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A matrix is a Q0-matrix if for every k∈{1,2,…,n}, the sum of all k×k principal minors is nonnegative. In this paper, we study some necessary and sufficient conditions for a digraph to have Q0-completion. Later on we discuss the relationship between Q and Q0-matrix completion problem. Finally, a classification of the digraphs of order up to four is done based on Q0-completion.

The purpose of this paper is to establish and implement a direct topological reanalysis algorithm for general successive structural modifications, based on the updating matrix triangular factorization (UMTF) method for non-topological modification proposed by Song et al. [Computers and Structures, 143(2014):60-72].

In this method, topological modifications are viewed as a union of symbolic and numerical change of structural matrices. The numerical part is dealt with UMTF by directly updating the matrix triangular factors. For symbolic change, an integral structure which consists of all potential nodes/elements is introduced to avoid side effects on the efficiency during successive modifications. Necessary pre- and post processing are also developed for memory-economic matrix manipulation.

The new reanalysis algorithm is applicable to successive general structural modifications for arbitrary modification amplitudes and locations. It explicitly updates the factor matrices of the modified structure and thus guarantees the accuracy as full direct analysis while greatly enhancing the efficiency.

Examples including evolutionary structural optimization and sequential construction analysis show the capability and efficiency of the algorithm.

This innovative paper makes direct topological reanalysis be applicable for successive structural modifications in many different areas.

Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE) based sensor simulations for the inverse problem of electrical capacitance tomography. Two known computational bottlenecks are the assembly of the FE equation system as well as the computation of the Jacobian. Here, existing computation techniques like adjoint field approaches require additional simulations. This paper aims to present fast numerical techniques for the sensor simulation and computations with the Jacobian matrix.

For the FE equation system, a solution strategy based on Green’s functions is derived. Its relation to the solution of a standard FE formulation is discussed. A fast stiffness matrix assembly based on an eigenvector decomposition is shown. Based on the properties of the Green’s functions, Jacobian operations are derived, which allow the computation of matrix vector products with the Jacobian for free, i.e. no additional solves are required. This is demonstrated by a Broyden–Fletcher–Goldfarb–Shanno-based image reconstruction algorithm.

MATLAB-based time measurements of the new methods show a significant acceleration for all calculation steps compared to reference implementations with standard methods. E.g. for the Jacobian operations, improvement factors of well over 100 could be found.

The paper shows new methods for solving known computational tasks for solving inverse problems. A particular advantage is the coherent derivation and elaboration of the results. The approaches can also be applicable to other inverse problems.

Mining user-concerned actionable and interpretable hot topics will help management departments fully grasp the latest events and make timely decisions. Existing topic models primarily integrate word embedding and matrix decomposition, which only generates keyword-based hot topics with weak interpretability, making it difficult to meet the specific needs of users. Mining phrase-based hot topics with syntactic dependency structure have been proven to model structure information effectively. A key challenge lies in the effective integration of the above information into the hot topic mining process.

This paper proposes the nonnegative matrix factorization (NMF)-based hot topic mining method, semantics syntax-assisted hot topic model (SSAHM), which combines semantic association and syntactic dependency structure. First, a semantic–syntactic component association matrix is constructed. Then, the matrix is used as a constraint condition to be incorporated into the block coordinate descent (BCD)-based matrix decomposition process. Finally, a hot topic information-driven phrase extraction algorithm is applied to describe hot topics.

The efficacy of the developed model is demonstrated on two real-world datasets, and the effects of dependency structure information on different topics are compared. The qualitative examples further explain the application of the method in real scenarios.

Most prior research focuses on keyword-based hot topics. Thus, the literature is advanced by mining phrase-based hot topics with syntactic dependency structure, which can effectively analyze the semantics. The development of syntactic dependency structure considering the combination of word order and part-of-speech (POS) is a step forward as word order, and POS are only separately utilized in the prior literature. Ignoring this synergy may miss important information, such as grammatical structure coherence and logical relations between syntactic components.

The author studies forms over finite fields obtained as the determinant of Hermitian matrices and use these determinatal forms to define and study the base polynomial of a square matrix over a finite field.

The authors give full proofs for the new results, quoting previous works by other authors in the proofs. In the introduction, the authors quoted related references.

The authors get a few theorems, mainly describing some monic polynomial arising as a base polynomial of a square matrix.

As far as the author knows, all the results are new, and the approach is also new.

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

The purpose of this study is to present and explain a new customer segmentation approach inspired by failure mode and effect analysis (FMEA) which can help classify customers into more accurate segments.

The present study offers a look at the three most commonly used approaches to assessing customer loyalty:net promoter score, loyalty ladder and loyalty matrix. A survey on the quality of restaurant services compares the results of categorizing customers according to these three most frequently used approaches.

A new way of categorizing customers through loyalty priority number (LPN) is proposed. LPN was designed as a major segmentation criterion consisting of customer loyalty rate, frequency of purchase of products or services and value of purchases. Using the proposed approach allows to categorize customers into four more comprehensive groups: random, bronze, silver and gold – according to their loyalty and value to the organization.

Survey will bring a more accurate way of categorizing customers even in those sectors where transaction data are not available. More accurate customer categorization will enable organizations to use targeting tools more effectively and improve product positioning.

The most commonly used categorization approaches such as net promoter score, loyalty ladder or loyalty matrix offer relatively general information about customer groups. The present study combines the benefits of these approaches with the principles of FMEA. The case study not only made it possible to offer a view of the real application of the proposed approach but also made it possible to make a uniform comparison of the accuracy of customer categorization.

This study aims to create actionable guidelines for pricing decision-making by employing game a theory matrix to forecast the correlation between the average daily rate and the latest ambiance of hotels.

Utilizing a vector error correction model, the research employs game theory to assess the influence of the average daily rate on the hotel's newest atmosphere during both peak season (April–September) and valley season (October–March).

Findings indicate that during the peak season, when the average daily rate rises in resorts and falls in suburban areas, the hotel’s newest atmosphere is at its best in both types of accommodations. During the off-peak season, the hotel’s newest atmosphere is achieved when both resorts and suburban accommodations increase their average daily rates.

There are two study constraints. One is the assumption that hotel guests in both parties prefer not to change hotels, but in fact they would. Two is a limited sample of two resort and suburban markets.

This suggests that the hotel’s newest atmosphere can draw both leisure and business travelers to suburban areas during the low season and more leisure travelers to resorts during the high season.

The study’s findings have implications for revenue related to the hotel’s newest atmosphere and cleanliness for both suburban and resort hotels, particularly when promoting tourism collaboratively.

The study provides valuable insights for hotel managers in analyzing pricing strategies using matrices.

With the continuous increase of users, resources and tags, social tagging systems gradually present the characteristics of “big data” such as large number, fast growth, complexity and unreliable quality, which greatly increases the complexity of recommendation. The contradiction between the efficiency and effectiveness of recommendation service in social tagging is increasingly becoming prominent. The purpose of this study is to incorporate topic optimization into collaborative filtering to enhance both the effectiveness and the efficiency of personalized recommendations for social tagging.

Combining the idea of optimization before service, this paper presents an approach that incorporates topic optimization into collaborative recommendations for social tagging. In the proposed approach, the recommendation process is divided into two phases of offline topic optimization and online recommendation service to achieve high-quality and efficient personalized recommendation services. In the offline phase, the tags' topic model is constructed and then used to optimize the latent preference of users and the latent affiliation of resources on topics.

Experimental evaluation shows that the proposed approach improves both precision and recall of recommendations, as well as enhances the efficiency of online recommendations compared with the three baseline approaches. The proposed topic optimization–incorporated collaborative recommendation approach can achieve the improvement of both effectiveness and efficiency for the recommendation in social tagging.

With the support of the proposed approach, personalized recommendation in social tagging with high quality and efficiency can be achieved.

This study proposes spatial origin-destination threshold Tobit to address spatial interdependence among bilateral trade flows while accounting for zero trade volumes.

This model is designed to capture multiple forms of spatial autocorrelation embedded in “directional” trade flows. The authors apply this improved model to export flows among 32 Asian countries in 1990.

The empirical results indicate the presence of all three types of spatial dependence: exporter-based, importer-based and exporter-to-importer-based. After further considering multifaceted spatial correlation in bilateral trade flows, the authors find that the effect of conventional trade variables changes in a noticeable way.

This finding implies that the standard gravity model may produce biased estimates if it does not take spatial dependence into account.

This paper attempts to offer an improved model of the standard gravity model by taking spatial dependence into account.