Supplemental Jurisdiction over Permissive Counterclaims in Light of Exxon v. Allapattah

This comment examines the development of supplemental jurisdiction as applied to counterclaims, as well as the circuit slit with regard to supplemental jurisdiction over permissive counterclaims

Instability of pulses in gradient reaction-diffusion systems: A symplectic approach

In a scalar reaction-diffusion equation, it is known that the stability of a steady state can be determined from the Maslov index, a topological invariant that counts the state's critical points. In particular, this implies that pulse solutions are unstable. We extend this picture to pulses in reaction-diffusion systems with gradient nonlinearity. In particular, we associate a Maslov index to any asymptotically constant state, generalizing existing definitions of the Maslov index for homoclinic orbits. It is shown that this index equals the number of unstable eigenvalues for the linearized evolution equation. Finally, we use a symmetry argument to show that any pulse solution must have nonzero Maslov index, and hence be unstable.Comment: 19 pages, 1 figure. To appear in Philos. Trans. Roy. Soc.

Planar Homography Estimation from Traffic Streams via Energy Functional Minimization

The 3x3 homography matrix specifies the mapping between two images of the same plane as viewed by a pinhole camera. Knowledge of the matrix allows one to remove the perspective distortion and apply any similarity transform, effectively making possible the measurement of distances and angles on the image. A rectified road scene for instance, where vehicles can be segmented and tracked, gives rise to ready estimates of their velocities and spacing or categorization of their type. Typical road scenes render the classical approach to homography estimation difficult. The Direct Linear Transform is highly susceptible to noise and usually requires refining via an further nonlinear penalty minimization. Additionally, the penalty is a function of the displacement between measured and calibrated coordinates, a quantity unavailable in a scene for which we have no knowledge of the road coordinates. We propose instead to achieve metric rectification via the minimization of an energy that measures the violation of two constraints: the divergence-free nature of the traffic flow and the orthogonality of the flow and transverse directions under the true transform. Given that an homography is only determined up to scale, the minimization is performed on the Lie group $SL(3)$, for which we develop a gradient descent algorithm. While easily expressed in the world frame, the energy must be computed from measurements made in the image and thus must be pulled back using standard differential geometric machinery to the image frame. We develop an enhancement to the algorithm by incorporating optical flow ideas and apply it to both a noiseless test case and a suite of real-world video streams to demonstrate its efficacy and convergence. Finally, we discuss the extension to a 3D-to-planar mapping for vehicle height inference and an homography that is allowed to vary over the image, invoking a minimization on Diff$(SL(3))$

Optically controlled grippers for manipulating micron-sized particles

We report the development of a joystick controlled gripper for the real-time manipulation of micron-sized objects, driven using holographic optical tweezers (HOTs). The gripper consists of an arrangement of four silica beads, located in optical traps, which can be positioned and scaled in order to trap an object indirectly. The joystick can be used to grasp, move (lateral or axial), and change the orientation of the target object. The ability to trap objects indirectly allows us to demonstrate the manipulation of a strongly scattering micron-sized metallic particle

Avoiding ‘starburst’: The need to identify common metrics of evaluating strengths-based programmes in prison

The notions of strengths-based working in health and justice are not new and areas as diverse as positive psychology and criminology, mental health and addictions recovery, and therapeutic jurisprudence and restorative approaches in the justice field all share a common set of principles and values that may offer some insights into questions of evaluation, effectiveness and measurement. The first part of this paper will examine the shared foundations of strengths- based approaches and this will inform a second section examining common principles in these models. Part Three will then provide three illustrative examples of strengths-based programmes in prisons in the United Kingdom (UK), before the final section, Part Four, outlines a two-tier model of strengths-measurement that will help to avoid 'starburst', that is, where the benefit is so short-lived that it has no lasting impact on the wellbeing of the prison or its constituents

Transfer pricing: strategies, practices, and tax minimization

Using a survey of tax executives from multinational corporations, we document that some firms set their transfer pricing strategy to minimize tax payments, but more firms focus on tax compliance. We estimate that a firm focusing on minimizing taxes has a GAAP effective tax rate that is 6.6 percentage points lower and generates about $43 million more in tax savings, on average, than a firm focusing on tax compliance. Available COMPUSTAT data on sample firms confirm our survey‐based inferences. We also find that transfer pricing‐related tax savings are greater when higher foreign income, tax haven use, and R&D activities are combined with a tax minimization strategy. Finally, compliance‐focused firms report lower FIN 48 tax reserves than tax‐minimizing firms, consistent with the former group using less uncertain transfer pricing arrangements. Collectively, our study provides direct evidence that multinational firms have differing internal priorities for transfer pricing, and that these differences are strongly related to the taxes reported by these firms.First author draf