The Convergence of Least-Squares Progressive Iterative Approximation for Singular Least-Squares Fitting System

Data fitting is an extensively employed modeling tool in geometric design. With the advent of the big data era, the data sets to be fitted are made larger and larger, leading to more and more leastsquares fitting systems with singular coefficient matrices. LSPIA (least-squares progressive iterative approximation) is an efficient iterative method for the least-squares fitting. However, the convergence of LSPIA for the singular least-squares fitting systems remains as an open problem. In this paper, the authors showed that LSPIA for the singular least-squares fitting systems is convergent. Moreover, in a special case, LSPIA converges to the Moore-Penrose (M-P) pseudo-inverse solution to the leastsquares fitting result of the data set. This property makes LSPIA, an iterative method with clear geometric meanings, robust in geometric modeling applications. In addition, the authors discussed some implementation detail of LSPIA, and presented an example to validate the convergence of LSPIA for the singular least-squares fitting systems.     

Prediction of end-use energy consumption in a region of Northwest China

End-use energy consumption can reflect the industrial development of a country and the living standards of its residents. The study of end-use energy consumption can provide a solid basis for industrial restructuring, energy saving, and emission reduction. In this paper, we analyzed the end-use energy consumption of a region in Northwestern China, and applied the Markov prediction method to forecast the future demand of different types of end-use energy. This provides a reference for the energy structure optimization in the Northwestern China.     

Laccases of prokaryotic origin: enzymes at the interface of protein science and protein technology

The ubiquitous members of the multicopper oxidase family of enzymes oxidize a range of aromatic substrates such as polyphenols, methoxy-substituted phenols, amines and inorganic compounds, concomitantly with the reduction of molecular dioxygen to water. This family of enzymes can be broadly divided into two functional classes: metalloxidases and laccases. Several prokaryotic metalloxidases have been described in the last decade showing a robust activity towards metals, such as Cu(I), Fe(II) or Mn(II) and have been implicated in the metal metabolism of the corresponding microorganisms. Many laccases, with a superior efficiency for oxidation of organic compounds when compared with metals, have also been identified and characterized from prokaryotes, playing roles that more closely conform to those of intermediary metabolism. This review aims to present an update of current knowledge on prokaryotic multicopper oxidases, with a special emphasis on laccases, anticipating their enormous potential for industrial and environmental applications.     

How Research on Microbiomes is Changing Biology: A Discussion on the Concept of the Organism

Multicellular organisms contain numerous symbiotic microorganisms, collectively called microbiomes. Recently, microbiomic research has shown that these microorganisms are responsible for the proper functioning of many of the systems (digestive, immune, nervous, etc.) of multicellular organisms. This has inclined some scholars to argue that it is about time to reconceptualise the organism and to develop a concept that would place the greatest emphasis on the vital role of microorganisms in the life of plants and animals. We believe that, unfortunately, there is a problem with this suggestion, since there is no such thing as a universal concept of the organism which could constitute a basis for all biological sciences. Rather, the opposite is true: numerous alternative definitions exist. Therefore, comprehending how microbiomics is changing our understanding of organisms may be a very complex matter. In this paper we will demonstrate that this pluralism proves that claims about a change in our understanding of organisms can be treated as both true and untrue. Mainly, we assert that the existing concepts differ substantially, and that only some of them have to be reconsidered in order to incorporate the discoveries of microbiomics, while others are already flexible enough to do so. Taking into account the plurality of conceptualisations within different branches of modern biology, we will conduct our discussion using the developmental and the cooperation–conflict concepts of the organism. Then we will explain our results by referring to the recent philosophical debate on the nature of the concept of the organism within biology.     

Free Information Flow Benefits Truth Seeking

How can we approach the truth in a society? It may depend on various factors. In this paper, using a well-established truth seeking model, the authors show that the persistent free information flow will bring us to the truth. Here the free information flow is modeled as the environmental random noise that could alter one's cognition. Without the random noise, the model predicts that the truth can only be captured by the truth seekers who own actively perceptive ability of the truth and their believers, while the other individuals may stick to falsehood. But under the influence of the random noise, the authors strictly prove that even there is only one truth seeker in the group, all individuals will finally approach the truth.     

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

In this paper, the input-to-state stability (ISS) analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.     

Systemic Thinking and Practice Toward Facilitating Inclusive Education: Reflections on a Case of Co-Generated Knowledge and Action in South Africa

This article offers our reflections around a case of facilitating systemic thinking and practice in which the first author of the article (Tlale) interacted with research participants/participant researchers with the intention of strengthening systemic thought and action toward fostering inclusive education in the setting (a rural school in the Eastern Cape in South Africa). We reflect upon the process and also how our engagement was perceived by participants, as expressed in feedback received from them. We point to how Tlale introduced the idea of systemic thinking (to teachers, school management team, school governing body, and a district officer for the district) as tied to the possibility of acting to generate transformation toward a more inclusive educational context for the benefit of the learners at the school in question, thus acting as a systemic mediator on their behalf.     

The Ordering and Replacement Policy for the System with Two Types of Failures

In this paper, the optimal maintenance policy is investigated for a system with stochastic lead time and two types of failures. The system has two types of failures, one type is repairable, when the repairable failure occurs, the system will be repaired by repairman, and the system after repair is not "as good as new". The other type of failure is unrepairable, and when the unrepairable failure occurs the system must be replaced by a new and identical one. The spare system for replacement is available only by order, and the lead time for delivering the spare system is stochastic. The successive survival times of the system form a stochastically decreasing geometric process, the consecutive repair times after failures of the system form a renewal process. By using the renewal process theory and geometric process theory, the explicit expression of the long-run average cost per unit time under ordering policy(N-1) is derived, and the corresponding optimal can be found analytically. Finally,the numerical analyses are given.