Coefficient Vector Research Articles

Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using lepton+jets events from proton-proton collisions at s=13 TeV

Measurements of the polarization and spin correlation in top quark pairs (tt¯) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data from the LHC at s=13 TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb−1. All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed inclusively and in bins of additional observables, such as the mass of the tt¯ system and the top quark scattering angle in the tt¯ rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the tt¯ spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for tt¯ states at the production threshold and at high masses of the tt¯ system. Entanglement is observed for the first time in events at high tt¯ mass, where a large fraction of the tt¯ decays are spacelike separated, with an expected and observed significance of above 5 standard deviations. © 2024 CERN, for the CMS Collaboration 2024 CERN

OPTIMIZATION OF THE SCATTERING MATRIX OF FREQUENCY -DETUNED ADD/DROP FILTERS FOR MULTIPLEXERS BUILT ON SYSTEMS OF OPTICAL DIELECTRIC RESONATORS WITH WHISPERING GALLERY MODES

Background. A significant increase in the speed of information transmission in fiber-optic communication networks is determined by the strict requirements imposed on the elemental base of receiving and transmitting devices. One of the important components of such devices is diplexers built on different notch and bandpass filters, which are often performed on dielectric resonators (DR) with whispering gallery mode (WGM) oscillations. Calculation and optimization of the parameters of multilink filters and diplexers built on DR is impossible without further development of the theory of their design. The development of the theory of diplexers today is often based on electrodynamic modelling, which is built on preliminary calculations of filter scattering parameters in various transmission lines with a complex topology of connections. Objective. The aim of this study is to construct electrodynamics' models of wave scattering on complex multi-connected DR structures with degenerate types of WGM natural oscillations, which contain several frequency-detuned bandpass or notch filters located in one or several transmission lines. To solve the scattering problem, we proposed a system of equations derived from perturbation theory for Maxwell's equations [24], modified to describe the DR fields with whispering gallery oscillations in transmission lines. The construction of such solutions is complicated by the fact that each of the partial optical resonators of the filters, in the case of excitation of azimuthally inhomogeneous WGM in it, has, as a rule, two degenerate types of natural oscillations. Moreover, each such type of oscillation is characterized by different complex values of the coupling coefficients with the line, open space, and also with other resonators. The latter circumstance leads to the fact that the systems of equations for the amplitudes of natural and forced oscillations of resonators are doubled. The signs of the coefficients of mutual coupling are usually different, this leads to the fact that the behaviour of DRs in the system becomes more difficult to predict, therefore the second objective of this work is to study the patterns of the scattering characteristics of line waves on systems of frequency-detuned DRs with degenerate types of oscillations with the possibility of constructing multiplexers for modern optical communication systems. Methods. The methods of technical electrodynamics are used for calculating and analysing scattering matrices. The end result is obtaining new analytical equations and formulas for new complex structures of coupled dielectric resonators with whispering gallery oscillations in the different transmission lines. Results. Frequency dependences of scattering matrices on complex structures of frequency-detuned filters built on coupled optical DR with whispering gallery oscillations located in one or more transmission lines are considered. Electromagnetic models of bandstop and add/drop filters are built, consisting of various optical resonators with degenerate types of natural oscillations. General analytical expressions of vector coefficients and matrices for building systems of equations describing coupled oscillations, as well as forced oscillations of resonators in cases of their use in optical filters with serial and parallel arrangement, are given. General solutions for the scattering field on frequency-detuned resonators located in different optical transmission lines have been found. Examples of calculating frequency dependences of the scattering matrix for the most interesting structures consisting of two different frequency-detuned filters are given. The frequency scattering characteristics of several types of devices are calculated, which consist of two notch filters with different blocking bands, made on detuned DRs in one transmission line. The possibilities of the earlier proposed method are demonstrated in the example of calculating the scattering characteristics of known types of diplexers built on the basis of the use of two add/drop filters with different frequency bandwidths. The frequency dependences of the scattering matrices of the two most common types of devices, located in parallel between two or four regular transmission lines of add/drop filters with different numbers of resonators; laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel side-coupled integrated space sequence of resonators (SCISSORs), were studied. New scattering models of diplexers consisting of optical resonators of different connection topologies were built: serial, parallel with the use of laterally coupled add/drop filters; parallel-coupled add/drop filters; twisted double-channel SCISSORs. The frequency dependences scattering matrix of the diplexers were also calculated. The characteristics of the designed diplexers obtained from the examined filters of different types were compared. Conclusions. The theory of diplexer construction, which takes place on the simultaneous optimization of the scattering matrix of several filters built on complex systems of dielectric resonators with degenerate types of whispering gallery oscillations is expanded. A calculation method was developed and new analytical relations were found for the scattering matrix coefficients of optical diplexers of various types.

General Expression of Best Equivariant Estimators of Regression Coefficients in Seemingly Unrelated Regression Models

ABSTRACTSeemingly unrelated regression models have been commonly employed as regression models with multiple explanatory variables and multiple response variables having cross‐correlations. This paper discusses equivariant estimation of the regression coefficient vector and derives the best equivariant estimator under a generalized quadratic loss function. The result of this paper is shown to include the results of previous best equivariant estimators under specific loss functions as special cases.

MANAGEMENT OF INFORMATION EXCHANGE IN WIRELESS SENSOR NETWORKS USING MOBILE AGENTS

The proposed method provides a simple search for the optimal number of routes with energy consumption constraints, as well as minimization of traffic in the network. The delivery speed is regulated by applying controlled Markov processes under the constraints on the required energy consumption of the sensors. When controlled by mobile agents, energy costs for data delivery are reduced, which is especially important for sensor networks with non-renewable energy sources. The control problem is to optimally determine the wear coefficient vector and the diffusion coefficient matrix, which minimize the traffic volume with a limit on energy consumption and taking into account the asymmetry of the communication quality between consecutive nodes.

A Small Sigma Asymptomatic Approach Generalized Quasi Minimax and Mock Minimax Estimators in Linear Regression Model

In this paper concern with priority two generalized classes of estimators utilizing both types of information apriori and sample, for the estimation of coefficient vector in classical linear regression model in the presence of ellipsoidal Constraints on the parameter vector when the variance of the distribution are unknown. A vectors mean square matrices and weighted quadratic risk are found employing small sigma asymptotic. Some better estimators in the sense of having lesser risk than those of the estimators.

A reduced-dimension method of Crank-Nicolson finite element solution coefficient vectors for the unsteady Burgers equation

This paper primarily focuses on the dimensionality reduction of finite element (FE) solution coefficient vectors for the unsteady Burgers equation, solved using the Crank-Nicolson FE (CNFE) method. The proper orthogonal decomposition (POD) basis is constructed from the snapshot matrix, which is formed using the first L solutions, where L is significantly smaller than the total number of time steps N of the CNFE method. By reconstructing the matrix form of the CNFE method, a reduced-dimension Crank-Nicolson finite element (RDCNFE) method is proposed and stability analysis and error estimates are discussed. Numerical tests are implemented to verify the theoretical results and demonstrate the high efficiency of the RDCNFE method.

A novel dimension reduction model based on POD and two-grid Crank–Nicolson mixed finite element methods for 3D nonlinear elastodynamic sine–Gordon problem

Earthquake, petroleum and gas extraction, and underground nuclear test all could cause nonlinear tectonic deformation. It is of great significance to effectively predict and evaluate the disasters and impacts of these geological structure deformation. In this end, a three-dimension (3D) nonlinear elastodynamic sine–Gordon model that can be used to describe nonlinear tectonic deformation including 3D displacement vector, 3 × 3 symmetric stress tensor matrix, nonlinear sin term, and singular initial value functions is first proposed. Then, a new time semi-discrete mixed Crank–Nicolson (TSDMCN) scheme for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TSDMCN solutions are proved. Next, a new two-grid mixed finite element Crank–Nicolson (TGMFECN) method with unconditional stability for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TGMFECN solutions are proved. Thenceforth, it is the most important thing is that a novel reduced-dimensional iterative TGMFECN (RDITGMFECN) method in matrix form is established by resorting to proper orthogonal decomposition only to lower the unknown TGMFECN solution coefficient vectors and keep TGMFECN basis functions unchanged, which can ensure that the RDITGMFECN method has the same accuracy as the usual TGMFECN method, but can greatly lower the dimension of the unknown TGMFECN solution coefficient vectors so as to mitigate calculated workload, save CPU operating-time, improve computing efficiency, and improve real-time calculating accuracy. In theory, the existence, stability, and error estimates of RDITGMFECN solutions are demonstrated by matrix analysis such that the theoretical analysis becomes very intuitive and easy to be understood by the public, which is a new attempt of theoretical analysis. In application, two numerical examples are used to simulate the 3D nonlinear tectonic deformation caused by earthquake and to verify the correctness of our theoretical results and the effectiveness of the RDITGMFECN method.

Two-grid reduced-dimension extrapolated method of Crank-Nicolson finite element solution coefficient vectors for nonlinear parabolic equation

Two-grid reduced-dimension extrapolated method of Crank-Nicolson finite element solution coefficient vectors for nonlinear parabolic equation

Global and local identifiability analysis of a nonlinear biphasic constitutive model in confined compression.

Application of biomechanical models relies on model parameters estimated from experimental data. Parameter non-identifiability, when the same model output can be produced by many sets of parameter values, introduces severe errors yet has received relatively little attention in biomechanics and is subtle enough to remain unnoticed in the absence of deliberate verification. The present work develops a global identifiability analysis method in which cluster analysis and singular value decomposition are applied to vectors of parameter-output variable correlation coefficients. This method provides a visual representation of which specific experimental design elements are beneficial or harmful in terms of parameter identifiability, supporting the correction of deficiencies in the test protocol prior to testing physical specimens. The method was applied to a representative nonlinear biphasic model for cartilaginous tissue, demonstrating that confined compression data does not provide identifiability for the biphasic model parameters. This result was confirmed by two independent analyses: local analysis of the Hessian of a sum-of-squares error cost function and observation of the behaviour of two optimization algorithms. Therefore, confined compression data are insufficient for the calibration of general-purpose biphasic models. Identifiability analysis by these or other methods is strongly recommended when planning future experiments.

The Reduced-Dimension Method for Crank–Nicolson Mixed Finite Element Solution Coefficient Vectors of the Extended Fisher–Kolmogorov Equation

A reduced-dimension (RD) method based on the proper orthogonal decomposition (POD) technology and the linearized Crank–Nicolson mixed finite element (CNMFE) scheme for solving the 2D nonlinear extended Fisher–Kolmogorov (EFK) equation is proposed. The method reduces CPU runtime and error accumulation by reducing the dimension of the unknown CNMFE solution coefficient vectors. For this purpose, the CNMFE scheme of the above EFK equation is established, and the uniqueness, stability and convergence of the CNMFE solutions are discussed. Subsequently, the matrix-based RDCNMFE scheme is derived by applying the POD method. Furthermore, the uniqueness, stability and error estimates of the linearized RDCNMFE solution are proved. Finally, numerical experiments are carried out to validate the theoretical findings. In addition, we contrast the RDCNMFE method with the CNMFE method, highlighting the advantages of the dimensionality reduction method.

Robust multi-outcome regression with correlated covariate blocks using fused LAD-lasso

Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust fused LAD-lasso method for multiple outcomes is presented that addresses the challenges of non-normal outcome distributions and outlying observations. Measured covariate data from space or time, or spectral bands or genomic positions often have natural correlation structure arising from measuring distance between the covariates. The proposed multi-outcome approach includes handling of such covariate blocks by a group fusion penalty, which encourages similarity between neighboring regression coefficient vectors by penalizing their differences, for example, in sequential data situation. Properties of the proposed approach are illustrated by extensive simulations using BIC-type criteria for model selection. The method is also applied to a real-life skewed data on retirement behavior with longitudinal heteroscedastic explanatory variables.

Wind Speed Modeling under Quasi‐Linear Autoregressive Neural Network Model for Prediction of Production Power

Accurate wind speed modeling is beneficial for the design of wind energy conversion systems. Models of wind speed are used to assess the adequacy and dependability of a power supply. However, precise wind speed modeling is challenging due to the sporadic availability of wind speed. In this note, we propose a wind speed model with an autoregressive (AR) structure. A hybrid model is developed under linear and nonlinear parts based on a quasi‐linear autoregressive exogenous neural network (Q‐ARX‐NN). The model's structure is composed of a regression vector and its coefficients. The coefficients are divided into linear and nonlinear coefficients. A set of linear coefficients is identified under the algorithm of least square error (LSE), and a set of nonlinear coefficients is modeled by using a neural network to refine the residual error of the nonlinear part. Some artificial neural network (ANN) models can be set as nonlinear part sub‐models to sharpen the model's accuracy. The proposed model is tested for wind speed modeling to estimate wind energy production. Various nonlinear parts of the sub‐model are tested, such as neural networks, radial basis function networks, and ANN networks. Moreover, we evaluate the effects of the order of the model by varying hidden and output nodes, which can be summarized as the number of coefficients of the regression vector. Using specific wind turbine performance data, prediction models estimate production power. © 2024 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A novel dimensionality reduction iterative method for the unknown coefficient vectors in TGFECN solutions of unsaturated soil water flow problem

The main purpose of this paper is to reduce the dimensionality of unknown coefficient vectors in finite element (FE) solutions of two-grid FE Crank-Nicolson (CN) (TGFECN) format for the unsaturated soil water flow (USWF) problem with two strong nonlinear terms by using proper orthogonal decomposition (POD). For this purpose, our first step involves designing a time semi-discrete CN (TSDCN) scheme for the USWF problem and demonstrate the existence, boundedness, and error estimations of TSDCN solutions. Thereafter, we discretize the TSDCN scheme using the two-grid FE method to create a new TGFECN format and prove the existence, boundedness, and error estimations of TGFECN solutions. The primary focus should be on reducing the dimension of unknown coefficient vectors of TGFECN solutions through the utilization of the POD technique in creating a novel format, referred to as dimension reduction iterative TGFECN (DRITGFECN) format, while establishing the existence, boundedness, and error estimations for DRITGFECN solutions. Lastly, we use two sets of numerical tests to exhibit the advantage of the DRITGFECN format. Due to the presence of two highly nonlinear terms in the unsaturated soil flow problem, the development and analysis of DRITGFECN format pose greater challenges and necessitates more advanced technical skills compared to previous studies. However, the significance and broad applications of this research make it a valuable subject for investigation.

Finite-frequency model order reduction of linear and bilinear systems via low-rank approximation

In this paper, we first investigate the finite-frequency model order reduction for linear systems based on low-rank Gramian approximations. An efficient algorithm for computing low-rank approximations of the finite-frequency and frequency-dependent Gramians based on Laguerre functions is proposed. The approach constructs the low-rank decomposition factors of the finite-frequency Gramians or frequency-dependent Gramians through a recursive formula of Laguerre functions expansion coefficient vectors and then combines the low-rank square root method and frequency-dependent balanced truncation method to obtain the reduced-order models. In this process, it avoids dealing with the matrix-valued functions and solving the related (generalized) Lyapunov matrix equations directly, making them computationally efficient. Furthermore, the above method is successfully extended to bilinear systems, and a corresponding efficient computation method for low-rank approximations of the finite-frequency Gramians of bilinear systems is derived. Finally, some numerical simulations are provided to illustrate the effectiveness of our proposed algorithms.

Statistically optimal firstorder algorithms: a proof via orthogonalization

Abstract We consider a class of statistical estimation problems in which we are given a random data matrix ${\boldsymbol{X}}\in{\mathbb{R}}^{n\times d}$ (and possibly some labels ${\boldsymbol{y}}\in{\mathbb{R}}^{n}$) and would like to estimate a coefficient vector ${\boldsymbol{\theta }}\in{\mathbb{R}}^{d}$ (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g. sparse regression). Firstorder methods proceed by iteratively multiplying current estimates by ${\boldsymbol{X}}$ or its transpose. Examples include gradient descent or its accelerated variants. Under the assumption that the data matrix ${\boldsymbol{X}}$ is standard Gaussian, Celentano, Montanari, Wu (2020, Conference on Learning Theory, pp. 1078–1141. PMLR) proved that for any constant number of iterations (matrix vector multiplications), the optimal firstorder algorithm is a specific approximate message passing algorithm (known as ‘Bayes AMP’). The error of this estimator can be characterized in the high-dimensional asymptotics $n,d\to \infty $, $n/d\to \delta $, and provides a lower bound to the estimation error of any firstorder algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of firstorder algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof is simpler, does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications.

Can stronger governance and institutional quality drive growth through inward foreign direct investments in BRICS nations?

Background: This research focusses on the significance of institutional quality (INSQ) and governance in shaping the relationship between foreign direct investments (FDI) and growth. It specifically examines the BRICS nations (Brazil, Russia, India, China and South Africa) because of their economic significance in the global economy.Aim: This study aims to analyse the impact of INSQ and governance on sustainable growth, with a particular focus on its effects through the channels of FDI in the BRICS countries.Setting: Annual panel data from the Organisation for Economic Cooperation and Development (OECD) statistics, the United Nations Conference on Trade and Development (UNCTAD) statistics and the World Bank indicators spanning two decades (2000–2022) are used to analyse BRICS nations.Methods: The research study employed the Bayesian time-varying coefficient vector autoregression (BTVC-VAR) model to achieve the objective of the study.Results: The findings indicate that there is no long-term relationship between FDI, INSQ and economic growth in the BRICS countries. However, there is a noticeable co-movement among these variables in the short run.Conclusion: Given the obtained results, the policymakers should prioritise efforts to strengthen institutional capacity in the short term while focussing on the Sustainable Development Goals (SDG-8 and SDG-16).Contribution: The existing studies have assumed static economic, social and political conditions, potentially failing to accurately depict the complexities of an actual economy. This study offers methodological innovation by employing Bayesian time-varying coefficient vector autoregression (BTVC-VAR), enabling coefficients to adapt to evolving economic conditions over time. This effectively captures the dynamic nature of variables and provides reliable estimates.

Wavelet-based convolutional neural network for non-intrusive load monitoring of next generation shipboard Power Systems

In this study, a non-intrusive load monitoring (NILM) framework is developed for next generation shipboard power systems (SPS) based on a discrete wavelet transform signal processing and a convolutional neural network (CNN). We have applied the developed NILM method to a four-zone medium voltage direct current (MVDC) SPS to evaluate the effectiveness of the proposed method. Each zone of the MVDC SPS consists of multiple components, such as propulsion load, pulsed load, high ramp rate load, cooling load, and hotel load. The current signals from the main generators are the main inputs to the NILM model. The current signals are first processed through a discrete wavelet transform to create a coefficient vector that reflects the status of all the components in each zone. Then, a multi-class classification problem is formulated and solved using a CNN architecture model to monitor the load statuses in real time. The results of case studies show that the developed NILM model in comparison with benchmark methods can (i) accurately monitor the status of all components with a total accuracy of over 98%, (ii) identify unique pulsed loads with a total accuracy of over 99%, and (iii) sustain the functionality of load monitoring under extreme events such as cyber/physical attacks, load uncertainty, and noisy inputs.

Drone Swarm Robust Cooperative Formation Pursuit through Relative Positioning in a Location Denial Environment

This paper considers the pursuit problem of a moving target by a swarm of drones through a flexible-configuration formation. The drones are modeled by second-order systems subject to uncertain damping ratios, whereas the moving target follows a polynomial-type trajectory whose coefficient vectors are fully unknown. Due to location denial, drones cannot obtain their absolute positions, but they can obtain their positions relative to other neighboring drones and the target. To achieve a robust formation pursuit, a robust cooperative control protocol is synthesized, which comprises three key components, namely, the pseudo drone position estimator, the pseudo target position estimator, and the local internal model control (IMC) law. The pseudo drone position estimator and the pseudo target position estimator aim to recover for each drone the position of itself and the target, respectively, but are subject to some common unknown constant bias in a distributed manner. By subtracting the pseudo target position from the pseudo drone position, each drone can acquire its position relative to the target, which facilitates the design of a local IMC law to fulfill formation pursuit in the presence of system parametric uncertainties. Both pure numerical simulation and hardware-in-the-loop (HIL) simulation are performed to verify the effectiveness of the proposed control protocol.

Performance analysis of unconstrained partitioned-block frequency-domain adaptive filters in under-modeling scenarios

The unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) offers superior computational efficiency over its constrained counterpart. However, the correlation matrix governing the natural modes of the unconstrained PBFDAF is not full rank. Consequently, the mean coefficient behavior of the algorithm depends on the initialization of adaptive coefficients and the Wiener solution is non-unique. To address the above problems, a new theoretical model for the deficient-length unconstrained PBFDAF is proposed by constructing a modified filter weight vector within a system identification framework. Specifically, we analyze the transient and steady-state convergence behavior. Our analysis reveals that modified weight vector is independent of its initialization in the steady state. The deficient-length unconstrained PBFDAF converges to a unique Wiener solution, which does not match the true impulse response of the unknown plant. However, the unconstrained PBFDAF can recover more coefficients of the parameter vector of the unknown system than the constrained PBFDAF in certain cases. Also, the modified filter coefficient yields better mean square deviation (MSD) performance than previously assumed. The presented alternative performance analysis provides new insight into convergence properties of the deficient-length unconstrained PBFDAF. Simulations validate the analysis based on the proposed theoretical model.

Temporal dominance of Sensations: Do different concepts of “dominance” affect the results?

The purpose of this study was to understand the role of “dominance” definitions in the results of TDS applied to consumers. This study compared two temporal dominance of sensations (TDS) approaches − TDS-I − that attracts the most attention and TDS-II − most intense/strongest sensation − in the context of evaluating artisanal Minas cheeses from the Serra da Canastra and chocolate with different cocoa concentrations samples. TDS curves were constructed and a trajectory-based principal component analysis (PCA) was performed dominance rates at ten equally spaced time points. Additionally, difference curves, multiple factor analysis (MFA) and regression vector coefficient (RV coefficient) were performed to compare the two approaches. The findings showed that the two approaches produced similar results, suggesting that consumers interpret the terms dominant and intense in a similar way during TDS evaluations, the results were even closer at the chocolate study than at the cheese study. However, in both approaches were observed low dominance rates and differences between the sensation perception time, mainly in the evaluation of cheese flavor. This variability may be attributed to the complexity of the cheese’s flavor and the varied interpretations of dominance among evaluators. Despite these differences, the approaches showed similar characterizations across the same samples, demonstrating high reproducibility and a strong ability to differentiate between samples. This study demonstrates that the choice between the terms dominant (which captures more attention) or intense (stronger) to guide consumers in performing the sensory test does not significantly influence the results. Consequently, it is possible to adopt greater freedom and flexibility in the terminology used to instruct participants in conducting the test.