The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Getting the measure of derivational morphology in adult speech a corpus analysis using MorphoQuantics

This paper describes the methodology used to compile a corpus called MorphoQuantics that contains a comprehensive set of 17,943 complex word types extracted from the spoken component of the British National Corpus (BNC). The categorisation of these complex words was derived primarily from the classification of Prefixes, Suffixes and Combining Forms proposed by Stein (2007). The MorphoQuantics corpus has been made available on a website of the same name; it lists 554 word-initial and 281 word-final morphemes in English, their etymology and meaning, and records the type and token frequencies of all the associated complex words containing these morphemes from the spoken element of the BNC, together with their Part of Speech. The results show that, although the number of word-initial affixes is nearly double that of word-final affixes, the relative number of each observed in the BNC is very similar; however, word-final affixes are more productive in that, on average, the frequency with which they attach to different bases is three times that of word-initial affixes. Finally, this paper considers how linguists, psycholinguists and psychologists may use MorphoQuantics to support their empirical work in first and second language acquisition, and clinical and educational research.

Probability functions to build composite indicators: a methodology to measure environmental impacts of genetically modified crops

There is an on-going debate on the environmental effects of genetically modified crops to which this paper aims to contribute. First, data on environmental impacts of genetically modified (GM) and conventional crops are collected from peer-reviewed journals, and secondly an analysis is conducted in order to examine which crop type is less harmful for the environment. Published data on environmental impacts are measured using an array of indicators, and their analysis requires their normalisation and aggregation. Taking advantage of composite indicators literature, this paper builds composite indicators to measure the impact of GM and conventional crops in three dimensions: (1) non-target key species richness, (2) pesticide use, and (3) aggregated environmental impact. The comparison between the three composite indicators for both crop types allows us to establish not only a ranking to elucidate which crop is more convenient for the environment but the probability that one crop type outperforms the other from an environmental perspective. Results show that GM crops tend to cause lower environmental impacts than conventional crops for the analysed indicators.

A moment problem for random discrete measures

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures η on X which are of the form η =

A methodology to measure the environmental impact of ICT operating systems across different device platforms

Abstract: A new methodology was created to measure the energy consumption and related green house gas (GHG) emissions of a computer operating system (OS) across different device platforms. The methodology involved the direct power measurement of devices under different activity states. In order to include all aspects of an OS, the methodology included measurements in various OS modes, whilst uniquely, also incorporating measurements when running an array of defined software activities, so as to include OS application management features. The methodology was demonstrated on a laptop and phone that could each run multiple OSs, results confirmed that OS can significantly impact the energy consumption of devices. In particular, the new versions of the Microsoft Windows OS were tested and highlighted significant differences between the OS versions on the same hardware. The developed methodology could enable a greater awareness of energy consumption, during both the software development and software marketing processes.

On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Let λ1,…,λn be real numbers in (0,1) and p1,…,pn be points in Rd. Consider the collection of maps fj:Rd→Rd given by fj(x)=λjx+(1−λj)pj. It is a well known result that there exists a unique nonempty compact set Λ⊂Rd satisfying Λ=∪nj=1fj(Λ). Each x∈Λ has at least one coding, that is a sequence (ϵi)∞i=1 ∈{1,…,n}N that satisfies limN→∞fϵ1…fϵN(0)=x. We study the size and complexity of the set of codings of a generic x∈Λ when Λ has positive Lebesgue measure. In particular, we show that under certain natural conditions almost every x∈Λ has a continuum of codings. We also show that almost every x∈Λ has a universal coding. Our work makes no assumptions on the existence of holes in Λ and improves upon existing results when it is assumed Λ contains no holes.

“TEEP: A Course-Driven Assessment Measure”

Conference proceedings paper in Alexander, O. (Ed.) 2007, Proceedings of the 2005 joint BALEAP/SATEFL conference: New Approaches to Materials Development for Language Learning. Bern: Peter Lang.