Enabling Entrepreneurial Ecosystems

Inspired by research on the importance of entrepreneurship for sustained economic growth and improved wellbeing, many governments and non-governmental grantmaking organizations have sought over the past decade to implement policies and programs intended to support entrepreneurs. Over this interval, growing appreciation of the limits of strategies focused narrowly on financing or training entrepreneurs has prompted a number of such entities to shift their efforts toward more broadbased strategies aimed at enabling "entrepreneurial ecosystems" at the city or sub-national regional scale.This paper takes the metaphor of the "ecosystem" seriously, seeking to draw lessons from evolutionary biology and ecology to inform policy for entrepreneurship. In so doing, the paper provides a framework for data gathering and analysis of practical value in assessing the vibrancy of entrepreneurial ecosystems

Use of the Neurological Pupil Index to Predict Postoperative Visual Function After Resection of a Tuberculum Sellae Meningioma: A Case Report.

The Neurological Pupil index (NPi) is a standardized method for evaluating pupil reactivity that removes inter-examiner variability. Changes in the NPi can predict clinical deterioration in patients with traumatic brain injury (TBI); however, its use to predict visual impairment after the resection of parasellar meningiomas has not been described. A 71-year-old female underwent a modified expanded bifrontal craniotomy for resection of a 3.1 cm tuberculum sella meningioma that caused compression of the optic chiasm and resulted in left temporal and right superior temporal visual field deficits. Postoperatively, she lost vision in the right eye. Pupillometer measurements demonstrated an asymmetrically low NPi at that time, which improved to normal prior to partial vision recovery. The average NPi in the right pupil was 1.67 during the time of vision loss compared to 3.47 in the left pupil (p=1.7x10-10). Statistical analysis was performed with the Student's t-test and the significance level was set at p-value < 0.01. Resection of parasellar meningiomas is challenging because of the proximity of the optic apparatus. We report a case of unilateral vision loss after resection of a tuberculum sella meningioma in which the impaired eye's NPi value correlated closely with visual function. NPi values that decrease below 3 predict spikes in intracranial pressure in TBI patients; similarly, increases in the NPi value above 2.5-3 predict improvement in vision in the case reported here. By monitoring the proximal portion of the oculomotor reflex, the NPi can be a marker of visual impairment after surgery

A Nielsen theory for coincidences of iterates

As the title suggests, this paper gives a Nielsen theory of coincidences of iterates of two self maps f, g of a closed manifold. The ideas is, as much as possible, to generalize Nielsen type periodic point theory, but there are many obstacles. Many times we get similar results to the "classical ones" in Nielsen periodic point theory, but with stronger hypotheses.Comment: 30 page

Uncertainty in projections of streamflow changes due to climate change in California

Understanding the uncertainty in the projected impacts of climate change on hydrology will help decision-makers interpret the confidence in different projected future hydrologic impacts. We focus on California, which is vulnerable to hydrologic impacts of climate change. We statistically bias correct and downscale temperature and precipitation projections from 10 GCMs participating in the Coupled Model Intercomparison Project. These GCM simulations include a control period (unchanging CO2 and other forcing) and perturbed period (1%/year CO2 increase). We force a hydrologic model with the downscaled GCM data to generate streamflow at strategic points. While the different GCMs predict significantly different regional climate responses to increasing atmospheric CO2, hydrological responses are robust across models: decreases in summer low flows and increases in winter flows, and a shift of flow to earlier in the year. Summer flow decreases become consistent across models at lower levels of greenhouse gases than increases in winter flows do

A Primal-Dual Augmented Lagrangian

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual $\ell$1 linearly constrained Lagrangian (pd$\ell$1-LCL) method

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time