Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Energy average formula of photon gas rederived by using the generalized Hermann-Feynman theorem

By virtue of the generalized Hermann-Feynmam theorem and the method of characteristics we rederive energy average formula of photon gas, this is another useful application of the theorem.Comment: 2 page

Entangled Husimi distribution and Complex Wavelet transformation

Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.Comment: 7 page

Refining grain structure and porosity of an aluminium alloy with intensive melt shearing

The official published version of the article can be obtained at the link below.Intensive melt shearing was achieved using a twin-screw machine to condition an aluminium alloy prior to solidification. The results show that intensive melt shearing has a significant grain-refining effect. In addition, the intensive melt shearing reduces both the volume fraction and the size of porosity. It can reduce the density index from 10.50% to 2.87% and the average size of porosity in the samples solidified under partial vacuum from around 1 mm to 100 μm.Financial support was obtained from the EPSRC and the Technology Strategy Board

Interpretable and Generalizable Person Re-Identification with Query-Adaptive Convolution and Temporal Lifting

For person re-identification, existing deep networks often focus on representation learning. However, without transfer learning, the learned model is fixed as is, which is not adaptable for handling various unseen scenarios. In this paper, beyond representation learning, we consider how to formulate person image matching directly in deep feature maps. We treat image matching as finding local correspondences in feature maps, and construct query-adaptive convolution kernels on the fly to achieve local matching. In this way, the matching process and results are interpretable, and this explicit matching is more generalizable than representation features to unseen scenarios, such as unknown misalignments, pose or viewpoint changes. To facilitate end-to-end training of this architecture, we further build a class memory module to cache feature maps of the most recent samples of each class, so as to compute image matching losses for metric learning. Through direct cross-dataset evaluation, the proposed Query-Adaptive Convolution (QAConv) method gains large improvements over popular learning methods (about 10%+ mAP), and achieves comparable results to many transfer learning methods. Besides, a model-free temporal cooccurrence based score weighting method called TLift is proposed, which improves the performance to a further extent, achieving state-of-the-art results in cross-dataset person re-identification. Code is available at https://github.com/ShengcaiLiao/QAConv.Comment: This is the ECCV 2020 version, including the appendi

SU(N) Coherent States

We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labelled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.Comment: 25 pages, LaTex, no figure

Using schema transformation pathways for data lineage tracing

With the increasing amount and diversity of information available on the Internet, there has been a huge growth in information systems that need to integrate data from distributed, heterogeneous data sources. Tracing the lineage of the integrated data is one of the problems being addressed in data warehousing research. This paper presents a data lineage tracing approach based on schema transformation pathways. Our approach is not limited to one specific data model or query language, and would be useful in any data transformation/integration framework based on sequences of primitive schema transformations

Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model

Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model and tail operators are expressed in terms of bosonized vertex operators in the $A^{(1)}_{n-1}$ model. Correlation functions of $(\mathbb{Z}/n\mathbb{Z})$-symmetric model can be obtained by using these objects, in principle. In particular, we calculate spontaneous polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available at http://stacks.iop.org/1751-8121/42/16521

Coherent States with SU(N) Charges

We define coherent states carrying SU(N) charges by exploiting generalized Schwinger boson representation of SU(N) Lie algebra. These coherent states are defined on $2 (2^{N - 1} - 1)$ complex planes. They satisfy continuity property and provide resolution of identity. We also exploit this technique to construct the corresponding non-linear SU(N) coherent states.Comment: 18 pages, LaTex, no figure