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David Anderson

Publications and source records attributed to David Anderson.

At least 37 records · Page 2Linked to original sources
arXiv2023

The development of HISPEC for Keck and MODHIS for TMT: science cases and predicted sensitivities

HISPEC is a new, high-resolution near-infrared spectrograph being designed for the W.M. Keck II telescope. By offering single-shot, R=100,000 between 0.98 - 2.5 um, HISPEC will enable spectroscopy of transiting and non-transiting exoplanets in close orbits, direct high-contrast detection and spectroscopy of spatially separated substellar companions, and exoplanet dynamical mass and orbit measurements using precision radial velocity monitoring calibrated with a suite of state-of-the-art absolute and relative wavelength references. MODHIS is the counterpart to HISPEC for the Thirty Meter Telescope and is being developed in parallel with similar scientific goals. In this proceeding, we provide a brief overview of the current design of both instruments, and the requirements for the two spectrographs as guided by the scientific goals for each. We then outline the current science case for HISPEC and MODHIS, with focuses on the science enabled for exoplanet discovery and characterization. We also provide updated sensitivity curves for both instruments, in terms of both signal-to-noise ratio and predicted radial velocity precision.

astro-ph.IM↗
arXiv2023

Infinite flags and Schubert polynomials

We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched Schubert polynomials. We also construct an embedding of the type C flag variety, and study the corresponding pullback map on (equivariant) cohomology rings.

math.AG↗
arXiv2023

Integral equivariant cohomology of affine Grassmannians

We give explicit presentations of the integral equivariant cohomology of the affine Grassmannians and flag varieties in type A, arising from their natural embeddings in the corresponding infinite (Sato) Grassmannian and flag variety. These presentations are compared with results obtained by Lam and Shimozono, for rational equivariant cohomology of the affine Grassmannian, and by Larson, for the integral cohomology of the moduli stack of vector bundles on $\mathbb{P}^1$.

math.AG↗
arXiv2023

Strong equivariant positivity for homogeneous varieties and back-stable coproduct coefficients

Using a transversality argument, we demonstrate the positivity of certain coefficients in the equivariant cohomology and K-theory of a generalized flag manifold. This strengthens earlier equivariant positivity theorems (of Graham and Anderson-Griffeth-Miller) by further constraining the roots which can appear in these coefficients. As an application, we deduce that structure constants for comultiplication in the equivariant K-theory of an infinite flag manifold exhibit an unusual positivity property, establishing conjectures of Lam-Lee-Shimozono. Along the way, we present alternative formulas for the back stable Grothendieck polynomials defined by those authors, as well as a new method for computing the coproduct coefficients.

math.AG↗
arXiv2022

Panoramic SETI: Program Update and High-Energy Astrophysics Applications

Optical SETI (Search for Extraterrestrial Intelligence) instruments that can explore the very fast time domain, especially with large sky coverage, offer an opportunity for new discoveries that can complement multimessenger and time domain astrophysics. The Panoramic SETI experiment (PANOSETI) aims to observe optical transients with nanosecond to second duration over a wide field-of-view ($\thicksim$2,500 sq.deg.) by using two assemblies of tens of telescopes to reject spurious signals by coincidence detection. Three PANOSETI telescopes, connected to a White Rabbit timing network used to synchronize clocks at the nanosecond level, have been deployed at Lick Observatory on two sites separated by a distance of 677 meters to distinguish nearby light sources (such as Cherenkov light from particle showers in the Earth's atmosphere) from astrophysical sources at large distances. In parallel to this deployment, we present results obtained during four nights of simultaneous observations with the four 12-meter VERITAS gamma-ray telescopes and two PANOSETI telescopes at the Fred Lawrence Whipple Observatory. We report PANOSETI's first detection of astrophysical gamma rays, comprising three events with energies in the range between $\thicksim$15 TeV and $\thicksim$50 TeV. These were emitted by the Crab Nebula, and identified as gamma rays using joint VERITAS observations.

astro-ph.IM↗
arXiv2022

Whittaker functions from motivic Chern classes

We prove a `motivic' analogue of the Weyl character formula, computing the Euler characteristic of a line bundle on a generalized flag manifold $G/B$ multiplied either by a motivic Chern class of a Schubert cell, or a Segre analogue of it. The result, given in terms of Demazure-Lusztig (D-L) operators, recovers formulas found by Brubaker, Bump and Licata for the Iwahori-Whittaker functions of the principal series representation of a $p$-adic group. In particular, we obtain a new proof of the classical Casselman-Shalika formula for the spherical Whittaker function. The proofs are based on localization in equivariant K theory, and require a geometric interpretation of how the Hecke dual (or inverse) of a D-L operator acts on the class of a point. We prove that the Hecke dual operators give Grothendieck-Serre dual classes of the motivic classes, a result which might be of independent interest. In an Appendix joint with Dave Anderson we show that if the line bundle is trivial, we recover a generalization of a classical formula by Kostant, Macdonald, Shapiro and Steinberg for the Poincar{é} polynomial of $G/B$; the generalization we consider is due to Akyıldız and Carrell and replaces $G/B$ by any smooth Schubert variety.

math.AG↗
arXiv2022

Interpretable Climate Change Modeling With Progressive Cascade Networks

Typical deep learning approaches to modeling high-dimensional data often result in complex models that do not easily reveal a new understanding of the data. Research in the deep learning field is very actively pursuing new methods to interpret deep neural networks and to reduce their complexity. An approach is described here that starts with linear models and incrementally adds complexity only as supported by the data. An application is shown in which models that map global temperature and precipitation to years are trained to investigate patterns associated with changes in climate.

cs.LG↗
arXiv2022

EACELEB: An East Asian Language Speaking Celebrity Dataset for Speaker Recognition

Large datasets are very useful for training speaker recognition systems, and various research groups have constructed several over the years. Voxceleb is a large dataset for speaker recognition that is extracted from Youtube videos. This paper presents an audio-visual method for acquiring audio data from Youtube given the speaker's name as input. The system follows a pipeline similar to that of the Voxceleb data acquisition method. However, our work focuses on fast data acquisition by using face-tracking in subsequent frames once a face has been detected -- this is preferable over face detection for every frame considering its computational cost. We show that applying audio diarization to our data after acquiring it can yield equal error rates comparable to Voxceleb. A secondary set of experiments showed that we could further decrease the error rate by fine-tuning a pre-trained x-vector system with the acquired data. Like Voxceleb, the work here focuses primarily on developing audio for celebrities. However, unlike Voxceleb, our target audio data is from celebrities in East Asian countries. Finally, we set up a speaker verification task to evaluate the accuracy of our acquired data. After diarization and fine-tuning, we achieved an equal error rate of approximately 4\% across our entire dataset.

cs.SD↗
arXiv2021

The multiplicity of a singularity in a vexillary Schubert variety

In a classical-type flag variety, we consider a Schubert variety associated to a vexillary (signed) permutation, and establish a combinatorial formula for the Hilbert-Samuel multiplicity of a point on such a Schubert variety. The formula is expressed in terms of excited Young diagrams, and extends results for Grassmannians due to Krattenthaler, Lakshmibai-Raghavan-Sankaran, and for the maximal isotropic (symplectic and orthogonal) Grassmannians to Ghorpade-Raghavan, Raghavan-Upadhyay, Kreiman, and Ikeda-Naruse. We also provide a new proof of a theorem of Li-Yong in the type A vexillary case. The main ingredient is an isomorphism between certain neighborhoods of fixed points, known as Kazhdan-Lusztig varieties, which, in turn, relies on a direct sum embedding previously used by Anderson-Fulton to relate vexillary loci to Grassmannian loci.

math.AG↗
arXiv2021

TIC 454140642: A Compact, Coplanar, Quadruple-lined Quadruple Star System Consisting of Two Eclipsing Binaries

We report the discovery of a compact, coplanar, quadruply-lined, eclipsing quadruple star system from TESS data, TIC 454140642, also known as TYC 0074-01254-1. The target was first detected in Sector 5 with 30-min cadence in Full-Frame Images and then observed in Sector 32 with 2-min cadence. The light curve exhibits two sets of primary and secondary eclipses with periods of PA = 13.624 days (binary A) and PB = 10.393 days (binary B). Analysis of archival and follow-up data shows clear eclipse-timing variations and divergent radial velocities, indicating dynamical interactions between the two binaries and confirming that they form a gravitationally-bound quadruple system with a 2+2 hierarchy. The Aa+Ab binary, Ba+Bb binary, and A-B system are aligned with respect to each other within a fraction of a degree: the respective mutual orbital inclinations are 0.25 degrees (A vs B), 0.37 degrees (A vs A-B), and 0.47 degrees (B vs A-B). The A-B system has an orbital period of 432 days - the second shortest amongst confirmed quadruple systems - and an orbital eccentricity of 0.3.

astro-ph.SR↗
arXiv2021

Identities for Schur-type determinants and pfaffians

We give a simple formula for some determinants, and an analogous formula for pfaffians, both of which are polynomial identities. The second involve some expressions that interpolate between determinants and pfaffians. We give several tableau formulas for difference operators in Types A and C, as well as other operators that appear in the "enriched", or "back-stable" Schubert polynomials. There are also tableau formulas for the enriched Schubert polynomials for vexillary and $321$-avoiding permutations.

math.CO↗
arXiv2021

Schubert Polynomials in Types A and C

Enriched versions of type A Schubert polynomials are constructed with coefficients in a polynomial ring in variables $c_1, c_2, \ldots$. Specializing these variables to $0$ recovers the double Schubert polynomials of Lascoux and Schützenberger; specializing them to certain power series recovers the back-stable double Schubert polynomials of Lam, Lee, and Shimozono; specializing them to Schur Q-polynomials relates them to the type C double Schubert polynomials of Ikeda, Mihalcea, and Naruse. Many formulas for classical Schubert polynomials generalize to this setting. They give, and are characterized by, formulas for degeneracy loci.

math.CO↗
arXiv2020

The Breakthrough Listen Search for Intelligent Life: Public Data, Formats, Reduction and Archiving

Breakthrough Listen is the most comprehensive and sensitive search for extraterrestrial intelligence (SETI) to date, employing a collection of international observational facilities including both radio and optical telescopes. During the first three years of the Listen program, thousands of targets have been observed with the Green Bank Telescope (GBT), Parkes Telescope and Automated Planet Finder. At GBT and Parkes, observations have been performed ranging from 700 MHz to 26 GHz, with raw data volumes averaging over 1PB / day. A pseudo-real time software spectroscopy suite is used to produce multi-resolution spectrograms amounting to approximately 400 GB hr^-1 GHz^-1 beam^-1. For certain targets, raw baseband voltage data is also preserved. Observations with the Automated Planet Finder produce both 2-dimensional and 1-dimensional high resolution (R~10^5) echelle spectral data. Although the primary purpose of Listen data acquisition is for SETI, a range of secondary science has also been performed with these data, including studies of fast radio bursts. Other current and potential research topics include spectral line studies, searches for certain kinds of dark matter, probes of interstellar scattering, pulsar searches, radio transient searches and investigations of stellar activity. Listen data are also being used in the development of algorithms, including machine learning approaches to modulation scheme classification and outlier detection, that have wide applicability not just for astronomical research but for a broad range of science and engineering. In this paper, we describe the hardware and software pipeline used for collection, reduction, archival, and public dissemination of Listen data. We describe the data formats and tools, and present Breakthrough Listen Data Release 1.0 (BLDR 1.0), a defined set of publicly-available raw and reduced data totalling 1 PB.

astro-ph.IM↗
arXiv2020

On the finiteness of quantum K-theory of a homogeneous space

We show that the product in the quantum K-ring of a generalized flag manifold $G/P$ involves only finitely many powers of the Novikov variables. In contrast to previous approaches to this finiteness question, we exploit the finite difference module structure of quantum K-theory. At the core of the proof is a bound on the asymptotic growth of the $J$-function, which in turn comes from an analysis of the singularities of the zastava spaces studied in geometric representation theory. An appendix by H. Iritani establishes the equivalence between finiteness and a quadratic growth condition on certain shift operators.

math.AG↗
arXiv2020

Indicator patterns of forced change learned by an artificial neural network

Many problems in climate science require the identification of signals obscured by both the "noise" of internal climate variability and differences across models. Following previous work, we train an artificial neural network (ANN) to identify the year of input maps of temperature and precipitation from forced climate model simulations. This prediction task requires the ANN to learn forced patterns of change amidst a background of climate noise and model differences. We then apply a neural network visualization technique (layerwise relevance propagation) to visualize the spatial patterns that lead the ANN to successfully predict the year. These spatial patterns thus serve as "reliable indicators" of the forced change. The architecture of the ANN is chosen such that these indicators vary in time, thus capturing the evolving nature of regional signals of change. Results are compared to those of more standard approaches like signal-to-noise ratios and multi-linear regression in order to gain intuition about the reliable indicators identified by the ANN. We then apply an additional visualization tool (backward optimization) to highlight where disagreements in simulated and observed patterns of change are most important for the prediction of the year. This work demonstrates that ANNs and their visualization tools make a powerful pair for extracting climate patterns of forced change.

physics.ao-ph↗
arXiv2020

First SETI Observations with China's Five-hundred-meter Aperture Spherical radio Telescope (FAST)

The Search for Extraterrestrial Intelligence (SETI) attempts to address the possibility of the presence of technological civilizations beyond the Earth. Benefiting from high sensitivity, large sky coverage, an innovative feed cabin for China's Five-hundred-meter Aperture Spherical radio Telescope (FAST), we performed the SETI first observations with FAST's newly commisioned 19-beam receiver; we report preliminary results in this paper. Using the data stream produced by the SERENDIP VI realtime multibeam SETI spectrometer installed at FAST, as well as its off-line data processing pipelines, we identify and remove four kinds of radio frequency interference(RFI): zone, broadband, multi-beam, and drifting, utilizing the Nebula SETI software pipeline combined with machine learning algorithms. After RFI mitigation, the Nebula pipeline identifies and ranks interesting narrow band candidate ET signals, scoring candidates by the number of times candidate signals have been seen at roughly the same sky position and same frequency, signal strength, proximity to a nearby star or object of interest, along with several other scoring criteria. We show four example candidates groups that demonstrate these RFI mitigation and candidate selection. This preliminary testing on FAST data helps to validate our SETI instrumentation techniques as well as our data processing pipeline.

astro-ph.IM↗
arXiv2019

Tier structure of strongly endotactic reaction networks

Reaction networks are mainly used to model the time-evolution of molecules of interacting chemical species. Stochastic models are typically used when the counts of the molecules are low, whereas deterministic models are used when the counts are in high abundance. In 2011, the notion of `tiers' was introduced to study the long time behavior of deterministically modeled reaction networks that are weakly reversible and have a single linkage class. This `tier' based argument was analytical in nature. Later, in 2014, the notion of a strongly endotactic network was introduced in order to generalize the previous results from weakly reversible networks with a single linkage class to this wider family of networks. The point of view of this later work was more geometric and algebraic in nature. The notion of strongly endotactic networks was later used in 2018 to prove a large deviation principle for a class of stochastically modeled reaction networks. We provide an analytical characterization of strongly endotactic networks in terms of tier structures. By doing so, we shed light on the connection between the two points of view, and also make available a new proof technique for the study of strongly endotactic networks. We show the power of this new technique in two distinct ways. First, we demonstrate how the main previous results related to strongly endotactic networks, both for the deterministic and stochastic modeling choices, can be quickly obtained from our characterization. Second, we demonstrate how new results can be obtained by proving that a sub-class of strongly endotactic networks, when modeled stochastically, is positive recurrent. Finally, and similarly to recent independent work by Agazzi and Mattingly, we provide an example which closes a conjecture in the negative by showing that stochastically modeled strongly endotactic networks can be transient (and even explosive).

math.PR↗