How many zeros of a random polynomial are real?

We provide an elementary geometric derivation of the Kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients. We show that the expected number of real zeros is simply the length of the moment curve $(1,t,\ldots,t^n)$ projected onto the surface of the unit sphere, divided by $\pi$. The probability density of the real zeros is proportional to how fast this curve is traced out. We then relax Kac's assumptions by considering a variety of random sums, series, and distributions, and we also illustrate such ideas as integral geometry and the Fubini-Study metric.Comment: 37 page

Evidence for a Weak Wind from the Young Sun

The early history of the solar wind has remained largely a mystery due to the difficulty of detecting winds around young stars that can serve as analogs for the young Sun. Here we report on the detection of a wind from the 500 Myr old solar analog π1 UMa (G1.5 V), using spectroscopic observations from the Hubble Space Telescope. We detect H I Lyα absorption from the interaction region between the stellar wind and interstellar medium, i.e., the stellar astrosphere. With the assistance of hydrodynamic models of the π1 UMa astrosphere, we infer a wind only half as strong as the solar wind for this star. This suggests that the Sun and solar-like stars do not have particularly strong coronal winds in their youth.Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program GO-12596

Artificial Intelligence for mental health support during COVID-19: Experiences of graduate counseling students

The purpose of this study was to examine how an AI chatbot could provide mental health support to counselors-in-training during the COVID-19 pandemic. The chatbot “Tess” was available to participants for two weeks. Participants responded to questions about their experience and the content of this qualitative data was analyzed. Themes emerged that focused on mental health during the pandemic, utility of the AI chatbot during the pandemic, and potential therapeutic use in general. Findings were mixed and suggest some skepticism among counseling students towards the use of an AI chatbot

The Embryonic Transcriptome Of The Red-Eared Slider Turtle (Trachemys Scripta)

The bony shell of the turtle is an evolutionary novelty not found in any other group of animals, however, research into its formation has suggested that it has evolved through modification of conserved developmental mechanisms. Although these mechanisms have been extensively characterized in model organisms, the tools for characterizing them in non-model organisms such as turtles have been limited by a lack of genomic resources. We have used a next generation sequencing approach to generate and assemble a transcriptome from stage 14 and 17 Trachemys scripta embryos, stages during which important events in shell development are known to take place. The transcriptome consists of 231,876 sequences with an N-50 of 1,166 bp. GO terms and EC codes were assigned to the 61,643 unique predicted proteins identified in the transcriptome sequences. All major GO categories and metabolic pathways are represented in the transcriptome. Transcriptome sequences were used to amplify several cDNA fragments designed for use as RNA in situ probes. One of these, BMP5, was hybridized to a T. scripta embryo and exhibits both conserved and novel expression patterns. The transcriptome sequences should be of broad use for understanding the evolution and development of the turtle shell and for annotating any future T. scripta genome sequences

Error analysis of free probability approximations to the density of states of disordered systems

Theoretical studies of localization, anomalous diffusion and ergodicity breaking require solving the electronic structure of disordered systems. We use free probability to approximate the ensemble- averaged density of states without exact diagonalization. We present an error analysis that quantifies the accuracy using a generalized moment expansion, allowing us to distinguish between different approximations. We identify an approximation that is accurate to the eighth moment across all noise strengths, and contrast this with the perturbation theory and isotropic entanglement theory.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

Epistemic Beliefs: Relationship to Future Expectancies and Quality of Life in Cancer Patients.

CONTEXT: Expectations about the future (future expectancies) are important determinants of psychological well-being among cancer patients, but the strategies patients use to maintain positive and cope with negative expectancies are incompletely understood. OBJECTIVES: To obtain preliminary evidence on the potential role of one strategy for managing future expectancies: the adoption of epistemic beliefs in fundamental limits to medical knowledge. METHODS: A sample of 1307 primarily advanced-stage cancer patients participating in a genomic tumor testing study in community oncology practices completed measures of epistemic beliefs, positive future expectancies, and mental and physical health-related quality of life (HRQOL). Descriptive and linear regression analyses were conducted to assess the relationships between these factors and test two hypotheses: 1) epistemic beliefs affirming fundamental limits to medical knowledge ( fallibilistic epistemic beliefs ) are associated with positive future expectancies and mental HRQOL, and 2) positive future expectancies mediate this association. RESULTS: Participants reported relatively high beliefs in limits to medical knowledge (M = 2.94, s.d.=.67) and positive future expectancies (M = 3.01, s.d.=.62) (range 0-4), and relatively low mental and physical HRQOL. Consistent with hypotheses, fallibilistic epistemic beliefs were associated with positive future expectancies (b = 0.11, SE=.03, P\u3c 0.001) and greater mental HRQOL (b = 0.99, SE=.34, P = 0.004); positive expectancies also mediated the association between epistemic beliefs and mental HRQOL (Sobel Z=4.27, P\u3c0.001). CONCLUSIONS: Epistemic beliefs in limits to medical knowledge are associated with positive future expectancies and greater mental HRQOL; positive expectancies mediate the association between epistemic beliefs and HRQOL. More research is needed to confirm these relationships and elucidate their causal mechanisms

Large Scale Cross-Correlations in Internet Traffic

The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network `Renater'. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues--up to a rescaling which exhibits a typical correlation time of the order 10 minutes--and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between connections. The study of the most correlated connections reveals the existence of `active centers' which are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the WWW traffic.Comment: 7 pages, 6 figures, final versio

ACED: Accelerated Computational Electrochemical systems Discovery

Large-scale electrification is vital to addressing the climate crisis, but many engineering challenges remain to fully electrifying both the chemical industry and transportation. In both of these areas, new electrochemical materials and systems will be critical, but developing these systems currently relies heavily on computationally expensive first-principles simulations as well as human-time-intensive experimental trial and error. We propose to develop an automated workflow that accelerates these computational steps by introducing both automated error handling in generating the first-principles training data as well as physics-informed machine learning surrogates to further reduce computational cost. It will also have the capacity to include automated experiments "in the loop" in order to dramatically accelerate the overall materials discovery pipeline.Comment: 4 pages, 1 figure, accepted to NeurIPS Climate Change and AI Workshop 2020, updating acknowledgements and citation