Towards a molecular understanding of the electronic metal-support interaction(EMSI)in heterogeneous catalysis

Tailoring the electronic metal-support interaction(EMSI)has attracted considerable interests as one of the most efficient approaches to improve both the activity and stability of metal catalysts in heterogeneous catalysis.In this viewpoint,we illustrate the methodology and relevant fundamentals on the disentanglement,characterization,and interpretation of EMSI.Under the choice of monometallic catalyst over inert support,a combination of optimal experiment design,multimodal techniques,in situ characterization,with a comprehensive understanding of the underlying measurement protocols is highly desirable for a reliable determination of EMSI.Accordingly,not only the d-band filling but also d-band energy within the EMSI should be taken into consideration for providing general principles to guide the electron-promoting catalytic reaction.

MERACLE:Constructive Layer-Wise Conversion of a Tensor Train into a MERA

In this article,two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz(MERA).The Tucker core tensor is never explicitly computed but stored as a tensor train instead,resulting in both computationally and storage efficient algorithms.Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error.In addition,an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors,which are a crucial component in the construction of a low-rank MERA.Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train.

Quantum Recoil Effects of Spontaneous Emission on Disentanglement

By taking into account spatial degrees of freedom of atoms, we study the internal-state disentanglement dynamics of two atoms interacting with a vacuum multi-mode noise field. We show that the complete internal-state disentanglement of the two atoms, caused due to the atomic spontaneous emission can be achieved in a finite time.

Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials

The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.

Facial landmark disentangled network with variational autoencoder

Learning disentangled representation of data is a key problem in deep learning.Specifically,disentangling 2D facial landmarks into different factors(e.g.,identity and expression)is widely used in the applications of face reconstruction,face reenactment and talking head et al..However,due to the sparsity of landmarks and the lack of accurate labels for the factors,it is hard to learn the disentangled representation of landmarks.To address these problem,we propose a simple and effective model named FLD-VAE to disentangle arbitrary facial landmarks into identity and expression latent representations,which is based on a Variational Autoencoder framework.Besides,we propose three invariant loss functions in both latent and data levels to constrain the invariance of representations during training stage.Moreover,we implement an identity preservation loss to further enhance the representation ability of identity factor.To the best of our knowledge,this is the first work to end-to-end disentangle identity and expression factors simultaneously from one single facial landmark.

Wave functions of a new kind of nonlinear single-mode squeezed state

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.

New Convenient Way for Deriving Exponential Operators' Disentangling Formulas and Their Applications

We recommend a new convenient method for disentangling some exponential operators and derive a set of new operator identities. Especially, we derive the normal odering form of exp [fa^＋a ＋ ga^2＋ ＋ ka^2] without appealing to Lie algebra method. Application of these formulas in solving some dynamic Hamiltonian is presented.

Disentanglement of Two Qubits Coupled to an XY Spin Chain at Finite Temperature

The disentanglement evolution of bipartite spin-1/2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied in this letter. The dynamical process of the entanglement is numerically and analytically investigated. We find that thermal effects can enhance disentanglement if the entangled initial state of the central spins does not in the decoherence free space. The critical phenomenon of quantum phase transitions reflected in the disentanglement can be washed out by the thermal effect eventually.

New Convenient Way for Deriving Exponential Operators' Disentangling Formulas and Their Applications(Ⅱ)

In the preceding paper [Commun. Theor. Phys. 51 （2009） 321] we have recommended a convenient method for disentangling exponential operators in the form of exp{B ＋ C}, trying to find an operator A that satisfies [A, B] = C, and [A, [A, B]] = 0, then from the Baker-Hausdorff formula we have exp{B ＋C} ： exp（B ＋ [A, B]} = e^A e^B e^-A. After arranging e^Ae^B = e^B e^A e^W, the disentangling exp{B ＋ C} = e^B e^W is obtained. In this work we use this method to two-mode case, especially, derive the normal ordering form of exp[h（a^＋a ＋ b^＋b） ＋ ga^＋b^＋ ＋ kab] without appealing to Lie algebra method.

Disentanglement of Qubit in Dephasing Model

We investigate the entanglement evolution of two qubits that are initially in Werner state under the classical phase noise. We discuss the influence of mixture degree on disentanglement. It is showed that the more mixed the state, the shorter is the time of disentanglement.

Quantum Disentanglement as the Physics behind Dark Energy

A straightforward simple proof is given that dark energy is the natural conse-quence of a quantum disentanglement physical process. Thus while the ordinary energy density of the cosmos is equal to half that of Hardy’s quantum probability of Entanglement i.e. where , the density of cosmic dark energy is consequently one minus divided by two i.e. . This result is in full agreement with all the numerous previous theoretical predictions as well as being in remarkable agreement with the overwhelming majority of cosmic accurate measurements and observations.

Disentanglement of a Singlet Spin State in a Coincidence Stern-Gerlach Device

We analyze the spin coincidence experiment considered by Bell in the derivation of Bells theorem. We solve the equation of motion for the spin system with a spin Hamiltonian, Hz, where the magnetic field is only in the z-direction. For the specific case of the coincidence experiment where the two magnets have the same orientation the Hamiltonian Hz commutes with the total spin Iz, which thus emerges as a constant of the motion. Bells argument is then that an observation of spin up at one magnet A necessarily implies spin down at the other B. For an isolated spin system A-B with classical translational degrees of freedom and an initial spin singlet state there is no force on the spin particles A and B. The spins are fully entangled but none of the spin particles A or B are deflected by the Stern-Gerlach magnets. This result is not compatible with Bells assumption that spin 1/2 particles are deected in a Stern-Gerlach device. Assuming a more realistic Hamiltonian Hz + Hx including a gradient in x direction the total Iz is not conserved and fully entanglement is not expected in this case. The conclusion is that Bells theorem is not applicable to spin coincidence measurement originally discussed by Bell.

Texture-based latent space disentanglement for enhancement of a training dataset for ANN-based classification of fruit and vegetables

The capability of Convolutional Neural Networks(CNNs)for sparse representation has significant application to complex tasks like Representation Learning(RL).However,labelled datasets of sufficient size for learning this representation are not easily obtainable.The unsupervised learning capability of Variational Autoencoders(VAEs)and Generative Adversarial Networks(GANs)provide a promising solution to this issue through their capacity to learn representations for novel data samples and classification tasks.In this research,a texture-based latent space disentanglement technique is proposed to enhance learning of representations for novel data samples.A comparison is performed among different VAEs and GANs with the proposed approach for synthesis of new data samples.Two different VAE architectures are considered,a single layer dense VAE and a convolution based VAE,to compare the effectiveness of different architectures for learning of the representations.The GANs are selected based on the distance metric for disjoint distribution divergence estimation of complex representation learning tasks.The proposed texture-based disentanglement has been shown to provide a significant improvement for disentangling the process of representation learning by conditioning the random noise and synthesising texture rich images of fruit and vegetables。

Shear and extensional rheology of entangled polymer melts: Similarities and differences

This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into "dead knots" in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.

How to disentangle microbially functional complexity: an insight from the network analysis of C, N, P and S cycling genes

A complete ecosystem is also a complex network in which multifarious species interact with each other to achieve system-level functions, such as nutrient biogeochemistry (1)Microbial community is commonly considered as the primary driving force of ecosystem nutrient mobilization and metabolism, especially carbon (C), nitrogen (N), phosphorus (P), sulfur (S) and methane coupling process (2)The rise of metagenomics and high-throughput array (e.g. PhyloChip, GeoChip, etc.

BROWNIAN MOTION MODEL OF ENTANGLED POLYMERS AND SIMULATION FOR DISENTANGLEMENT

The dynamics of the center-of-mass of entangled polymer is assumed to be of 1-dimen-sional Brownian motion in a constrained tube. When the length fluctuation of the constrain-ed tube is neglected, the asymptotic relation between the relaxation time for disentangle-ment τ and the chain length N is obtained, i.e. τ～N^3. Under conditions of the finite chainlength and the length fluctuation of an effective constrained tube, the dependence relation τ～N^(3.40±0.16) is obtained by computer simulation. This conclusion elucidates reasonably the knownexperimental results about the dynamics of real entangled polymers.

A Review of Disentangled Representation Learning for Remote Sensing Data

representation that can identify and isolate different potential variables hidden in the highdimensional observations.Disentangled representation learning can capture information about a single change factor and control it by the corresponding potential subspace,providing a robust representation for complex changes in the data.In this paper,we first introduce and analyze the current status of research on disentangled representation and its causal mechanisms and summarize three crucial properties of disentangled representation.Then,disentangled representation learning algorithms are classified into four categories and outlined in terms of both mathematical description and applicability.Subsequently,the loss functions and objective evaluation metrics commonly used in existing work on disentangled representation are classified.Finally,the paper summarizes representative applications of disentangled representation learning in the field of remote sensing and discusses its future development.