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We introduce discontinuous solutions to nonlinear impulsive control systems with state time delays in the dynamics and derive necessary optimality conditions in the form of a maximum principle for associated optimal control problems. In the case without delays, if the measure control is scalar valued, the corresponding discontinuous state trajectory, understood as a limit of classical state trajectories for absolutely continuous controls approximating the measure, is unique. For vector-valued measure controls, however, the limiting trajectory is not unique and a full description of the control must include additional "attached" controls affecting instantaneous state evolution at a discontinuity. For impulsive control systems with time delays we reveal a new phenomenon, namely, that the limiting state trajectory resulting from different approximations of a given measure control needs not to be unique, even in the scalar case. Correspondingly, our framework allows for additional attached controls, even though the measure control is scalar valued. [ABSTRACT FROM AUTHOR]

Congenital stationary night blindness (CSNB) is an ocular disorder characterized by nyctalopia. An autosomal recessive missense mutation in glutamate metabotropic receptor 6 (GRM6 c.533C>T, p.(Thr178Met)), called CSNB2, was previously identified in one Tennessee Walking Horse and predicted to reduce binding affinity of the neurotransmitter glutamate, impacting the retinal rod ON‐bipolar cell signaling pathway. Thus, the first aim was to identify the allele frequency (AF) of CSNB2 in breeds with reported cases of CSNB and breeds closely related to the Tennessee Walking Horse. The second aim was to perform ocular examinations in multiple breeds to confirm the link between genotype and CSNB phenotype. In evaluating 3518 horses from 14 breeds, the CSNB2 allele was identified in nine previously unreported breeds. The estimated AF was highest in pacing Standardbreds (0.17) and lowest in American Quarter Horses (0.0010). Complete ophthalmic examinations and electroretinograms (ERG) were performed on 19 horses from three breeds, including one CSNB2 homozygote from each breed. All three CSNB2/CSNB2 horses had an electronegative ERG waveform under scotopic light conditions consistent with CSNB. The remaining 16 horses (seven CSNB2/N and nine N/N) had normal scotopic ERG results. All horses had normal photopic ERGs. This study provides additional evidence that GRM6 c.533C>T homozygosity is likely causal to CSNB in Tennessee Walking Horses, Standardbreds, and Missouri Fox Trotting Horses. Genetic testing is recommended for breeds with the CSNB2 allele to limit the production of affected horses. This study represents the largest across‐breed identification of CSNB in the horse and suggests that this disorder is likely underdiagnosed. [ABSTRACT FROM AUTHOR]

We consider a constrained optimal control problem and an extension of it, in which the set of strict-sense trajectories is enlarged. Extension is a common procedure in optimal control used to derive necessary and sufficient optimality conditions for the original problem from the extended one, which usually admits a minimizer and has a more regular structure. However, this procedure fails if the two problems have different infima. Therefore, it is relevant to identify such situations. Following on from earlier work by Warga but adopting perturbation techniques developed in nonsmooth analysis, we investigate the relation between the occurrence of an infimum gap and the abnormality of necessary conditions. For the notion of a local minimizer based on control distance and an extension, including the impulsive one, we prove that (i) a local extended minimizer that is not a local minimizer of the original problem, and (ii) a local strict-sense minimizer that is not a local minimizer of the extended problem both satisfy the extended maximum principle in abnormal form. The main novelty is result (ii), as until now, it has only been shown that a strict-sense minimizer that is not an extended minimizer is abnormal for an 'averaged version' of the maximum principle. [ABSTRACT FROM AUTHOR]

In optimal control theory one sometimes extends the minimization domain of a given problem, with the aim of achieving the existence of an optimal control. However, this issue is naturally confronted with the possibility of a gap between the original infimum value and the extended one. Avoiding this phenomenon is not a trivial issue, especially when the trajectories are subject to endpoint constraints. However, since the seminal works by Warga, some authors have recognized "normality"" of an extended minimizer as a condition guaranteeing the absence of an infimum gap. Yet, normality is far from being necessary for this goal, a fact that makes the search for weaker assumptions a reasonable aim. In relation to a control-affine system with unbounded controls, in this paper we prove a sufficient no-gap condition based on a notion of higher order normality, which is less demanding than the standard normality and involves iterated Lie brackets of the vector fields defining the dynamics. [ABSTRACT FROM AUTHOR]

In optimal control theory, infimum gap means that there is a gap between the infimum values of a given minimum problem and an extended problem, obtained by enlarging the set of original solutions and controls. The gap phenomenon is somewhat "dual" to the problem of the controllability of the original control system to an extended solution. In this paper we present sufficient conditions for the absence of an infimum gap and for controllability for a wide class of optimal control problems subject to endpoint and state constraints. These conditions are based on a nondegenerate version of the nonsmooth constrained maximum principle, expressed in terms of subdifferentials. In particular, under some new constraint qualification conditions, we prove that (i) if an extended minimizer is a nondegenerate normal extremal, then no gap shows up; (ii) given an extended solution verifying the constraints, either it is a nondegenerate abnormal extremal or the original system is controllable to it. An application to the impulsive extension of a free end-time, nonconvex optimization problem with control-polynomial dynamics illustrates the results. [ABSTRACT FROM AUTHOR]

In this paper we extend the notions of sample and Euler stabilizability to a set of a control system to a wide class of systems with unbounded controls, which includes nonlinear control-polynomial systems. In particular, we allow discontinuous stabilizing feedbacks, which are unbounded approaching the target. As a consequence, sampling trajectories may present a chattering behaviour and Euler solutions have in general an impulsive character. We also associate to the control system a cost and provide sufficient conditions, based on the existence of a special Lyapunov function, which allow for the existence of a stabilizing feedback that keeps the cost of all sampling and Euler solutions starting from the same point below the same value, in a uniform way. [ABSTRACT FROM AUTHOR]

We consider a nonlinear system, affine with respect to an unbounded control u which is allowed to range in a closed cone. With this system we associate a Bolza type minimum problem, with a Lagrangian having sublinear growth with respect to u. This lack of coercivity gives the problem an impulsive character, meaning that minimizing sequences of trajectories happen to converge towards discontinuous paths. As is known, a distributional approach does not make sense in such a nonlinear setting, where, instead, a suitable embedding in the graph space is needed. We provide higher-order necessary optimality conditions for properly defined impulsive minima in the form of equalities and inequalities involving iterated Lie brackets of the dynamical vector fields. These conditions are derived under very weak regularity assumptions and without any constant rank conditions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Given a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u and a closed target set S depending both on the state and on the control u, we study the minimum time problem with a bound on the total variation of u and u constrained in a closed, convex set U, possibly with empty interior. We revisit several concepts of generalized control and solution considered in the literature and show that they all lead to the same minimum time function T. Then we obtain sufficient conditions for the existence of an optimal generalized trajectory-control pair and study the possibility of Lavrentiev-type gap between the minimum time in the spaces of regular (that is, absolutely continuous) and generalized controls. Finally, under a convexity assumption on the dynamics, we characterize T as the unique lower semicontinuous solution of a regular HJ equation with degenerate state constraints. [ABSTRACT FROM AUTHOR]

Optimal unbounded control problems with affine control dependence may fail to have minimizers in the class of absolutely continuous state trajectories. For this reason, extended impulsive versions - which cannot be of measure-theoretic type - have been investigated, in which the domain is enlarged to include discontinuous state trajectories of bounded variation, and for which existence of minimizers is guaranteed. It is of interest to know whether the passage from the original optimal control problem to its extension introduces an infimum gap. This paper provides sufficient conditions for the absence of an infimum gap based on normality of extremals. In certain cases, the normality conditions reduce to simple verifiable criteria, which improve on earlier, directly-derived sufficient conditions for no infimum gap. [ABSTRACT FROM AUTHOR]

Objective Assess vascular permeability of the snake spectacle to sodium fluorescein during resting and shedding phases of the ecdysis cycle. Animal studied Ball python (Python regius). Procedures The snake was anesthetized, and spectral domain optic coherence tomography was performed prior to angiographic procedures. An electronically controlled digital single-lens reflex camera with a dual-head flash equipped with filters suitable for fluorescein angiography was used to make images. Sodium fluorescein (10%) solution was administered by intracardiac injection. Angiographic images were made as fluorescein traversed the vasculature of the iris and spectacle. Individually acquired photographic frames were assessed and sequenced into pseudovideo image streams for further evaluation Conclusions Fluorescein angiograms of the snake spectacle were readily obtained. Vascular permeability varied with the phase of ecdysis. Copious leakage of fluorescein occurred during the shedding phase. This angiographic method may provide diverse opportunities to investigate vascular aspects of snake spectacle ecdysis, dysecdysis, and the integument in general. [ABSTRACT FROM AUTHOR]

Objective The purpose of this study was to determine impact of needle gauge, type, and orientation on average volume of drop dispensed. Procedure Five needle gauges (22G, 23G, 25G, 27G, and 30G) were examined. For each gauge, volume of drop delivered was determined for standard sharp beveled tip, blunt tip, and after breaking off of the sharp needle from the hub. Vertical and horizontal orientation of the needle was tested for effect on drop volume for 22-G and 30-G sharp beveled needles. Results Mean drop volume was affected by needle gauge, needle orientation, and whether the needle had been broken off from its hub. Mean drop volume scaled directly with needle diameter with drop volumes of 25.0 μL (±20.2) and 83.9 μL (±16.5) being found for 30-gauge and 22-gauge needles, respectively. Intermediate gauges (27, 25, 23G) yielded intermediate drop volumes. Blunt needles tended to produce larger drop volumes compared to sharp beveled needles, but these differences did not reach statistical significance. Breaking off of the needle from the hub produced substantially larger drop volumes with little difference being found between needle gauges. Average volumes of 1 drop from a 22-G vertical, 22-G horizontal, 30-G vertical, and 30-G horizontal sharp beveled needle were 20.2, 9.1, 10.1, and 3.3 μL, respectively. Conclusions These findings have relevance for controlled delivery of topical ophthalmic medications to patients. [ABSTRACT FROM AUTHOR]

ABSTRACT The murine dorsum dermal excisional wound model has been widely utilized with or without splint application. However, variations in experimental methods create challenges for direct comparison of results provided in the literature and for design of new wound healing studies. Here, we investigated the effects of wound location and size, number of wounds, type of adhesive used for splint fixation on wound healing using splinted or unsplinted dorsum excisional full thickness wound models. One or two 6- or 8-mm full thickness wounds were made with or without splinting in genetically diabetic but heterozygous mice ( Dock7 m + / + Lepr db). Two different adhesives: tissue adhesive and an over the counter cyanoacrylate adhesive (OTCA) 'Krazy glue' were used to fix splints. Wound contraction, wound closure, and histopathological parameters including reepithelialization, collagen deposition and inflammation were compared between groups. No significant effect of wound number (1 vs. 2), side (left vs. right and cranial vs. caudal) or size on wound healing was observed. The OTCA group had a significantly higher splint success compared to the tissue adhesive group that resulted in significantly higher reepithelialization and collagen deposition in the OTCA group. Understanding the outcomes and effects of the variables will help investigators choose appropriate experimental conditions for the study purpose and interpret data. [ABSTRACT FROM AUTHOR]

Topical application of platelet-derived growth factor-BB (PDGF-BB) is considered to accelerate tissue repair of impaired chronic wounds. However, the vast literature is plagued with conflicting reports of its efficacy in animal models and this is often influenced by a wide array of experimental variables making it difficult to compare the results across the studies. To mitigate the confounding variables that influence the efficacy of topically applied PDGF-BB, we used a controlled full thickness splinted excisional wound model in db/db mice (type 2 diabetic mouse model) for our investigations. A carefully-defined silicone-splinted wound model, with reduced wound contraction, controlled splint and bandage maintenance, allowing for healing primarily by reepithelialization was employed. Two splinted 8 mm dorsal full thickness wounds were made in db/db mice. Wounds were topically treated once daily with either 3 µg PDGF-BB in 30 µl of 5% PEG-PBS vehicle or an equal volume of vehicle for 10 days. Body weights, wound contraction, wound closure, reepithelialization, collagen content, and wound bed inflammation were evaluated clinically and histopathologically. The bioactivity of PDGF-BB was confirmed by in vitro proliferation assay. PDGF-BB, although bioactive in vitro, failed to accelerate wound healing in vivo in the db/db mice using the splinted wound model. Considering that the predominant mechanism of wound healing in humans is by re-epeithelialization, the most appropriate model for evaluating therapeutics is one that uses splints to prevent excessive wound contraction. Here, we report that PDGF-BB does not promote wound closure by re-epithelialization in a murine splinted wound model. Our results highlight that the effects of cytoactive factors reported in vivo ought to be carefully interpreted with critical consideration of the wound model used. [ABSTRACT FROM AUTHOR]