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Ying Xu

Publications and source records attributed to Ying Xu.

At least 109 records · Page 6Linked to original sources
arXiv2012

Classification of quasifinite representations of a Lie algebra related to Block type

A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra $\BB$ related to Block type, with basis {L_{\a,i},C|a,i\in\Z, i\ge0} and relations [L_{\a,i},L_{\b,j}]=((i+1)\b-(j+1)\a)L_{\a+\b,i+j}+\d_{\a+\b,0}\d_{i+j,0}\frac{\a^3-\a}{6}C, [C,L_{\a,i}]=0.Namely, an irreducible quasifinite $\BB$-module is either a highest weight module, a lowest weight module or a module of the intermediate series.

math.RT↗
arXiv2011

Quantizations of the extended affine Lie algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$

The extended affine Lie algebra $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ is quantized from three different points of view in this paper, which produces three noncommutative and noncocommutative Hopf algebra structures, and yield other three quantizations by an isomorphism of $\widetilde{\frak{sl}_2(\mathbb{C}_q)}$ correspondingly. Moreover, two of these quantizations can be restricted to the extended affine Lie algebra ${sl_2(\mathbb{C}_q)}$.

math.QA↗
arXiv2011

Multi-task GLOH feature selection for human age estimation

In this paper, we propose a novel age estimation method based on GLOH feature descriptor and multi-task learning (MTL). The GLOH feature descriptor, one of the state-of-the-art feature descriptor, is used to capture the age-related local and spatial information of face image. As the exacted GLOH features are often redundant, MTL is designed to select the most informative feature bins for age estimation problem, while the corresponding weights are determined by ridge regression. This approach largely reduces the dimensions of feature, which can not only improve performance but also decrease the computational burden. Experiments on the public available FG-NET database show that the proposed method can achieve comparable performance over previous approaches while using much fewer features.

cs.CV↗
arXiv2011

Quasifinite representations of a class of Block type Lie algebras $\BB$

Intrigued by a well-known theorem of Mathieu's on Harish-Chandra modules over the Virasoro algebra, we give an analogous result for a class of Block type Lie algebras $\BB$, where the parameter $q$ is a nonzero complex number. We also classify quasifinite irreducible highest weight $\BB$-modules and irreducible $\BB$-modules of the intermediate series. In particular, we obtain that an irreducible $\BB$-module of the intermediate series may be a nontrivial extension of a $\Vir$-module of the intermediate series if $q$ is half of a negative integer, where $\Vir$ is a subalgebra of $\BB$ isomorphic to the Virasoro algebra.

math.RT↗
arXiv2011

The U(1) Lattice Gauge Theory Universally Connects All Classical Models with Continuous Variables, Including Background Gravity

We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged) four-dimensional lattice gauge theory (LGT) with gauge group U(1). This result is very general that it includes models in different dimensions with different symmetries. In particular, we show that a U(1) LGT defined in a curved spacetime can be mapped to a U(1) LGT with a flat background metric. The result is achieved by expressing the U(1) LGT partition function as an inner product between two quantum states.

quant-ph↗
arXiv2010

Entanglement in Valence-Bond-Solid States

This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Renyi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.

quant-ph↗
arXiv2010

Derivations and automorphism groups of completed Witt Lie algebra

In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a byproduct, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad-locally finite element.

math.RA↗
arXiv2009

Pricing strategies for viral marketing on Social Networks

We study the use of viral marketing strategies on social networks to maximize revenue from the sale of a single product. We propose a model in which the decision of a buyer to buy the product is influenced by friends that own the product and the price at which the product is offered. The influence model we analyze is quite general, naturally extending both the Linear Threshold model and the Independent Cascade model, while also incorporating price information. We consider sales proceeding in a cascading manner through the network, i.e. a buyer is offered the product via recommendations from its neighbors who own the product. In this setting, the seller influences events by offering a cashback to recommenders and by setting prices (via coupons or discounts) for each buyer in the social network. Finding a seller strategy which maximizes the expected revenue in this setting turns out to be NP-hard. However, we propose a seller strategy that generates revenue guaranteed to be within a constant factor of the optimal strategy in a wide variety of models. The strategy is based on an influence-and-exploit idea, and it consists of finding the right trade-off at each time step between: generating revenue from the current user versus offering the product for free and using the influence generated from this sale later in the process. We also show how local search can be used to improve the performance of this technique in practice.

cs.DS↗
arXiv2008

Entanglement of Valence-Bond-Solid on an Arbitrary Graph

The Affleck-Kennedy-Lieb-Tasaki (AKLT) spin interacting model can be defined on an arbitrary graph. We explain the construction of the AKLT Hamiltonian. Given certain conditions, the ground state is unique and known as the Valence-Bond-Solid (VBS) state. It can be used in measurement-based quantum computation as a resource state instead of the cluster state. We study the VBS ground state on an arbitrary connected graph. The graph is cut into two disconnected parts: the block and the environment. We study the entanglement between these two parts and prove that many eigenvalues of the density matrix of the block are zero. We describe a subspace of eigenvectors of the density matrix corresponding to non-zero eigenvalues. The subspace is the degenerate ground states of some Hamiltonian which we call the block Hamiltonian.

quant-ph↗
arXiv2008

Block Spin Density Matrix of the Inhomogeneous AKLT Model

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.

quant-ph↗
arXiv2008

Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.

quant-ph↗
arXiv2007

Binary Quantum Search

Database search has wide applications and is used as a subroutine in many important algorithms. We shall consider a database with one target item. Quantum algorithm finds the target item in a database faster than any classical algorithm. It frequently occurs in practice that only a portion of information about the target item is interesting, or we need to find a group of items sharing some common feature as the target item. This problem is in general formulated as search for a part of the database [a block] containing the target item, instead of the item itself. This is partial search. Partial search trades accuracy for speed, i.e. it works faster than a full search. Partial search algorithm was discovered by Grover and Radhakrishnan. We shall consider optimized version of the algorithm and call it GRK. It can be applied successively [in a sequence]. First the database is partitioned into blocks and we use GRK to find the target block. Then this target block is partitioned into sub-blocks and we use GRK again to find the target sub-block. [We can call it binary quantum search.] Another possibility is to partition the database into sub-blocks directly and use GRK to find the target sub-block in one time. In this paper we prove that the latter is faster [makes less queries to the oracle].

quant-ph↗
arXiv2006

Conductance oscillation and quantization in monoatomic Al wires

We present first-principles calculations for the transport properties of monoatomic Al wires sandwiched between Al(100) electrodes. The conductance of the monoatomic Al wires oscillates with the number of the constituent atoms as a function of the wire length, either with a period of four-atom for wires with the typical interatomic spacing or a period of six-atom with the interatomic spacing of the bulk fcc aluminum, indicating a dependence of the period of conductance oscillation on the interatomic distance of the monoatomic Al wires.

cond-mat.mes-hall↗
arXiv2006

Current rectification by asymmetric molecules: An ab initio study

We study current rectification effect in an asymmetric molecule HOOC-C$_6$H$_4$-(CH$_2$)$_n$ sandwiched between two Aluminum electrodes using an {\sl ab initio} nonequilibrium Green function method. The conductance of the system decreases exponentially with the increasing number $n$ of CH$_2$. The phenomenon of current rectification is observed such that a very small current appears at negative bias and a sharp negative differential resistance at a critical positive bias when $n\ge 2$. The rectification effect arises from the asymmetric structure of the molecule and the molecule-electrode couplings. A significant rectification ratio of $\sim$38 can be achieved when $n=5$.

cond-mat.mes-hall↗
arXiv2006

Effects of relative orientation of the molecules on electron transport in molecular devices

Effects of relative orientation of the molecules on electron transport in molecular devices are studied by non-equilibrium Green's function method based on density functional theory. In particular, two molecular devices, with the planer Au$_{7}$ and Ag$_{3}$ clusters sandwiched between the Al(100) electrodes are studied. In each device, two typical configurations with the clusters parallel and vertical to the electrodes are considered. It is found that the relative orientation affects the transport properties of these two devices completely differently. In the Al(100)-Au$_7$-Al(100) device, the conductance and the current of the parallel configuration are much larger than those in the vertical configuration, while in the Al(100)-Ag$_{3}$-Al(100) device, an opposite conclusion is obtained.

cond-mat.mes-hall↗