
In NIST/SEMATECH eHandbook of Statistical Methods (2012), 7.2.6.2
Abstract
[Excerpt: Definitions of order statistics and ranks] For a series of measurements Y1, …, YN, denote the data ordered in increasing order of magnitude by Y〈1〉, …, Y〈N〉. These ordered data are called order statistics. If Y〈j〉 is the order statistic that corresponds to the measurement Yᵢ, then the rank for Yᵢ is j; i.e., [::] Y〈j〉 ∼ Yᵢ, rᵢ=j. [Definition of percentiles] Order statistics provide a way of estimating proportions of the data that should fall above and below a ...


Abstract
There are a large number of different definitions used for sample quantiles in statistical computer packages. Often within the same package one definition will be used to compute a quantile explicitly, while other definitions may be used when producing a boxplot, a probability plot, or a QQ plot. We compare the most commonly implemented sample quantile definitions by writing them in a common notation and investigating their motivation and some of their properties. We argue that there is a need to ...


In Research Trends in Science, Technology and Mathematics Education (May 2006), pp. 5590
Abstract
People have a natural desire to organize, classify, label, and define the things, events, and patterns of their daily lives. But their bestlaid plans are overwhelmed by the inevitable change, growth, innovation, progress, evolution, diversity, and entropy. These rapid changes, which create difficulties for people, are far more disruptive for the fragile databases and knowledge bases in computer systems. The term knowledge soup better characterizes the fluid, dynamically changing nature of the information that people learn, reason about, act upon, and ...


Abstract
Fuzziness is explored as an alternative to randomness for describing uncertainty. The new setsaspoints geometric view of fuzzy sets is developed. This view identifies a fuzzy set with a point in a unit hypercube and a nonfuzzy set with a vertex of the cube. Paradoxes of twovalued logic and set theory, such as Russell's paradox, correspond to the midpoint of the fuzzy cube. The fundamental questions of fuzzy theory—How fuzzy is a fuzzy set? How much is one fuzzy set a ...


MathWorks Technical Articles and Newsletters, Vol. 1 (1990), 92036v00
Abstract
If the average of two numbers is three, what are the numbers? The solution to this problem is not unique, and the problem is illdefined, but that does not mean that MATLAB® cannot solve it. [\n] In this article from 1990, Cleve Moler explores this simple yet impossible problem and others like it using MATLAB to find answers with the fewest nonzero components and other “nice” solutions. ...


Abstract
The fate of dimensions of dimensioned quantities that are inserted into the argument of transcendental functions such as logarithms, exponentiation, trigonometric, and hyperbolic functions is discussed. Emphasis is placed on common misconceptions that are not often systematically examined in undergraduate courses of physical sciences. The argument of dimensional inhomogeneity of the terms of a Taylor expansion of a transcendental function presented in some nonpeerreviewed popular Internet sites is shown to be false. ...


(February 2014)
Abstract
List of indexed keywords within the transdisciplinary set of domains which relate to the Integrated Natural Resources Modelling and Management (INRMM). In particular, the list of keywords maps the semantic tags in the INRMM Metainformation Database (INRMMMiD). [\n] The INRMMMiD records providing this list are accessible by the special tag: inrmmlistoftags ( http://mfkp.org/INRMM/tag/inrmmlistoftags ). ...


Abstract
In this paper, the author extends his previous treatment of 'The Bargaining Problem" to a wider class of situations in which threats can play a role. A new approach is introduced involving the elaboration of the threat concept. [Introduction] The theory presented here was developed to treat economic (or other) situations involving two individuals whose interests are neither completely opposed nor completely coincident. The word cooperative is used because the two individuals are supposed to be able to discuss the situation ...


Abstract
Rejoinder to "Brownian distance covariance" by Gábor J. Székely and Maria L. Rizzo [arXiv:1010.0297] ...


Abstract
We consider two desired properties of learning algorithms: *sparsity* and *algorithmic stability*. Both properties are believed to lead to good generalization ability. We show that these two properties are fundamentally at odds with each other: a sparse algorithm cannot be stable and vice versa. Thus, one has to trade off sparsity and stability in designing a learning algorithm. In particular, our general result implies that $\ell_1$regularized regression (Lasso) cannot be stable, while $\ell_2$regularized regression is known to have strong stability properties ...


Abstract
[Abstract] Cluster analysis is aimed at classifying elements into categories on the basis of their similarity. Its applications range from astronomy to bioinformatics, bibliometrics, and pattern recognition. We propose an approach based on the idea that cluster centers are characterized by a higher density than their neighbors and by a relatively large distance from points with higher densities. This idea forms the basis of a clustering procedure in which the number of clusters arises intuitively, outliers are automatically spotted and excluded ...


Abstract
Many tools designed to help programmers view and manipulate source code exploit the formal structure of the programming language. Languagebased tools use information derived via linguistic analysis to offer services that are impractical for purely textbased tools. In order to be effective, however, languagebased tools must be designed to account properly for the documentary structure of source code: a structure that is largely orthogonal to the linguistic but no less important. Documentary structure includes, in addition to the language text, all ...


Abstract
While XP principles are independent of the languages in which software is developed, we can distinguish properties of programming languages that affect the agility of development. Some languages are inherently more agile than others, and the experience of developing software in these languages reflects this. A family of languages descended from the mathematics notation developed at Harvard in the 1950s by Iverson [1] shares properties of extreme terseness and abstractive power with weak data typing. The history of software development in ...


Abstract
[Significance] The maximum entropy principle (MEP) states that for many statistical systems the entropy that is associated with an observed distribution function is a maximum, given that prior information is taken into account appropriately. Usually systems where the MEP applies are simple systems, such as gases and independent processes. The MEP has found thousands of practical applications. Whether a MEP holds for complex systems, where elements interact strongly and have memory and path dependence, remained unclear over the past half century. ...


Abstract
[Significance] Hilly landscapes are typically mantled with soil and underlain by a weathered bedrock zone that may extend tens of meters beneath the surface before reaching fresh bedrock. The weathered bedrock zone influences water runoff to channels, the chemistry of that water, the rates and processes of erosion, and atmospheric processes due to plant uptake of moisture and return to the atmosphere. However, the spatial pattern of the underlying freshbedrock surface is essentially unknown. We present a testable model that predicts ...


Abstract
Highly heterogeneous degree distributions yield efficient spreading of simple epidemics through networks, but can be inefficient with more complex epidemiological processes. We study diseases with nonlinear force of infection whose prevalences can abruptly collapse to zero while decreasing the transmission parameters. We find that scalefree networks can be unable to support diseases that, on the contrary, are able to persist at high endemic levels in homogeneous networks with the same average degree. ...


No. 2002/c. (2002)
Abstract
In many projects 20% of the total effort yields 80% of the total outcome. This phenomenon is usually termed Pareto’s 80/20 law. In this paper we propose a theory to explain this empirical observation. The yield gained by the subdivision of a project into several tasks is measured. The requirements for such a yield lead to the axioms of Shannon Information. With the right adjustment of units for cost and yield this gives the definition of Entropic Yield. Pareto’s 80/20 law thus results from an economic optimization of Entropic ...


Abstract
The Pareto 80/20 Rule, also known as the Pareto principle or law, states that a small number of causes (20%) is responsible for a large percentage (80%) of the effect. Although widely recognized as a heuristic rule, this proportion has not been theoretically based. The article considers derivation of this 80/20 rule and some other standard quotients from the mean and its interval estimation for the total value defined by the product of two variables in the random partitioning model. ...


Abstract
[Significance] Humans usually punish free riders but refuse to sanction those who cooperate but do not punish. However, such secondorder punishment is essential to maintain cooperation. The central authorities established in modern societies punish both free riders and tax evaders. This is a paradox: would individuals who do not engage in secondorder punishment strive for an authority that does? We address this puzzle with a mathematical model and an economic experiment. When individuals can choose between authorities by migrating between different ...


Abstract
It is argued that formal verifications of programs, no matter how obtained, will not play the same key role in the development of computer science and software engineering as proofs do in mathematics. Furthermore the absence of continuity, the inevitability of change, and the complexity of specification of significantly many real programs make the formal verification process difficult to justify and manage. It is felt that ease of formal verification should not dominate program language design. ...


Abstract
[Excerpt] "I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, ...


In Canadian Conference on Computer & Electrical Engineering (1990)
Abstract
Prolog can be extended by a system of constraints on closed intervals to perform declarative relational arithmetic. Imposing constraints on an interval can narrow its range and propagate the narrowing to other intervals related to it by constraint equations or inequalities. Relational interval arithmetic can be used to contain floating point errors and, when combined with Prolog backtracking, to obtain numeric solutions to linear and nonlinear rational constraint satisfaction problems over the reals (e.g. ndegree polynomial equations). This technique differs from ...


Abstract
As the first editorinchief of Management Science, I expressed my ambition for the society (TIMS) and its journal. My notion was that a society and journal in the subject of a science of management would investigate how humans can manage their affairs well. For me, “well” means “ethically,” or in the best interest of humanity in a world of filthy oppression and murder (I'm a philosopher and therefore have a philosophical bias, the same bias Plato had when he wrote the ...


Abstract
One starting point for a dialogue between literacy education and science education is the way in which science uses multiple literacies. Literacy education usually begins with an emphasis on language and on texts: how they're made, what they mean. Science education begins with questions about how things happen in the world. We might imagine a scientist studying literacy to be a bit like an ethnographer. An ethnographer of science and its literacies will come across other scientists making and using texts, ...


Abstract
The 1979 ACM 7bring Award was presented to Kenneth E. Iverson by Walter Carlson, Chairman of the Awards Committee, at the ACM Annual Conference in Detroit, Michigan, October 29, 1979. in making its selection, the General Technical Achievement Award Committee cited Iverson for his pioneering effort in programming languages and mathematical notation resulting in what the computing field now knows as APL. Iverson's contributions to the implementation of interactive systems, to the educational uses of APL, and to programming language theory and ...
