Bivariate Matrix Research Articles

Psychological Experiences of Parents of Pediatric Cancer Patients during and after COVID-19 Pandemic.

Family members dealing with the devastating impact of a cancer diagnosis are now facing even greater vulnerability due to the COVID-19 pandemic. Alongside the already overwhelming trauma, they must also bear the distressing burden of the infection risks. The purpose of this study was to examine and explore the effects in parents of pediatric cancer patients two years after the start of the COVID-19 pandemic to compare these data with the previous data. We conducted a single-center prospective observational study, enrolling 75 parents of 42 pediatric oncology patients. Four questionnaires (IES-R; PSS; STAI-Y and PedsQL) were given to the parents 2 years after the first evaluation. The bivariate matrix of correlation found a strong significant positive correlation between IES-R and PSS scores (r = 0.526, p < 0.001) as in T1. Stress symptoms (t = 0.00, p < 0.001) and levels of anxiety (trait) (t = 0.32, p < 0.001) remained unchanged; anxiety state levels appeared to have increased (t = 0.425, p < 0.001); there was a significant decrease in the PedsQL tot (t = 5.25, p < 0.001). The COVID-19 pandemic has influenced the levels of stress and anxiety of parents and the quality of life of patients, also correlating with the traumatic impact of the diagnosis.

Psychological Impact of COVID-19 on Parents of Pediatric Cancer Patients.

The changes and general alarm of the current COVID-19 pandemic have amplified the sense of precariousness and vulnerability for family members who, in addition to the emotional trauma of the cancer diagnosis, add the distress and fear of the risks associated with infection. The primary objectives of the present study were to investigate the psychological impact of the COVID-19 pandemic on the parents of pediatric cancer patients, and the level of stress, anxiety, and the child’s quality of life perceived by the parents during the COVID-19 epidemic. The parents of 45 consecutive children with solid and hematological tumors were enrolled. Four questionnaires (Impact of Event Scale-Revised – IES-R; Perceived Stress Scale – PSS; Spielberger State – Trait Anxiety Inventory – STAI-Y; Pediatric Quality of Life Inventory – PedsQL) were administered to the parents at the beginning of the pandemic lockdown. A 75% of parents exhibited remarkable levels of anxiety, with 60 subjects in state scale and 45 subjects in trait scale having scores that reached and exceeded the STAI-Y cut off. The bivariate matrix of correlation found a significant positive correlation between the IES-R and PSS scores (r = 0.55, P < 0.001). There was a positive correlation between the PSS and PedsQL (emotional needs) scale (P < 0.001) and a negative correlation between IES-R and STAI-Y (P < 0.001). The results confirm that parents of pediatric cancer patients have a high psychological risk for post-traumatic symptoms, high stress levels, and the presence of clinically significant levels of anxiety.

Dynamic Bayesian temporal modeling and forecasting of short-term wind measurements

Abstract We present a new Bayesian modeling approach for joint analysis of wind components and short-term wind prediction. This approach considers a truncated bivariate matrix Bayesian dynamic linear model (TMDLM) that jointly models the u (zonal) and v (meridional) wind components of observed hourly wind speed and direction data. The TMDLM takes into account calm wind observations and provides joint forecasts of hourly wind speed and direction at a given location. The proposed model is compared to alternative empirically-based time series approaches that are often used for short-term wind prediction, including the persistence method (naive predictor), as well as univariate and bivariate ARIMA models. Model performance is measured predictively in terms of mean squared errors associated to 1-h and 24-h ahead forecasts. We show that our approach generally leads to more accurate short term predictions than these alternative approaches in the context of analysis and forecasting of hourly wind measurements in 3 locations in Northern California for winter and summer months.

Detecting chimeras by eigenvalue decomposition of the bivariate local order parameter

It has been shown that the eigenvalue decomposition of the matrix of the bivariate phase synchronization measure can be used for the detection of cluster synchronization. It has also been shown that other measures, such as the strength of incoherence and various local order parameters, can be used to quantitatively characterize chimeras, or chimera states. Here we bridge these two domains by showing that the eigenvalue decomposition method can also be used for the detection of chimeras. We compute the local order parameter for all oscillator pairs and apply the eigenvalue decomposition on the bivariate matrix. We show that, in contrast to cluster synchronization, there are more eigenvalues above one than the number of synchronized clusters in the network. The corresponding eigenvectors correspond to synchronized groups, while the oscillators that are not represented by the eigenvectors form the chimeras. We demonstrate our approach on coupled Liénard equations and FitzHugh-Nagumo neurons.

A Competitive Multiattribute Group Decision-Making Approach for the Game between Manufacturers.

Under the competitive market environment, the game between manufacturers comes down to the competitive multiattribute group decision-making problem. In this study, the evaluation information of experts is given in the form of 2-dimension 2-tuple linguistic variables, and an approach is proposed for the competitive multiattribute group decision-making problem based on game theory and evidence theory. Firstly, based on the evidence theory, the attribute values of each situation are obtained by aggregating the 2-dimension 2-tuple linguistic evaluation information given by experts. Secondly, according to the attribute values of every situation, the evidence theory is applied for the second aggregation to obtain the overall values of every situation, and then the game matrix of competitive multiattribute group decision problem is formed. Then, according to the bivariate game matrix, the Nash equilibrium point of competitive multiattribute group decision-making problem is determined based on game theory. Finally, a practical case about the alternative selections for a duopoly problem is used to illustrate the effectiveness and applicability of the proposed approach for the competitive multiattribute group decision-making problem.

Bivariate Jacobsthal and bivariate Jacobsthal-Lucas matrix polynomial sequences

In this study, we consider sequences named bivariate Jacobsthal, bivariate Jacobsthal Lucas polynomial sequences. After that, by using these sequences, we define bivariate Jacobsthal and bivariate Jacobsthal-Lucas matrix polynomial sequences. Finally we investigate some properties of these sequences, present some important relationship between bivariate Jacobsthal matrix polynomial sequence and bivariate Jacobsthal Lucas matrix polynomial sequences.

Conditioning of the matrix-matrix exponentiation

If A has no eigenvalues on the closed negative real axis, and B is arbitrary square complex, the matrix-matrix exponentiation is defined as A B := e log(A)B . It arises, for instance, in Von Newmann’s quantum-mechanical entropy, which in turn finds applications in other areas of science and engineering. In this paper, we revisit this function and derive new related results. Particular emphasis is devoted to its Frechet derivative and conditioning. We propose a new definition of bivariate matrix function and derive some general results on their Frechet derivatives, which hold, not only to the matrix-matrix exponentiation but also to other known functions, such as means of two matrices, second order Frechet derivatives and some iteration functions arising in matrix iterative methods. The numerical computation of the Frechet derivative is discussed and an algorithm for computing the relative condition number of A B is proposed. Some numerical experiments are included.

Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree

A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares. We show more generally that every nonnegative quadratic form on a real projective variety $X$ of minimal degree is a sum of $\dim(X)+1$ squares of linear forms. This strengthens one direction of a recent result due to Blekherman, Smith, and Velasco. Our upper bound is the best possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares. We determine the number of equivalence classes of sum-of-squares representations of general quadratic forms on surfaces of minimal degree, generalizing the count for ternary quartics by Powers, Reznick, Scheiderer, and Sottile.

The Phase I Dispersion Charts for Bivariate Process Monitoring

Multivariate control charts are usually implemented in statistical process control to monitor several correlated quality characteristics. Process dispersion charts are used to determine the stability of process variation (which is typically done before monitoring the process location/mean). A Phase-I study is generally used when population parameters are unknown. This article develops Phase-I |S| and |G| control charts, to monitor the dispersion of a bivariate normal process. The charting constants are determined to achieve the required nominal false alarm probability (FAP0). The performance of the proposed charts is evaluated in terms of (i) the attained false rate and (ii) the probability of signaling for out-of-control situations. The analysis shows that the proposed Phase-I bivariate charts correctly control the FAP (the false alarm probability) and detect a shift occurring in the bivariate dispersion matrix with adequate probability. An example is given to explain the practical implementation of these charts. Copyright © 2015 John Wiley & Sons, Ltd.

Maintaining the integrity of sources in complex learning systems: intraference and the correlation preserving transform.

The correlation preserving transform (CPT) is introduced to perform bivariate component analysis via decorrelating matrix decompositions, while at the same time preserving the integrity of original bivariate sources. Specifically, unlike existing bivariate uncorrelating matrix decomposition techniques, CPT is designed to preserve both the order of the data channels within every bivariate source and their mutual correlation properties. We introduce the notion of intraference to quantify the effects of interchannel mixing artifacts within recovered bivariate sources, and show that the integrity of separated sources is compromised when not accounting for the intrinsic correlations within bivariate sources, as is the case with current bivariate matrix decompositions. The CPT is based on augmented complex statistics and involves finding the correct conjugate eigenvectors associated with the pseudocovariance matrix, making it possible to maintain the physical meaning of the separated sources. The benefits of CPT are illustrated in the source separation and clustering scenarios, for both synthetic and real-world data.

SPIKY: A graphical user interface for tracking spike train similarity

Modern electrophysiology is developing fast and it sometimes provides more data than available algorithms and methods can handle and process. In particular, there is an increasing demand for methods which provide the possibility to study similarity patterns of activity across many neurons. Accordingly, a wide variety of approaches to quantify the similarity (or dissimilarity) between two or more spike trains has been suggested. Recently, the ISI- and the SPIKE-distance [1,2] have been proposed as parameter-free and time-scale independent measures of spike train synchrony. The key property of both measures is that they are time-resolved since they rely on instantaneous estimates of spike train dissimilarity. This makes it possible to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. The SPIKE-distance also comes in a causal variant [2] which is defined such that the instantaneous values of dissimilarity are defined from past information only so that time-resolved spike train synchrony can be estimated in real-time. For both the regular and the real-time SPIKE-distance, there are several levels of information reduction [3]. The starting point is the most detailed representation in which one instantaneous value is obtained for each pair of spike trains. This results in a matrix of size ’number of sampled time instants’ × ’squared number of spike trains’ (i.e. #(tn)N2). By selecting a pair of spike trains one obtains a bivariate dissimilarity profile whereas the selection of a time instant yields an instantaneous matrix of pairwise spike train dissimilarities which can be used to divide the spike trains into instantaneous clusters, i.e., groups of spike trains with low intra-group and high inter-group dissimilarity. Another way to reduce the information is averaging. The spatial average over spike train pairs yields a dissimilarity profile for the selected (sub)population, whereas temporal averaging leads to a bivariate distance matrix for the selected interval or the selected trigger points. Finally, application of the remaining average results in one distance value which describes the overall level of synchrony for a group of spike trains over a given time interval. The Matlab source codes for calculating and visualizing both the ISI- and the SPIKE-distance have been made publicly available and have already been widely used in various contexts. However, the use of these codes is not very intuitive and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and accessible interface. Here we address this need and present an advanced version of the graphical user interface SPIKY [4,5]. This interactive program facilitates the application of the ISI- and the SPIKE-distance to both simulated and real data. Once given a set of spike train data (importable from many different formats), SPIKY calculates the desired measure and allows visualization of different representations such as measure profiles and pairwise dissimilarity matrices. SPIKY also includes the possibility to generate movies which are very useful in order to track the varying patterns of (dis)similarity. Finally, SPIKY has been optimized with respect to both computation speed (by using MEX-files, i.e. C-based Matlab executables) and memory demand (by taking advantage of the piecewise linear nature of the dissimilarity profiles).

Linearization of bivariate polynomial matrices expressed in non monomial basis

The paper proposes a two step algorithm that reduces a bivariate polynomial matrix $$T\left( s,z\right) $$ T s , z expressed in Newton or Lagrange base to a bivariate matrix pencil $$A+E_{1}s+E_{2}z$$ A + E 1 s + E 2 z with the same invariant polynomials and zero structure.

Bivariate matrix functions

A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing results on linear matrix equations and derivatives of matrix functions.

A Bivariate Matrix Padé-Type Method of the 2-D Filters

In this paper,according to the special generating polynomial, a class of bivariate matrix Padé-type approximation (BMPTA) is given by introducing a bivariate matrix-valued linear functional on the scalar polynomial space.An application in state-space realization of the 2-D filters is also given in the end.

SPIKY: a graphical user interface for monitoring spike train synchrony

With the growing availability of multi-unit recordings there is increasing demand for methods which provide the possibility to study similarity patterns of activity across many neurons. Accordingly, a wide variety of approaches to quantify the similarity (or dissimilarity) between two or more spike trains has been suggested. Recently, the ISI- and the SPIKE-distance [1,2] have been proposed as parameter-free and time-scale independent measures of spike train synchrony. The key property of both measures is that they are time-resolved since they rely on instantaneous estimates of spike train dissimilarity. This makes it possible to track changes in instantaneous clustering, i.e., time-localized patterns of (dis)similarity among multiple spike trains. The SPIKE-distance also comes in a causal variant [2] which is defined such that the instantaneous values of dissimilarity are defined from past information only so that time-resolved spike train synchrony can be estimated in real-time. For both the regular and the real-time SPIKE-distance, there are several levels of information reduction [3]. The starting point is the most detailed representation in which one instantaneous value is obtained for each pair of spike trains. This results in a matrix of size 'number of sampled time instants' × 'squared number of spike trains' (i.e. #(tn)N2). By selecting a pair of spike trains one obtains a bivariate dissimilarity profile whereas the selection of a time instant yields an instantaneous matrix of pairwise spike train dissimilarities which can be used to divide the spike trains into instantaneous clusters, i.e., groups of spike trains with low intra-group and high inter-group dissimilarity. Another way to reduce the information is averaging. The spatial average over spike train pairs yields a dissimilarity profile for the selected (sub)population, whereas temporal averaging leads to a bivariate distance matrix for the selected interval or the selected trigger points. Finally, application of the remaining average results in one distance value which describes the overall level of synchrony for a group of spike trains over a given time interval. The Matlab source codes for calculating and visualizing both the ISI- and the SPIKE-distance have been made publicly available and have already been widely used in various contexts. However, the use of these codes is not very intuitive and their application requires some basic knowledge of Matlab. Thus it became desirable to provide a more user-friendly and accessible interface. Here we address this need and present the graphical user interface SPIKY [4,5]. This interactive program facilitates the application of the ISI- and the SPIKE-distance to both simulated and real data. SPIKY includes a spike train generator for testing purposes, as well as masks for selecting the analysis window and the neuronal subpopulation of interest. Once given a set of spike train data, it calculates the desired measure and allows visualization of all the different representations mentioned above (such as measure profiles and pairwise dissimilarity matrices). It even includes the possibility to generate movies which are very useful in order to track the varying patterns of (dis)similarity. Finally, we also have increased the high computation speed even further by transferring the most time-consuming parts of the original Matlab code to Matlab executables (MEX) with the new subroutines written in C.

On stabilisability of 2-D MIMO shift-invariant systems

We concentrate on the linear spatially distributed time-invariant two-dimensional systems with multiple inputs and multiple outputs and with control action based on an array of sensors and actuators connected to the system. The system is described by the bivariate matrix polynomial fraction. Stabilisation of such systems is based on the relationship between stability of a bivariate polynomial and positiveness of a related polynomial matrix on the unit circle. Such matrices are not linear in the controller parameters, however, in simple cases, a linearising factorisation exists. It allows to describe the control design in the form of a linear matrix inequality. In more complicated cases, linear sufficient conditions are given. This concept is applied to a system with multiple outputs—a heat conduction in a long thin metal rod equipped with an array of temperature sensors and heaters, where heaters are placed in larger distances than sensors.

A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the form motivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are based on the generalized inverse for a matrix which is introduced by C. Gu the author of this paper, and it is effective in continued fraction interpolation. The algorithm and some other important conclusions such as divisibility and characterization are given. In the end, two examples are also given to show the effectiveness of the algorithm. The numerical results of the second example show that the algorithm of this paper is better than the method of Thieletype matrix-valued rational interpolant in Gu (1997).

New results on multivariate polynomial matrix factorizations

Multivariate (n-D) polynomial matrix factorizations are basic research problems in multidimensional systems and signal processing. In this paper several extensions of the existing results on multivariate matrix factorizations are proved. Moreover, by means of the general theory of multivariate matrix factorizations recently developed, a new proof is given to the bivariate polynomial matrix factorizations. This new approach produces also a recursive algorithm for the actual computation of the general bivariate matrix factorizations, which relies on the algorithm of the Gröbner bases for modules and does not involve calculations over the function fields.

An effective hybrid algorithm for computing symbolic determinants

A hybrid algorithm for computing the determinant of a matrix whose entries are polynomials is presented. It is based on the dimension-decreasing algorithm [22] and the parallel algorithm for computing a symbolic determinant of [19]. First, through the dimension-decreasing algorithm, a given multivariate matrix can be converted to a bivariate matrix. Then, the parallel algorithm can be applied to effectively compute the determinant of the bivariate matrix. Experimental results show that the new algorithm can not only reduce enormously the intermediate expression swell in the process of symbolic computation, but also achieve higher degree of parallelism, compared with the single parallel algorithm given in [19].

Generalized Homogeneous Multivariate Matrix PadÉ-Type Approximants and PadÉ Approximants

Generalized homogeneous multivariate matrix Pade-type approximants (GHMPTA) and Pade approximants are studied in ways similar to those of Brezinski and Kida in the scalar cases. By choosing an arbitrary monic bivariate scalar polynomial from the triangular form as the generating one of the approximant, we discuss their several typical important properties and study the connection between generalized homogeneous bivariate matrix Pade-type approximants and Pade approximants. The arguments given in detail in two variables can be extended directly to the case of d variables (d ges 2).