Statistical and Variational Methods for Problems in Visual Control

2009 ◽  
Author(s):  
Allen Tannenbaum
Keyword(s):  
Variational Methods ◽  
Visual Control

Transscleral Extraction of an Intraocular Foreign Body From the Posterior Segment of the Eye Without Pars Plana Vitrectomy

2020 ◽  
Vol 76 (1) ◽  
pp. 14-23
Author(s):  
Štěpán Rusňák ◽  
Lenka Hecová
Keyword(s):  
Foreign Body ◽  
Pars Plana Vitrectomy ◽  
Young Patients ◽  
Vitreous Body ◽  
Visual Control ◽  
Intraocular Foreign Body ◽  
Survey Study ◽  
Surgical Method ◽  
Eye Trauma ◽  
Pars Plana

Purpose: Penetrating eye trauma with an intraocular foreign body is very frequent, especially in men in their productive age. Pars plana vitrectomy would be the standard surgical method at our department. However, in indicated cases (metallic intraocular bodies in the posterior eye segment in young patients with well transparent ocular media without detached ZSM and without any evident vitreoretinal traction) transscleral extraction of the intraocular foreign body is performed using the exo magnet, eventually endo magnet with a minimal PPV without PVD induction under the visual control of endo-illumination. Materials and Methods: Between June 2003 and June 2018, 66 eyes of 66 patients diagnosed with a penetrating eye trauma caused by an intraocular foreign body located in the posterior eye segment were treated. In 18 eyes (27,3 %) with a metallic foreign body in vitreous (body) or in retina, no PPV or a minimal PPV without PVD was used as a surgical method. In the remaining 48 eyes (72,7 %), a standard 20G, respectively 23G PPV method were used together with PVD induction and the foreign body extraction via endo or exo magnet. Conclusions: As demonstrated by our survey/study, in the cases of a thoroughly considered indication an experimented vitreoretinal surgeon can perform a safe NCT transscleral extraction from the posterior eye segment via exo magnet, eventually endo magnet under the visual control of a contact display system with a minimal PPV. Thereby, the surgeon can enhance the patient´s chance to preserve their own lens and its accommodative abilities as well as reduce the risk of further surgical interventions of the afflicted eye.

Autonomous Visual Control of a Mobile Robot

1994 ◽  
Author(s):  
Michael R. Blackburn ◽  
Hoa G. Nguyen
Keyword(s):  
Mobile Robot ◽  
Visual Control

scholarly journals Multiple positive solutions for nonlocal elliptic problems involving the Hardy potential and concave–convex nonlinearities

2020 ◽  
pp. 2050008
Author(s):  
Shaya Shakerian
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Variational Approach ◽  
Nehari Manifold ◽  
Multiple Positive Solutions ◽  
Hardy Potential ◽  
Smooth Bounded Domain ◽  
Existence And Multiplicity ◽  
The Nehari Manifold

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].

Variational Methods for Machine Learning with Applications to Deep Networks

2021 ◽  
Author(s):  
Lucas Pinheiro Cinelli ◽  
Matheus Araújo Marins ◽  
Eduardo Antônio Barros da Silva ◽  
Sérgio Lima Netto
Keyword(s):  
Machine Learning ◽  
Variational Methods ◽  
Deep Networks

scholarly journals Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth

2020 ◽  
Vol 10 (1) ◽  
pp. 732-774
Author(s):  
Zhipeng Yang ◽  
Fukun Zhao
Keyword(s):  
Small Parameter ◽  
Variational Methods ◽  
Critical Exponent ◽  
Laplace Operator ◽  
Sobolev Inequality ◽  
Fractional Laplacian ◽  
Singularly Perturbed ◽  
Choquard Equation ◽  
Fractional Choquard Equation ◽  
Fractional Laplace Operator

Abstract In this paper, we study the singularly perturbed fractional Choquard equation $$\begin{equation*}\varepsilon^{2s}(-{\it\Delta})^su+V(x)u=\varepsilon^{\mu-3}(\int\limits_{\mathbb{R}^3}\frac{|u(y)|^{2^*_{\mu,s}}+F(u(y))}{|x-y|^\mu}dy)(|u|^{2^*_{\mu,s}-2}u+\frac{1}{2^*_{\mu,s}}f(u)) \, \text{in}\, \mathbb{R}^3, \end{equation*}$$ where ε > 0 is a small parameter, (−△)s denotes the fractional Laplacian of order s ∈ (0, 1), 0 < μ < 3, $2_{\mu ,s}^{\star }=\frac{6-\mu }{3-2s}$is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality and fractional Laplace operator. F is the primitive of f which is a continuous subcritical term. Under a local condition imposed on the potential V, we investigate the relation between the number of positive solutions and the topology of the set where the potential attains its minimum values. In the proofs we apply variational methods, penalization techniques and Ljusternik-Schnirelmann theory.

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