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Sensors (Basel, Switzerland) Mar 2021We developped an open source library called RcdMathLib for solving multivariate linear and nonlinear systems. RcdMathLib supports on-the-fly computing on low-cost and...
We developped an open source library called RcdMathLib for solving multivariate linear and nonlinear systems. RcdMathLib supports on-the-fly computing on low-cost and resource-constrained devices, e.g., microcontrollers. The decentralized processing is a step towards ubiquitous computing enabling the implementation of Internet of Things (IoT) applications. RcdMathLib is modular- and layer-based, whereby different modules allow for algebraic operations such as vector and matrix operations or decompositions. RcdMathLib also comprises a utilities-module providing sorting and filtering algorithms as well as methods generating random variables. It enables solving linear and nonlinear equations based on efficient decomposition approaches such as the Singular Value Decomposition (SVD) algorithm. The open source library also provides optimization methods such as Gauss-Newton and Levenberg-Marquardt algorithms for solving problems of regression smoothing and curve fitting. Furthermore, a positioning module permits computing positions of IoT devices using algorithms for instance trilateration. This module also enables the optimization of the position by performing a method to reduce multipath errors on the mobile device. The library is implemented and tested on resource-limited IoT as well as on full-fledged operating systems. The open source software library is hosted on a GitLab repository.
PubMed: 33804494
DOI: 10.3390/s21051689 -
Optics Express Nov 2018With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount...
With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount importance. Highly precise techniques for measuring the polarisation, frequency, and arrival time of a photon have been developed. However, the transverse spatial degree of freedom still lacks a measurement scheme that allows the reconstruction of its full transverse structure with a simple implementation and a high level of accuracy. Here we show a method to measure the azimuthal and radial modes of Laguerre-Gaussian beams with a greater than 99 % accuracy, using a single phase screen. We compare our technique with previous commonly used methods and demonstrate the significant improvements it presents for quantum key distribution and state tomography of high-dimensional quantum states of light. Moreover, our technique can be readily extended to any arbitrary family of spatial modes, such as mutually unbiased bases, Hermite-Gauss, and Ince-Gauss. Our scheme will significantly enhance existing quantum and classical communication protocols that use the spatial structure of light, as well as enable fundamental experiments on spatial-mode entanglement to reach their full potential.
PubMed: 30650772
DOI: 10.1364/OE.26.031925 -
Nanomaterials (Basel, Switzerland) Jan 2023This paper presents an efficient method to generate high-order Bessel-Gauss beams carrying orbital angular momentum (OAM) by using a thin and compact optical element...
This paper presents an efficient method to generate high-order Bessel-Gauss beams carrying orbital angular momentum (OAM) by using a thin and compact optical element such as a multilevel spiral axicon. This approach represents an excellent alternative for diffraction-free OAM beam generation instead of complex methods based on a doublet formed by a physical spiral phase plate and zero-order axicon, phase holograms loaded on spatial light modulators (SLMs), or the interferometric method. Here, we present the fabrication process for axicons with 16 and 32 levels, characterized by high mode conversion efficiency and good transmission for visible light (λ = 633 nm wavelength). The Bessel vortex states generated with the proposed diffractive optical elements (DOEs) can be exploited as a very useful resource for optical and quantum communication in free-space channels or in optical fibers.
PubMed: 36770540
DOI: 10.3390/nano13030579 -
PeerJ 2020The native structure of a protein is important for its function, and therefore methods for exploring protein structures have attracted much research. However, rather few...
The native structure of a protein is important for its function, and therefore methods for exploring protein structures have attracted much research. However, rather few methods are sensitive to topologic-geometric features, the examples being knots, slipknots, lassos, links, and pokes, and with each method aimed only for a specific set of such configurations. We here propose a general method which transforms a structure into a "fingerprint of topological-geometric values" consisting in a series of real-valued descriptors from mathematical Knot Theory. The extent to which a structure contains unusual configurations can then be judged from this fingerprint. The method is not confined to a particular pre-defined topology or geometry (like a knot or a poke), and so, unlike existing methods, it is general. To achieve this our new algorithm, GISA, as a key novelty produces the descriptors, so called Gauss integrals, not only for the full chains of a protein but for all its sub-chains. This allows fingerprinting on any scale from local to global. The Gauss integrals are known to be effective descriptors of global protein folds. Applying GISA to sets of several thousand high resolution structures, we first show how the most basic Gauss integral, the writhe, enables swift identification of pre-defined geometries such as pokes and links. We then apply GISA with no restrictions on geometry, to show how it allows identifying rare conformations by finding rare invariant values only. In this unrestricted search, pokes and links are still found, but also knotted conformations, as well as more highly entangled configurations not previously described. Thus, an application of the basic scan method in GISA's tool-box revealed 10 known cases of knots as the top positive writhe cases, while placing at the top of the negative writhe 14 cases in cis-trans isomerases sharing a spatial motif of little secondary structure content, which possibly has gone unnoticed. Possible general applications of GISA are fold classification and structural alignment based on local Gauss integrals. Others include finding errors in protein models and identifying unusual conformations that might be important for protein folding and function. By its broad potential, we believe that GISA will be of general benefit to the structural bioinformatics community. GISA is coded in C and comes as a command line tool. Source and compiled code for GISA plus read-me and examples are publicly available at GitHub (https://github.com).
PubMed: 32566389
DOI: 10.7717/peerj.9159 -
International Journal of Environmental... Mar 2022The Corona Virus Disease 2019 (COVID-19) is spreading all over the world. Quantitative analysis of the effects of various factors on the spread of the epidemic will help...
The Corona Virus Disease 2019 (COVID-19) is spreading all over the world. Quantitative analysis of the effects of various factors on the spread of the epidemic will help people better understand the transmission characteristics of SARS-CoV-2, thus providing a theoretical basis for governments to develop epidemic prevention and control strategies. This article uses public data sets from The Center for Systems Science and Engineering at Johns Hopkins University (JHU CSSE), Air Quality Open Data Platform, China Meteorological Data Network, and WorldPop website to construct experimental data. The epidemic situation is predicted by Dual-link BiGRU Network, and the relationship between epidemic spread and various feature factors is quantitatively analyzed by the Gauss-Newton iteration Method. The study found that population density has the greatest positive correlation to the spread of the epidemic among the selected feature factors, followed by the number of landing flights. The number of newly diagnosed daily will increase by 1.08% for every 1% of the population density, the number of newly diagnosed daily will increase by 0.98% for every 1% of the number of landing flights. The results of this study show that the control of social distance and population movement has a high priority in epidemic prevention and control strategies, and it can play a very important role in controlling the spread of the epidemic.
Topics: COVID-19; China; Disease Outbreaks; Epidemics; Humans; SARS-CoV-2
PubMed: 35328880
DOI: 10.3390/ijerph19063187 -
Optics Express Dec 2022We analyze the effects of atmospheric turbulence on the mode power spectrum of beams carrying orbital angular momentum represented by Laguerre-Gauss (LG) modes. For an...
We analyze the effects of atmospheric turbulence on the mode power spectrum of beams carrying orbital angular momentum represented by Laguerre-Gauss (LG) modes. For an input (p,m) LG mode, i.e. pump, we calculate the power transferred to other modes (p',m') due to turbulence. Our analysis is validated against split-step beam propagation simulations and shows agreement into the strong turbulence regime. These results have applications for the design and characterization of free-space laser communication systems.
PubMed: 36522955
DOI: 10.1364/OE.475896 -
Entropy (Basel, Switzerland) Dec 2021Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a...
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond to the likelihood and prior-probability models, respectively. The Bayesian approach gives more flexibility in choosing these terms and, in particular, the prior term via hierarchical models and hidden variables. However, the Bayesian computations can become very heavy computationally. The machine learning (ML) methods such as classification, clustering, segmentation, and regression, based on neural networks (NN) and particularly convolutional NN, deep NN, physics-informed neural networks, etc. can become helpful to obtain approximate practical solutions to inverse problems. In this tutorial article, particular examples of image denoising, image restoration, and computed-tomography (CT) image reconstruction will illustrate this cooperation between ML and inversion.
PubMed: 34945979
DOI: 10.3390/e23121673 -
Frontiers in Big Data 2022We introduce a supervised learning framework for target functions that are well approximated by a sum of (few) separable terms. The framework proposes to approximate...
We introduce a supervised learning framework for target functions that are well approximated by a sum of (few) separable terms. The framework proposes to approximate each component function by a B-spline, resulting in an approximant where the underlying coefficient tensor of the tensor product expansion has a low-rank polyadic decomposition parametrization. By exploiting the multilinear structure, as well as the sparsity pattern of the compactly supported B-spline basis terms, we demonstrate how such an approximant is well-suited for regression and classification tasks by using the Gauss-Newton algorithm to train the parameters. Various numerical examples are provided analyzing the effectiveness of the approach.
PubMed: 35224482
DOI: 10.3389/fdata.2022.688496 -
Sensors (Basel, Switzerland) Dec 2022This study addressed the problem of localization in an ultrawide-band (UWB) network, where the positions of both the access points and the tags needed to be estimated....
This study addressed the problem of localization in an ultrawide-band (UWB) network, where the positions of both the access points and the tags needed to be estimated. We considered a fully wireless UWB localization system, comprising both software and hardware, featuring easy plug-and-play usability for the consumer, primarily targeting sport and leisure applications. Anchor self-localization was addressed by two-way ranging, also embedding a Gauss-Newton algorithm for the estimation and compensation of antenna delays, and a modified isolation forest algorithm working with low-dimensional set of measurements for outlier identification and removal. This approach avoids time-consuming calibration procedures, and it enables accurate tag localization by the multilateration of time difference of arrival measurements. For the assessment of performance and the comparison of different algorithms, we considered an experimental campaign with data gathered by a proprietary UWB localization system.
Topics: Wireless Technology; Sports; Algorithms; Computers; Technology
PubMed: 36502064
DOI: 10.3390/s22239363 -
Optics Express May 2023X-rays have developed into an essential tool in variety of fields, such as biology, materials, chemistry, and physics etc. Numerous X-ray types, including the orbital...
X-rays have developed into an essential tool in variety of fields, such as biology, materials, chemistry, and physics etc. Numerous X-ray types, including the orbital angular momentum (OAM), the Laguerre-Gauss, and the Hermite-Gauss states, have been proposed. This greatly enhances the depth of application of X-ray. The X-ray states described above are mostly produced by binary amplitude diffraction elements. In light of this, this paper proposes a flat X-ray diffraction grating based on caustic theory to generate Airy-type X-ray. It is proved by the simulation of multislice method that the proposed grating can generate the Airy beam in the X-ray field. The results show that the generated beams have a secondary parabolic trajectory deflection with the propagation distance, which is consistent with the theory. Inspired by the success of Airy beam in light-sheet microscope, the Airy-type X-ray can be anticipated to enable novel image capability for bio or nanoscience.
PubMed: 37381524
DOI: 10.1364/OE.492003