Semi-Supervised Multimodal Relevance Vector Regression Improves Cognitive Performance Estimation from Imaging and Biological Biomarkers

Accurate estimation of cognitive scores for patients can help track the progress of neurological diseases. In this paper, we present a novel semi-supervised multimodal relevance vector regression (SM-RVR) method for predicting clinical scores of neurological diseases from multimodal imaging and biological biomarker, to help evaluate pathological stage and predict progression of diseases, e.g., Alzheimer’s diseases (AD). Unlike most existing methods, we predict clinical scores from multimodal (imaging and biological) biomarkers, including MRI, FDG-PET, and CSF. Considering that the clinical scores of mild cognitive impairment (MCI) subjects are often less stable compared to those of AD and normal control (NC) subjects due to the heterogeneity of MCI, we use only the multimodal data of MCI subjects, but no corresponding clinical scores, to train a semi-supervised model for enhancing the estimation of clinical scores for AD and NC subjects. We also develop a new strategy for selecting the most informative MCI subjects. We evaluate the performance of our approach on 202 subjects with all three modalities of data (MRI, FDG-PET and CSF) from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. The experimental results show that our SM-RVR method achieves a root-mean-square error (RMSE) of 1.91 and a correlation coefficient (CORR) of 0.80 for estimating the MMSE scores, and also a RMSE of 4.45 and a CORR of 0.78 for estimating the ADAS-Cog scores, demonstrating very promising performances in AD studies

International Congress of Mathematicians: 2022 July 6–14: Proceedings of the ICM 2022

Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022. Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress. The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described