Precision Measurement of the Ds∗+−Ds+D_s^{*+}- D_s^+ Mass Difference

We have measured the vector-pseudoscalar mass splitting $M(D_s^{*+})-M(D_s^+) = 144.22\pm 0.47\pm 0.37 MeV$, significantly more precise than the previous world average. We minimize the systematic errors by also measuring the vector-pseudoscalar mass difference $M(D^{*0})-M(D^0)$ using the radiative decay $D^{*0}\rightarrow D^0\gamma$, obtaining $[M(D_s^{*+})-M(D_s^+)]-[M(D^{*0})-M(D^0)] = 2.09\pm 0.47\pm 0.37 MeV$. This is then combined with our previous high-precision measurement of $M(D^{*0})-M(D^0)$, which used the decay $D^{*0}\rightarrow D^0\pi^0$. We also measure the mass difference $M(D_s^+)-M(D^+)=99.5\pm 0.6\pm 0.3$ MeV, using the $\phi\pi^+$ decay modes of the $D_s^+$ and $D^+$ mesons.Comment: 18 pages uuencoded compressed postscript (process with uudecode then gunzip). hardcopies with figures can be obtained by sending mail to: [email protected]

Myoclonus-dystonia : distinctive motor and non-motor phenotype from other dystonia syndromes

Background: myoclonus-dystonia (M-D) due to a pathogenic variant of SGCE is an autosomal dominant inherited movement disorder. Apart from motor symptoms, psychiatric disorders are highly prevalent in patients with MD. Previous studies suggest, but never tested directly, that the type of psychiatric disorder differs between dystonia syndromes, probably related to disease specific pathology. Little is known about other non-motor symptoms (NMS) in M.D. Here, we systematically study NMS in M-D in direct comparison to other types of dystonia and healthy controls. Methods: Standardized questionnaires were used to assess type and severity of psychiatric co-morbidity, sleep problems, fatigue and quality of life. Results of M-D patients with a pathogenic variant of SGCE were compared to results of idiopathic cervical dystonia (CD) patients, dopa-responsive dystonia (DRD) patients with a pathogenic variant of GCH1 and controls. Results: We included 164 participants: 41 M-D, 51 CD, 19 DRD patients, 53 controls. Dystonia patients (M-D, CD and DRD) had an increased prevalence of psychiatric disorders compared to controls (56-74% vs. 29%). In M-D we found a significantly increased prevalence of obsessive-compulsive disorder (OCD) and psychosis compared to CD and DRD. All dystonia patients had more sleep problems (49-68% vs. 36%) and fatigue (42-73% vs. 15%) than controls. Compared to other dystonia subtypes, M-D patients reported less excessive daytime sleepiness and fatigue. Conclusion: Psychiatric comorbidity is frequent in all dystonia types, but OCD and psychosis are more common in M-D patients. Further research is necessary to elucidate underlying pathways

Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes

We give a partial "quasi-stratification" of the secant varieties of the order $d$ Veronese variety $X_{m,d}$ of $\mathbb {P}^m$. It covers the set $\sigma_t(X_{m,d})^{\dagger}$ of all points lying on the linear span of curvilinear subschemes of $X_{m,d}$, but two "quasi-strata" may overlap. For low border rank two different "quasi-strata" are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each $P\in \sigma_t(X_{m,d})^{\dagger}$ the minimal label of a quasi-stratum containing it.Comment: 16 page

FPS-SFT: A Multi-dimensional Sparse Fourier Transform Based on the Fourier Projection-slice Theorem

We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are parameterized by random slopes and offsets. The discrete Fourier transform (DFT) along those lines represents projections of M-D DFT of the M-D data onto those lines. The M-D sinusoids that are contained in the signal can be reconstructed from the DFT along lines with a low sample and computational complexity provided that the signal is sparse in the frequency domain and the lines are appropriately designed. The performance of FPS-SFT is demonstrated both theoretically and numerically. A sparse image reconstruction application is illustrated, which shows the capability of the FPS-SFT in solving practical problems