Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

Standardized evaluation of algorithms for computer-aided diagnosis of dementia based on structural MRI: The CADDementia challenge

Algorithms for computer-aided diagnosis of dementia based on structural MRI have demonstrated high performance in the literature, but are difficult to compare as different data sets and methodology were used for evaluation. In addition, it is unclear how the algorithms would perform on previously unseen data, and thus, how they would perform in clinical practice when there is no real opportunity to adapt the algorithm to the data at hand. To address these comparability, generalizability and clinical applicability issues, we organized a grand challenge that aimed to objectively compare algorithms based on a clinically representative multi-center data set. Using clinical practice as the starting point, the goal was to reproduce the clinical diagnosis. Therefore, we evaluated algorithms for multi-class classification of three diagnostic groups: patients with probable Alzheimer's disease, patients with mild cognitive impairment and healthy controls. The diagnosis based on clinical criteria was used as reference standard, as it was the best available reference despite its known limitations. For evaluation, a previously unseen test set was used consisting of 354 T1-weighted MRI scans with the diagnoses blinded. Fifteen research teams participated with a total of 29 algorithms. The algorithms were trained on a small training set (n = 30) and optionally on data from other sources (e.g., the Alzheimer's Disease Neuroimaging Initiative, the Australian Imaging Biomarkers and Lifestyle flagship study of aging). The best performing algorithm yielded an accuracy of 63.0% and an area under the receiver-operating-characteristic curve (AUC) of 78.8%. In general, the best performances were achieved using feature extraction based on voxel-based morphometry or a combination of features that included volume, cortical thickness, shape and intensity. The challenge is open for new submissions via the web-based framework: http://caddementia.grand-challenge.org.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Assessing the ability of rural agrarian areas to provide Cultural Ecosystem Services (CES): a Multi Scale Social Indicator Framework (MSIF)

Assessing the ways in which rural agrarian areas provide Cultural Ecosystem Services (CES) is proving difficult to achieve. This research has developed an innovative methodological approach named as Multi Scale Indicator Framework (MSIF) for capturing the CES embedded into the rural agrarian areas. This framework reconciles a literature review with a trans-disciplinary participatory workshop. Both of these sources reveal that societal preferences diverge upon judgemental criteria which in turn relate to different visual concepts that can be drawn from analysing attributes, elements, features and characteristics of rural areas. We contend that it is now possible to list a group of possible multi scale indicators for stewardship, diversity and aesthetics. These results might also be of use for improving any existing European indicators frameworks by also including CES. This research carries major implications for policy at different levels of governance, as it makes possible to target and monitor policy instruments to the physical rural settings so that cultural dimensions are adequately considered. There is still work to be developed on regional specific values and thresholds for each criteria and its indicator set. In practical terms, by developing the conceptual design within a common framework as described in this paper, a considerable step forward towards the inclusion of the cultural dimension in European wide assessments can be made.

The origins of small wars: from special operations to ideological insurgencies

This edited volume explores the origins of the term small wars and traces it to special operations. In the 17th century, such "guerrilla/petite guerre" special operations grew out of training and winter operations of the regular forces as practiced in the 16th century. In the 18th century, they fused with a tradition going back to Antiquity, of employing special ethnic groups (such as the Hungarian Hussars) for special operations. Side by side with these special operations, however, there was the even older genealogy of uprisings and insurgencies, which since the Spanish Guerrilla of 1808-1812 has been associated with this term. All three traditions have influenced each other.

National experiences with insurgencies and counterinsurgencies: are there “National styles”?

There are clearly identifiable patterns in the way in which insurgents operate in certain geographic areas and cultures, and in which states deal with them. These have been stressed by writing about national "ways of war", strategic culture, or national styles. Nevertheless, there have been important ruptures and changes in some of these, so that for Britain, for example, three successive phases corresponding to patterns can be identified. For France, two pronounced rivaling traditions coincided over two centuries. Algerians by contrast changed fundamentally in their fighting style with the different political ideologies they were following. Palestinian insurgency against Israel is also marked by change in approach. Russia and China possibly show the longest continuity in their handling of insurgencies.

The Cold War in retrospect : 25 years after its end

This special issue of Cold War History offers a retrospective on the end of the Cold War, 25 years after its peaceful conclusion. This peaceful conclusion is an achievement that cannot be celebrated enough, and we must continue to build international relations in conflict and co-operation on this awareness of our common humanity and our common human fallibility.

La mefiance de son propre gouvernement dans le cinema du « monde libre »

The tradition of criticizing one's own government which in the Western (mainly English-speaking) Liberal Democracies goes back at least to the 14th century founds its expression also in American and British Cold War films. Several reflect the suspicion that the Cold War was in some way aggravated by the USA and the UK in order to serve particular interests of the government or arms industries. Such films, often based on novels, include "1984", "Fahrenheit 451", "The Three Days of the Condor", "The Quiet American", and most recently, "V for Vendetta", as well as many anti-war films. Paradoxically, it is a sign of Western liberalism that these films have been made and mostly received a wide distribution.

Insurgencies and counterinsurgency strategies: patterns and dilemmas

The roots of insurgencies and counterinsurgency go back to Antiquity, and consistent patterns can be traced. These include the state's use of its own armed forces against insurgents who tend to be inferior in terms of armaments, and states' attempts to delegitimize violent aimed to overthrow it, and the need for insurgents to recur to illegal means to challenge the state's power. Very often insurgents have to team up with criminal networks in order to do so, undermining their ability to claim legitimacy.

Paix et guerre selon Christine de Pizan

Analysis of the thinking on just war and conflict mediation of the only classical woman strategist, who lived around 1400, and wrote this with a view to the Hundred Years' War and civil wars and insurgencies taking place in her lifetime. Christine de Pizan's Feats of Arms and Chivalry would later become the first printed and widely distributed field manual, translated into English and printed by Caxton for Henry VII Tudor.

Mens rea in joint enterprise: a role for endorsement?

This paper argues that the problems commonly associated with the joint enterprise doctrine might be alleviated by supplementing the cognitive mens rea standard of foresight with a volitional element that looks to how the defendant related to the foreseen risk. A re-examination of the case law suggests that a mens rea conception of foresight plus endorsement might be within interpretative reach. The paper considers possible objections to such a development but ultimately rejects them. It concludes that it is not necessary to wait for Parliament to put in place reforms: joint enterprise is a creature of the common law, and the common law is able to tame it unaided.

Evolution PDEs and augmented eigenfunctions. half line.

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is no suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of augmented eigenfunctions, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.

Neurocognitive control in dance perception and performance

Dance is a rich source of material for researchers interested in the integration of movement and cognition. The multiple aspects of embodied cognition involved in performing and perceiving dance have inspired scientists to use dance as a means for studying motor control, expertise, and action-perception links. The aim of this review is to present basic research on cognitive and neural processes implicated in the execution, expression, and observation of dance, and to bring into relief contemporary issues and open research questions. The review addresses six topics: 1) dancers’ exemplary motor control, in terms of postural control, equilibrium maintenance, and stabilization; 2) how dancers’ timing and on-line synchronization are influenced by attention demands and motor experience; 3) the critical roles played by sequence learning and memory; 4) how dancers make strategic use of visual and motor imagery; 5) the insights into the neural coupling between action and perception yielded through exploration of the brain architecture mediating dance observation; and 6) a neuroaesthetics perspective that sheds new light on the way audiences perceive and evaluate dance expression. Current and emerging issues are presented regarding future directions that will facilitate the ongoing dialogue between science and dance.