Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere

In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from $\mathbb{R}^2$ into $S^2$.Comment: 14 pages, 5 figures, final version to be published in Nonlinearit

Phenotypic characteristics of the p.Asn215Ser (p.N215S) GLA mutation in male and female patients with Fabry disease: A multicenter Fabry Registry study.

BackgroundThe p.Asn215Ser or p.N215S GLA variant has been associated with late-onset cardiac variant of Fabry disease.MethodsTo expand on the scarce phenotype data, we analyzed natural history data from 125 p.N215S patients (66 females, 59 males) enrolled in the Fabry Registry (NCT00196742) and compared it with data from 401 patients (237 females, 164 males) harboring mutations associated with classic Fabry disease. We evaluated interventricular septum thickness (IVST), left ventricular posterior wall thickness (LVPWT), estimated glomerular filtration rate and severe clinical events.ResultsIn p.N215S males, mildly abnormal mean IVST and LVPWT values were observed in patients aged 25-34 years, and values gradually increased with advancing age. Mean values were similar to those of classic males. In p.N215S females, these abnormalities occurred primarily in patients aged 55-64 years. Severe clinical events in p.N215S patients were mainly cardiac (males 31%, females 8%) while renal and cerebrovascular events were rare. Renal impairment occurred in 17% of p.N215S males (mostly in patients aged 65-74 years), and rarely in females (3%).Conclusionp.N215S is a disease-causing mutation with severe clinical manifestations found primarily in the heart. Cardiac involvement may become as severe as in classic Fabry patients, especially in males

Collapse of an Instanton

We construct a two parameter family of collapsing solutions to the 4+1 Yang-Mills equations and derive the dynamical law of the collapse. Our arguments indicate that this family of solutions is stable. The latter fact is also supported by numerical simulations.Comment: 17 pages, 1 figur

Quantum lump dynamics on the two-sphere

It is well known that the low-energy classical dynamics of solitons of Bogomol'nyi type is well approximated by geodesic motion in M_n, the moduli space of static n-solitons. There is an obvious quantization of this dynamics wherein the wavefunction evolves according to the Hamiltonian H_0 equal to (half) the Laplacian on M_n. Born-Oppenheimer reduction of analogous mechanical systems suggests, however, that this simple Hamiltonian should receive corrections including k, the scalar curvature of M_n, and C, the n-soliton Casimir energy, which are usually difficult to compute, and whose effect on the energy spectrum is unknown. This paper analyzes the spectra of H_0 and two corrections to it suggested by work of Moss and Shiiki, namely H_1=H_0+k/4 and H_2=H_1+C, in the simple but nontrivial case of a single CP^1 lump moving on the two-sphere. Here M_1=TSO(3), a noncompact kaehler 6-manifold invariant under an SO(3)xSO(3) action, whose geometry is well understood. The symmetry gives rise to two conserved angular momenta, spin and isospin. A hidden isometry of M_1 is found which implies that all three energy spectra are symmetric under spin-isospin interchange. The Casimir energy is found exactly on the zero section of TSO(3), and approximated numerically on the rest of M_1. The lowest 19 eigenvalues of H_i are found for i=0,1,2, and their spin-isospin and parity compared. The curvature corrections in H_1 lead to a qualitatively unchanged low-level spectrum while the Casimir energy in H_2 leads to significant changes. The scaling behaviour of the spectra under changes in the radii of the domain and target spheres is analyzed, and it is found that the disparity between the spectra of H_1 and H_2 is reduced when the target sphere is made smaller.Comment: 35 pages, 3 figure

The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps

The most fruitful approach to studying low energy soliton dynamics in field theories of Bogomol'nyi type is the geodesic approximation of Manton. In the case of vortices and monopoles, Stuart has obtained rigorous estimates of the errors in this approximation, and hence proved that it is valid in the low speed regime. His method employs energy estimates which rely on a key coercivity property of the Hessian of the energy functional of the theory under consideration. In this paper we prove an analogous coercivity property for the Hessian of the energy functional of a general sigma model with compact K\"ahler domain and target. We go on to prove a continuity property for our result, and show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive in the degree 1 sector. We present numerical evidence which suggests that the Hessian is globally coercive in a certain equivariance class of the degree n sector for n>1. We also prove that, within the geodesic approximation, a single CP^1 lump moving on S^2 does not generically travel on a great circle.Comment: 29 pages, 1 figure; typos corrected, references added, expanded discussion of the main function spac

Optical markers of magnetic phase transition in CrSBr

Here, we investigate the role of the interlayer magnetic ordering of CrSBr in the framework of $\textit{ab initio}$ calculations and by using optical spectroscopy techniques. These combined studies allow us to unambiguously determine the nature of the optical transitions. In particular, photoreflectance measurements, sensitive to the direct transitions, have been carried out for the first time. We have demonstrated that optically induced band-to-band transitions visible in optical measurement are remarkably well assigned to the band structure by the momentum matrix elements and energy differences for the magnetic ground state (A-AFM). In addition, our study reveals significant differences in electronic properties for two different interlayer magnetic phases. When the magnetic ordering of A-AFM to FM is changed, the crucial modification of the band structure reflected in the direct-to-indirect band gap transition and the significant splitting of the conduction bands along the $\Gamma-Z$ direction are obtained. In addition, Raman measurements demonstrate a splitting between the in-plane modes $B^2_{2g}$/$B^2_{3g}$, which is temperature dependent and can be assigned to different interlayer magnetic states, corroborated by the DFT+U study. Moreover, the $B^2_{2g}$ mode has not been experimentally observed before. Finally, our results point out the origin of interlayer magnetism, which can be attributed to electronic rather than structural properties. Our results reveal a new approach for tuning the optical and electronic properties of van der Waals magnets by controlling the interlayer magnetic ordering in adjacent layers.Comment: 33 pages, 15 figure

Disturbance and Predictability of Flowering Patterns in Bird-Pollinated Cloud Forest Plants

The distribution and flowering patterns of hummingbird—pollinated plants were compared from July 1981 to June 1983 in three patch types in cloud forest at Monteverde, Costa Rica. Study plots were: (1) four recent, large (1100—2500 m2) disturbances ("cutovers") produced by cutting vegetation, (2) six recent, smaller (200—600 m2) disturbances caused by treefalls, and (3) four plots (1600—1800 m2) of canopied forest. Based on published literature dealing with communities that characterize different regimes of disturbance, we tested one assumption and two hypotheses. Assumption: Plant species composition differs among the three patch types. Hypothesis 1: Phenotypic specialization by plants for co—evolved interactions with hummingbirds will be lowest in large gaps, highest in forest, and intermediate in treefalls. Hypothesis 2: Predictability of flowering phenologies and nectar production will be lowest in large gaps, highest in forest, intermediate in treefalls. Neither the assumption nor the hypotheses were supported by the results. The patch mosaic in this cloud forest was not associated with major differences in species composition of bird—pollinated plants. Most species studied were self—compatible. Most abundant in cutovers were species with long corollas, relatively specialized for attracting long—billed hummingbirds. Species with short corollas, which can be visited by many hummingbird species and some insects, were most abundant in treefalls and forest. Variation in phenological patterns showed no consistent trends among patch types. Predictability of flower and nectar production tended to be greatest in treefalls, which are foci of concentrated flowering activity by all species. Discrepancies between our results and previous studies can be ascribed to two facts. (1) Much of the literature dealing with ecological consequences of disturbance has dealt with large—scale anthropogenic disturbances such as old fields of the eastern USA, whereas we studied small, natural, or quasi—natural disturbances. (2) Studies of forest disturbance have focused on the tree layer, whereas we studied the understory herbs, shrubs, and epiphytes. Natural disturbance usually involves death and replacement of one or more trees, whereas individuals of other life forms may persist through the disturbance

Cardiac Involvement in Fabry Disease: JACC Review Topic of the Week

Fabry disease (FD) is a rare X-linked inherited lysosomal storage disorder caused by deficient α-galactosidase A activity that leads to an accumulation of globotriasylceramide (Gb3) in affected tissues, including the heart. Cardiovascular involvement usually manifests as left ventricular hypertrophy, myocardial fibrosis, heart failure, and arrhythmias, which limit quality of life and represent the most common causes of death. Following the introduction of enzyme replacement therapy, early diagnosis and treatment have become essential to slow disease progression and prevent major cardiac complications. Recent advances in the understanding of FD pathophysiology suggest that in addition to Gb3 accumulation, other mechanisms contribute to the development of Fabry cardiomyopathy. Progress in imaging techniques have improved diagnosis and staging of FD-related cardiac disease, suggesting a central role for myocardial inflammation and setting the stage for further research. In addition, with the recent approval of oral chaperone therapy and new treatment developments, the FD-specific treatment landscape is rapidly evolving

Safety and efficacy of pegunigalsidase alfa in patients with Fabry disease who were previously treated with agalsidase alfa: results from BRIDGE, a phase 3 open-label study

BACKGROUND: Pegunigalsidase alfa is a novel, PEGylated α-galactosidase-A enzyme-replacement therapy approved in the EU and US to treat patients with Fabry disease (FD). OBJECTIVE/METHODS: BRIDGE is a phase 3 open-label, switch-over study designed to assess safety and efficacy of 12 months of pegunigalsidase alfa (1 mg/kg every 2 weeks) treatment in adults with FD who had been previously treated with agalsidase alfa (0.2 mg/kg every 2 weeks) for ≥ 2 years. RESULTS: Twenty-seven patients were screened; 22 met eligibility criteria; and 20 (13 men, 7 women) completed the study. Pegunigalsidase alfa was well-tolerated, with 97% of treatment-emergent adverse events (TEAEs) being of mild or moderate severity. The incidence of treatment-related TEAEs was low, with 2 (9%) discontinuations due to TEAEs. Five patients (23%) reported infusion-related reactions. Overall mean (SD; n = 22) baseline estimated glomerular filtration rate (eGFR) was 82.5 (23.4) mL/min/1.73 m2 and plasma lyso-Gb3 level was 38.3 (41.2) nmol/L (men: 49.7 [45.8] nmol/L; women: 13.8 [6.1] nmol/L). Before switching to pegunigalsidase alfa, mean (standard error [SE]) annualized eGFR slope was − 5.90 (1.34) mL/min/1.73 m2/year; 12 months post-switch, the mean eGFR slope was − 1.19 (1.77) mL/min/1.73 m2/year; and mean plasma lyso-Gb3 reduced by 31%. Seven (35%) out of 20 patients were positive for pegunigalsidase alfa antidrug antibodies (ADAs) at ≥ 1 study timepoint, two of whom had pre-existing ADAs at baseline. Mean (SE) changes in eGFR slope for ADA-positive and ADA-negative patients were + 5.47 (3.03) and + 4.29 (3.15) mL/min/1.73 m2/year, respectively, suggesting no negative impact of anti-pegunigalsidase alfa ADAs on eGFR slope. CONCLUSION: Pegunigalsidase alfa may offer a safe and effective treatment option for patients with FD, including those previously treated with agalsidase alfa. TRN: NCT03018730. Date of registration: January 2017