Minimum Trace Research Articles

Numerical investigation of the role of masonry typology on shear strength

The force-displacement behavior of masonry elements depends on the properties of their constituents, mortar and unit, as well as on their typology, i.e., the shape and size of the units and the patterns they generate. Up until now, only few numerical studies investigated the influence of the masonry typology on the mechanical properties of the masonry. The lack of research is caused by both the difficulty of generating specific stone masonry typologies, which vary depending on geographical regions, construction periods, and building technology, and the difficulty of conducting detailed micro-modeling analyses. Building on our recent developments of a typology generator and a detailed micro-modeling method based on cohesive elements, we investigate the relation between masonry typology and maximum shear resistance. After calibration of the model for shear-compression tests, the study examines the validity of Mann and Müller’s theory at the nonlinear stage, clarifies the role of the line of minimum trace in characterizing effective interlocking, and investigates the correlation of maximum shear resistance with various indexes. We show that the effect of the interlocking between units on the shear strength is overestimated by the Mann-Müller model. This study provides a fundamental contribution to our understanding of the influence of masonry typology on the masonry shear strength.

Assessing the Performance of Hierarchical Forecasting Methods on the Retail Sector.

Retailers need demand forecasts at different levels of aggregation in order to support a variety of decisions along the supply chain. To ensure aligned decision-making across the hierarchy, it is essential that forecasts at the most disaggregated level add up to forecasts at the aggregate levels above. It is not clear if these aggregate forecasts should be generated independently or by using an hierarchical forecasting method that ensures coherent decision-making at the different levels but does not guarantee, at least, the same accuracy. To give guidelines on this issue, our empirical study investigates the relative performance of independent and reconciled forecasting approaches, using real data from a Portuguese retailer. We consider two alternative forecasting model families for generating the base forecasts; namely, state space models and ARIMA. Appropriate models from both families are chosen for each time-series by minimising the bias-corrected Akaike information criteria. The results show significant improvements in forecast accuracy, providing valuable information to support management decisions. It is clear that reconciled forecasts using the Minimum Trace Shrinkage estimator (MinT-Shrink) generally improve on the accuracy of the ARIMA base forecasts for all levels and for the complete hierarchy, across all forecast horizons. The accuracy gains generally increase with the horizon, varying between 1.7% and 3.7% for the complete hierarchy. It is also evident that the gains in forecast accuracy are more substantial at the higher levels of aggregation, which means that the information about the individual dynamics of the series, which was lost due to aggregation, is brought back again from the lower levels of aggregation to the higher levels by the reconciliation process, substantially improving the forecast accuracy over the base forecasts.

Controlled tracking in urban terrain: Closing the loop

AbstractWe investigate the challenging problem of integrating detection, signal processing, target tracking, and adaptive waveform scheduling with lookahead in urban terrain. We propose a closed‐loop active sensing system to address this problem by exploiting three distinct levels of diversity: (1) spatial diversity through the use of coordinated multistatic radars; (2) waveform diversity by adaptively scheduling the transmitted waveform; and (3) motion model diversity by using a bank of parallel filters matched to different motion models. Specifically, at every radar scan, the waveform that yields the minimum trace of the one‐step‐ahead error covariance matrix is transmitted; the received signal goes through a matched‐filter, and curve fitting is used to extract range and range‐rate measurements that feed the LMIPDA‐VSIMM algorithm for data association and filtering. Monte Carlo simulations demonstrate the effectiveness of the proposed system in an urban scenario contaminated by dense and uneven clutter, strong multipath, and limited line‐of‐sight.

On equivalence of major relaxation methods for minimum ellipsoid covering intersection of ellipsoids

This paper investigates the problem on the minimum trace or volume ellipsoid covering intersection of ellipsoids. This problem can be solved by three major relaxation methods involving semi-definite programming relaxation, S-procedure relaxation and parameterized bounding ellipsoid relaxation. They are proposed from the different ideas or viewpoints, so that it is difficult to judge which relaxation method is the most suitable for the different practical implementations. To the best of our knowledge, the problem of proving the convexity of the optimization problem derived by the third relaxation method remains open. By rigorous analysis, we reveal the equivalence among the three relaxation methods, and address the open problem, i.e., the optimization problem derived by the third relaxation method can be equivalently transformed to a convex optimization problem. The computation complexity of these relaxation methods are also discussed, and the equivalent result is helpful to set membership filter and multisensor fusion obtaining a tighter ellipsoid to contain the state with lower computation complexity. Finally, the performance of each method is evaluated by several typical numerical examples in information fusion and filtering.

Evaluation of the Antibacterial Effect of Ethanol and Ethyl Acetate Extracts of Myrtus communis Against Antibiotic-Resistant Pseudomonas aeruginosa

Background: Pseudomonas aeruginosa is a human and plant pathogen. The aim of this study was to investigate the antibacterial effects of ethanol and ethyl acetate extracts of Myrtus communis against antibiotic-resistant P. aeruginosa isolates. Methods: The plant was collected from the plains of Kerman province, and its ethanol and ethyl acetate extracts were prepared using a rotary machine. Pseudomonas aeruginosa strains were isolated from urine and blood samples of patients in Zabol, Iran. Antibiotic resistance pattern was determined by the agar diffusion method. Finally, the minimum inhibitory concentration (MIC) and minimum trace concentration (MTC) were determined by the microdilution method. Results: The antibiotic-resistance patterns of the standard and clinical strains showed that P. aeruginosa was resistant to all antibiotics at the following rates: Azithromycin (25%), ampicillin (12.5%), gentamycin (0%), amoxi-clav (12.5%), cefazolin (12%), and amikacin (12.5%). The study of the effect of ethanol extract on clinical and standard P. aeruginosa strains showed that the MIC of the ethanolic extract against the standard strain of P. aeruginosa was 25 ppm. Conclusions: The results of this study showed good antimicrobial effects of the plant extracts against antibiotic-resistant P. aeruginosa, which can be used to treat Pseudomonas infections.

Distributed Set-Membership Filtering for Multirate Systems Under the Round-Robin Scheduling Over Sensor Networks.

In this paper, the distributed set-membership filtering problem is dealt with for a class of time-varying multirate systems in sensor networks with the communication protocol. For relieving the communication burden, the round-Robin (RR) protocol is exploited to orchestrate the transmission order, under which each sensor node only broadcasts partial information to both the corresponding local filter and its neighboring nodes. In order to meet the practical transmission requirements as well as reduce communication cost, the multirate strategy is proposed to govern the sampling/update rate of the plant, the sensors, and the filters. By means of the lifting technique, the augmented filtering error system is established with a unified sampling rate. The main purpose of the addressed filtering problem is to design a set of distributed filters such that, in the simultaneous presence of the RR transmission protocol, the multirate mechanism, and the bounded noises, there exists a certain ellipsoid that includes all possible error states at each time instant. Then, the desired distributed filter gains are obtained by minimizing such an ellipsoid in the sense of the minimum trace of the weighted matrix. The proposed resource-efficient filtering algorithm is of a recursive form, thereby facilitating the online implementation. A numerical simulation example is given to demonstrate the effectiveness of the proposed protocol-based distributed filter design method.

Asymptotic behaviors of semidefinite programming with a covariance perturbation

In this paper, we study asymptotic behaviors of semidefinite programming with a covariance perturbation. We obtain some moderate deviations, Cramer-type moderate deviations and a law of the iterated logarithm of estimates of the respective optimal value and optimal solutions when the covariance matrix is estimated by its sample covariance. As an example, we also apply the main results to the Minimum Trace factor Analysis.

A 2D typology generator for historical masonry elements

The mechanical response of stone masonry depends on the properties of the components and also on the typology created by the stone units and the mortar joints. While the influence of the component strength on masonry is relatively well studied, few studies have been devoted to its influence on masonry properties mainly because of the difficulty of varying the masonry typology systematically. This paper focuses on generation and calibration of masonry typologies, which serves as foundation for further numerical investigation. To this purpose, we develop a typology generator based on relevant research in computer vision. To characterize different typologies quantitatively, we also develop an objective method to compute the line of minimum trace directly from the image of stone masonry based on graph theory. The code and recommendations for the parameter choices are publicly available online. Altogether, this paper provides a useful tool for researchers to study systematically the influence of historical stone masonry typologies.

Statistical inference of semidefinite programming

In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions when the ‘true’ covariance matrix is estimated by its sample counterpart. The analysis is based on perturbation theory of semidefinite programming. As an example we consider asymptotics of the so-called minimum trace factor analysis. We also discuss the minimum rank matrix completion problem and its SDP counterparts.

Factor Analysis From Quadratic Sampling

Factor analysis decomposition, i.e., decomposition of a covariance matrix as a sum of a low-rank positive semidefinite matrix and a diagonal matrix is an important problem in a variety of areas, such as signal processing, machine learning, system identification, and statistical inference. In this letter, the focus is on computing the factor analysis decomposition from a set of quadratic (or symmetric rank-one) measurements of a covariance matrix. Commonly used minimum trace factor analysis heuristic can be adapted to solve this problem when all the measurements are available. However, the resulting convex program is not suitable for processing large-scale or streaming data. Therefore, this letter presents a low-complexity iterative algorithm, which recovers the unknowns through a series of rank-one updates. The iterative algorithm performs better than the convex program when only a finite number of data snapshots are available.

An Airborne Target Localization Algorithm Based on UKF and Optimal Maneuver Strategy

The airborne bearing-only passive target localization performance is relevant with the specific filter and maneuver model. This paper presents a combination of Unscented Kalman Filtering (UKF) with control inputs and optimal route planning algorithm to improve the performance. Taking the minimum trace of unbiased UKF estimation covariance matrix as criteria, single-step heading traverse method is applied to reach every optimal solution. A single flight path simulation and Monte Carlo analysis validate that the optimal strategy can improve both the convergence and localization accuracy.

On the minimum trace norm/energy of (0,1)-matrices

The trace norm of a matrix is the sum of its singular values. This paper presents results on the minimum trace norm ψn(m) of (0,1)-matrices of size n×n with exactly m ones. It is shown that:(1) if n≥2 and n<m≤2n, then ψn(m)≤m+2(m−1), with equality if and only if m is a prime;(2) if n≥4 and 2n<m≤3n, then ψn(m)≤m+22⌊m/3⌋, with equality if and only if m is a prime or a double of a prime;(3) if 3n<m≤4n, then ψn(m)≤m+2m−2, with equality if and only if there is an integer k≥1 such that m=12k±2 and 4k±1,6k±1,12k±1 are primes.

Comparing the Effects of Different Smoothing Algorithms on the Assessment of Dimensionality of Ordered Categorical Items with Parallel Analysis.

The analysis of polychoric correlations via principal component analysis and exploratory factor analysis are well-known approaches to determine the dimensionality of ordered categorical items. However, the application of these approaches has been considered as critical due to the possible indefiniteness of the polychoric correlation matrix. A possible solution to this problem is the application of smoothing algorithms. This study compared the effects of three smoothing algorithms, based on the Frobenius norm, the adaption of the eigenvalues and eigenvectors, and on minimum-trace factor analysis, on the accuracy of various variations of parallel analysis by the means of a simulation study. We simulated different datasets which varied with respect to the size of the respondent sample, the size of the item set, the underlying factor model, the skewness of the response distributions and the number of response categories in each item. We found that a parallel analysis and principal component analysis of smoothed polychoric and Pearson correlations led to the most accurate results in detecting the number of major factors in simulated datasets when compared to the other methods we investigated. Of the methods used for smoothing polychoric correlation matrices, we recommend the algorithm based on minimum trace factor analysis.

Asynchronous Multi-Sensor Fusion Algorithm Based on the Steady-State Kalman Filter

The paper studies an asynchronous multi-sensor fusion problem based a kind of asynchronous multi-sensor dynamic system. Firstly, this paper presents a centralized fusion algorithm based on the Kalman filter without ignoring the correlation between process noise and augmented measurement noise. It is optimal in minimum mean square error. Then using the steady-state Kalman filter to estimate and fuse. Secondly, in the condition that the local sensor estimation error is associated, a distributed fusion algorithm is given by utilizing S.L. Sun optimal information fusion criterion in minimum error covariance matrix trace at fusion center. In distributed algorithm, the value transmitting to the fusion center is determined by the local sensor estimation based on the steady-state Kalman filter and one step predictive value. Since both optimal fusion algorithm standards are different, so the fusion precision will vary. Finally the effectiveness of the algorithm is verified by computer simulation.

Negativity of quantumness and its interpretations

We analyze the general nonclassicality of correlations of a composite quantum systems as measured by the negativity of quantumness. The latter corresponds to the minimum entanglement, as quantified by the negativity, that is created between the system and an apparatus that is performing local measurements on a selection of subsystems. The negativity of quantumness thus quantifies the degree of nonclassicality on the measured subsystems. We demonstrate a number of possible different interpretations for this measure, and for the concept of quantumness of correlations in general. In particular, for general bipartite states in which the measured subsystem is a qubit, the negativity of quantumness acquires a geometric interpretation as the minimum trace distance from the set of classically correlated states. This can be further reinterpreted as minimum disturbance, with respect to trace norm, due to a local measurement or a nontrivial local unitary operation. We calculate the negativity of quantumness in closed form for Werner and isotropic states, and for all two-qubit states for which the reduced state of the system that is locally measured is maximally mixed---this includes all Bell diagonal states. We discuss the operational significance and potential role of the negativity of quantumness in quantum information processing.

A new estimation with minimum trace of asymptotic covariance matrix for incomplete longitudinal data with a surrogate process

Missing data is a very common problem in medical and social studies, especially when data are collected longitudinally. It is a challenging problem to utilize observed data effectively. Many papers on missing data problems can be found in statistical literature. It is well known that the inverse weighted estimation is neither efficient nor robust. On the other hand, the doubly robust (DR) method can improve the efficiency and robustness. As is known, the DR estimation requires a missing data model (i.e., a model for the probability that data are observed) and a working regression model (i.e., a model for the outcome variable given covariates and surrogate variables). Because the DR estimating function has mean zero for any parameters in the working regression model when the missing data model is correctly specified, in this paper, we derive a formula for the estimator of the parameters of the working regression model that yields the optimally efficient estimator of the marginal mean model (the parameters of interest) when the missing data model is correctly specified. Furthermore, the proposed method also inherits the DR property. Simulation studies demonstrate the greater efficiency of the proposed method compared with the standard DR method. A longitudinal dementia data set is used for illustration.

Cost performance trade-off in thermoelectric modules with low fractional area coverage

ABSTRACTWe report a comprehensive study of the cost of materials used in the thermoelectric module as the elements, substrate, and metal interconnect are optimized for maximum output power. The power conversion cost [$/W] is analyzed. The maximum power output is found by matching both thermal and electrical impedances to the external load and heat sink. The fractional area coverage or fill factor of the thermoelement (leg) in the module is a key factor which affects the overall cost of the waste heat recovery system. Thermal spreading resistance is a function of the thermal conductivity and the thickness of the substrates. Also the air gap between the legs contributes to parasitic heat loss from the hot to the cold substrate through heat conduction and radiative heat transfer. The optimum fill factor under atmospheric air-pressure is found to be on the order of a few percent. We also take into account the three-dimensional current flow and the effect of the metallization thickness on the series resistance in the module. Calculations identify the minimum metal trace thickness needed to have a minimum impact on output power generation.

Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspace $U$ that ensures any positive semidefinite matrix $L$ with column space $U$ can be recovered from $D+L$ for any diagonal matrix $D$ using a convex optimization-based heuristic known as minimum trace factor analysis. This result leads to a new understanding of the structure of rank-deficient correlation matrices and a simple condition on a set of points that ensures there is a centered ellipsoid passing through them.

Positive Definiteness via Off-diagonal Scaling of a Symmetric Indefinite Matrix

Indefinite symmetric matrices that are estimates of positive definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based theory for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a matrix to achieve positive definiteness. As a contrast to recently developed ridge procedures, the proposed method does not need variables to contain measurement errors. When minimum trace factor analysis is used to implement the theory, only correlations that are associated with Heywood cases are shrunk.

다목적 다변량 자료분석을 위한 변수선택

다변량 자료분석에서 최근의 추세는 관측개체의 수 n이 커지는 외에 변수의 수 p가 큰사례들이 많아지고 있다는 것이다. n개 개체 각각에서 획득된 p개 변수들 <TEX>$X_1$</TEX>, <TEX>$X_2$</TEX>, <TEX>$\ldots$</TEX>, <TEX>$X_p$</TEX> 가운데는 이름이나 개념적으로는 구분이 가능하지 만 실제로 거의 중복이 되는 변수들이 있을 수 있는데, 이들 변수들이 모두 분석에 포함되면 여러 문제가 유발될 수 있다. 예컨대 주성분 분석이나 인자분석에서는 중복 변수들이 주축(主軸, principal axis) 결정에, 관측개체 군집 화에서는 개체간 거리 산출에 왜곡된 영향을 줄 수 있다. 또한 목적변수가 지정된 지도학습(supervised learning)에서 설명변수들의 중복성은 추정모형의 안정성을 해치는 결과를 초래한다. 실제 자료 분석에서는 한 자료 세트가 여러 기법으로 탐색되고 다수의 모형이 추출되므로 변수세트를 최대한 절약적(parsimonious)으로 구성할 필요가 있다. 본 연구의 목적은 <TEX>$X_1$</TEX>, <TEX>$X_2$</TEX>, <TEX>$\ldots$</TEX>, <TEX>$X_p$</TEX> 중에서 필요한 변수들은 선적하고 불필요한 변수들은 제거함으로써 주어진 변수세트를 보다 적은 크기의 변수세트로 대치하는 방법을 제시하는 데 있다. 제안 방법을 몇 개의 수치적 사례에 적용해 봄으로써 선적 변수와 제거변수간 관계의 시각화, 회귀모형에서의 유용성, 범주형 자료분석에서의 활용 등에 대해 논의 하고자 한다. Recently we frequently analyze multivariate data with quite large number of variables. In such data sets, virtually duplicated variables may exist simultaneously even though they are conceptually distinguishable. Duplicate variables may cause problems such as the distortion of principal axes in principal component analysis and factor analysis and the distortion of the distances between observations, i.e. the input for cluster analysis. Also in supervised learning or regression analysis, duplicated explanatory variables often cause the instability of fitted models. Since real data analyses are aimed often at multiple purposes, it is necessary to reduce the number of variables to a parsimonious level. The aim of this paper is to propose a practical algorithm for selection of a subset of variables from a given set of p input variables, by the criterion of minimum trace of partial variances of unselected variables unexplained by selected variables. The usefulness of proposed method is demonstrated in visualizing the relationship between selected and unselected variables, in building a predictive model with very large number of independent variables, and in reducing the number of variables and purging/merging categories in categorical data.