Exploring Quadrupolar Interactions of 23Na and 35Cl with Triple-Quantum MRS/MRI

Magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) can be used to investigate the quadrupolar nuclei 23Na and 35Cl, each with a nuclear spin of 3/2. The Na+ cations and Cl- anions are involved in cellular functions and can undergo quadrupolar interactions with oppositely charged macromolecules. These interactions give rise to triple-quantum (TQ) signals. Compromised physiological functions change the macromolecular composition and ion content, which can be investigated with TQ MRI/MRS. The goal was to develop a sequence to acquire single-quantum (SQ) and TQ images and to map relaxation parameters in vivo within one measurement. First, a density-adapted radial MRI technique (DA-R) was implemented at a 9.4 T scanner. Phantom images demonstrated superior image quality and measurement time efficiency. High-resolution 23Na and 35Cl images allowed for distinction of anatomical features in rat. Second, TQ spectroscopy with time-proportional phase incrementation (TQ-TPPI) was used to acquire data in cells and in rat head. The results revealed interesting discrepancies in 23Na and 35Cl TQ signals, uncovering differences in the quadrupolar interactions of Na+ and Cl- on a molecular level. Finally, TQ-TPPI was combined with DA-R to create TQ and SQ TPPI imaging (TASTI). The sequence was sucsessfully applied to rat head. For the first time, localized ratios between TQ and SQ signal were mapped in different head regions. Furthermore, it enabled the distinction between TQ signal fractions in the intra- and extracellular space. With its ability to analyze local changes in ion content, relaxation times and TQ signal, the TASTI sequence has the potential to become the one tool to combine all major approaches to address 23Na NMR

Coresets for Wasserstein Distributionally Robust Optimization Problems

Wasserstein distributionally robust optimization (\textsf{WDRO}) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of \textsf{WDRO} can be prohibitive in practice since solving its ``minimax'' formulation requires a great amount of computation. Recently, several fast \textsf{WDRO} training algorithms for some specific machine learning tasks (e.g., logistic regression) have been developed. However, the research on designing efficient algorithms for general large-scale \textsf{WDRO}s is still quite limited, to the best of our knowledge. \textit{Coreset} is an important tool for compressing large dataset, and thus it has been widely applied to reduce the computational complexities for many optimization problems. In this paper, we introduce a unified framework to construct the $\epsilon$-coreset for the general \textsf{WDRO} problems. Though it is challenging to obtain a conventional coreset for \textsf{WDRO} due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of \textsf{WDRO}. Also, the error introduced by the dual coreset can be theoretically guaranteed for the original \textsf{WDRO} objective. To construct the dual coreset, we propose a novel grid sampling approach that is particularly suitable for the dual formulation of \textsf{WDRO}. Finally, we implement our coreset approach and illustrate its effectiveness for several \textsf{WDRO} problems in the experiments

Coresets for Relational Data and The Applications

A coreset is a small set that can approximately preserve the structure of the original input data set. Therefore we can run our algorithm on a coreset so as to reduce the total computational complexity. Conventional coreset techniques assume that the input data set is available to process explicitly. However, this assumption may not hold in real-world scenarios. In this paper, we consider the problem of coresets construction over relational data. Namely, the data is decoupled into several relational tables, and it could be very expensive to directly materialize the data matrix by joining the tables. We propose a novel approach called ``aggregation tree with pseudo-cube'' that can build a coreset from bottom to up. Moreover, our approach can neatly circumvent several troublesome issues of relational learning problems [Khamis et al., PODS 2019]. Under some mild assumptions, we show that our coreset approach can be applied for the machine learning tasks, such as clustering, logistic regression and SVM

A Novel Sequential Coreset Method for Gradient Descent Algorithms

A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational complexity. {\em Coreset} is a popular data compression technique that has been extensively studied before. However, most of existing coreset methods are problem-dependent and cannot be used as a general tool for a broader range of applications. A key obstacle is that they often rely on the pseudo-dimension and total sensitivity bound that can be very high or hard to obtain. In this paper, based on the ''locality'' property of gradient descent algorithms, we propose a new framework, termed ''sequential coreset'', which effectively avoids these obstacles. Moreover, our method is particularly suitable for sparse optimization whence the coreset size can be further reduced to be only poly-logarithmically dependent on the dimension. In practice, the experimental results suggest that our method can save a large amount of running time compared with the baseline algorithms

Tracking protein function with sodium multi quantum spectroscopy in a 3D-tissue culture based on microcavity arrays

The aim of this study was to observe the effects of strophanthin induced inhibition of the Na-/KATPase in liver cells using a magnetic resonance (MR) compatible bioreactor. A microcavity array with a high density three-dimensional cell culture served as a functional magnetic resonance imaging (MRI) phantom for sodium multi quantum (MQ) spectroscopy. Direct contrast enhanced (DCE) MRI revealed the homogenous distribution of biochemical substances inside the bioreactor. NMR experiments using advanced bioreactors have advantages with respect to having full control over a variety of physiological parameters such as temperature, gas composition and fluid flow. Simultaneous detection of single quantum (SQ) and triple quantum (TQ) MR signals improves accuracy and was achieved by application of a pulse sequence with a time proportional phase increment (TQTPPI). The time course of the Na-/KATPase inhibition in the cell culture was demonstrated by the corresponding alterations of sodium TQ/ SQ MR signals