Hankel operators on vector-valued Bergman spaces with exponential weights

Let $\mathcal{H}$ be a separable Hilbert space and let $A^{2}_{\varphi}(\mathcal{H})$ be the $\mathcal{H}$-valued Bergman spaces with exponential weights. In the present paper, we give the complete characterizations for the boundedness and compactness of Hankel operators on $A^{2}_{\varphi}(\mathcal{H})$. For $p\geq2$, the Schatten $p$-classes of the Hankel operator with conjugate analytic symbols are studied.Comment: 16 page

Regularizing Face Verification Nets For Pain Intensity Regression

Limited labeled data are available for the research of estimating facial expression intensities. For instance, the ability to train deep networks for automated pain assessment is limited by small datasets with labels of patient-reported pain intensities. Fortunately, fine-tuning from a data-extensive pre-trained domain, such as face verification, can alleviate this problem. In this paper, we propose a network that fine-tunes a state-of-the-art face verification network using a regularized regression loss and additional data with expression labels. In this way, the expression intensity regression task can benefit from the rich feature representations trained on a huge amount of data for face verification. The proposed regularized deep regressor is applied to estimate the pain expression intensity and verified on the widely-used UNBC-McMaster Shoulder-Pain dataset, achieving the state-of-the-art performance. A weighted evaluation metric is also proposed to address the imbalance issue of different pain intensities.Comment: 5 pages, 3 figure; Camera-ready version to appear at IEEE ICIP 201

Deterministic realization of collective measurements via photonic quantum walks

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information processing and for exploring the intriguing physics behind this power.Comment: Close to the published versio

rac-6-Hy­droxy-4-(4-nitro­phen­yl)-5-(2-thienyl­carbon­yl)-6-(trifluoro­meth­yl)-3,4,5,6-tetra­hydro­pyrimidin-2(1H)-one monohydrate

The title compound, C16H12F3N3O5S·H2O, was prepared by reaction of 4-nitro­benzaldehyde, 4,4,4-trifluoro-1-(thio­phen-2-yl)butane-1,3-dione and urea. The asymmetric unit contains two independent mol­ecules, with essentially identical geom­etries and conformations. The dihydro­pyrimidine rings adopt a half-chair conformation. The dihedral angles between the benzene ring and the thio­phene ring are 54.82 (8) and 58.72 (8)° in the two mol­ecules. The mol­ecular conformation of one of the mol­ecules is stabilized by two intra­molecular O—H⋯O hydrogen bonds, generating an S(6) ring. The crystal structure is stabilized by inter­molecular O—H⋯O and N—H⋯O hydrogen bonds