Impact of boundaries on fully connected random geometric networks

Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the transition to full connectivity is strongly influenced by details of the boundary, but observe an alternative form of universality. Our approach correctly distinguishes connectivity properties of networks in domains with equal bulk contributions. It also facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension.Comment: 6 pages, 3 figure

Local BRST cohomology in minimal D=4, N=1 supergravity

The local BRST cohomology is computed in old and new minimal supergravity, including the coupling to Yang-Mills gauge multiplets. This covers the determination of all gauge invariant local actions for these models, the classification of all the possible counterterms that are invariant on-shell, of all candidate gauge anomalies, and of the possible nontrivial (continuous) deformations of the standard actions and gauge transformations. Among others it is proved that in old minimal supergravity the most general gauge invariant action can indeed be constructed from well-known superspace integrals, whereas in new minimal supergravity there are only a few additional (but important) contributions which cannot be constructed in this way without further ado. Furthermore the results indicate that supersymmetry itself is not anomalous in minimal supergravity and show that the gauge transformations are extremely stable under consistent deformations of the models. There is however an unusual deformation converting new into old minimal supergravity with local R-invariance which is reminiscent of a duality transformation.Comment: 58 pages, latex 2.09, no figures; final version, minor corrections, Comment added in conclusions (footnote), refs. update

Economic Analysis of Knowledge: The History of Thought and the Central Themes

Following the development of knowledge economies, there has been a rapid expansion of economic analysis of knowledge, both in the context of technological knowledge in particular and the decision theory in general. This paper surveys this literature by identifying the main themes and contributions and outlines the future prospects of the discipline. The wide scope of knowledge related questions in terms of applicability and alternative approaches has led to the fragmentation of research. Nevertheless, one can identify a continuing tradition which analyses various aspects of the generation, dissemination and use of knowledge in the economy

Investigating the influence of haemodynamic stimuli on intracranial aneurysm inception

We propose a novel method to reconstruct the hypothetical geometry of the healthy vasculature prior to intracranial aneurysm (IA) formation: a Frenet frame is calculated along the skeletonization of the arterial geometry; upstream and downstream boundaries of the aneurysmal segment are expressed in terms of the local Frenet frame basis vectors; the hypothetical healthy geometry is then reconstructed by propagating a closed curve along the skeleton using the local Frenet frames so that the upstream boundary is smoothly morphed into the downstream boundary. This methodology takes into account the tortuosity of the arterial vasculature and requires minimal user subjectivity. The method is applied to 22 clinical cases depicting IAs. Computational fluid dynamic simulations of the vasculature without IA are performed and the haemodynamic stimuli in the location of IA formation are examined. We observe that locally elevated wall shear stress (WSS) and gradient oscillatory number (GON) are highly correlated (20/22 for WSS and 19/22 for GON) with regions susceptible to sidewall IA formation whilst haemodynamic indices associated with the oscillation of the WSS vectors have much lower correlations

Patient-Specific Modelling of Intracranial Aneurysm Evolution

Intracranial aneurysms appear as sac-like outpouchings of the cerebral vasculature wall; inflated by the pressure of the blood that fills them. They are relatively common and affect up to 5% of the adult population. Fortunately, most remain asymptomatic. However, there is a small but inherent risk of rupture: 0.1% to 1% of detected aneurysms rupture every year. If rupture does occur there is a 30% to 50% chance of fatality. Consequently, if an aneurysm is detected, clinical intervention may be deemed appropriate. Therapy is currently aimed at pre-rupture detection and preventative treatment. However, interventional procedures are not without risk to the patient. The improvement and optimization of interventional techniques is an important concern for patient welfare and is necessary for rationalisation of healthcare priorities. Hence there is a need to develop methodologies to assist in identifying those ICAs most at risk of rupture. We focus on the mathematical modelling and computational simulation of ICA evolution. Models must take into consideration: (i) the biomechanics of the arterial wall; (ii) the biology of the arterial wall and (iii) the complex interplay between (i) and (ii), i.e. the mechanobiology of the arterial wall. The ultimate ambition of such models is to aid clinical diagnosis on a patient-specific basis. However, due to the significant biological complexity coupled with limited histological information such models are still in their relative infancy. Current research focuses on simulating the evolution of an ICA with an aim to yield insight into the growth and remodelling (G&R) processes that give rise to inception, enlargement, stabilisation and rupture. We present a novel Fluid-Structure-Growth computational framework for modelling aneurysm evolution