The Claremont Graduate University (CGU) is a private, all-graduate research university in Claremont, California. Founded in 1925, CGU is a member of the Claremont Colleges which includes five undergraduate (Pomona College, Claremont McKenna College, Harvey Mudd College, Scripps College, Pitzer College) and two graduate (CGU and Keck Graduate Institute of Applied Life Sciences) institutions of higher education.The university is organized into seven separate units: the School of Arts & Humanities; School of Community & Global Health; Drucker School of Management; School of Educational Studies; the School of Social Science, Policy, & Evaluation; the Center for Information Systems & Technology; and the Institute of Mathematical Sciences. It is classified among "R2: Doctoral Universities – High research activity.
The task of separating a superposition of signals into its individual components is a common challenge encountered in various signal processing applications, especially in domains such as audio and radar signals. A previous paper by Chui and Mhaskar proposes a method called Signal Separation Operator (SSO) to find the instantaneous frequencies and amplitudes of such superpositions where both of these change continuously and slowly over time. In this paper, we amplify and modify this method in order to separate chirp signals in the presence of crossovers, a very low SNR, and discontinuities. We give a theoretical analysis of the behavior of SSO in the presence of noise to examine the relationship between the minimal separation, minimal amplitude, SNR, and sampling frequency. Our method is illustrated with a few examples, and numerical results are reported on a simulated dataset comprising 7 simulated signals.
While the disparity is narrowing, Hispanic/Latinx students remain underrepresented in science, technology, engineering, and mathematics (STEM) majors. Prior research has shown that STEM identity is an important predictor of a sense of belonging and persistence for underrepresented minorities in STEM. Guided by social identity theory, the present study examined how culturally responsive teaching practices (CRTP) interact with negative ingroup stereotype endorsement and ethnic identification to predict STEM identification among a sample of 349 Hispanic/Latinx undergraduates across 12 Hispanic-Serving Institutions on the West Coast of the United States. Results indicated significant positive main effects of CRTP and ethnic identity on STEM identity. Additionally, CRTP moderated the relationship between students’ ethnic and STEM identities; ethnic identity was positively related to STEM identity among students reporting average or high perceived CRTP in their undergraduate courses, but not among those reporting low CRTP. Negative ingroup stereotype endorsement was negatively related to STEM identity at the bivariate level, but the association was no longer significant in the interaction model including CRTP and ethnic identity. Overall, these findings suggest that CRTP could be an identity-relevant contextual factor in which underrepresented students’ ethnic and STEM identities are more strongly aligned.
A central problem in machine learning is often formulated as follows: Given a dataset [Formula: see text] , which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model f such that f(x) ≈ y for any (x, y) drawn from the same distribution. Neural networks and kernel-based methods are commonly employed for this task due to their capacity for fast and parallel computation. The approximation capabilities, or expressive power, of these methods have been extensively studied over the past 35 years. In this paper, we will present examples of key ideas in this area found in the literature. We will discuss emerging trends in machine learning including the role of shallow/deep networks, approximation on manifolds, physics-informed neural surrogates, neural operators, and transformer architectures. Despite function approximation being a fundamental problem in machine learning, approximation theory does not play a central role in the theoretical foundations of the field. One unfortunate consequence of this disconnect is that it is often unclear how well trained models will generalize to unseen or unlabeled data. In this review, we examine some of the shortcomings of the current machine learning framework and explore the reasons for the gap between approximation theory and machine learning practice. We will then review some of recent work that achieves function approximation on unknown manifolds without the need to learn specific manifold features, such as the eigen-decomposition of the Laplace-Beltrami operator or atlas construction. In many machine learning problems, particularly classification tasks, the labels yj are drawn from a finite set of values. We summarize another recent paper that establishes a deep connection between signal separation problems and classification problems, proposing that classification tasks should be approached as instances of signal separation. We conclude by identifying several open research problems that warrant further investigation.
The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields both the number of classes, and a perfect classification using a minimal number of queried labels. Our approach uses localized trigonometric polynomial kernels initially developed for the point source signal separation problem in signal processing. Rather than point sources, we argue that the various classes come from different probability measures. The localized kernel technique developed for separating point sources is then shown to separate the supports of these measures. This is done in a hierarchical manner in our MASC algorithm to accommodate touching/overlapping class boundaries. We illustrate our theory on several simulated and real life datasets, including the Salinas and Indian Pines hyperspectral datasets and a document dataset.
INTRODUCTION:Complete blood count (CBC) discrimination indices are widely used as low-cost triage tools for microcytosis, but their diagnostic utility in population-based samples with ferritin-defined iron status is uncertain. We evaluated whether commonly used indices distinguish ferritin-defined iron-deficient from noniron-deficient microcytosis among women aged 18-49 years. METHODS:We analyzed the National Health and Nutrition Examination Survey (NHANES) 2015-2016, 2017-2018, and August 2021-August 2023 data among nonpregnant women aged 18-49 years with CBC, serum ferritin, and survey design variables. Among microcytic (MCV < 80 fL) women, iron-deficient microcytosis was defined as ferritin < 15 ng/mL and noniron-deficient microcytosis as ferritin ≥ 15 ng/mL. Mentzer, England-Fraser, Srivastava, and red cell distribution width (RDW) indices were evaluated at conventional cutoffs. Sensitivity analyses used ferritin < 30 ng/mL and C-reactive protein (CRP) restrictions of ≤ 5 and ≤ 3 mg/L. All estimates were survey-weighted. RESULTS:Among 3991 women, 507 had microcytosis. Ferritin-defined noniron-deficient microcytosis comprised 40.8% (95% CI, 35.5-46.2) and remained 37.0% and 33.6% after CRP restrictions of ≤ 5 and ≤ 3 mg/L. With ferritin ≥ 30 ng/mL, the corresponding proportions were 26.5%, 22.6%, and 20.2%. All four indices showed high sensitivity (92.9%-97.6%) but poor specificity (6.7%-35.3%). RDW had the highest specificity but still misclassified most noniron-deficient cases. CONCLUSIONS:Classic CBC indices had limited utility as standalone triage tools for ferritin-defined microcytosis. Ferritin-based assessment, interpreted in the relevant clinical and inflammatory context, should remain central. Persistent microcytosis without evidence of reduced iron stores should prompt diagnostic reconsideration and, when appropriate, hemoglobinopathy-aware evaluation.
