Numerical Analysis

Acknowledgements: This article will appear in the forthcoming Princeton Companion to Mathematics, edited by Timothy Gowers with June Barrow-Green, to be published by Princeton University Press.\ud \ud In preparing this essay I have benefitted from the advice of many colleagues who corrected a number of errors of fact and emphasis. I have not always followed their advice, however, preferring as one friend put it, to "put my head above the parapet". So I must take full responsibility for errors and omissions here.\ud \ud With thanks to: Aurelio Arranz, Alexander Barnett, Carl de Boor, David Bindel, Jean-Marc Blanc, Mike Bochev, Folkmar Bornemann, Richard Brent, Martin Campbell-Kelly, Sam Clark, Tim Davis, Iain Duff, Stan Eisenstat, Don Estep, Janice Giudice, Gene Golub, Nick Gould, Tim Gowers, Anne Greenbaum, Leslie Greengard, Martin Gutknecht, Raphael Hauser, Des Higham, Nick Higham, Ilse Ipsen, Arieh Iserles, David Kincaid, Louis Komzsik, David Knezevic, Dirk Laurie, Randy LeVeque, Bill Morton, John C Nash, Michael Overton, Yoshio Oyanagi, Beresford Parlett, Linda Petzold, Bill Phillips, Mike Powell, Alex Prideaux, Siegfried Rump, Thomas Schmelzer, Thomas Sonar, Hans Stetter, Gil Strang, Endre Süli, Defeng Sun, Mike Sussman, Daniel Szyld, Garry Tee, Dmitry Vasilyev, Andy Wathen, Margaret Wright and Steve Wright

Visualization of Data by Method of Elastic Maps and Its Applications in Genomics, Economics and Sociology

Technology of data visualization and data modeling is suggested. The basic of the technology is original idea of elastic net and methods of its construction and application. A short review of relevant methods has been made. The methods proposed are illustrated by applying them to the real economical, sociological and biological datasets and to some model data distributions. The basic of the technology is original idea of elastic net - regular point approximation of some manifold that is put into the multidimensional space and has in a certain sense minimal energy. This manifold is an analogue of principal surface and serves as non-linear screen on what multidimensional data are projected. Remarkable feature of the technology is its ability to work with and to fill gaps in data tables. Gaps are unknown or unreliable values of some features. It gives a possibility to predict plausibly values of unknown features by values of other ones. So it provides technology of constructing different prognosis systems and non-linear regressions. The technology can be used by specialists in different fields. There are several examples of applying the method presented in the end of this paper

Graphics calculators in upper secondary courses

This paper has been produced on request of the Secondary Education Authority, as part of a process of considering the potential impact of graphics calculators on upper secondary school courses. The paper provides background on this matter for the Authority and for committee members, including syllabus committees that may be affected by the decision to permit the use of graphics calculators in Tertiary Entrance Examinations

LANGUAGE DOCUMENTATION ON JAVANESE: A SHIFT TOWARDS RECOGNIZING AND CELEBRATING COLLOQUIAL VARIETIES

Javanese has benefitted from a long history of linguistic study. To focus on grammars, Javanese boasts grammars in French by Favre (1866); in Dutch by Kiliaan (1919), Prijohoetomo (1937), Arps et al. (2000); in Indonesian by Suharno (1982), Sudaryanto (1991; ed), Wedhawati et al. (2006); in English by Horne (1961), Keeler (1992), Robson (2014); among others. Although Javanese already has a stable scholarly tradition, the focus has been almost exclusively on the Standard variety, spoken in the principalities of Yogyakarta and Solo, constituting a small sliver of the attested language. Given its vast dialectal variation, there is still a huge need for linguistic research on Javanese. With the advent of establishing language documentation as a branch of linguistics (Himmelmann 1991), some progress has been made in the documentation and description of colloquial varieties: for example, Suwadji (1981) on Javanese varieties on the north coast of Central Java; Conners (2008) on Tengger Javanese; Hoogervorst (2010) on Surabayan Javanese; Vander Klok (2012) on Paciran Javanese. These works represent a shift towards the recognition and validation of non-standard varieties of Javanese, which were unnoticed in the past. We advocate for the continuation of this trend. In particular, we present our work on the documentation of two colloquial varieties of Javanese, Malang Javanese and Semarang Javanese, for which the outcome of this project is a reference grammar. We end by highlighting the importance of such documentation, especially of non-standard varieties, for language maintenance: even large languages are susceptible to language endangerment, and Javanese is no exception (e.g. Kurniasih 2006; Smith-Hefner 2009; Cohn et al. 2013)

Architecture and Design of Medical Processor Units for Medical Networks

This paper introduces analogical and deductive methodologies for the design medical processor units (MPUs). From the study of evolution of numerous earlier processors, we derive the basis for the architecture of MPUs. These specialized processors perform unique medical functions encoded as medical operational codes (mopcs). From a pragmatic perspective, MPUs function very close to CPUs. Both processors have unique operation codes that command the hardware to perform a distinct chain of subprocesses upon operands and generate a specific result unique to the opcode and the operand(s). In medical environments, MPU decodes the mopcs and executes a series of medical sub-processes and sends out secondary commands to the medical machine. Whereas operands in a typical computer system are numerical and logical entities, the operands in medical machine are objects such as such as patients, blood samples, tissues, operating rooms, medical staff, medical bills, patient payments, etc. We follow the functional overlap between the two processes and evolve the design of medical computer systems and networks.Comment: 17 page

Screening of energy efficient technologies for industrial buildings' retrofit

This chapter discusses screening of energy efficient technologies for industrial buildings' retrofit

Efficient resolution of the Colebrook equation

A robust, fast and accurate method for solving the Colebrook-like equations is presented. The algorithm is efficient for the whole range of parameters involved in the Colebrook equation. The computations are not more demanding than simplified approximations, but they are much more accurate. The algorithm is also faster and more robust than the Colebrook solution expressed in term of the Lambert W-function. Matlab and FORTRAN codes are provided

Field Study for Remote Sensing: An instructor's manual

The need for and value of field work (surface truthing) in the verification of image identification from high atitude infrared and multispectral space sensor images are discussed in this handbook which presents guidelines for developing instructional and research procedures in remote sensing of the environment

QIP = PSPACE

We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a class of semidefinite programs that captures the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows immediately from the well-known equality IP = PSPACE, the equality QIP = PSPACE follows.Comment: 21 pages; v2 includes corrections and minor revision