On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Only connect: an annotated bibliography reflecting the breadth and diversity of systems thinking

The field of systems thinking is both broad and diverse. This paper tries to provide assistance to outsiders wishing to find out what systems thinking is and also to insiders interested in exploring areas of the systems movement other than their own. A selection of books, papers and articles is given. Each has a full reference and a brief annotation, this being an account of, and a critical comment on, its content. The selection does not aim to be definitive or authoritative and obviously displays the predilections of the authors. However, the hope is that it will convey a sense of the intellectual and practical endeavours that, to the authors, constitute systems thinking and that it may aid the exploration of the range of holistic ideas that people have found useful in thinking about and acting in the world.

On the longitudinal extent of magnetopause reconnection pulses

The open magnetosphere model of cusp ion injection, acceleration and precipitation is used to predict the dispersion characteristics for fully pulsed magnetic reconnection at a low-latitude magnetopause X-line. The resulting steps, as would be seen by a satellite moving meridionally and normal to the ionospheric projection of the X-line, are compared with those seen by satellites moving longitudinally, along the open/closed boundary. It is shown that two observed cases can be explained by similar magnetosheath and reconnection characteristics, and that the major differences between them are well explained by the different satellite paths through the events. Both cases were observed in association with poleward-moving transient events seen by ground-based radar, as also predicted by the theory. The results show that the reconnection is pulsed but strongly imply it cannot also be spatially patchy, in the sense of isolated X-lines which independently are intermittently active. Furthermore they show that the reconnection pulses responsible for the poleward-moving events and the cusp ion steps, must cover at least 3 h of magnetic local time, although propagation of the active reconnection region may mean that it does not extend this far at any one instant of time.

Dependence of convective flows and particle precipitation in the high-latitude dayside ionosphere on theXandYcomponents of the interplanetary magnetic field

The asymmetries in the convective flows, current systems, and particle precipitation in the high-latitude dayside ionosphere which are related to the equatorial plane components of the interplanetary magnetic field (IMF) are discussed in relation to the results of several recent observational studies. It is argued that all of the effects reported to date which are ascribed to the y component of the IMF can be understood, at least qualitatively, in terms of a simple theoretical picture in which the effects result from the stresses exerted on the magnetosphere consequent on the interconnection of terrestrial and interplanetary fields. In particular, relaxation under the action of these stresses allows, in effect, a partial penetration of the IMF into the magnetospheric cavity, such that the sense of the expected asymmetry effects on closed field lines can be understood, to zeroth order, in terms of the “dipole plus uniform field” model. In particular, in response to IMF By, the dayside cusp should be displaced in longitude about noon in the same sense as By in the northern hemisphere, and in the opposite sense to By in the southern hemisphere, while simultaneously the auroral oval as a whole should be shifted in the dawn-dusk direction in the opposite sense with respect to By. These expected displacements are found to be consistent with recently published observations. Similar considerations lead to the suggestion that the auroral oval may also undergo displacements in the noon-midnight direction which are associated with the x component of the IMF. We show that a previously published study of the position of the auroral oval contains strong initial evidence for the existence of this effect. However, recent results on variations in the latitude of the cusp are more ambiguous. This topic therefore requires further study before definitive conclusions can be drawn.

Cultural geography and enchantment: the affirmative constitution of geographical research

Thrift [2008. Non-representational theory: space, politics, affect, 65. Abingdon: Routledge] has identified disenchantment as “[o]ne of the most damaging ideas” within social scientific and humanities research. As we have argued elsewhere, “[m]etanarratives of disenchantment and their concomitant preoccupation with destructive power go some way toward accounting for the overwhelmingly ‘critical’ character of geographical theory over the last 40 years” [Woodyer, T. and Geoghegan, H., 2013. (Re)enchanting geography? The nature of being critical and the character of critique in human geography. Progress in Human Geography, 37 (2), 195–214]. Through its experimentation with different ways of working and writing, cultural geography plays an important role in challenging extant habits of critical thinking. In this paper, we use the concept of “enchantment” to make sense of the deep and powerful affinities exposed in our research experiences and how these might be used to pursue a critical, yet more cheerful way of engaging with the geographies of the world.

Object-love at the Science Museum: cultural geographies of museum storerooms

The field of museum geography is taking on new significance as geographers and museum-studies scholars make sense of the spatial relations between the people, things, practices and buildings that make and remake museums. In order to strengthen this spatial interest in museums, this paper makes important connections between recent work in cultural geography and museum studies on love, materiality and the museum effect. This paper marks a departure from the preoccupation with the public spaces of museums to go behind the scenes of the Science Museum in London to explore its rarely visited, but nonetheless lively, small-to-medium-sized object storerooms at Blythe House. Incorporating field diary entries and interview extracts from two research projects based upon the museum storerooms at Blythe House, this paper brings to life the social interactions that take place between museum curators and conservators and the objects they care for. This focus on object-love enables scholars to consider anew what museums are and what they are for, the life of the museum object in the storeroom, and the emotional practices of professional curatorship and conservation. This journey into the storeroom at Blythe House makes explicit how object-love shapes museum space.

Resilience as transformative capacity: exploring the quadripartite cycle of structuration in a Mozambican resettlement programme

The concept of resilience has emerged out of a complex literature that has sought to make sense of an increasingly interconnected world that appears ever more beset by crises. Resilience’s appeal is reflected by the burgeoning mass of literature that has appeared on the subject in the past five years. However, there is ongoing debate surrounding its usage, with some commentators claiming that the term is inherently too conservative a one to be usefully applied to situations of vulnerability in which more radical social change is required. This article extends existing efforts to formulate more transformative notions of resilience by reframing it as a double-edged outcome of the pre-reflective and critical ways in which actors draw upon their internal structures following the occurrence of a negative event, thus reproducing or changing the external structural context that gave rise to the event in the first place. By employing a structuration-inspired analysis to the study of small-scale farmer responses to a flood-induced resettlement programme in central Mozambique, the article presents a systematic approach to the examination of resilience in light of this reframing. The case study findings suggest that more attention should be paid to the facilitative, as well as constraining, nature of structures if vulnerable populations are to be assisted in their efforts to exert transformative capacity over the wider conditions that give rise to their difficulties.

Intuitions in the Face of Diversity

In recent decades, intuitions' role in philosophy has been hotly debated. Many claim intuitions play an important role. Others, some armed with data, challenge the use of intuitions. This thesis reflects on this debate and advances the debate in two main ways. Having a clear understanding of the challenge which intuition-use in philosophy faces is important. Part I focuses on this. Chapters 1-2 introduce the topic of intuitions, motivate the methodological study of intuitions, and present the historical background to recent empirical challenges to intuition-use. Chapters 3-5 concern the contemporary challenge. I present the empirical evidence the challenge uses, present what I argue to be the strongest version of the challenge, and defend that challenge against some objections. How one characterises intuitions is incredibly important in philosophical methodology. If we are to properly evaluate philosophical methods vis-a-vis their use of something called intuitions { if we are to assess the empirical challenge { it is important to be clear exactly what we mean by `intuitions'. Part II focuses on this. Chapter 6 argues there is little consensus among philosophers as to what intuitions are and their role in philosophy. Chapter 7 questions whether philosophers have developed an idiolect in which `intuition' has distinctive meaning | as frequently supposed. Chapter 8 points out a common misunderstanding about intuitions in philosophy; using quantitative tools to challenge the idea that an increased use of `intuition' in philosophy is the result of an increased use of intuition. So, the developing picture is one of confusion, without a clear idea of what sense of `intuition' is important. Fortunately, Chapter 9 sets us back on the right track. It sets out a positive programme for evaluative methodology: methodologists should adopt a permissive conception of intuitions and make fine distinctions between different intuitions, so long as we can track those distinctions while philosophising.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

How Pragmatically Odd! Interface Delays and Pronominal Subject Distribution in the L2 Spanish of English Natives

Sorace (2000, 2005) has claimed that while L2 learners can easily acquire properties of L2 narrow syntax they have significant difficulty with regard to interpretation and the discourse distribution of related properties, resulting in so-called residual optionality. However, there is no consensus as to what this difficulty indicates. Is it related to an insurmountable grammatical representational deficit (in the sense of representation deficit approaches; e.g. Beck 1998, Franceschina 2001, Hawkins 2005), is it due to cross-linguistic interference, or is it just a delay due to a greater complexity involved in the acquisition of interface-conditioned properties? In this article, I explore the L2 distribution of null and overt subject pronouns of English speaking learners of L2 Spanish. While intermediate learners clearly have knowledge of the syntax of Spanish null subjects, they do not have target-like pragmatic knowledge of their distribution with overt subjects. The present data demonstrate, however, that this difficulty is overcome at highly advanced stages of L2 development, thus suggesting that properties at the syntax-pragmatics interface are not destined for inevitable fossilization.

How students view the boundaries between their science and religious education concerning the origins of life and the universe

Internationally in secondary schools, lessons are typically taught by subject specialists, raising the question of how to accommodate teaching which bridges the sciences and humanities. This is the first study to look at how students make sense of the teaching they receive in two subjects (science and religious education) when one subject’s curriculum explicitly refers to cross-disciplinary study and the other does not. Interviews with 61 students in seven schools in England suggested that students perceive a permeable boundary between science and their learning in science lessons and also a permeable boundary between religion and their learning in RE lessons, yet perceive a firm boundary between science lessons and RE lessons. We concluded that it is unreasonable to expect students to transfer instruction about cross-disciplinary perspectives across such impermeable subject boundaries. Finally we consider the implications of these findings for the successful management of cross-disciplinary education.

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

Rawls and Rousseau: 'amour-propre' and the strains of commitment

In this paper I try to illuminate the Rawlsian architectonic through an interpretation of what Rawls’ Lectures on the History of Political Philosophy say about Rousseau. I argue that Rawls’ emphasis there when discussing Rousseau on interpreting amour-propre so as to make it compatible with a life in at least some societies draws attention to, and helps explicate, an analogous feature of his own work, the strains of commitment broadly conceived. Both are centrally connected with protecting a sense of self which is vital for one’s own agency. This allows us to appreciate better than much of the literature presently does the requirement for Rawls that justice and the good are congruent, that a society of justice does not disfigure citizens’ ability to live out lives relatively unmarked by relations of domination. Some comments on G. A. Cohen’s critiques of Rawls are made.

The dark side of brand attachment: a conceptual framework of brand attachment's detrimental outcomes

Brand attachment recently has received great attention among practitioners and academics alike. Scholars consider brand attachment a key requisite in consumer-brand relationships that create favourable consumer behaviours such as positive brand attitudes and brand loyalty. Few studies, however, examine the detrimental outcomes of brand attachment. In this paper, we develop a conceptual framework that explores how brand attachment may explain detrimental consumer behaviours, such as oppositional brand loyalty and antibrand actions. We investigate consumers' trash-talking and schadenfreude in brand communities and their subsequent outcomes. Our framework reveals that the link between brand attachment and oppositional brand loyalty is driven by consumers' social identity and sense of rivalry. Furthermore, we put forward that brand attachment leads to anti-brand actions when relationships deteriorate. We identify two factors behind the deterioration: (1) companies' opportunism activities, and (2) incongruity between consumers' values and the brand's values. Theoretical and managerial implications are discussed arising from our emerging 'dark side' brand attachment framework.

Resolution and discrimination - two sides of the same coin

The notions of resolution and discrimination of probability forecasts are revisited. It is argued that the common concept underlying both resolution and discrimination is the dependence (in the sense of probability theory) of forecasts and observations. More specifically, a forecast has no resolution if and only if it has no discrimination if and only if forecast and observation are stochastically independent. A statistical tests for independence is thus also a test for no resolution and, at the same time, for no discrimination. The resolution term in the decomposition of the logarithmic scoring rule, and the area under the Receiver Operating Characteristic will be investigated in this light.