 (encoded by DNM1L) is inactive, as shown by its phosphorylation state. All three patients harboured 15 decreased levels of DRP1 phosphorylated at serine residue 616 (P-DRP1S616), a post-translational modification known to activate DRP1, and increased levels of DRP1 phosphorylated at serine 637 (P-DRP1S637), associated with the inactive state of the DRP1 GTPase. Knockdown of STAT2 in SHSY5Y cells recapitulated the fission defect, with elongated mitochondria and decreased PDRP1 S616 levels. Furthermore the mitochondrial fission defect in patient fibroblasts was rescued following lentiviral transduction with wild-type STAT2 in all three patients, with normalization of mitochondrial length and increased P-DRP1S616 levels. Taken 20 together, these findings implicate STAT2 as a novel regulator of DRP1 phosphorylation at serine 616, and thus of mitochondrial fission, and suggest that there are interactions between immunity and mitochondria. This is the first study to link the innate immune system to mitochondrial dynamics and morphology. We hypothesize that variability in JAK-STAT signalling may contribute to the phenotypic heterogeneity of mitochondrial disease, and may explain why some patients with underlying mitochondrial disease decompensate after seemingly trivial viral infections. Modulating JAK-STAT activity may represent a novel 25 therapeutic avenue for mitochondrial diseases, which remain largely untreatable. This may also be relevant for more common neurodegenerative diseases, including Alzheimer’s, Huntington’s and Parkinson’s diseases, in which abnormalities of mitochondrial morphology have been implicated in disease pathogenesis