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.

Observation impact in data assimilation: the effect of non-Gaussian observation error.

Data assimilation methods which avoid the assumption of Gaussian error statistics are being developed for geoscience applications. We investigate how the relaxation of the Gaussian assumption affects the impact observations have within the assimilation process. The effect of non-Gaussian observation error (described by the likelihood) is compared to previously published work studying the effect of a non-Gaussian prior. The observation impact is measured in three ways: the sensitivity of the analysis to the observations, the mutual information, and the relative entropy. These three measures have all been studied in the case of Gaussian data assimilation and, in this case, have a known analytical form. It is shown that the analysis sensitivity can also be derived analytically when at least one of the prior or likelihood is Gaussian. This derivation shows an interesting asymmetry in the relationship between analysis sensitivity and analysis error covariance when the two different sources of non-Gaussian structure are considered (likelihood vs. prior). This is illustrated for a simple scalar case and used to infer the effect of the non-Gaussian structure on mutual information and relative entropy, which are more natural choices of metric in non-Gaussian data assimilation. It is concluded that approximating non-Gaussian error distributions as Gaussian can give significantly erroneous estimates of observation impact. The degree of the error depends not only on the nature of the non-Gaussian structure, but also on the metric used to measure the observation impact and the source of the non-Gaussian structure.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

Second Strike and you are (finally) out? The Quashing of the Prevention of Infiltration Law (Amendment no. 4)

The blog-post critically analyses the Israeli Supreme Court judgment (HCJ 8425/13 Anon v. Knesset et al) quashing the Prevention of Infiltration Law (Amendment no. 4), offering themes of comparative constitutional interest.

Radar observations of non-thermal plasmas at different aspect angles

Data are presented from the EISCAT CP-3-E experiment which show the presence of non-thermal plasma over a range of latitudes. The O+ ion-velocity distribution function is almost toroidal when the electric field reaches values of 125 mV m−1. The ion temperature derived from such data assuming a Maxwellian distribution function will overestimate the true ion temperature when the observing angle is large with respect to the magnetic field, and underestimate the temperature when the aspect angle is small. When the expressions for the distribution function are extended to include mixed ion composition, an improvement is sometimes found in fitting the observed data, and estimates of the composition can be made. Such an analysis suggests that N2+ can occasionally form a significant part of the total ion density in a narrow height region centred at 275 km.

Incoherent scatter radar observations of non-Maxwellian ion velocity distributions in the auroral F-region

Observations by the EISCAT experiments “POLAR” and Common Programme CP-3 reveal non-Maxwellian ion velocity distributions in the auroral F-region ionosphere. Analysis of data from three periods is presented. During the first period, convection velocities are large (≈2 km s-1) and constant over part of a CP-3 latitude scan; the second period is one of POLAR data containing a short-lived (<1 min.) burst of rapid (>1.5 km s-1) flow. We concentrate on these two periods as they allow the study of a great many features of the ion-neutral interactions which drive the plasma non-thermal and provide the best available experimental test for models of the 3-dimensional ion velocity distribution function. The third period is included to illustrate the fact that non-thermal plasma frequently exists in the auroral ionosphere: the data, also from the POLAR experiment, cover a three-hour period of typical auroral zone flow and analysis reveals that the ion distribution varies from Maxwellian to the threshold of a toroidal form.

Model predictions of the occurrence of non-Maxwellian plasmas, and analysis of their effects on EISCAT data

The recent identification of non-thermal plasmas using EISCAT data has been made possible by their occurrence during large, short-lived flow bursts. For steady, yet rapid, ion convection the only available signature is the shape of the spectrum, which is unreliable because it is open to distortion by noise and sampling uncertainty and can be mimicked by other phenomena. Nevertheless, spectral shape does give an indication of the presence of non-thermal plasma, and the characteristic shape has been observed for long periods (of the order of an hour or more) in some experiments. To evaluate this type of event properly one needs to compare it to what would be expected theoretically. Predictions have been made using the coupled thermosphere-ionosphere model developed at University College London and the University of Sheffield to show where and when non-Maxwellian plasmas would be expected in the auroral zone. Geometrical and other factors then govern whether these are detectable by radar. The results are applicable to any incoherent scatter radar in this area, but the work presented here concentrates on predictions with regard to experiments on the EISCAT facility.

The modelled occurrence of non-thermal plasma in the ionospheric F-region and the possible consequences for ion outflows into the magnetosphere

A global, time-dependent, three-dimensional, coupled ionosphere-thermosphere model is used to predict the spatial distribution of non-thermal plasma in the F-layer. It is shown that, even for steady-state conditions with Kp as low as 3, the difference between the ion and neutral velocities often exceeds the neutral thermal speed by a factor, D', which can be as large as 4. Theoretically, highly non-Maxwellian, and probably toroidal, ion velocity distributions are expected when D' exceeds about 1.5. The lack of response of the neutral winds to sunward ion drifts in the dawn sector of the auroral oval cause this to be the region most likely to contain toroidal distributions. The maximum in D' is found in the throat region of the convection pattern, where the strong neutral winds of the afternoon sector meet the eastward ion flows of the morning sector. These predictions are of interest, not only to radar scientists searching for non-thermal ionospheric plasma, but also as one possible explanation of the initial heating and upward flows of ions in the cleft ion fountain and nightside auroral oval, both of which are a major source of plasma for the magnetosphere.

Bargaining over strategies of non-cooperative games

We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner’s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games.

On the possibility of non-fat frying using molten glucose

Fried products impose a health concerns due to considerable amount of oil they contain. Production of snack foods with minimal oil content and good management of oil during frying to minimise the production of toxic compounds continue to be challenging aims. This paper aims to investigate the possibility of producing a fat-free food snack by replacing frying oil with a non-fat medium. Glucose was melted and its temperature was then brought to 185°C and used to fry potato strips, to obtain a product referred here as glucose fries. The resulting product was compared with French fries prepared conventionally under conditions that resulted in similar final moisture content. The resulting products were also examined for crust formation, texture parameters, colour development and glucose content. Stereo microscope images showed that similar crusts were formed in the glucose fries and French fries. Texture parameters were found to be similar for both products at 5mm and 2 mm penetration depth. The maximum hardness at 2mm penetration depth was also similar for both products, but different from cooked potato. The colour development which characterised French fries was also observed in glucose fries. The glucose content in glucose fries was found to be twice the content of French fries, which is to be expected since glucose absorbed or adhered to the surface. In conclusion, glucose fries, with similar texture and colour characteristics to that of French fries, can be prepared by using a non-fat frying medium.

The tragedy of non-ideal theory

This paper has three aims. First, it argues that the present use of ‘ideal theory’ is unhelpful, and that an earlier and apparently more natural use focusing on perfection would be preferable. Second, it has tried to show that revision of the use of the term would better expose two distinctive normative issues, and illustrated that claim by showing how some contributors to debates about ideal theory have gone wrong partly through not distinguishing them. Third, in exposing those two distinct normative issues, it has revealed a particular way in which ideal theory even under the more specific, revisionary definition will often be central to working out what to do in non-ideal circumstances. By clarifying the terms on which debates over ideal and non-ideal theory should take place, and highlighting the particular problems each deals with, it tries to clear the ground for turning to the actual problem, which is what to do in our non-ideal and often tragic circumstances.

Regulating non-international armed conflicts: a review essay of 'The Law of Non-International Armed Conflict' by Sandesh Sivakumaran

This review essay engages with Sandesh Sivakumaran’s book The Law of Non-International Armed Conflict, exploring its significance both in international humanitarian law and international law more generally.

The Hugh Sinclair Unit of Human Nutrition – 20 years of research 1995–2015

The Hugh Sinclair Unit of Human Nutrition (HSUHN) at the University of Reading was founded in October 1995 with the appointment of Christine Williams OBE as the first Hugh Sinclair Chair in Human Nutrition. This was made possible by the competitively won funds from the estate and legacy of the late Professor Hugh Macdonald Sinclair (1910–1990). The vision for the newly established HSUHN was to ‘strengthen the evidence base for dietary recommendations for prevention of degenerative chronic diseases’. This has remained the research focus of the HSUHN under the leadership of Professors Christine Williams (1995–2005), Ian Rowland (2006–2013) and Julie Lovegrove (2014-present). Our mission is to improve population health and evaluate mechanisms of action for the effects of dietary components on health, which reflects Hugh Sinclair’s life ambition within nutritional science. Over the past 20 years, the HSUHN has developed an international reputation within the nutrition science community, and in recognition of the 20th anniversary, this paper highlights Hugh Sinclair’s contributions to the field of nutrition and key research achievements by members of the Unit.

Civilian casualties – do we really care? The failure of the revolution in military affairs of non-lethal weapons in the U.S., Russia and Israel

Causing civilian casualties during military operations has become a much politicised topic in international relations since the Second World War. Since the last decade of the 20th century, different scholars and political analysts have claimed that human life is valued more and more among the general international community. This argument has led many researchers to assume that democratic culture and traditions, modern ethical and moral issues have created a desire for a world without war or, at least, a demand that contemporary armed conflicts, if unavoidable, at least have to be far less lethal forcing the military to seek new technologies that can minimise civilian casualties and collateral damage. Non-Lethal Weapons (NLW) – weapons that are intended to minimise civilian casualties and collateral damage – are based on the technology that, during the 1990s, was expected to revolutionise the conduct of warfare making it significantly less deadly. The rapid rise of interest in NLW, ignited by the American military twenty five years ago, sparked off an entirely new military, as well as an academic, discourse concerning their potential contribution to military success on the 21st century battlefields. It seems, however, that except for this debate, very little has been done within the military forces themselves. This research suggests that the roots of this situation are much deeper than the simple professional misconduct of the military establishment, or the poor political behaviour of political leaders, who had sent them to fight. Following the story of NLW in the U.S., Russia and Israel this research focuses on the political and cultural aspects that have been supposed to force the military organisations of these countries to adopt new technologies and operational and organisational concepts regarding NLW in an attempt to minimise enemy civilian casualties during their military operations. This research finds that while American, Russian and Israeli national characters are, undoubtedly, products of the unique historical experience of each one of these nations, all of three pay very little regard to foreigners’ lives. Moreover, while it is generally argued that the international political pressure is a crucial factor that leads to the significant reduction of harmed civilians and destroyed civilian infrastructure, the findings of this research suggest that the American, Russian and Israeli governments are well prepared and politically equipped to fend off international criticism. As the analyses of the American, Russian and Israeli cases reveal, the political-military leaderships of these countries have very little external or domestic reasons to minimise enemy civilian casualties through fundamental-revolutionary change in their conduct of war. In other words, this research finds that employment of NLW have failed because the political leadership asks the militaries to reduce the enemy civilian casualties to a politically acceptable level, rather than to the technologically possible minimum; as in the socio-cultural-political context of each country, support for the former appears to be significantly higher than for the latter.