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A frame $(x_j{)}_{j\in <\#comment/>J}$for a Hilbert space $H$is said to do phase retrieval if for all distinct vectors $x,y\in <\#comment/>H$the magnitudes of the frame coefficients $(|⟨<\#comment/>x,x_j⟩<\#comment/>|{)}_{j\in <\#comment/>J}$and $(|⟨<\#comment/>y,x_j⟩<\#comment/>|{)}_{j\in <\#comment/>J}$distinguish $x$from $y$(up to a unimodular scalar). A frame which does phase retrieval is said to do $C$-stable phase retrieval if the recovery of any vector $x\in <\#comment/>H$from the magnitude of the frame coefficients is $C$-Lipschitz. It is known that if a frame does stable phase retrieval then any sufficiently small perturbation of the frame vectors will do stable phase retrieval, though with a slightly worse stability constant. We provide new quantitative bounds on how the stability constant for phase retrieval is affected by a small perturbation of the frame vectors. These bounds are significant in that they are independent of the dimension of the Hilbert space and the number of vectors in the frame. 

Despite the rapid expansion of higher education, many young adults still enter the labor market without a college education. However, little research has focused on racial/ethnic earnings disadvantages faced by non-college-educated youth. We analyze the restricted-use data from the High School Longitudinal Study of 2009 to examine racial/ethnic earnings disparities among non-college-educated young men and women in their early 20s as of 2016, accounting for differences in premarket factors and occupation with an extensive set of controls. Results suggest striking earnings disadvantages for Black men relative to white, Latinx, and Asian men. Compared to white men, Latinx and Asian men do not earn significantly less, yet their earnings likely differ substantially by ethnic origin. While racial/ethnic earnings gaps are less prominent among women than men, women of all racial/ethnic groups have earnings disadvantages compared to white men. The results call for future studies into the heterogeneity within racial/ethnic groups and the intersectionality of race/ethnicity and gender among non-college-educated young adults. 

The STEM (science, technology, engineering, and mathematics) potential of youth with cognitive disabilities is often dismissed through problematic perceptions of STEM ability as natural and of youth with cognitive disabilities as unable. National data on more than 15,000 adolescents from the High School Longitudinal Study of 2009 first suggest that, among youth with disabilities, youth with medicated attention-deficit/hyperactivity disorder (ADHD) have the highest levels of STEM achievement, and youth with learning or intellectual disabilities typically have the lowest. Undergraduates with medicated ADHD or autism appear to be more likely to major in STEM than youth without cognitive disabilities, and youth with autism have the most positive STEM attitudes. Finally, results suggest that high school STEM achievement is more salient for college enrollment than STEM-positive attitudes across youth with most disability types, whereas attitudes are more salient than achievement for choosing a STEM major. 

Abstract We formulate general conditions which imply that $${\mathcal L}(X,Y)$$ , the space of operators from a Banach space X to a Banach space Y , has $$2^{{\mathfrak {c}}}$$ closed ideals, where $${\mathfrak {c}}$$ is the cardinality of the continuum. These results are applied to classical sequence spaces and Tsirelson-type spaces. In particular, we prove that the cardinality of the set ofclosed ideals in $${\mathcal L}\left (\ell _p\oplus \ell _q\right )$$ is exactly $$2^{{\mathfrak {c}}}$$ for all $$1<\infty $$ . 

Abstract Objective.Neural activity represents a functional readout of neurons that is increasingly important to monitor in a wide range of experiments. Extracellular recordings have emerged as a powerful technique for measuring neural activity because these methods do not lead to the destruction or degradation of the cells being measured. Current approaches to electrophysiology have a low throughput of experiments due to manual supervision and expensive equipment. This bottleneck limits broader inferences that can be achieved with numerous long-term recorded samples.Approach.We developed Piphys, an inexpensive open source neurophysiological recording platform that consists of both hardware and software. It is easily accessed and controlled via a standard web interface through Internet of Things (IoT) protocols.Main results.We used a Raspberry Pi as the primary processing device along with an Intan bioamplifier. We designed a hardware expansion circuit board and software to enable voltage sampling and user interaction. This standalone system was validated with primary human neurons, showing reliability in collecting neural activity in near real-time.Significance.The hardware modules and cloud software allow for remote control of neural recording experiments as well as horizontal scalability, enabling long-term observations of development, organization, and neural activity at scale.