arXiv subjects

Richard G. Spencer

Publications and source records attributed to Richard G. Spencer.

8 recordsLinked to original sources

arXiv2025

Structure and Dynamics of the Young Massive Star Cluster Westerlund 1

We present a structural analysis of the young massive star cluster Westerlund 1 (Wd 1). With multi-epoch Hubble Space Telescope (HST) observations, we measure the proper motions of $10346$ stars and determine their kinematic memberships by fitting a Gaussian mixture model to their proper motions. After correcting for extinction and completeness, we model the stellar density distribution and confirm the presence of an elongation with an eccentricity of $0.71$. The eccentricity decreases slightly with increasing mass. We fit the radial profile with the Elson, Fall, and Freeman model, observing a decrease in the core radius with increasing mass, indicative of weak but detectable mass segregation. This finding is further supported by a measured mass segregation ratio of $Λ_\mathrm{\rm MSR}=1.11\pm0.11$, only above $1$ by $1σ$, and slightly shorter minimum spanning tree length for higher mass bins. The cluster has a 1D velocity dispersion of $3.42 \pm 0.10~\mathrm{km}\,\mathrm{s}^{-1}$, suggesting it is subvirial. The subvirial state implies either exceptionally high star formation efficiency or inefficient stellar feedback caused by local gas expulsion before stars reach the cluster. The crossing time is $0.30$ Myr and the relaxation time is $0.26$ Gyr. Given the age of Wd 1 of $10.7$ Myr, we expect evident mass segregation for stars more massive than $10~M_\odot$, which accounts for the minor mass segregation found in the mass range of $1.00\unicode{x2013}12.14~M_\odot$ in this work. This suggests the overall mass segregation in Wd 1 is not primordial.

astro-ph.GA↗

arXiv2025

An Eigenfunction Approach to Conversion of the Laplace Transform of Point Masses on the Real Line to the Fourier Domain

Motivated by applications in magnetic resonance relaxometry, we consider the following problem: Given samples of a function $t\mapsto \sum_{k=1}^K A_k\exp(-tλ_k)$, where $K\ge 2$ is an integer, $A_k\in\mathbb{R}$, $λ_k>0$ for $k=1,\cdots, K$, determine $K$, $A_k$'s and $λ_k$'s. Unlike the case in which the $λ_k$'s are purely imaginary, this problem is notoriously ill-posed. Our goal is to show that this problem can be transformed into an equivalent one in which the $λ_k$'s are replaced by $iλ_k$. We show that this may be accomplished by approximation in terms of Hermite functions, and using the fact that these functions are eigenfunctions of the Fourier transform. We present a preliminary numerical exploration of parameter extraction from this formalism, including the effect of noise. We do not claim to have eliminated the inherent ill-posedness of the original problem, as reflected in the numerical results.

math.NA↗

arXiv2025

Input layer regularization and automated regularization hyperparameter tuning for myelin water estimation using deep learning

We propose a novel deep learning method which combines classical regularization with data augmentation for estimating myelin water fraction (MWF) in the brain via biexponential analysis. Our aim is to design an accurate deep learning technique for analysis of signals arising in magnetic resonance relaxometry. In particular, we study the biexponential model, one of the signal models used for MWF estimation. We greatly extend our previous work on \emph{input layer regularization (ILR)} in several ways. We now incorporate optimal regularization parameter selection via a dedicated neural network or generalized cross validation (GCV) on a signal-by-signal, or pixel-by-pixel, basis to form the augmented input signal, and now incorporate estimation of MWF, rather than just exponential time constants, into the analysis. On synthetically generated data, our proposed deep learning architecture outperformed both classical methods and a conventional multi-layer perceptron. On in vivo brain data, our architecture again outperformed other comparison methods, with GCV proving to be somewhat superior to a NN for regularization parameter selection. Thus, ILR improves estimation of MWF within the biexponential model. In addition, classical methods such as GCV may be combined with deep learning to optimize MWF imaging in the human brain.

q-bio.QM↗

arXiv2024

On the limits of neural network explainability via descrambling

We characterize the exact solutions to neural network descrambling--a mathematical model for explaining the fully connected layers of trained neural networks (NNs). By reformulating the problem to the minimization of the Brockett function arising in graph matching and complexity theory we show that the principal components of the hidden layer preactivations can be characterized as the optimal explainers or descramblers for the layer weights, leading to descrambled weight matrices. We show that in typical deep learning contexts these descramblers take diverse and interesting forms including (1) matching largest principal components with the lowest frequency modes of the Fourier basis for isotropic hidden data, (2) discovering the semantic development in two-layer linear NNs for signal recovery problems, and (3) explaining CNNs by optimally permuting the neurons. Our numerical experiments indicate that the eigendecompositions of the hidden layer data--now understood as the descramblers--can also reveal the layer's underlying transformation. These results illustrate that the SVD is more directly related to the explainability of NNs than previously thought and offers a promising avenue for discovering interpretable motifs for the hidden action of NNs, especially in contexts of operator learning or physics-informed NNs, where the input/output data has limited human readability.

cs.LG↗

arXiv2024

Hyperspectral Reconstruction of Skin Through Fusion of Scattering Transform Features

Hyperspectral imagery (HSI) is an established technique with an array of applications, but its use is limited due to both practical and technical issues associated with spectral devices. The goal of the ICASSP 2024 'Hyper-Skin' Challenge is to extract skin HSI from matching RGB images and an infrared band. To address this problem we propose a model using features of the scattering transform - a type of convolutional neural network with predefined filters. Our model matches and inverts those features, rather than the pixel values, reducing the complexity of matching while grouping similar features together, resulting in an improved learning process.

eess.IV↗

arXiv2023

The Galactic Center with Roman

We advocate for a Galactic center (GC) field to be added to the Galactic Bulge Time Domain Survey (GBTDS). The new field would yield high-cadence photometric and astrometric measurements of an unprecedented ${\sim}$3.3 million stars toward the GC. This would enable a wide range of science cases, such as finding star-compact object binaries that may ultimately merge as LISA-detectable gravitational wave sources, constraining the mass function of stars and compact objects in different environments, detecting populations of microlensing and transiting exoplanets, studying stellar flares and variability in young and old stars, and monitoring accretion onto the central supermassive black hole. In addition, high-precision proper motions and parallaxes would open a new window into the large-scale dynamics of stellar populations at the GC, yielding insights into the formation and evolution of galactic nuclei and their co-evolution with the growth of the supermassive black hole. We discuss the possible trade-offs between the notional GBTDS and the addition of a GC field with either an optimal or minimal cadence. Ultimately, the addition of a GC field to the GBTDS would dramatically increase the science return of Roman and provide a legacy dataset to study the mid-plane and innermost regions of our Galaxy.

astro-ph.IM↗

arXiv2022

Solution of Non-negative Least Squares Inverse Problems Using a Span of Regularized Solutions, with Application to Magnetic Resonance Relaxometry

We present a fundamentally new regularization method for the solution of the Fredholm integral equation of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method identifies solutions within a much larger function space, spanned by this set of regularized solutions, than is available to conventional regularizaton methods. Each of these solutions is regularized to a different extent. In effect, we combine the stability of solutions with greater degrees of regularization with the resolution of those that are less regularized. In contrast, current methods involve selection of a single, or in some cases several, regularization parameters that define an optimal degree of regularization. Because the identified solution is within the span of a set of differently-regularized solutions, we call this method \textit{span of regularizations}, or SpanReg. We demonstrate the performance of SpanReg through a non-negative least squares analysis employing a Gaussian basis, and demonstrate the improved recovery of bimodal Gaussian distribution functions as compared to conventional methods. We also demonstrate that this method exhibits decreased dependence of the end result on the optimality of regularization parameter selection. We further illustrate the method with an application to myelin water fraction mapping in the human brain from experimental magnetic resonance imaging relaxometry data. We expect SpanReg to be widely applicable as an effective new method for regularization of inverse problems.

stat.ME↗

arXiv2018

A Novel Extension to Fuzzy Connectivity for Body Composition Analysis: Applications in Thigh, Brain, and Whole Body Tissue Segmentation

Magnetic resonance imaging (MRI) is the non-invasive modality of choice for body tissue composition analysis due to its excellent soft tissue contrast and lack of ionizing radiation. However, quantification of body composition requires an accurate segmentation of fat, muscle and other tissues from MR images, which remains a challenging goal due to the intensity overlap between them. In this study, we propose a fully automated, data-driven image segmentation platform that addresses multiple difficulties in segmenting MR images such as varying inhomogeneity, non-standardness, and noise, while producing high-quality definition of different tissues. In contrast to most approaches in the literature, we perform segmentation operation by combining three different MRI contrasts and a novel segmentation tool which takes into account variability in the data. The proposed system, based on a novel affinity definition within the fuzzy connectivity (FC) image segmentation family, prevents the need for user intervention and reparametrization of the segmentation algorithms. In order to make the whole system fully automated, we adapt an affinity propagation clustering algorithm to roughly identify tissue regions and image background. We perform a thorough evaluation of the proposed algorithm's individual steps as well as comparison with several approaches from the literature for the main application of muscle/fat separation. Furthermore, whole-body tissue composition and brain tissue delineation were conducted to show the generalization ability of the proposed system. This new automated platform outperforms other state-of-the-art segmentation approaches both in accuracy and efficiency.

cs.CV↗