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

Fundamental Properties of Integrated-Depth Equations for Nonlinear Water Propagation in Porous Media

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Measurement of the Near-Bed Turbulence in a Laboratory Surf Zone

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Artificial Intelligence and Visual Analytics: A Deep-Learning Approach to Analyze Hotel Reviews & Responses

With a growing number of online reviews, consumers often rely on these reviews to make purchase decisions. However, little is known about managerial responses to online hotel reviews. This paper reports on a framework to integrate visual analytics and machine learning techniques to investigate whether hotel managers respond to positive and negative reviews differently and how to use a deep-learning approach to prioritize responses. In this study, forty 4- and 5-star hotels in London with 91,051 reviews and 70,397 responses were collected and analyzed. Visual analyses and machine learning were conducted. The results indicate most hotels (72.5%) showing no preference to respond to positive and negative reviews. Our proposed deep-learning approach outperformed existing algorithms to prioritize responses

Land Subsidence Caused by Groundwater Exploitation in Yunlin, Taiwan

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchive

Experimental and Numerical Study of Tsunami Wave Propagation and Run-Up on Sloping Beaches

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Clinical application of tumor volume in advanced nasopharyngeal carcinoma to predict outcome

<p>Abstract</p> <p>Background</p> <p>Current staging systems have limited ability to adjust optimal therapy in advanced nasopharyngeal carcinoma (NPC). This study aimed to delineate the correlation between tumor volume, treatment outcome and chemotherapy cycles in advanced NPC.</p> <p>Methods</p> <p>A retrospective review of 110 patients with stage III-IV NPC was performed. All patients were treated first with neoadjuvant chemotherapy, then concurrent chemoradiation, and followed by adjuvant chemotherapy as being the definitive therapy. Gross tumor volume of primary tumor plus retropharyngeal nodes (GTVprn) was calculated to be an index of treatment outcome.</p> <p>Results</p> <p>GTVprn had a close relationship with survival and recurrence in advanced NPC. Large GTVprn (≧13 ml) was associated with a significantly poorer local control, lower distant metastasis-free rate, and poorer survival. In patients with GTVprn ≧ 13 ml, overall survival was better after ≧4 cycles of chemotherapy than after less than 4 cycles.</p> <p>Conclusions</p> <p>The incorporation of GTVprn can provide more information to adjust treatment strategy.</p

Transcriptome analysis of Dnmt3l knock-out mice derived multipotent mesenchymal stem/stromal cells during osteogenic differentiation

Multipotent mesenchymal stem/stromal cells (MSCs) exhibit great potential for cell-based therapy. Proper epigenomic signatures in MSCs are important for the maintenance and the subsequent differentiation potential. The DNA methyltransferase 3-like (DNMT3L) that was mainly expressed in the embryonic stem (ES) cells and the developing germ cells plays an important role in shaping the epigenetic landscape. Here, we report the reduced colony forming ability and impaire