Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in $O(n\log n)$ complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D $n\times n\times n$ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\times L\times L$ lattice manifests the linear in $L$ computational work, $O(L)$, instead of the usual $O(L^3 \log L)$ scaling by the Ewald-type approaches

A Scalable Specification-Agnostic Multi-Sensor Anomaly Detection System for IIoT Environments

Advanced sensing is a key ingredient for intelligent control in Industrial Internet of Things (IIoT) environments. Coupled with enhanced communication capabilities, sensors are becoming increasingly vulnerable to cyberattacks, thereby jeopardizing the often safety-critical underlying cyber-physical system. One prominent approach to sensor-level attack detection in modern industrial environments, named PASAD, has recently been proposed in the literature. PASAD is a process-aware stealthy-attack detection mechanism that has shown promising capabilities in detecting anomalous, potentially malicious behavior through real-time monitoring of sensor measurements. Although fast and lightweight, a major limitation of PASAD is that it is univariate, meaning that only a single sensor can be monitored by one instance of the algorithm. This impediment poses serious concerns on its scalability, especially in modernized industrial environments, which typically employ a plethora of sensors. This paper generalizes PASAD to the multivariate case, where a plurality of sensors can be monitored concurrently with little added complexity. This generalization has the evident advantage of offering scalability potential for deployment in future-focused industrial environments, which are undergoing growing integration between the digital and physical worlds

The approach for complexity analysis of multivariate time series

This paper proposes to estimate the complexity of a multivariate time series by the spatio-temporal entropy based on multivariate singular spectrum analysis (M-SSA). In order to account for both within- and cross-component dependencies in multiple data channels the high dimensional block Toeplitz covariance matrix is decomposed as a Kronecker product of a spatial and a temporal covariance matrix and the multivariate spatio-temporal entropy is defined in terms of modulus and angle of the complex quantity constructed from the spatial and temporal components of the multivariate entropy. The benefits of the proposed approach are illustrated by simulations on complexity analysis of multivariate deterministic and stochastic processes

Bayesian latent time joint mixed-effects model of progression in the Alzheimer's Disease Neuroimaging Initiative.

IntroductionWe characterize long-term disease dynamics from cognitively healthy to dementia using data from the Alzheimer's Disease Neuroimaging Initiative.MethodsWe apply a latent time joint mixed-effects model to 16 cognitive, functional, biomarker, and imaging outcomes in Alzheimer's Disease Neuroimaging Initiative. Markov chain Monte Carlo methods are used for estimation and inference.ResultsWe find good concordance between latent time and diagnosis. Change in amyloid positron emission tomography shows a moderate correlation with change in cerebrospinal fluid tau (ρ = 0.310) and phosphorylated tau (ρ = 0.294) and weaker correlation with amyloid-β 42 (ρ = 0.176). In comparison to amyloid positron emission tomography, change in volumetric magnetic resonance imaging summaries is more strongly correlated with cognitive measures (e.g., ρ = 0.731 for ventricles and Alzheimer's Disease Assessment Scale). The average disease trends are consistent with the amyloid cascade hypothesis.DiscussionThe latent time joint mixed-effects model can (1) uncover long-term disease trends; (2) estimate the sequence of pathological abnormalities; and (3) provide subject-specific prognostic estimates of the time until onset of symptoms