Majorisation with applications to the calculus of variations

This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant. Theorem 6.2 describes a class of possible non-polyconvex but multiplicative quasiconvex isotropic functions. This class is not contained in a well known theorem of Ball (6.3 in this paper) which gives sufficient conditions for an isotropic and objective function to be polyconvex. We show here that there is a new way to prove directly the quasiconvexity (in the multiplicative form). Relevance of Schur convexity for the description of rank one convex hulls is explained.Comment: 13 page

Shareholder voting in mergers and acquisitions: evidence from the UK

This paper examines the determinants and consequences of shareholder voting on mergers and acquisitions using a sample of resolutions approved by shareholders of UK publicly listed firms from 1997 to 2015. We find that dissent on M&A resolutions is negatively related to bidder announcement returns and positively related to shareholders’ general dissatisfaction towards the management. Shareholder dissent is an important predictor of the announcement returns of subsequent M&A deals. We also report an increase in shareholder dissent after the 2007-2008 financial crisis

Jets and Topography: Jet Transitions and the Impact on Transport in the Antarctic Circumpolar Current

The Southern Ocean’s Antarctic Circumpolar Current (ACC) naturally lends itself to interpretations using a zonally averaged framework. Yet, navigation around steep and complicated bathymetric obstacles suggests that local dynamics may be far removed from those described by zonally symmetric models. In this study, both observational and numerical results indicate that zonal asymmetries, in the form of topography, impact global flow structure and transport properties. The conclusions are based on a suite of more than 1.5 million virtual drifter trajectories advected using a satellite altimetry–derived surface velocity field spanning 17 years. The focus is on sites of “cross front” transport as defined by movement across selected sea surface height contours that correspond to jets along most of the ACC. Cross-front exchange is localized in the lee of bathymetric features with more than 75% of crossing events occurring in regions corresponding to only 20% of the ACC’s zonal extent. These observations motivate a series of numerical experiments using a two-layer quasigeostrophic model with simple, zonally asymmetric topography, which often produces transitions in the front structure along the channel. Significantly, regimes occur where the equilibrated number of coherent jets is a function of longitude and transport barriers are not periodic. Jet reorganization is carried out by eddy flux divergences acting to both accelerate and decelerate the mean flow of the jets. Eddy kinetic energy is amplified downstream of topography due to increased baroclinicity related to topographic steering. The combination of high eddy kinetic energy and recirculation features enhances particle exchange. These results stress the complications in developing consistent circumpolar definitions of the ACC fronts

Closed-range posinormal operators and their products

We focus on two problems relating to the question of when the product of two posinormal operators is posinormal, giving (1) necessary conditions and sufficient conditions for posinormal operators to have closed range, and (2) sufficient conditions for the product of commuting closed-range posinormal operators to be posinormal with closed range. We also discuss the relationship between posinormal operators and EP operators (as well as hypo-EP operators), concluding with a new proof of the Hartwig-Katz Theorem, which characterizes when the product of posinormal operators on \CC^n is posinormal

Bandit Models of Human Behavior: Reward Processing in Mental Disorders

Drawing an inspiration from behavioral studies of human decision making, we propose here a general parametric framework for multi-armed bandit problem, which extends the standard Thompson Sampling approach to incorporate reward processing biases associated with several neurological and psychiatric conditions, including Parkinson's and Alzheimer's diseases, attention-deficit/hyperactivity disorder (ADHD), addiction, and chronic pain. We demonstrate empirically that the proposed parametric approach can often outperform the baseline Thompson Sampling on a variety of datasets. Moreover, from the behavioral modeling perspective, our parametric framework can be viewed as a first step towards a unifying computational model capturing reward processing abnormalities across multiple mental conditions.Comment: Conference on Artificial General Intelligence, AGI-1

Severe Malignant Hypertension following Renal Artery Embolization: A Crucial Role for the Renal Microcirculation in the Pathogenesis of Hypertension?

Malignant hypertension is the most severe form of hypertension that is usually fatal if not properly managed. It is usually associated with evidence of microvascular damage such as retinopathy and nephropathy. Renal artery embolization is a widely utilised tool for the management of a wide range of conditions including drug resistant renovascular hypertension in patients with end stage renal failure. In this report we describe two patients with mild-to-moderate hypertension who underwent renal artery embolization for reasons unrelated to their hypertension. Contrary to conventional wisdom, in both patients hypertension became more severe and difficult to control. This report describes the cases and discusses the implications for current theory and the possible role of the microcirculation in the causation of hypertension

Knot polynomial invariants in classical Abelian Chern-Simons field theory

Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant $t^{I\left( \mathcal{L} \right) }$ is constructed for a link $\mathcal{L}$, where $I$ is the abelian Chern-Simons action and $t$ a formal constant. For oriented knotted vortex lines, $t^{I}$ satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, $t^{I}$ satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.Comment: 15 pages, 8 figure