Entanglement and elementary excitations in quantum spin chain

The entanglement induced by elementary excitations in the XX spin chain is investigated by Bethe ansatz method. The reduced density matrix and correlation function between any pair of spins can be obtained for ground and all excited states with N qubits. Rely on them we show the explicit and general relations between entanglement and elementary excitations in XX spin chain. We further show our method can be extend to other integrable models.     

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schrödinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrödinger functional technique turns out to be much more efficient than the known alternatives.     

A novel in silico platform for a fully automatic personalized brain tumor growth

Glioblastoma Multiforme is the most common and most aggressive type of brain tumors. Although accurate prediction of Glioblastoma borders and shape is absolutely essential for neurosurgeons, there are not many in silico platforms that can make such predictions. In the current study, an automatic patient-specific simulation of Glioblastoma growth would be described. A finite element approach is used to analyze the magnetic resonance images from patients in the early stages of their tumors. For segmentation of the tumor, the Support Vector Machine (SVM) method, which is an automatic segmentation algorithm, is used. Using in situ and in vivo data, the main parameters of tumor prediction and growth are estimated with high precision in proliferation-invasion partial differential equation, using the genetic algorithm optimization method. The results show that for a C57BL mouse, the differences between the area and perimeter of in vivo test and simulation prediction data, as the objective function, are 3.7% and 17.4%, respectively.     

基于太赫兹光谱-统计分析的大气PM2.5监测研究

应用太赫兹技术对大气中动力学直径小于2.5 μm(PM_2.5)的细颗粒物进行了定量研究。PM_2.5质量和太赫兹吸光度之间存在线性关系,相关系数为0.86。应用主成分分析的方法,可证明随着PM_2.5质量的增加,与吸收系数存在相似的趋势。为了提高预测精度,采用偏最小二乘,支持向量机和反向传播人工神经网络对PM_2.5进行定量研究。与单一的线性模型相比,统计模型具有较大的预测相关性和较小的误差。对于神经网络模型,训练集与预测集的相关系数和均方根误差分别达到0.999和0.016 mg,0.912和0.207 mg。因此,THz技术和统计学方法的结合可提供较高精度的预测,作为一种监测PM_2.5的有效手段。     

Transfer Matrix Functional Relations for the Generalized τ2 (t q ) Model

The N-state chiral Potts model in lattice statistical mechanics can be obtained as a “descendant” of the six-vertex model, via an intermediate “Q” or “τ₂ (t _q )” model. Here we generalize this to obtain a column-inhomogeneous τ₂ (t _q ) model, and derive the functional relations satisfied by its row-to-row transfer matrix. We do not need the usual chiral Potts relations between the Nth powers of the rapidity parameters a _p , b _p , c _p , d _p of each column. This enables us to readily consider the case of fixed-spin boundary conditions on the left and right-most columns. We thereby re-derive the simple direct product structure of the transfer matrix eigenvalues of this model, which is closely related to the superintegrable chiral Potts model with fixed-spin boundary conditions.     

Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity

We have analyzed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnès and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π⁺ and π⁰ production on the proton as well as π⁻ production on the neutron, in the energy range 160 MeV ⩽ E_γ ⩽ 420 MeV. The lack of high precision data on the neutron and of polarization observables leads to some limitations of our results. Especially the multipole M₁₋ connected with the Roper resonance P₁₁ (1440) cannot be determined to the required precision. Our predictions for the threshold amplitudes are in good agreement with both the data and chiral perturbation theory. In the region of the Δ(1232) we have determined the ratio of electric quadrupole and magnetic dipole excitation. The position of the resonance pole is obtained in exellent agreement with pion-nucleon scattering, and the complex residues of the multipoles are determined with the speed-plot technique.     

Ensemble Linear Subspace Analysis of High-Dimensional Data

Regression models provide prediction frameworks for multivariate mutual information analysis that uses information concepts when choosing covariates (also called features) that are important for analysis and prediction. We consider a high dimensional regression framework where the number of covariates (p) exceed the sample size (n). Recent work in high dimensional regression analysis has embraced an ensemble subspace approach that consists of selecting random subsets of covariates with fewer than p covariates, doing statistical analysis on each subset, and then merging the results from the subsets. We examine conditions under which penalty methods such as Lasso perform better when used in the ensemble approach by computing mean squared prediction errors for simulations and a real data example. Linear models with both random and fixed designs are considered. We examine two versions of penalty methods: one where the tuning parameter is selected by cross-validation; and one where the final predictor is a trimmed average of individual predictors corresponding to the members of a set of fixed tuning parameters. We find that the ensemble approach improves on penalty methods for several important real data and model scenarios. The improvement occurs when covariates are strongly associated with the response, when the complexity of the model is high. In such cases, the trimmed average version of ensemble Lasso is often the best predictor.     

Transfer tensor method in statistical mechanics

We generalize the transfer matrix method to get exact solutions of d-dimensional classical spin lattice models in statistical mechanics.     

基于局域相关向量机回归模型的小尺度网络流量的非线性预测

基于非线性时间序列局域预测法与相关向量机回归模型, 本文提出了局域相关向量机预测方法, 并应用于预测实际的小尺度网路流量序列. 应用基于信息准则的局域预测法邻近点的选取方法来选取局域相关向量机回归模型的邻近点个数. 对比分析了局域相关向量机预测法、前馈神经网络模型与局域线性预测法对网络流量序列的预测性能, 其中前馈神经网络模型的参数采用粒子群优化算法来优化. 实验结果表明: 邻近点优化后的局域相关向量机回归模型能够有效地预测小尺度网络流量序列, 归一化均方误差很小; 局域相关向量机回归模型生成的时间序列具有与原网络流量时间序列相一致的概率分布; 局域相关向量机回归模型的预测精度好于前馈神经网络模型的与局域线性预测法的. 关键词： 小尺度网络流量 非线性时间序列预测方法 局域预测法 相关向量机回归模型     

Boundary symmetries in linear differential and integral equation problems applied to the self-consistent Green’s function formalism of acoustic and electromagnetic scattering

Explicit symmetry relations for the Green’s function subject to homogeneous boundary conditions are derived for arbitrary linear differential or integral equation problems in which the boundary surface has a set of symmetry elements. For corresponding homogeneous problems subject to inhomogeneous boundary conditions implicit symmetry relations involving the Green’s function are obtained. The usefulness of these symmetry relations is illustrated by means of a recently developed self-consistent Green’s function formalism of electromagnetic and acoustic scattering problems applied to the exterior scattering problem. One obtains explicit symmetry relations for the volume Green’s function, the surface Green’s function, and the interaction operator, and the respective symmetry relations are shown to be equivalent. This allows us to treat boundary symmetries of volume-integral equation methods, boundary-integral equation methods, and the T matrix formulation of acoustic and electromagnetic scattering under a common theoretical framework. By specifying a specific expansion basis the coordinate-free symmetry relations of, e.g., the surface Green’s function can be brought into the form of explicit symmetry relations of its expansion coefficient matrix. For the specific choice of radiating spherical wave functions the approach is illustrated by deriving unitary reducible representations of non-cubic finite point groups in this basis, and by deriving the corresponding explicit symmetry relations of the coefficient matrix. The reducible representations can be reduced by group-theoretical techniques, thus bringing the coefficient matrix into block-diagonal form, which can greatly reduce ill-conditioning problems in numerical applications.     

K 0 regeneration in nuclei

Recent data onK ⁰ regeneration are critically analysed by means of both dispersion relations and a Regge pole model for kaon-nucleon scattering. Theoretical limits on the precision level are established.     

From CFT to graphs

In this paper, we pursue the discussion of the connections between rational conformal field theories (CFT) and graphs. We generalise our recent work on the relations of operator product algebra (OPA) structure constants of sl(2) theories with the Pasquier algebra attached to the graph. We show that in a variety of CFT's built on sl(n) (typically conformal embeddings and orbifolds), similar considerations enable one to write a linear system satisfied by the matrix elements of the Pasquier algebra in terms of conformal data (quantum dimensions and fusion coefficients). In some cases this provides sufficient information for the determination of all the eigenvectors of an adjacency matrix, and hence of a graph.     

X射线荧光光谱测定地质样品中27种组分分析结果不确定度的评估

建立了一种X射线荧光光谱分析方法分析结果不确定度的评估模式。以大量有可靠值的硅酸盐类地质样品的偏振能量色散X射线荧光光谱的分析结果为研究对象,对27个组分分别采用浓度分段,分别评估不同浓度段内各个组分分析方法精密度引入的相对不确定度(n=6,一个浓度段内各水平相对标准偏差的平均值)和准确度引入的相对不确定度(一个浓度段内各个水平的相对偏差的相对标准偏差),依据误差传递理论,合成精密度和准确度分别引入的相对不确定度得到总的相对不确定度。这种基本模式可以解决一定浓度范围内常规大量类似基体未知地质样品不确定度评估难的问题,不必对每个未知样品的分析结果都进行不确定度的评估,可以从这种模式统计的结果中给出不确定度的值。这种评估模式是一种基本的具有实际应用价值的统计模式,可以为后续的不确定度评估的函数模式的建立提供有力的基础。但是该不确定度评估模式涉及的有可靠值的样品数量较多,难以简单应用到其他基体样品分析结果的不确定度评估。争取以本研究为基础尽快建立一种合理的数理统计函数模式以适用于不同类型样品X射线荧光光谱分析结果不确定度的评估。     

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the ¹ S ₀ channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=?8 and ?4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.     

An optimal scheme for top quark mass measurement near the tt threshold at future e+e- colliders

A top quark mass measurement scheme near the tt production threshold in future e⁺e^- colliders, e.g.the Circular Electron Positron Collider (CEPC), is simulated. A χ² fitting method is adopted to determine the number of energy points to be taken and their locations. Our results show that the optimal energy point is located near the largest slope of the cross section v. beam energy plot, and the most efficient scheme is to concentrate all luminosity on this single energy point in the case of one-parameter top mass fitting. This suggests that the so-called data-driven method could be the best choice for future real experimental measurements. Conveniently, the top mass statistical uncertainty can also be calculated directly by the error matrix even without any sampling and fitting. The agreement of the above two optimization methods has been checked. Our conclusion is that by taking 50 fb^-1 total effective integrated luminosity data, the statistical uncertainty of the top potential subtracted mass can be suppressed to about 7 MeV and the total uncertainty is about 30 MeV. This precision will help to identify the stability of the electroweak vacuum at the Planck scale.     

Q-phonon scheme in the collective nuclear model

The Q-phonon scheme developed on the basis of the algebraic collective nuclear model is discussed. It is shown that, within this scheme, low-lying collective states of even-even nuclei can be described to a precision higher than 90% of the norm by using one or, at maximum, two components of the Q-phonon basis constructed by applying a fixed number of the quadrupole operators Q to the exact ground state of the system. Various applications of this approximate scheme are discussed. It is shown that, by using this scheme, the relations between several E2-transition probabilities or between the energies of the collective states can be derived. It is also shown that the Q-phonon scheme can be used to extract information about the equilibrium shapes of nuclei and their fluctuations from data on the E2-transition probabilities.     

Phenomenological relations for neutrino masses and mixing parameters

Phenomenological relations for masses, angles, and CP phases in the neutrino mixing matrix are proposed with allowance for available experimental data. For the case of CP violation in the lepton sector, an analysis of the possible structure of the neutrino mass matrix and a calculation of the neutrino mass features and the Dirac CP phase for the bimodal-neutrino model are performed. The values obtained in this way can be used to interpret and predict the results of various neutrino experiments.     

Generalized Heisenberg algebra and algebraic method: The example of an infinite square-well potential

We discuss the role of generalized Heisenberg algebras (GHA) in obtaining an algebraic method to describe physical systems. The method consists in finding the GHA associated to a physical system and the relations between its generators and the physical observables. We choose as an example the infinite square-well potential for which we discuss the representations of the corresponding GHA. We suggest a way of constructing a physical realization of the generators of some GHA and apply it to the square-well potential. An expression for the position operator x in terms of the generators of the algebra is given and we compute its matrix elements.     

Precise measurement of positronium hyperfine splitting using the Zeeman effect

Positronium is an ideal system for the research of the quantum electrodynamics (QED) in bound state. The hyperfine splitting (HFS) of positronium, Δ_HFS, gives a good test of the bound state calculations and probes new physics beyond the Standard Model. A new method of QED calculations has revealed the discrepancy by 15 ppm (3.9σ) of Δ_HFS between the QED prediction and the experimental average. There would be possibility of new physics or common systematic uncertainties in the previous all experiments. We describe a new experiment to reduce possible systematic uncertainties and will provide an independent check of the discrepancy. We are now taking data and the current result of Δ_HFS?=?203.395 1 ±0.002 4 (stat., 12 ppm) ±0.001 9 (sys., 9.5 ppm) GHz has been obtained so far. A measurement with a precision of O(ppm) is expected within a year.     

On the initial-boundary value problems for soliton equations

We present a novel approach to solving initial-boundary value problems on the segment and the half line for soliton equations. Our method is illustrated by solving a prototypal and widely applied dispersive soliton equation—the celebrated nonlinear Schroedinger equation. It is well known that the basic difficulty associated with boundaries is that some coefficients of the evolution equation of the (x) scattering matrix S(k, t) depend on unknown boundary data. In this paper, we overcome this difficulty by expressing the unknown boundary data in terms of elements of the scattering matrix itself to obtain a nonlinear integrodifferential evolution equation for S(k, t). We also sketch an alternative approach in the semiline case on the basis of a nonlinear equation for S(k, t), which does not contain unknown boundary data; in this way, the “linearizable” boundary value problems correspond to the cases in which S(k, t) can be found by solving a linear Riemann-Hilbert problem.