Advances in quantitative analysis of astrocytes using machine learning

Astrocytes, a subtype of glial cells, are starshaped cells that are involved in the homeostasis and blood flow control of the central nervous system (CNS). They are known to provide structural and functional support to neurons, including the regulation of neuronal activation through extracellular ion concentrations, the regulation of energy dynamics in the brain through the transfer of lactate to neurons, and the modulation of synaptic transmission via the release of neurotransmitters such as glutamate and adenosine triphosphate. In addition, astrocytes play a critical role in neuronal reconstruction after brain injury, including neurogenesis, synaptogenesis, angiogenesis, repair of the blood-brain barrier, and glial scar formation after traumatic brain injury (Zhou et al., 2020). The multifunctional role of astrocytes in the CNS with tasks requiring close contact with their targets is reflected by their morphological complexity, with processes and ramifications occurring over multiple scales where interactions are plastic and can change depending on the physiological conditions. Another major feature of astrocytes is reactive astrogliosis, a process occurring in response to traumatic brain injury, neurological diseases, or infection which involves substantial morphological alterations and is often accompanied by molecular, cytoskeletal, and functional changes that ultimately play a key role in the disease outcome (Schiweck et al., 2018). Because morphological changes in astrocytes correlate so significantly with brain injury and the development of pathologies of the CNS, there is a major interest in methods to reliably detect and accurately quantify such morphological alterations. We review below the recent progress in the quantitative analysis of images of astrocytes. We remark that, while our discussion is focused on astrocytes, the same methods discussed below can be applied to other types of complex glial cells.National Science Foundation grants Division of Mathmatical Scienc

Analysis and identification of multidimensional singularities using the continuous shearlet transform

Abstract In this chapter, we illustrate the properties of the continuous shearlet transform with respect to its ability to describe the set of singularities of multidimensional functions and distributions. This is of particular interest since singularities and other irregular structures typically carry the most essential information in multidimensional phenomena. Consider, for example, the edges of natural images or the moving fronts in the solutions of transport equations. In the following, we show that the continuous shearlet transform provides a precise geometrical characterization of the singularity sets of multidimensional functions and precisely characterizes the boundaries of 2D and 3D regions through its asymptotic decay at fine scales. These properties go far beyond the continuous wavelet transform and other classical methods, and set the groundwork for very competitive algorithms for edge detection and feature extraction of 2D and 3D data. Key words: analysis of singularities, continuous wavelet transform, shearlets, sparsity, wavefront set, wavelets

Robust and stable region-of-interest tomographic reconstruction using a robust width prior

Region-of-interest computed tomography (ROI CT) aims at reconstructing a region within the field of view by using only ROI-focused projections. The solution of this inverse problem is challenging and methods of tomographic reconstruction that are designed to work with full projection data may perform poorly or fail when applied to this setting. In this work, we study the ROI CT problem in the presence of measurement noise and formulate the reconstruction problem by relaxing data fidelity and consistency requirements. Under the assumption of a robust width prior that provides a form of stability for data satisfying appropriate sparsity-inducing norms, we derive reconstruction performance guarantees and controllable error bounds. Based on this theoretical setting, we introduce a novel iterative reconstruction algorithm from ROI-focused projection data that is guaranteed to converge with controllable error while satisfying predetermined fidelity and consistency tolerances. Numerical tests on experimental data show that our algorithm for ROI CT is competitive with state-of-the-art methods especially when the ROI radius is small

FACE, GENDER AND RACE CLASSIFICATION USING MULTI-REGULARIZED FEATURES LEARNING

This paper investigates a new approach for face, gender and race classification, called multi-regularized learning (MRL). This approach combines ideas from the recently proposed algorithms called multi-stage learning (MSL) and multi-task features learning (MTFL). In our approach, we first reduce the dimensionality of the training faces using PCA. Next, for a given a test (probe) face, we use MRL to exploit the relationships among multiple shared stages generated by changing the regularization parameter. Our approach results in convex optimization problem that controls the trade-off between the fidelity to the data (training) and the smoothness of the solution (probe). Our MRL algorithm is compared against different state-of-the-art methods on face recognition (FR), gender classification (GC) and race classification (RC) based on different experimental protocols with AR, LFW, FEI, Lab2 and Indian databases. Results show that our algorithm performs very competitively

Optimal restoration of noisy 3D X-ray data via shearlet

decomposition

Automated detection of GFAP-labeled astrocytes in micrographs using YOLOv5

Astrocytes, a subtype of glial cells with a complex morphological structure, are active players in many aspects of the physiology of the central nervous system (CNS). However, due to their highly involved interaction with other cells in the CNS, made possible by their morphological complexity, the precise mechanisms regulating astrocyte function within the CNS are still poorly understood. This knowledge gap is also due to the current limitations of existing quantitative image analysis tools that are unable to detect and analyze images of astrocyte with sufficient accuracy and efficiency. To address this need, we introduce a new deep learning framework for the automated detection of GFAP-immunolabeled astrocytes in brightfield or fluorescent micrographs. A major novelty of our approach is the applications of YOLOv5, a sophisticated deep learning platform designed for object detection, that we customized to derive optimized classification models for the task of astrocyte detection. Extensive numerical experiments using multiple image datasets show that our method performs very competitively against both conventional and state-of-the-art methods, including the case of images where astrocytes are very dense. In the spirit of reproducible research, our numerical code and annotated data are released open source and freely available to the scientific community.National Science Foundation ; National Institutes of Healt

Spectral calibration of exponential Lévy Models [2]

The calibration of financial models has become rather important topic in recent years mainly because of the need to price increasingly complex options in a consistent way. The choice of the underlying model is crucial for the good performance of any calibration procedure. Recent empirical evidences suggest that more complex models taking into account such phenomenons as jumps in the stock prices, smiles in implied volatilities and so on should be considered. Among most popular such models are Levy ones which are on the one hand able to produce complex behavior of the stock time series including jumps, heavy tails and on other hand remain tractable with respect to option pricing. The work on calibration methods for financial models based on Lévy processes has mainly focused on certain parametrisations of the underlying Lévy process with the notable exception of Cont and Tankov (2004). Since the characteristic triplet of a Lévy process is a priori an infinite-dimensional object, the parametric approach is always exposed to the problem of misspecification, in particular when there is no inherent economic foundation of the parameters and they are only used to generate different shapes of possible jump distributions. In this work we propose and test a non-parametric calibration algorithm which is based on the inversion of the explicit pricing formula via Fourier transforms and a regularisation in the spectral domain.Using the Fast Fourier Transformation, the procedure is fast, easy to implement and yields good results in simulations in view of the severe ill-posedness of the underlying inverse problem