Improved classification for compositional data using the α\alpha-transformation

In compositional data analysis an observation is a vector containing non-negative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of proportions that sum to one. Data of this type arise in many areas including geology, archaeology, biology, economics and political science. In this paper we investigate methods for classification of compositional data. Our approach centres on the idea of using the $\alpha$-transformation to transform the data and then to classify the transformed data via regularised discriminant analysis and the k-nearest neighbours algorithm. Using the $\alpha$-transformation generalises two rival approaches in compositional data analysis, one (when $\alpha=1$) that treats the data as though they were Euclidean, ignoring the compositional constraint, and another (when $\alpha=0$) that employs Aitchison's centred log-ratio transformation. A numerical study with several real datasets shows that whether using $\alpha=1$ or $\alpha=0$ gives better classification performance depends on the dataset, and moreover that using an intermediate value of $\alpha$ can sometimes give better performance than using either 1 or 0.Comment: This is a 17-page preprint and has been accepted for publication at the Journal of Classificatio

A data-based power transformation for compositional data

Compositional data analysis is carried out either by neglecting the compositional constraint and applying standard multivariate data analysis, or by transforming the data using the logs of the ratios of the components. In this work we examine a more general transformation which includes both approaches as special cases. It is a power transformation and involves a single parameter, {\alpha}. The transformation has two equivalent versions. The first is the stay-in-the-simplex version, which is the power transformation as defined by Aitchison in 1986. The second version, which is a linear transformation of the power transformation, is a Box-Cox type transformation. We discuss a parametric way of estimating the value of {\alpha}, which is maximization of its profile likelihood (assuming multivariate normality of the transformed data) and the equivalence between the two versions is exhibited. Other ways include maximization of the correct classification probability in discriminant analysis and maximization of the pseudo R-squared (as defined by Aitchison in 1986) in linear regression. We examine the relationship between the {\alpha}-transformation, the raw data approach and the isometric log-ratio transformation. Furthermore, we also define a suitable family of metrics corresponding to the family of {\alpha}-transformation and consider the corresponding family of Frechet means.Comment: Published in the proceddings of the 4th international workshop on Compositional Data Analysis. http://congress.cimne.com/codawork11/frontal/default.as

Interlocal Contractual Arrangements in the Provision of Public Safety

The range of interlocal contractual arrangements in the realm of public safety in Florida provides a research site to examine the extent to which these arrangements have been used by local governments. We developed a contractual perspective on interlocal contractual arrangements as relational contracts by arguing that their institutional designs are partly an effort of involved parties to reduce transaction costs that are the product of the properties of the services themselves; and partly by state statutes that allowed mix approaches to contractual arrangements. A relational contract is advantageous because it specified the activities to be rendered without unnecessarily intruding on the authority of the other jurisdictions. It is nonobligatory, voluntary, and easily terminated without legal consequences to either party. Alternatively, in the presence of regional politics and avoid future disputes, municipality and county governments can choose a more legally binding contract by using non-relational contract such as interlocal agreements, contracts or leases. Utilizing the data compiled by the Florida Department of Community Affairs, we identified 2,251 interlocal contractual agreements in the provision of public safety. Our results show that there is a positive and significant association between city-county relations and the type of contractual arrangement chosen to govern those relations. There are also evidence when specialized investment required in the provision of public safety services, a non relational contract was preferred; and when measuring and monitoring the outcomes of the services are relative difficult, a relational contract was preferred. A single functional service area with similar policy and goal preferences also affected the transaction costs of negotiating, operating, and enforcing contractual arrangement; so did the number of collaborators involved in an agreement

Electrically driven spin resonance in a bent disordered carbon nanotube

Resonant manipulation of carbon nanotube valley-spin qubits by an electric field is investigated theoretically. We develop a new analysis of electrically driven spin resonance exploiting fixed physical characteristics of the nanotube: a bend and inhomogeneous disorder. The spectrum is simulated for an electron valley-spin qubit coupled to a hole valley-spin qubit and an impurity electron spin, and features that coincide with a recent measurement are identified. We show that the same mechanism allows resonant control of the full four-dimensional spin-valley space.Comment: 11 pages, 7 figure

Better by design: Business preferences for environmental regulatory reform

We present the preferences for environmental regulatory reform expressed by 30 UK businesses and industry bodies from 5 sectors. While five strongly preferred voluntary regulation, seven expressed doubts about its effectiveness, and 18 expressed no general preference between instrument types. Voluntary approaches were valued for flexibility and lower burdens, but direct regulation offered stability and a level playing field. Respondents sought regulatory frameworks that: are coherent; balance clarity, prescription and flexibility; are enabled by positive regulatory relationships; administratively efficient; targeted according to risk magnitude and character; evidence-based and that deliver long-term market stability for regulatees. Anticipated differences in performance between types of instrument can be undermined by poor implementation. Results underline the need for policy makers and regulators to tailor an effective mix of instruments for a given sector, and to overcome analytical, institutional and political barriers to greater coherence, to better coordinate existing instruments and tackle new environmental challenges as they emerge

Opinion: A new approach to financial regulation

It has been five years since the US Congress enacted the landmark Dodd–Frank Wall Street Reform and Consumer Protection Act; and despite the fact that about 20% of the Act has yet to be implemented (1), several legislative initiatives are now attempting to soften or roll back key provisions. This pattern of regulatory action and reaction is not new. The financial excesses of one period often lead to asset bubbles that burst, ushering in a new period of much greater regulation. This, in turn, is systematically weakened over time as markets recover and we forget the reasons why we imposed such stringent regulations in the first place. Even before Dodd–Frank, the financial industry was among the most highly regulated of industries in the world. However, the many layers of regulation and multiple regulatory agencies were insufficient to prevent financial crisis. Why

Quantum information transport to multiple receivers

The importance of transporting quantum information and entanglement with high fidelity cannot be overemphasized. We present a scheme based on adiabatic passage that allows for transportation of a qubit, operator measurements and entanglement, using a 1-D array of quantum sites with a single sender (Alice) and multiple receivers (Bobs). Alice need not know which Bob is the receiver, and if several Bobs try to receive the signal, they obtain a superposition state which can be used to realize two-qubit operator measurements for the generation of maximally entangled states.Comment: Modified in view of referee's comments, new author added, natural scheme for operator measurements identified, hence W state preparation replaced with GHZ state preparation via operator measurements. 4 pages, 3 figure