The problem this paper addresses is the tension between descriptive and normative approaches to design theory and methodology. Descriptive approaches typically seek to document, formalize and/or automate existing ad hoc design methods, towards the goal of making current best practices available to all. In contrast, normative approaches attempt to improve upon existing design practices, towards ...

In this paper we study the properties of systems of bounded arithmetic capturing small complexity classes and state conditions sufficient for such systems to capture the corresponding complexity class tightly. Our class of systems of bounded arithmetic is the class of secondorder systems with comprehension axiom for a syntactically restricted class of formulas Φ ⊂ Σ 1 based on a logic in the de...

Quantitative methods for the study of the statistical properties of spontaneously occurring spike trains from single neurons have recently been presented. Such measurements suggest a number of descriptive mathematical models. One of these, based on a random walk towards an absorbing barrier, can describe a wide range of neuronal activity in terms of two parameters. These parameters are readily ...

Despite available therapies, mental disorders are the predominant chronic diseases of young people. Increasing the validity of descriptive psychiatry is now essential. Mathematical approaches can help characterise clinical phenotypes and aid both causal research and therapeutics in the community and the clinic.

Statistics is a broad mathematical discipline dealing with techniques for the collection, analysis, interpretation, and presentation of numerical data. Data are information used for reasoning, discussion, or calculation; data are the foundation of modern scientific inference. Data may be obtained by a formal sampling procedure, by recording responses to experimental conditions, or by observing ...

From a study of values of indices c 2 , g 2 and s 2 in the statistical reduction method and the k-index in Zwicky's subsequent division method applied to the same population, it is concluded that indices of the same general type of clustering, but formulated in different ways mathematically, sometimes lead to opposite results. The pattern of clustering of galaxies is by no means intrinsically e...

The computational and descriptive complexity of finite domain fixed template constraint satisfaction problem (CSP) is a well developed topic that combines several areas in mathematics and computer science. Allowing the domain to be infinite provides a way larger playground which covers many more computational problems and requires further mathematical tools. I will talk about some of the resear...

Mathematical modelling is essential for teaching and learning of mathematics aimed at improving students’ competence in solving real-world problems with mathematical means. Innovative technology-rich approaches can provide new paradigms education, which may produce opportunities the modelling. On other hand, there be a few challenges to successful use technology Although several studies have fo...

We describe our development and use of DescriptiveEnvironment (DE). This is a program to aid researchers in Finite Model Theory and students of logic to automatically generate examples, counterexamples of conjectures, reductions between problems, and visualizations of structures and queries. DescriptiveEnvironment is available for free use under an ISC license at http://www.cs.umass.edu/∼immerm...