There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Data Mining Practical Machine Learning Tools and Techniques

We are in the midst of a technological revolution whereby, for the first time, researchers can link daily word use to a broad array of real-world behaviors. This article reviews several computerized text analysis methods and describes how Linguistic Inquiry and Word Count (LIWC) was created and validated. LIWC is a transparent text analysis program that counts words in psychologically meaningful categories. Empirical results using LIWC demonstrate its ability to detect meaning in a wide variety of experimental settings, including to show attentional focus, emotionality, social relationships, thinking styles, and individual differences.

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The psychological meaning of words: LIWC and computerized text analysis methods

What Video Games Have to Teach Us about Learning and Literacy

Статья посвящена вопросам влияния власти на поведение человека. Авторы рассматривают данные различных источников, в которых увеличение власти связывается с напористостью, а ее уменьшение - с подавленностью. Конкретно, власть ассоциируется с: а) позитивным аффектом; б) вниманием к вознаграждению и к свойствам других, удовлетворяющим личные цели; в) автоматической переработкой информации и резкими суждениями; г) расторможенным социальным поведением. Уменьшение власти, напротив, ассоциируется с: а) негативным аффектом; б) вниманием к угрозам и наказаниям, к интересам других и к тем характеристикам я, которые отвечают целям других; в) контролируемой переработкой информации и совещательным типом рассуждений; г) подавленным социальным поведением. Обсуждаются также последствия этих паттернов поведения, связанных с властью, и потенциальные модераторы.

Power, approach, and inhibition. Власть, напористость и подавленность

Advances in computational linguistics and discourse processing have made it possible to automate many language- and text-processing mechanisms. We have developed a computer tool called Coh-Metrix, which analyzes texts on over 200 measures of cohesion, language, and readability. Its modules use lexicons, part-of-speech classifiers, syntactic parsers, templates, corpora, latent semantic analysis, and other components that are widely used in computational linguistics. After the user enters an English text, Coh-Metrix returns measures requested by the user. In addition, a facility allows the user to store the results of these analyses in data files (such as Text, Excel, and SPSS). Standard text readability formulas scale texts on difficulty by relying on word length and sentence length, whereas Coh-Metrix is sensitive to cohesion relations, world knowledge, and language and discourse characteristics.

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Coh-Metrix: Analysis of text on cohesion and language

We propose a multiscale finite element method for solving second order elliptic equations with rapidly oscillating coefficients. The main purpose is to design a numerical method which is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution. This is accomplished by incorporating the local microstructures of the differential operator into the finite element base functions. As a consequence, the base functions are adapted to the local properties of the differential operator. In this paper, we provide a detailed convergence analysis of our method under the assumption that the oscillating coefficient is of two scales and is periodic in the fast scale. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain a useful asymptotic solution structure. The issue of boundary conditions for the base functions will be discussed. Our numerical experiments demonstrate convincingly that our multiscale method indeed converges to the correct solution, independently of the small scale in the homogenization limit. Application of our method to problems with continuous scales is also considered.

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Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

Coh-Metrix is among the broadest and most sophisticated automated textual assessment tools available today. Automated Evaluation of Text and Discourse with Coh-Metrix describes this computational tool, as well as the wide range of language and discourse measures it provides. Section I of the book focuses on the theoretical perspectives that led to the development of Coh-Metrix, its measures, and empirical work that has been conducted using this approach. Section II shifts to the practical arena, describing how to use Coh-Metrix and how to analyze, interpret, and describe results. Coh-Metrix opens the door to a new paradigm of research that coordinates studies of language, corpus analysis, computational linguistics, education, and cognitive science. This tool empowers anyone with an interest in text to pursue a wide array of previously unanswerable research questions.

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Automated Evaluation of Text and Discourse with Coh-Metrix

This paper develops a least-squares functional that arises from recasting general second-order uniformly elliptic partial differential equations in $n=2$ or $3$ dimensions as a system of first-order equations. In part I [Z. Cai, R. D. Lazarov, T. Manteuffel, and S. McCormick, SIAM J. Numer. Anal., 31 (1994), pp. 1785--1799] a similar functional was developed and shown to be elliptic in the $H(\divv) \times H^1$ norm and to yield optimal convergence for finite element subspaces of $H(\divv) \times H^1$. In this paper the functional is modified by adding a compatible constraint and imposing additional boundary conditions on the first-order system. The resulting functional is proved to be elliptic in the $(H^1)^{n+1}$ norm. This immediately implies optimal error estimates for finite element approximation by standard subspaces of $(H^1)^{n+1}$. Another direct consequence of this ellipticity is that multiplicative and additive multigrid algorithms applied to the resulting discrete functionals are optimally convergent. As an alternative to perturbation-based approaches, the least-squares approach developed here applies directly to convection--diffusion--reaction equations in a unified way and also admits a fast multigrid solver, historically a missing ingredient in least-squares methodology.

https://www.jstor.org/stable/pdfplus/2951987.pdf

First-order system least squares for second-order partial differential equations: part I

The finite volume element method (FVE) is a discretization technique for partial differential equations. It uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations, then restricts the admissible functions to a finite element space to discretize the solution. this paper develops discretization error estimates for general selfadjoint elliptic boundary value problems with FVE based on triangulations with linear finite element spaces and a general type of control volume. We establishO(h) estimates of the error in a discreteH 1 semi-norm. Under an additional assumption of local uniformity of the triangulation the estimate is improved toO(h 2). Results on the effects of numerical integration are also included.

Zhiqiang Cai

Papers

Coh-Metrix: Analysis of text on cohesion and language

Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients

Automated Evaluation of Text and Discourse with Coh-Metrix

First-order system least squares for second-order partial differential equations: part I

On the finite volume element method