In-betweenness: a geometric monotonicity property for operator means

We introduce the notions of in-betweenness and monotonicity with respect to a metric, for operator means. These notions can be seen as generalising their natural counterpart for scalar means, and as a relaxation of the notion of geodesity. We exhibit two classes of non-trivial means that are monotonic with respect to the Euclidean metric. We also show that all Kubo-Ando means are monotonic with respect to the trace metric, which is the natural metric for the geometric mean.Comment: 15 pages; a preliminary version has been presented at the June 2010 ILAS Conference in Pisa, Ital

Turning asylum seekers into ‘dangerous criminals’:experiences of the criminal justice system of those seeking sanctuary

Since the events of 9/11 in the US in 2001 and, four years later, the 7/7 London bombings in the UK, warnings of terrorist attacks are high on the public agenda in many western countries. Politicians and tabloid press in the UK have continued to make direct and indirect connections between asylum seekers, terrorism and crime. This has increasingly resulted in harsh policy responses to restrict the movement of ‘third-world’ nationals, criminalisation of immigration and asylum policy, and making the violation of immigration laws punishable through criminal courts. This paper largely highlights the narratives of five asylum seekers who committed ‘crime’ by breaching immigration laws and were consequently treated as ‘dangerous criminals’ by the state authorities. More importantly it shows how these individuals experienced this treatment. The aim of this paper is to give voice to the victims of state abuse, claim space for victim agency, gather victim testimonies, challenge official explanations and in the process confront criminal and racist state practices

Influence of Slippery Pacemaker Leads on Lead-Induced Venous Occlusion

The use of medical devices such as pacemakers and implantable cardiac defibrillators have become commonplace to treat arrhythmias. Pacing leads with electrodes are used to send electrical pulses to the heart to treat either abnormally slow heart rates, or abnormal rhythms. Lead induced vessel occlusion, which is commonly seen after placement of pacemaker or implantable cardiac defibrillators leads, may result in lead malfunction and/or superior vena cava syndrome, and makes lead extraction difficult. The association between the anatomic locations at risk for thrombosis and regions of venous stasis have been reported previously. The computational studies reveal obvious flow stasis in the proximity of the leads, due to the no-slip boundary condition imposed on the lead surface. With recent technologies capable of creating slippery surfaces that can repel complex fluids including blood, we explore computationally how local structures may be altered in the regions around the leads when the no-slip boundary condition on the lead surface is relaxed using various slip lengths. The slippery surface is modeled by a Navier slip boundary condition. Analytical studies are performed on idealized geometries, which were then used to validate numerical simulations. A patient-specific model is constructed and studied numerically to investigate the influence of the slippery surface in a more physiologically realistic environment. The findings evaluate the possibility of reducing the risk of lead-induced thrombosis and occlusion by implementing a slippery surface conditions on the leads

Derivatives of Multilinear Functions of Matrices

Perturbation or error bounds of functions have been of great interest for a long time. If the functions are differentiable, then the mean value theorem and Taylor's theorem come handy for this purpose. While the former is useful in estimating $\|f(A+X)-f(A)\|$ in terms of $\|X\|$ and requires the norms of the first derivative of the function, the latter is useful in computing higher order perturbation bounds and needs norms of the higher order derivatives of the function. In the study of matrices, determinant is an important function. Other scalar valued functions like eigenvalues and coefficients of characteristic polynomial are also well studied. Another interesting function of this category is the permanent, which is an analogue of the determinant in matrix theory. More generally, there are operator valued functions like tensor powers, antisymmetric tensor powers and symmetric tensor powers which have gained importance in the past. In this article, we give a survey of the recent work on the higher order derivatives of these functions and their norms. Using Taylor's theorem, higher order perturbation bounds are obtained. Some of these results are very recent and their detailed proofs will appear elsewhere.Comment: 17 page