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© 2018 American College of Veterinary Ophthalmologists. Objective: To estimate the prevalence of ocular disease and obtain normative ocular data for free-living hummingbirds. Animals studied: Two hundred and sixty-three free-living, adult Hummingbirds from coastal and inland central California were studied, including Anna's (Calypte anna, n = 186) and Black-chinned (Archilochus alexandri; n = 77) hummingbirds. Procedures: Slit lamp biomicroscopy and indirect ophthalmoscopy were performed on all individuals. Rebound tonometry, measurement of horizontal palpebral fissure length, and streak retinoscopy were performed on select individuals. Five conscious Anna's Hummingbirds underwent ocular imaging including fundus photography, digital slit lamp photography, and anterior segment and retinal optical coherence tomography. Results: The prevalence of ocular disease in this population was 2.28%. Ocular imaging revealed a thin cornea, shallow anterior chamber, large lens, and a single central, deep convexiclivate fovea. Mean ± SD intraocular pressure was 11.21 ± 2.23 mm Hg. Mean ± SD eyelid length was 2.59 ± 0.19 mm. All eyes were emmetropic or mildly hyperopic with a mean (range) ± SD refractive error of +0.32 (-0.25 to +1) ± 0.33 diopters. Conclusions: Consistent with previous reports, these data suggest that hummingbirds have visual characteristics found in predatory and prey species, as well as a low prevalence of spontaneous ocular disease. This work provides a set of reference values and clinical findings that can be used in the future research on hummingbird vision and ocular disease. It also provides representative diagnostic images of normal birds and demonstrates that advanced ocular imaging can be performed on manually restrained hummingbirds without pharmacologic dilation.

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics., arXiv admin note: text overlap with arXiv:1503.03448

Parallel session; International audience; For a CONTROL SYSTEM of the form _ x = f (x; u; v) + Σm =1 g (x)u_ ; on [0;T]; (x; u)(0) = ( x; u); with x : [0;T] ! IRn; u : [0;T] ! U IRm; v : [0;T] ! V IRl ; we rely on the notion of LIMIT SOLUTION, and we investigate whether minimum problems with L1controls are PROPER EXTENSIONS of regular problems with more regular controls (AC or BV). Motivation: optimality conditions, numerical methods, etc.

Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.

In this paper we analyze nonlinear systems whose vector fields are driven by both an ordinary control $v$ and the derivative $\dot u$ of a second control $u$. It is clear that the presence of the derivative $\dot u$ causes some problems in the attempt to define a robust notion of trajectory corresponding to a discontinuous control $u$. On one hand, the nonlinearity of the systems under consideration makes a mere extension of the notion of solution by means of a measure--theoretical approach impossible. On the other hand, the interaction occurring between the derivative $\dot u$ of the {\it impulsive} control $u$ and the ordinary control $v$ prevent us from applying the results of [5], where a space--time extension of the concept of solution was already considered. Indeed in [5] the control $(u,v)$ had equibounded variation, whereas in the present work $v$ is just a measurable bounded map. After giving a stable notion of (space--time) solution to our problem we investigate the topological structure of the set of trajectories: as a consequence of having suppressed the restraint on the variation of $v$ we find that this set is no longer compact. This motivates the search for conditions under which the set of trajectories turns out to be closed again. Finally, in view of several applications we also analyze the case where the derivative $\dot u$ is constrained to range over a closed cone.