Crystal and molecular structures of two modifications of a chelate compound of Pb[(<Emphasis Type="Italic">iso</Emphasis>-C<Subscript>4</Subscript>H<Subscript>9</Subscript>)<Subscript>2</Subscript>PS<Subscript>2</Subscript>]<Subscript>2</Subscript>

A chelate compound Pb[(iso-C₄H₉)₂PS₂]² is synthesized. Using X-ray diffraction data, the crystal structures of two modifications of this compound are determined (X8 APEX diffractometer, MoK _α radiation, 14169 F _hkl , R = 0.0480 for the low temperature α-form and 6261 F _hkl , R = 0.0387 for the β-form studied at ambient temperature). The crystals are triclinic: a = 11.047(2) Å, b = 14.486(3) Å, c = 32.048(6) Å; α = 91.30(3)°, β = 99.73(3)°, γ = 101.61(3)°, V = 4942.9(17) ų, Z = 8, ρ_calc = 1.682 g/cm³ (α-modification) and a = 11.2124(5) Å, b = 14.6989(7) Å, c = 17.1644(6) Å; α = 109.393(1)°, β = 94.989(2)°, γ = 101.649(1)°, V = 2576.83(19) ų, Z = 4, ρ_calc = 1.613 g/cm³ (β-modification), space group \(P\bar 1\) for both polymorphs. The structures are molecular, coordination cores of PbS₄ are tetragonal pyramids with Pb atoms in the vertices and S atoms in the base. In both structures intermolecular Pb...S contacts yield supramolecular ensembles comprising by four molecules, where PbS₄₊₂ cores form planar aggregates of edge-sharing octahedra. The ensembles are joined by weak intermolecular S...S interactions resulting in the development of polymeric chains along the a axis.     

Eigen microstates and their evolutions in complex systems

Emergence refers to the existence or formation of collective behaviors in complex systems. Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system. In this framework, the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N × M matrix A, whose columns represent microstates and order of row is consist with the time. The ensemble matrix A can be decomposed as ■, where r= min(N,M), eigenvalue σIbehaves as the probability amplitude of the eigen microstate U_I so that ■ and U_I evolves following V_I. In a disorder complex system, there is no dominant eigenvalue and eigen microstate. When a probability amplitude σIbecomes finite in the thermodynamic limit, there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases. This indicates the emergence of U_I and a phase transition in complex system. Our framework has been applied successfully to equilibrium threedimensional Ising model, climate system and stock markets. We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters, such as phase transitions of collective motion and tipping points in climate systems and ecosystems.     

Microcanonical and Canonical Ensembles for fMRI Brain Networks in Alzheimer’s Disease

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of Alzheimer’s disease and identify stages in the disease progression. We employ methods of network neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for network construction and analysis. In network construction, we vary thresholds in establishing BOLD time series correlation between nodes, yielding variations in topological and other network characteristics. For network analysis, we employ methods developed for modelling statistical ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical ensemble are analogous to two different fMRI network representations. In the former case, there is zero variance in the number of edges in each network, while in the latter case the set of networks have a variance in the number of edges. Ensemble methods describe the macroscopic properties of a network by considering the underlying microscopic characterisations which are in turn closely related to the degree configuration and network entropy. When applied to fMRI data in populations of Alzheimer’s patients and controls, our methods demonstrated levels of sensitivity adequate for clinical purposes in both identifying brain regions undergoing pathological changes and in revealing the dynamics of such changes.     

Unsupervised Anomaly Detection with Distillated Teacher-Student Network Ensemble

We address the problem of unsupervised anomaly detection for multivariate data. Traditional machine learning based anomaly detection algorithms rely on specific assumptions of normal patterns and fail to model complex feature interactions and relations. Recently, existing deep learning based methods are promising for extracting representations from complex features. These methods train an auxiliary task, e.g., reconstruction and prediction, on normal samples. They further assume that anomalies fail to perform well on the auxiliary task since they are never trained during the model optimization. However, the assumption does not always hold in practice. Deep models may also perform the auxiliary task well on anomalous samples, leading to the failure detection of anomalies. To effectively detect anomalies for multivariate data, this paper introduces a teacher-student distillation based framework Distillated Teacher-Student Network Ensemble (DTSNE). The paradigm of the teacher-student distillation is able to deal with high-dimensional complex features. In addition, an ensemble of student networks provides a better capability to avoid generalizing the auxiliary task performance on anomalous samples. To validate the effectiveness of our model, we conduct extensive experiments on real-world datasets. Experimental results show superior performance of DTSNE over competing methods. Analysis and discussion towards the behavior of our model are also provided in the experiment section.     

The average stress tensor in systems with interacting particles

The derivation of an expression of the macroscopic stress tensor in terms of microscopic variables in systems of finite interacting particles is discussed from different points of view. It is shown that in volume averaging the introduction of a fictitious “interaction stress field”T ^I with special boundary conditions on the boundary of the averaging volume is needed. In ensemble averaging similar results are obtained by using a multipole expansion of the local stress and force fields. In the appropriate limiting cases, the obtained results are shown to be consistent with the results of kinetic theories of polymer solutions. Paper, presented at the First Conference of European Rheologists at Graz, April 14 – 16, 1982.     

总体经验模态分解能量向量用于ECG能量分布的研究

总体经验模态分解(EEMD)改进了经验模态分解(EMD)存在的模态混叠问题, 依据信号自身的波动特点将信号分解, 特别适合非线性非平稳信号的分析处理. ECG信号能量分布有一定的规律, 疾病会引起能量分布的变化, 研究ECG能量分布的改变对心脏疾病的研究和临床诊断有重要意义. 本文将ECG信号通过EEMD方法分解为多个本征模态函数(IMF)分量, 观察IMF分量的波动规律, 指出了ECG信号在不同时间尺度上的波动特点和物理意义. 将IMF分量分别计算能量, 得到ECG的能量向量, 并对健康人和三种心脏疾病患者能量向量进行对比分析. 结果表明心脏疾病导致EEMD能量向量的高频分量显著降低, 尤其是p₁分量具有较好的区分度, 可以作为心脏疾病诊断的参考依据. 相比较传统的频域分析方法单纯关注频率而忽略信号自身特点和信号成分之间的相互作用, EEMD的分解结果依赖于ECG信号本身, 因此更能够反映ECG信号的真实情况, 揭示年龄和疾病对ECG能量分布的影响.     

The exciton many-body theory extended to any kind of composite bosons

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between N excitons can be treated exactly through a set of dimensionless “Pauli scatterings” between two excitons. Many-body effects with free excitons turn out to be rather simple because these excitons are the exact one-pair eigenstates of the semiconductor Hamiltonian, in the absence of localized traps. They consequently form a complete orthogonal basis for one-pair states. As essentially all quantum particles known as bosons are composite bosons, it is highly desirable to extend this free exciton many-body theory to other kinds of “cobosons” — a contraction for composite bosons — the physically relevant ones being possibly not the exact one-pair eigenstates of the system Hamiltonian. The purpose of this paper is to derive the “Pauli scatterings” and the “interaction scatterings” of these cobosons in terms of their wave functions and the interactions which exist between the fermions from which they are constructed. It is also explained how to calculate many-body effects in such a very general composite boson system.     

Gibbs and Bose-Einstein distributions for an ensemble of self-adjoint operators in classical mechanics

We introduce the notion of an ensemble of self-adjoint operators and formulate theorems relating the occupation numbers to the number of eigenvalues of the ensemble. We formulate a theorem for the Gibbs distribution in classical mechanics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 312–316, May, 2008.     

Consistency of Microcanonical and Canonical Finite-Size Scaling

Typically, in order to obtain finite-size scaling laws for quantities in the microcanonical ensemble, an assumption is taken as a starting point. In this paper, consistency of such a Microcanonical Finite-Size Scaling Assumption with its commonly accepted canonical counterpart is shown, which puts Microcanonical Finite-Size Scaling on a firmer footing.