Tensor multivariate trace inequalities and their applications

In linear algebra, the trace of a square matrix is defined as the sum of elements on the main diagonal. The trace of a matrix is the sum of its eigenvalues (counted with multiplicities), and it is invariant under the change of basis. This charac-terization can be used to define the trace of a tensor in general. Trace inequalities are mathematical relations between different multivariate trace functionals involving linear operators. These relations are straightforward equalities if the involved linear operators commute, however, they can be difficult to prove when the non-commuting linear operators are involved. Given two Hermitian tensors H1 and H2 that do not commute. Does there exist a method to transform one of the two tensors such that they commute without completely destroying the structure of the original tensor? The spectral pinching method is a tool to resolve this problem. In this work, we will apply such spectral pinching method to prove several trace inequalities that extend the Araki–Lieb–Thirring (ALT) inequality, Golden–Thompson(GT) inequality and logarithmic trace inequality to arbitrary many tensors. Our approaches rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transpar-ent mechanism to treat generic tensor multivariate trace inequalities. As an example application of our tensor extension of the Golden–Thompson inequality, we give the tail bound for the independent sum of tensors. Such bound will play a fundamental role in high-dimensional probability and statistical data analysis

New Efficient Approach to Solve Big Data Systems Using Parallel Gauss–Seidel Algorithms

In order to perform big-data analytics, regression involving large matrices is often necessary. In particular, large scale regression problems are encountered when one wishes to extract semantic patterns for knowledge discovery and data mining. When a large matrix can be processed in its factorized form, advantages arise in terms of computation, implementation, and data-compression. In this work, we propose two new parallel iterative algorithms as extensions of the Gauss–Seidel algorithm (GSA) to solve regression problems involving many variables. The convergence study in terms of error-bounds of the proposed iterative algorithms is also performed, and the required computation resources, namely time-and memory-complexities, are evaluated to benchmark the efficiency of the proposed new algorithms. Finally, the numerical results from both Monte Carlo simulations and real-world datasets are presented to demonstrate the striking effectiveness of our proposed new methods

Improvement of LiDAR Data Accuracy Using 12 Parameter Affine Transformation

LiDAR data in a local coordinate system may need to be georeferenced and converted into a geographic or projected system. In coordinate transformation, the 7-parameter Helmet transformation method is usually used in measurements to eliminate the systematic errors made by a laser scanner. However, 7-parameter coordinate transformation assumes that there is only one scale error in all of the systematic errors. This study used 12 parameter affine transformation for coordinate transformation of airborne LiDAR data and terrestrial LiDAR data. The LiDAR data accuracy results upon 6-parameter similarity transformation, 7-parameter similarity transformation, and 12-parameter affine transformation were compared. The results showed that using 12-parameter affine transformation the airborne LiDAR and terrestrial LiDAR data have 2-3 times greater accuracy than do 7-parameter or 6-parameter transformations

A Survey of Blind Modulation Classification Techniques for OFDM Signals

Blind modulation classification (MC) is an integral part of designing an adaptive or intelligent transceiver for future wireless communications. Blind MC has several applications in the adaptive and automated systems of sixth generation (6G) communications to improve spectral efficiency and power efficiency, and reduce latency. It will become a integral part of intelligent software-defined radios (SDR) for future communication. In this paper, we provide various MC techniques for orthogonal frequency division multiplexing (OFDM) signals in a systematic way. We focus on the most widely used statistical and machine learning (ML) models and emphasize their advantages and limitations. The statistical-based blind MC includes likelihood-based (LB), maximum a posteriori (MAP) and feature-based methods (FB). The ML-based automated MC includes k-nearest neighbors (KNN), support vector machine (SVM), decision trees (DTs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), and long short-term memory (LSTM) based MC methods. This survey will help the reader to understand the main characteristics of each technique, their advantages and disadvantages. We have also simulated some primary methods, i.e., statistical- and ML-based algorithms, under various constraints, which allows a fair comparison among different methodologies. The overall system performance in terms bit error rate (BER) in the presence of MC is also provided. We also provide a survey of some practical experiment works carried out through National Instrument hardware over an indoor propagation environment. In the end, open problems and possible directions for blind MC research are briefly discussed

Cerebral hemorrhagic infarction following cranioplasty in a shunted patient with tension pneumocephalus resulting from depressed skull and craniodural defect

SummaryA 34-year-old female sustained a severe traumatic brain injury that was treated with decompressive craniectomy and subsequent cranioplasty, then with ventriculoperitoneal shunt about 10 years previously. However, the skull flap was found to be depressed ever since. She was admitted to our hospital for a headache and left hemiparesis with sudden onset. The computed tomography scan displayed tension pneumocephalus in the right frontoparietal region. First, she underwent emergency burr hole drainage and placement of a subdural drain with external ventricular drainage tube. Then her symptoms improved considerably. Unfortunately, 6 months later she was admitted again to our hospital because of headache and left hemiparesis with sudden onset, and the brain computed tomography showed tension pneumocephalus in the right frontoparietal region. She underwent craniectomy to remove the previous depressed skull and simultaneous cranioplasty with Ti-Mesh. On the day of her operation, generalized seizure occurred and her consciousness deteriorated. The magnetic resonance imaging showed hemorrhagic infarction on both sides of the thalamus and the right parieto-occipital region. We think it probable that a sudden increase of cerebral blood flow in the cerebral hemisphere where the cranioplasty had been performed caused reperfusion injury and resulted in hemorrhagic infarction

The Study on Antecedents of Consumer Buying Impulsiveness in an Online Context

The global recession caused by the financial tsunami has seriously impacted numerous industries. Although the market scale of global e-commerce market has declined, global online shopping continues to grow. Many previous researches focused on the effect of website design characteristics on online impulsive buying behavior, and few have explored such behavior from consumer individual internal factor perspectives. This paper aims to explore and integrate individual internal factors influencing consumer online buying impulsiveness, and further to recognize the relationships among these factors. The results showed as follows: (1) hedonic consumption needs, impulsive buying tendency, positive affect and normative evaluations positively influence buying impulsiveness, respectively; (2) hedonic consumption needs positively influence positive affect; (3) impulsive buying tendency positively influences normative evaluations; (4) normative evaluations positively influence positive affect