The ΛS-Householder matrices

AbstractLet A,S∈Mn(C) be given. Suppose that S is nonsingular and Hermitian. Then A is ΛS-orthogonal if A∗SA=S. Let u∈Cn be such that u∗Su≠0. The ΛS-Householder matrix of u is Su≡I-tuu∗S, where t=2u∗Su. We show that det Su=-1, so that products of ΛS-Householder matrices have determinant ±1. Let n⩾2 and let k be positive integers with k⩽n. Set Lk≡Ik⊕-In-k. We show that every ΛLk-orthogonal matrix having determinant ±1 can be written as a product of at most 2n+2 ΛLk-Householder matrices. We also determine the possible Jordan Canonical Forms of products of two ΛLk-Householder matrices

Impact of data quality in real-time big data systems

Data Quality is one of the main challenges in any type of Big Data System. Timeliness is one of the main factors in real-time Big Data. Limiting data quality evaluations to data sources may be insufficient in Big Data Systems with high Velocity and Variability. On the other hand, real-time Data Quality evaluations throughout the Big Data Pipeline can be costly (i.e., latency introduced by Data Quality Evaluations). This paper identifies four categories – embedded, parallel, in-line, and independent– of approaches for Big Data Quality Evaluation available in the literature. A real-time Big Data System based on the SmartCambridge Real-Time Data Platform is deployed and used as basis to implement a representative case for each one of the four categories identified. An application for bus catching dynamic prediction is used as case study to quantify the impact of these Data Quality Evaluations in the Real-Time Data Platform in terms of latency introduced in the system. Results suggests that the impact of Data Quality Evaluations differ depending on the type of method used, and that the main factors are the data transfers between Data Quality modules and the data processing algorithms, the synchronisation of messages, and the complexity of the Data Quality algorithms

13C NMR study of superconductivity near charge instability realized in beta"-(BEDT-TTF)4[(H3O)Ga(C2O4)3]C6H5NO2

To investigate the superconducting (SC) state near a charge instability, we performed ^{13}C NMR experiments on the molecular superconductor beta"-(BEDT-TTF)_{4}[(H_{3}O)Ga(C_{2}O_{4})_{3}]C_{6}H_{5}NO_{2}, which exhibits a charge anomaly at 100 K. The Knight shift which we measured in the SC state down to 1.5 K demonstrates that Cooper pairs are in spin-singlet state. Measurements of the nuclear spin-lattice relaxation time reveal strong electron-electron correlations in the normal state. The resistivity increase observed below 10 K indicates that the enhanced fluctuation has an electric origin. We discuss the possibility of charge-fluctuation-induced superconductivity.Comment: 5 pages, 4 figure

Tuning thermal properties and microphase separation in aliphatic polyester ABA copolymers

Four alkyl substituted β-lactones were investigated as monomers in ring opening polymerisation to produce a family of poly(3-hydroxyalkanoate)s. Homopolymers were synthesised using a robust aluminium salen catalyst, resulting in polymers with low dispersity (Đ < 1.1) and predictable molecular weights. ABA triblock copolymers were prepared using poly(L-lactic acid) as the A block and the afore- mentioned poly(3-hydroxyalkanoate) as the B block via a sequential addition method. Characterisation of these copolymers determined they were well controlled with low dispersities and predictable molecular weight. DSC analysis determined copolymers prepared from β-butyrolactone or β-valerolactone yielded polymers with tunable and predictable thermal properties. Copolymers prepared from β-heptanolactone yielded a microphase separated material as indicated by SAXS, with two distinct Tgs. The polymers could be readily cast into flexible films and their improved tensile properties were explored

Improving SIEM for critical SCADA water infrastructures using machine learning

Network Control Systems (NAC) have been used in many industrial processes. They aim to reduce the human factor burden and efficiently handle the complex process and communication of those systems. Supervisory control and data acquisition (SCADA) systems are used in industrial, infrastructure and facility processes (e.g. manufacturing, fabrication, oil and water pipelines, building ventilation, etc.) Like other Internet of Things (IoT) implementations, SCADA systems are vulnerable to cyber-attacks, therefore, a robust anomaly detection is a major requirement. However, having an accurate anomaly detection system is not an easy task, due to the difficulty to differentiate between cyber-attacks and system internal failures (e.g. hardware failures). In this paper, we present a model that detects anomaly events in a water system controlled by SCADA. Six Machine Learning techniques have been used in building and evaluating the model. The model classifies different anomaly events including hardware failures (e.g. sensor failures), sabotage and cyber-attacks (e.g. DoS and Spoofing). Unlike other detection systems, our proposed work helps in accelerating the mitigation process by notifying the operator with additional information when an anomaly occurs. This additional information includes the probability and confidence level of event(s) occurring. The model is trained and tested using a real-world dataset

Antiferromagnetic Heisenberg model on anisotropic triangular lattice in the presence of magnetic field

We use Schwinger boson mean field theory to study the antiferromagnetic spin-1/2 Heisenberg model on an anisotropic triangular lattice in the presence of a uniform external magnetic field. We calculate the field dependence of the spin incommensurability in the ordered spin spiral phase, and compare the results to the recent experiments in Cs$_{2}$CuCl$_{4}$ by Coldea et al. (Phys. Rev. Lett. 86, 1335 (2001)).Comment: 4 pages with 4 figures include

Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

Feynman scaling violation on baryon spectra in pp collisions at LHC and cosmic ray energies

A significant asymmetry in baryon/antibaryon yields in the central region of high energy collisions is observed when the initial state has non-zero baryon charge. This asymmetry is connected with the possibility of baryon charge diffusion in rapidity space. Such a diffusion should decrease the baryon charge in the fragmentation region and translate into the corresponding decrease of the multiplicity of leading baryons. As a result, a new mechanism for Feynman scaling violation in the fragmentation region is obtained. Another numerically more significant reason for the Feynman scaling violation comes from the fact that the average number of cutted Pomerons increases with initial energy. We present the quantitative predictions of the Quark-Gluon String Model (QGSM) for the Feynman scaling violation at LHC energies and at even higher energies that can be important for cosmic ray physics.Comment: 21 pages, 11 figures, and 1 table. arXiv admin note: substantial text overlap with arXiv:1107.1615, arXiv:1007.320