scholarly journals Robust Shape Reconstruction and Optimal Transportation

2013 ◽  
Vol 3 (1) ◽  
pp. 79-88
Author(s):  
Pierre Alliez ◽  
Simon Giraudot ◽  
David Cohen-Steiner
Keyword(s):  
Shape Reconstruction ◽  
Optimal Transportation

scholarly journals Design and analysis of a fiber-optic sensing system for shape reconstruction of a minimally invasive surgical needle

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Aizhan Issatayeva ◽  
Aida Amantayeva ◽  
Wilfried Blanc ◽  
Daniele Tosi ◽  
Carlo Molardi
Keyword(s):  
Performance Analysis ◽  
Minimally Invasive ◽  
Optical Fibers ◽  
Single Mode ◽  
Spectral Shift ◽  
Shape Reconstruction ◽  
Minimally Invasive Surgical ◽  
Working Principle ◽  
Doped Fibers ◽  
Distributed Measurement

AbstractThis paper presents the performance analysis of the system for real-time reconstruction of the shape of the rigid medical needle used for minimally invasive surgeries. The system is based on four optical fibers glued along the needle at 90 degrees from each other to measure distributed strain along the needle from four different sides. The distributed measurement is achieved by the interrogator which detects the light scattered from each section of the fiber connected to it and calculates the strain exposed to the fiber from the spectral shift of that backscattered light. This working principle has a limitation of discriminating only a single fiber because of the overlap of backscattering light from several fibers. In order to use four sensing fibers, the Scattering-Level Multiplexing (SLMux) methodology is applied. SLMux is based on fibers with different scattering levels: standard single-mode fibers (SMF) and MgO-nanoparticles doped fibers with a 35–40 dB higher scattering power. Doped fibers are used as sensing fibers and SMFs are used to spatially separate one sensing fiber from another by selecting appropriate lengths of SMFs. The system with four fibers allows obtaining two pairs of opposite fibers used to reconstruct the needle shape along two perpendicular axes. The performance analysis is conducted by moving the needle tip from 0 to 1 cm by 0.1 cm to four main directions (corresponding to the locations of fibers) and to four intermediate directions (between neighboring fibers). The system accuracy for small bending (0.1–0.5 cm) is 90$$\%$$ % and for large bending (0.6–1 cm) is approximately 92$$\%$$ % .

scholarly journals DNA-Guided Assembly for Fibril Proteins

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 404
Author(s):  
Alexandru Amărioarei ◽  
Frankie Spencer ◽  
Gefry Barad ◽  
Ana-Maria Gheorghe ◽  
Corina Iţcuş ◽  
...  
Keyword(s):  
Computational Model ◽  
Structural Properties ◽  
Self Assembly ◽  
Structural Characteristics ◽  
Computational Modelling ◽  
Shape Reconstruction ◽  
Raw Material ◽  
Dna Assembly ◽  
Mesh Structure ◽  
Elementary Fibril

Current advances in computational modelling and simulation have led to the inclusion of computer scientists as partners in the process of engineering of new nanomaterials and nanodevices. This trend is now, more than ever, visible in the field of deoxyribonucleic acid (DNA)-based nanotechnology, as DNA’s intrinsic principle of self-assembly has been proven to be highly algorithmic and programmable. As a raw material, DNA is a rather unremarkable fabric. However, as a way to achieve patterns, dynamic behavior, or nano-shape reconstruction, DNA has been proven to be one of the most functional nanomaterials. It would thus be of great potential to pair up DNA’s highly functional assembly characteristics with the mechanic properties of other well-known bio-nanomaterials, such as graphene, cellulos, or fibroin. In the current study, we perform projections regarding the structural properties of a fibril mesh (or filter) for which assembly would be guided by the controlled aggregation of DNA scaffold subunits. The formation of such a 2D fibril mesh structure is ensured by the mechanistic assembly properties borrowed from the DNA assembly apparatus. For generating inexpensive pre-experimental assessments regarding the efficiency of various assembly strategies, we introduced in this study a computational model for the simulation of fibril mesh assembly dynamical systems. Our approach was based on providing solutions towards two main circumstances. First, we created a functional computational model that is restrictive enough to be able to numerically simulate the controlled aggregation of up to 1000s of elementary fibril elements yet rich enough to provide actionable insides on the structural characteristics for the generated assembly. Second, we used the provided numerical model in order to generate projections regarding effective ways of manipulating one of the the key structural properties of such generated filters, namely the average size of the openings (gaps) within these meshes, also known as the filter’s aperture. This work is a continuation of Amarioarei et al., 2018, where a preliminary version of this research was discussed.

scholarly journals ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS

2021 ◽  
pp. 1-37
Author(s):  
Florian F. Gunsilius
Keyword(s):  
Convergence Rate ◽  
Poincaré Inequality ◽  
Optimal Transportation ◽  
Matching Theory ◽  
Economic Research ◽  
Poincare Inequality ◽  
Optimal Transportation Problem ◽  
Minimax Rate ◽  
The Cost ◽  
Kantorovich Problem

The theory of optimal transportation has experienced a sharp increase in interest in many areas of economic research such as optimal matching theory and econometric identification. A particularly valuable tool, due to its convenient representation as the gradient of a convex function, has been the Brenier map: the matching obtained as the optimizer of the Monge–Kantorovich optimal transportation problem with the euclidean distance as the cost function. Despite its popularity, the statistical properties of the Brenier map have yet to be fully established, which impedes its practical use for estimation and inference. This article takes a first step in this direction by deriving a convergence rate for the simple plug-in estimator of the potential of the Brenier map via the semi-dual Monge–Kantorovich problem. Relying on classical results for the convergence of smoothed empirical processes, it is shown that this plug-in estimator converges in standard deviation to its population counterpart under the minimax rate of convergence of kernel density estimators if one of the probability measures satisfies the Poincaré inequality. Under a normalization of the potential, the result extends to convergence in the $L^2$ norm, while the Poincaré inequality is automatically satisfied. The main mathematical contribution of this article is an analysis of the second variation of the semi-dual Monge–Kantorovich problem, which is of independent interest.

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