Polyharmonic approximation on the sphere

The purpose of this article is to provide new error estimates for a popular type of SBF approximation on the sphere: approximating by linear combinations of Green's functions of polyharmonic differential operators. We show that the $L_p$ approximation order for this kind of approximation is $\sigma$ for functions having $L_p$ smoothness $\sigma$ (for $\sigma$ up to the order of the underlying differential operator, just as in univariate spline theory). This is an improvement over previous error estimates, which penalized the approximation order when measuring error in $L_p$, p>2 and held only in a restrictive setting when measuring error in $L_p$, p<2.Comment: 16 pages; revised version; to appear in Constr. Appro

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Trouble in Paradise - A disabled person's right to the satisfaction of a self-defined need:Some conceptual and practical problems

This paper questions the usefulness of the rights-based approach to ameliorating the social situation of disabled people in Britain and advances two criticisms. First, that rights and self-de? ned needs have been under-theorised by disability theorists to the extent that they have insuf? ciently appreciated the problems that these approaches pose. The paper suggests that rights to appropriate resources to satisfy self-de? ned needs will generate vast numbers of competing rights claims and that the resulting tendency of rights to con? ict has been under-appreciated. Secondly, that there has been little consideration of how these con? icts might be reconciled. The ? rst two sections of the paper look at the concepts of ascribed and self-de? ned needs, respectively, whilst the ? nal one looks at some of the problems of the rights approach and some of the dif? culties of making self-de? ned need the basis of rights claims

Computational Controversy

Climate change, vaccination, abortion, Trump: Many topics are surrounded by fierce controversies. The nature of such heated debates and their elements have been studied extensively in the social science literature. More recently, various computational approaches to controversy analysis have appeared, using new data sources such as Wikipedia, which help us now better understand these phenomena. However, compared to what social sciences have discovered about such debates, the existing computational approaches mostly focus on just a few of the many important aspects around the concept of controversies. In order to link the two strands, we provide and evaluate here a controversy model that is both, rooted in the findings of the social science literature and at the same time strongly linked to computational methods. We show how this model can lead to computational controversy analytics that have full coverage over all the crucial aspects that make up a controversy.Comment: In Proceedings of the 9th International Conference on Social Informatics (SocInfo) 201

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Principles of Stakes Fairness in Sport

Fairness in sport is not just about assigning the top prizes to the worthiest competitors. It is also about the way the prize structure itself is organised. For many sporting competitions, although it may be acceptable for winners to receive more than losers, it can seem unfair for winners to take everything and for losers to get nothing. Yet this insight leaves unanswered some difficult questions about what stakes fairness requires and which principles of stakes fairness are appropriate for particular competitions. In this article I specify a range of different principles of stakes fairness (ten in total) that could regulate sporting competitions. I also put forward a theoretical method for pairing up appropriate principles of stakes fairness with given sporting competitions. Specifically, I argue that the underlying rationales for holding sporting competitions can provide useful guides for identifying appropriate principles of stakes fairness. I then seek to clarify and work through some of the implications of this method for a sample of real world controversies over sporting prize structures. I also attempt to refine the method in response to two possible objections from indeterminacy and relativism. Finally, I compare and contrast my conclusions with more general philosophical debates about justice

The Gtpase Rho Controls a P53-Dependent Survival Checkpoint during Thymopoiesis

During the early stages of thymopoiesis, cell survival is controlled by cytokines that regulate the expression of antiapoptotic proteins such as Bcl-2. At the pre-T cell stage, a critical checkpoint for β chain selection is monitored by the tumor suppressor p53: pre-T cells can survive and differentiate when p53 is removed genetically or when its proapoptotic function is inactivated physiologically as a consequence of signaling through the pre-T cell receptor complex. Previous work has shown that the guanine nucleotide binding protein Rho controls cell survival in T cell progenitors. Here we define the survival pathways controlled by Rho in pre-T cells and show that this GTPase is a pivotal regulator of the p53-mediated checkpoint operating at the time of β selection: loss of Rho function results in apoptosis in pre-T cells, but this cell death is prevented by loss of p53. The prevention of cell death by loss of p53 restored numbers of early T cell progenitors but did not fully restore thymic cellularity. Further analysis revealed that loss of Rho function caused survival defects in CD4/8 double-positive thymocytes that is independent of p53 but can be prevented by ectopic expression of Bcl-2. These studies highlight that the GTPase Rho is a crucial component of survival signaling pathways in at least two different thymocyte subpopulations: Rho controls the p53 survival checkpoint in pre-T cells and is also crucial for a p53 independent survival signaling pathway in CD4/8 double positives

National Security Risks? Uncertainty, Austerity and Other Logics of Risk in the UK government’s National Security Strategy

Risk scholars within Security studies have argued that the concept of security has gone through a fundamental transformation away from a threat-based conceptualisation of defence, urgency and exceptionality to one of preparedness, precautions and prevention of future risks, some of which are calculable, others of which are not. This article explores whether and how the concept of security is changing due to this ‘rise of risk’, through a hermeneutically grounded conceptual and discourse analysis of the United Kingdom government’s national security strategy (NSS) from 1998 to 2011. We ask how risk-security language is employed in the NSS; what factors motivate such discursive shifts; and what, if any, consequences of these shifts can be discerned in UK national security practices. Our aim is twofold: to better understand shifts in the security understandings and policies of UK authorities; and to contribute to the conceptual debate on the significance of the rise of risk as a component of the concept of security

On a clear day you can see forever : integrating values and skills in sex offender treatment

The topic of sex offender rehabilitation frequently evokes fierce reactions, ranging from strident demands for harsher sentences contrasted with calls for more imaginative and compassionate sentencing options. There seems to be a polarization of positions centred on the question of offenders\u27 moral standing: are they moral strangers or fellow travellers? This fundamental disagreement about offenders\u27 moral status is at the core of a number of independent, although related current practice and research issues confronting the field, namely: (1) risk management versus strength-based treatment approaches; (2) the utility of utilizing individually tailored versus manual-based programmes for offenders; (3) focusing on the technical aspects or therapy as opposed to relationship and therapist factors (what has been called process issues); and (4) the conflict between protecting the community versus promoting the interests of offenders. In this paper I suggest that an approach to sex offender treatment based on a combination of human rights theory (an ethical resource) and strengths-based approaches can help us navigate our way through the above dilemmas in a way that addressees both the needs of offenders and those of the community

Continuity and change in the institution of town and country planning: modelling the role of ideology

The institution of town and country planning rests upon ideas and concepts which will always be contested. Such concepts include ‘liberty’, ‘community’, ‘society’ and ‘the state’. It is a function of political ideology to seek to fix the meanings of contested concepts and thus exert control over political reality. By analysing the particular conceptual structure of the ideologies which seek to influence planning from positions of political power, the analyst can show how these ideologies are related to shifts in the conceptual and institutional structure of planning. The paper illustrates this analytical method in the context of the transition from the ideology of New Labour to the ideology of the Conservative-led Coalition government in England after 2010