An automatic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si128.svg"><mml:msub><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>-based regularization method for the analysis of FFC dispersion profiles with quadrupolar peaks

Landi, Germana; Spinelli, G.V.; Zama, Fabiana; Martino, Delia Chillura; Conte, Pellegrino; Meo, Paolo Lo; Bortolotti, Villiam

doi:10.1016/j.amc.2022.127809

Cited by 9 publications

(12 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, the integral form of Equation ( 2) unconstrainedly gives only the number of the possible correlation times describing the dynamics of the overall physical system. Instead, the typical approach used in FFC NMR relaxometry requests an ad-hoc mathematical model containing information about the number and meaning of the correlation times that describe a given system [12].…”

Section: The Parameter Identification Problemmentioning

confidence: 99%

“…The locally adapted L 2 regularization was originally introduced by Bortolotti et al in [11], where the regularization parameters are determined by applying the Uniform Penalty principle. The global L 1 regularization has been applied in [12], which addresses the more complex problem of data exhibiting spurious peaks caused by Quadrupolar Relaxation Enhancement. Finally, the coupling of locally adapted L 2 and global L 1 penalties was originally introduced by Bortolotti et al in [13] for inverting two-dimensional NMR relaxation data and has been adapted to NMRD profiles.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Bortolotti,

Conte,

Landi

et al. 2024

Computers

View full text Add to dashboard Cite

Fast-Field-Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a powerful, non-destructive magnetic resonance technique that enables, among other things, the investigation of slow molecular dynamics at low magnetic field intensities. FFC-NMR relaxometry measurements provide insight into molecular motion across various timescales within a single experiment. This study focuses on a model-free approach, representing the NMRD profile R1 as a linear combination of Lorentzian functions, thereby addressing the challenges of fitting data within an ill-conditioned linear least-squares framework. Tackling this problem, we present a comprehensive review and experimental validation of three regularization approaches to implement the model-free approach to analyzing NMRD profiles. These include (1) MF-UPen, utilizing locally adapted L2 regularization; (2) MF-L1, based on L1 penalties; and (3) a hybrid approach combining locally adapted L2 and global L1 penalties. Each method’s regularization parameters are determined automatically according to the Balancing and Uniform Penalty principles. Our contributions include the implementation and experimental validation of the MF-UPen and MF-MUPen algorithms, and the development of a “dispersion analysis” technique to assess the existence range of the estimated parameters. The objective of this work is to delineate the variance in fit quality and correlation time distribution yielded by each algorithm, thus broadening the set of software tools for the analysis of sample structures in FFC-NMR studies. The findings underline the efficacy and applicability of these algorithms in the analysis of NMRD profiles from samples representing different potential scenarios.

show abstract

Section: The Parameter Identification Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Bortolotti,

Conte,

Landi

et al. 2024

Computers

View full text Add to dashboard Cite

show abstract

“…For this reason, any assumption about the number of exponentials to use for modelling the FFC NMR relaxometry data is not necessary [15]. The NMRD pro les (i.e., R 1 = 1/T 1 -vs-n L curves) were modelled according to the free-model analysis elsewhere reported [17], to obtain the distribution of correlation times from which information about the dynamic domains in chocolates were obtained.…”

Section: Fast Field Cycling (Ffc) Nmr Relaxometrymentioning

confidence: 99%

“…3. For this reason, the model described elsewhere [17] has been applied. The inverse transformation of the function related to the relaxometry NMRD showed a time domain graph where different correlation times, each referred to the dynamic components of the chocolate matrixes, are reported (Fig.…”

Section: Rheologymentioning

confidence: 99%

Novel vegan and sugar-substituted chocolates. Part I: physical-chemical characterization

Torregrossa,

Cinquanta,

Corona

et al. 2023

Preprint

View full text Add to dashboard Cite

The confectionery industry is increasingly adopting new solutions and possible formulations to expand the ranges of chocolate products that support food styles linked to either cultural or health choices. The chemical-physical characteristics of chocolates (dark and milk) produced with traditional formulations or intended for vegan or demanding less simple sugars consumers (with a 10% reduction in calorific value), were analysed. The effects of the substitution of milk with coconut copra, almond and isolated soy proteins, and the replacement of sucrose with coconut sugars, stevia and erythritol, have been accounted for by analysing texture, rheology and water activity, differential scanning calorimetry (DSC) and fast field cycling (FFC) nuclear magnetic resonance (NMR) relaxometry. The plant-based sample showed lower values for hardness and adhesiveness in the texture analysis, and a larger peak in the melting behaviour at the DSC. Moreover, the substitution of milk powder caused more than a halving of the yield stress and a similar decrease in apparent and Casson viscosity. The crystallisation of cocoa butter in the substituted-sugar sample involved the β V form, the most desirable crystal form in high-quality chocolate. Results by FFC NMR relaxometry allowed identification of differently sized aggregates whose chemical nature is discussed. FFC NMR relaxometry data confirm those by rheological and DSC investigations.

show abstract

“…In clinical practice, modal methods used are based on Zernike polynomials, which have shown high accuracy in slightly deformed corneas and good robustness against noise present in equipment during the measurement acquisition process [ 3 ], which gives them a lower dependence on measurement acquisition errors [ 14 ]. However, these polynomials have some problems due to their global nature, that is, in corneas that present significant surface irregularities, such as in the case of advanced keratoconus; these polynomials require high orders to perform a reliable reconstruction of corneal geometry, for which they use fitting tools such as least squares (LSQ) [ 15 ], or sequential quadratic programming (SQP) [ 16 ], but both generate instabilities against local minima caused by the discontinuities as mentioned above [ 17 , 18 , 19 ]. Therefore, it would be of interest to develop a modal reconstruction procedure that is not only accurate when irregular surfaces are present but also computationally viable in clinical practice.…”

Section: Introductionmentioning

confidence: 99%

Novel Multivariable Evolutionary Algorithm-Based Method for Modal Reconstruction of the Corneal Surface from Sparse and Incomplete Point Clouds

Sáez-Gutiérrez,

Velázquez,

Alió del Barrio

et al. 2023

Bioengineering

View full text Add to dashboard Cite

Three-dimensional reconstruction of the corneal surface provides a powerful tool for managing corneal diseases. This study proposes a novel method for reconstructing the corneal surface from elevation point clouds, using modal schemes capable of reproducing corneal shapes using surface polynomial functions. The multivariable polynomial fitting was performed using a non-dominated sorting multivariable genetic algorithm (NS-MVGA). Standard reconstruction methods using least-squares discrete fitting (LSQ) and sequential quadratic programming (SQP) were compared with the evolutionary algorithm-based approach. The study included 270 corneal surfaces of 135 eyes of 102 patients (ages 11–63) sorted in two groups: control (66 eyes of 33 patients) and keratoconus (KC) (69 eyes of 69 patients). Tomographic information (Sirius, Costruzione Strumenti Oftalmici, Italy) was processed using Matlab. The goodness of fit for each method was evaluated using mean squared error (MSE), measured at the same nodes where the elevation data were collected. Polynomial fitting based on NS-MVGA improves MSE values by 86% compared to LSQ-based methods in healthy patients. Moreover, this new method improves aberrated surface reconstruction by an average value of 56% if compared with LSQ-based methods in keratoconus patients. Finally, significant improvements were also found in morpho-geometric parameters, such as asphericity and corneal curvature radii.

show abstract

An automatic L1-based regularization method for the analysis of FFC dispersion profiles with quadrupolar peaks

Cited by 9 publications

References 26 publications

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Robust Algorithms for the Analysis of Fast-Field-Cycling Nuclear Magnetic Resonance Dispersion Curves

Novel vegan and sugar-substituted chocolates. Part I: physical-chemical characterization

Novel Multivariable Evolutionary Algorithm-Based Method for Modal Reconstruction of the Corneal Surface from Sparse and Incomplete Point Clouds

Contact Info

Product

Resources

About