Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic observable at different time intervals -- reveals a negative answer i.e., the joint probabilities of sequential measurements do not agree with the ones obtained by inverting the moments. This is indeed a reflection of the non-existence of a bonafide grand joint probability distribution, consistent with all the physical marginal probability distributions. Here we explicitly demonstrate that given the set of moments, it is not possible to retrieve the three-time quantum joint probability distribution resulting from quantum sequential measurement of a single qubit dichotomic observable at three different times. Experimental results using a nuclear magnetic resonance (NMR) system are reported here to corroborate these theoretical observations viz., the incompatibility of the three-time joint probabilties with those extracted from the moment sequence.Comment: 7 pages, 5 figures, RevTe

Degenerate Kalman filter error covariances and their convergence onto the unstable subspace

The characteristics of the model dynamics are critical in the performance of (ensemble) Kalman filters. In particular, as emphasized in the seminal work of Anna Trevisan and coauthors, the error covariance matrix is asymptotically supported by the unstable-neutral subspace only, i.e., it is spanned by the backward Lyapunov vectors with nonnegative exponents. This behavior is at the core of algorithms known as assimilation in the unstable subspace, although a formal proof was still missing. This paper provides the analytical proof of the convergence of the Kalman filter covariance matrix onto the unstable-neutral subspace when the dynamics and the observation operator are linear and when the dynamical model is error free, for any, possibly rank-deficient, initial error covariance matrix. The rate of convergence is provided as well. The derivation is based on an expression that explicitly relates the error covariances at an arbitrary time to the initial ones. It is also shown that if the unstable and neutral directions of the model are sufficiently observed and if the column space of the initial covariance matrix has a nonzero projection onto all of the forward Lyapunov vectors associated with the unstable and neutral directions of the dynamics, the covariance matrix of the Kalman filter collapses onto an asymptotic sequence which is independent of the initial covariances. Numerical results are also shown to illustrate and support the theoretical findings

A Context-Responsive LSTM based IoT Enabled E- Healthcare Monitoring System for Arrhythmia Detection

Detecting Arrhythmia, a life-threatening cardiac condition, in real-time is crucial for timely intervention and improved healthcare outcomes. Traditional manual methods for Arrhythmia detection using Electrocardiogram (ECG) signals are error-prone and resource-intensive. To address these limitations, this paper presents an automated system based on the Context Responsive Long Short-Term Memory (CR-LSTM) model for real-time Arrhythmia classification. The system leverages IoT technology to continuously monitor vital signs and effectively combines contextual information with temporal sensor data to accurately discern different types of Arrhythmias. The CR-LSTM model achieves an impressive accuracy of 99.72% in multiclass classification of Arrhythmias, making it a promising solution for dynamic healthcare settings and proactive personalized care

Effect of lateral crushing on tensile property of bamboo, modal and tencel fibres

The effect of lateral crushing on the tensile properties of bamboo, modal and tencel fibres has been investigated. A fibre crushing apparatus has been used for the purpose of lateral crushing of fibres. The influence of transverse compression on the axial mechanical properties of these fibres has been analysed. The study reveals that modal fibre sustained a higher loss in tensile properties compared to bamboo and tencel. The general phenomenon obtained from the study is that the percentage loss of strength and breaking extension varies from one fibre to another based on the fibre type and morphology

r-2,c-6-Bis(4-methoxy­phenyl)-c-3,t-3-dimethyl-1-nitro­sopiperidin-4-one

In the title compound, C21H24N2O4, the piperidine ring adopts a distorted boat conformation. The crystal structure is stabilized by C—H⋯π inter­actions involving one of the methoxy­phenyl rings

Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case

Observation of direct and indirect magnetoelectricity in lead free ferroelectric (Na 0.5Bi 0.5TiO 3)-magnetostrictive (CoFe 2O 4) particulate composite

A particulate composite consisting of 65 mol. % Na 0.5Bi 0.5TiO 3 and 35 mol. % CoFe 2O 4 was synthesized, and it's structure, microstructure, ferroelectric, magnetostrictive, magnetic, and direct/indirect magnetoelectric properties were studied. The composite showed different magnetization behaviour under electrically poled and un-poled conditions. The percentage change in magnetization as a result of poling is approximately -15% at 500 Oe magnetic field. Magnetostriction measurements displayed a value of λ 11 = -57 × 10 -6 and piezomagnetic coefficient δλ 11/δH = 0.022 × 10 -6 kOe -1 at 2.2 kOe for the composite. The maximum magnetoelectric output varied from 1350 mV/cm to 2000 mV/cm with change in the electrical poling condition