On the uniformly continuity of the solution map for two dimensional wave maps

The aim of this paper is to analyse the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid ${\cal H}^2$ that is embedded in ${\cal R}^3$. The initial data are in ${\dot H}^1\times L^2$. We prove that the solution map is not uniformly continuous

Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected Controlled-NOT gate which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the pi/8 gate, are also explicitly implemented by quasihole braidings. Instead of the pi/8 gate we try to construct a topologically protected Toffoli gate, in terms of the Controlled-phase gate and CNOT or by a braid-group based Controlled-Controlled-Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g_3.Comment: 6 pages, 7 figures, RevTeX; version 3: introduced section names, new reference added; new comment added about the embedding of the one- and two- qubit gates into a three-qubit syste

Low-resource Multi-task Audio Sensing for Mobile and Embedded Devices via Shared Deep Neural Network Representations

Continuous audio analysis from embedded and mobile devices is an increasingly important application domain. More and more, appliances like the Amazon Echo, along with smartphones and watches, and even research prototypes seek to perform multiple discriminative tasks simultaneously from ambient audio; for example, monitoring background sound classes (e.g., music or conversation), recognizing certain keywords (‘Hey Siri’ or ‘Alexa’), or identifying the user and her emotion from speech. The use of deep learning algorithms typically provides state-of-the-art model performances for such general audio tasks. However, the large computational demands of deep learning models are at odds with the limited processing, energy and memory resources of mobile, embedded and IoT devices. In this paper, we propose and evaluate a novel deep learning modeling and optimization framework that speci cally targets this category of embedded audio sensing tasks. Although the supported tasks are simpler than the task of speech recognition, this framework aims at maintaining accuracies in predictions while minimizing the overall processor resource footprint. The proposed model is grounded in multi-task learning principles to train shared deep layers and exploits, as input layer, only statistical summaries of audio lter banks to further lower computations. We nd that for embedded audio sensing tasks our framework is able to maintain similar accuracies, which are observed in comparable deep architectures that use single-task learning and typically more complex input layers. Most importantly, on an average, this approach provides almost a 2.1⇥ reduction in runtime, energy, and memory for four separate audio sensing tasks, assuming a variety of task combinations.Microsoft Researc

Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers

We demonstrate that the differential magnetic susceptibility of a fractional quantum Hall disk, representing a Coulomb island in a Fabry--Perot interferometer, is exactly proportional to the island's conductance and its paramagnetic peaks are the equilibrium counterparts of the Coulomb blockade conductance peaks. Using as a thermodynamic potential the partition functions of the edge states' effective conformal field theory we find the positions of the Coulomb blockade peaks, when the area of the island is varied, the modulations of the distance between them as well as the thermal decay and broadening of the peaks when temperature is increased. The finite-temperature estimates of the peak's heights and widths could give important information about the experimental observability of the Coulomb blockade. In addition, the predicted peak asymmetry and displacement at finite temperature due to neutral multiplicities could serve to distinguish different fractional quantum Hall states with similar zero-temperature Coulomb blockade patterns.Comment: 6 pages, 6 figures; published versio

Origin of Nepheline-normative High-K Ankaramites and the Evolution of Eastern Srednogorie Arc in SE Europe

Eastern Srednogorie is part of the Apuseni-Banat-Timok-Srednogorie magmatic belt in SE Europe, the main arc related to the Late Cretaceous subduction and closure of the Tethys Ocean between Africa and Europe. Extrusive and shallow intrusive magmatism in the Eastern Srednogorie is abundant and extremely diverse in composition, covering a wide range from ultramafic volcanic rocks to granites; this provides a unique opportunity to study processes of primitive melt formation and magma evolution in an arc environment. In contrast to other parts of the belt, relatively mafic lavas predominate here. Three magmatic regions are distinguished within Eastern Srednogorie from south to north: Strandzha, Yambol-Burgas and East Balkan. Systematic differences exist between these regions, notably the increased alkalinity of samples from the Yambol-Burgas region in the central part. All rocks display a clear subduction-like signature in their trace-element patterns, particularly the enrichment in large ion lithophile elements and light rare earth elements relative to high field strength elements. A distinct primitive nepheline-normative ankaramite magma type is recognized among the mafic volcanic rocks from the Yambol-Burgas region and melt inclusions entrapped in olivine and clinopyroxene from a cumulitic rock. Lower crustal clinopyroxene and amphibole cumulates carried to the surface as xenoliths in a mafic dike represent a possible source for the ankaramite. Modeling of the melting process suggests that low degrees of batch melting of a clinopyroxene-rich, amphibole-bearing source similar to the cumulate xenoliths at 1 GPa, temperatures of 1240-1300°C, oxidized conditions and a water content of 0·2 wt % reproduce accurately most of the observed major- and trace-element characteristics of the studied ankaramites. The elevated Rb, K2O, Th, Ba content and higher Pb isotope ratios of the predicted liquids compared with the ankaramites are explained by mixing of the ankaramite magma with lherzolite partial melts derived from the subduction-modified mantle wedge. Underplating of such mantle-derived magmas at the crust-mantle boundary in an extensional environment as a response to slab roll-back provides also the necessary heat to melt lower crustal cumulates. Fractional crystallization of mainly clinopyroxene plus olivine and Fe-Ti oxides in a deep (equivalent to 8 kbar pressure) magma chamber produced most of the observed range of shoshonitic basalts and basaltic andesites in Eastern Srednogorie. The more evolved intermediate varieties were probably formed by mixing and crystallization at lower temperatures in lower pressure magma chambers. Whole-rock Sr and Pb isotope compositions indicate variable degrees of admixing of basement rocks to generate the intermediate to acid Late Cretaceous magmas, but assimilation was minimal for magmas with less than 53 wt % SiO2. The proposed model for the evolution of the magmatism in Eastern Srednogorie involves initial formation of the calc-alkaline and high-K arc magmatism in the Strandzha and East Balkan regions, followed by roll-back induced intra-arc rifting and the formation of high-K, shoshonitic and ultra-high-K magmatism, including primitive ankaramites in the Yambol-Burgas regio

Chemo-dynamical evolution of Globular Cluster Systems

We studied the relation between the ratio of rotational velocity to velocity dispersion and the metallicity (/\sigma_{v}-metallicity relation) of globular cluster systems (GCS) of disk galaxies by comparing the relation predicted from simple chemo-dynamical models for the formation and evolution of disk galaxies with the observed kinematical and chemical properties of their GCSs. We conclude that proto disk galaxies underwent a slow initial collapse that was followed by a rapid contraction and derive that the ratio of the initial collapse time scale to the active star formation time scale is \sim 6 for our Galaxy and \sim 15 for M31. The fundamental formation process of disk galaxies was simulated based on simple chemo-dynamical models assuming the conservation of their angular momentum. We suggest that there is a typical universal pattern in the /\sigma_{v}-metallicity relation of the GCS of disk galaxies. This picture is supported by the observed properties of GCSs in the Galaxy and in M31. This relation would deviate from the universal pattern, however, if large-scale merging events took major role in chemo-dynamical evolution of galaxies and will reflect the epoch of such merging events. We discuss the properties of the GCS of M81 and suggest the presence of past major merging event.Comment: 25 pages, 8 figures, Accepted for publication in the Astrophysical Journa

Impact of Subthalamic Deep Brain Stimulation Frequency on Upper Limb Motor Function in Parkinson's Disease

BACKGROUND: Whilst changes in the frequency of subthalamic deep brain stimulation (STN-DBS) have been proposed to improve control of tremor or axial motor features in Parkinson's disease (PD), little is known about the effects of frequency changes on upper limb motor function, particularly bradykinesia. OBJECTIVE: To investigate the acute effects of various STN-DBS frequencies (40-160 Hz, 40 Hz intervals) on upper limb motor function. METHODS: We carried out a randomised, double-blind study on 20 PD patients with chronic STN-DBS using the Simple and Assembly components of the Purdue Pegboard (PP) test and a modified upper limb version of the UPDRS-III (UL-UPDRS-III). RESULTS: There was no significant effect of frequency on bradykinesia on the Simple PP task or the UL-UPDRS-III. There was an effect of frequency on the Assembly PP score when comparing all frequencies (p = 0.019) and between 80 Hz and 130 Hz (p = 0.007), with lower frequencies yielding a better performance. Rigidity and Tremor scores were significantly reduced with higher (>80 Hz) compared to lower (40 Hz) frequencies. CONCLUSIONS: Our findings suggest that a wide range of frequencies are efficacious in improving acute upper-limb motor function. Reducing the frequency of stimulation down to 80 Hz is safe and has a similar clinical effect to higher frequencies. Therefore, a wider range of frequencies are available when it comes adjusting patients' acute settings without the risk of worsening bradykinesia

RDGB , a PtdIns-PtdOH transfer protein, regulates G-protein-coupled PtdIns(4,5)P2 signalling during Drosophila phototransduction

Many membrane receptors activate phospholipase C (PLC) during signalling, triggering changes in the levels of several plasma membrane lipids including phosphatidylinositol (PtdIns), phosphatidic acid (PtdOH) and phosphatidylinositol 4,5-bisphosphate [PtdIns(4,5)P2]. It is widely believed that exchange of lipids between the plasma membrane and endoplasmic reticulum (ER) is required to restore lipid homeostasis during PLC signalling, yet the mechanism remains unresolved. RDGBα (hereafter RDGB) is a multi-domain protein with a PtdIns transfer protein (PITP) domain (RDGB-PITPd). We find that, in vitro, the RDGB-PITPd binds and transfers both PtdOH and PtdIns. In Drosophila photoreceptors, which experience high rates of PLC activity, RDGB function is essential for phototransduction. We show that binding of PtdIns to RDGB-PITPd is essential for normal phototransduction; however, this property is insufficient to explain the in vivo function because another Drosophila PITP (encoded by vib) that also binds PtdIns cannot rescue the phenotypes of RDGB deletion. In RDGB mutants, PtdIns(4,5)P2 resynthesis at the plasma membrane following PLC activation is delayed and PtdOH levels elevate. Thus RDGB couples the turnover of both PtdIns and PtdOH, key lipid intermediates during G-protein-coupled PtdIns(4,5)P2 turnover

Optical monitoring of the z=4.40 quasar Q 2203+292

We report Cousins R-band monitoring of the high-redshift (z=4.40) radio quiet quasar Q 2203+292 from May 1999 to October 2007. The quasar shows maximum peak-to-peak light curve amplitude of ~0.3 mag during the time of our monitoring, and ~0.9 mag when combined with older literature data. The rms of a fit to the light curve with a constant is 0.08 mag and 0.2 mag, respectively. The detected changes are at ~3-sigma level. The quasar was in a stable state during the recent years and it might have undergone a brightening event in the past. The structure function analysis concluded that the object shows variability properties similar to those of the lower redshift quasars. We set a lower limit to the Q 2203+292 broad line region mass of 0.3-0.4 M_odot. Narrow-band imaging search for redshifted Ly_alpha from other emission line objects at the same redshift shows no emission line objects in the quasar vicinity.Comment: 9 pages, 8 figures, accepted for publication in MNRA