A Primal-Dual Analysis of Monotone Submodular Maximization

In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This problem and its special case, the maximum $k$-coverage problem, have a wide range of applications in various fields including operations research, machine learning, and economics. While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of any instance. This certificate may be used in practice to certify much stronger guarantees than the worst-case $(1-1/e)$ approximation factor

The infrared imaging spectrograph (IRIS) for TMT: the science case

The InfraRed Imaging Spectrograph (IRIS) is a first-light instrument being designed for the Thirty Meter Telescope (TMT). IRIS is a combination of an imager that will cover a 16.4" field of view at the diffraction limit of TMT (4 mas sampling), and an integral field unit spectrograph that will sample objects at 4-50 mas scales. IRIS will open up new areas of observational parameter space, allowing major progress in diverse fields of astronomy. We present the science case and resulting requirements for the performance of IRIS. Ultimately, the spectrograph will enable very well-resolved and sensitive studies of the kinematics and internal chemical abundances of high-redshift galaxies, shedding light on many scenarios for the evolution of galaxies at early times. With unprecedented imaging and spectroscopy of exoplanets, IRIS will allow detailed exploration of a range of planetary systems that are inaccessible with current technology. By revealing details about resolved stellar populations in nearby galaxies, it will directly probe the formation of systems like our own Milky Way. Because it will be possible to directly characterize the stellar initial mass function in many environments and in galaxies outside of the the Milky Way, IRIS will enable a greater understanding of whether stars form differently in diverse conditions. IRIS will reveal detailed kinematics in the centers of low-mass galaxies, allowing a test of black hole formation scenarios. Finally, it will revolutionize the characterization of reionization and the first galaxies to form in the universe.Comment: to appear in Proc. SPIE 773

The InfraRed Imaging Spectrograph (IRIS) for TMT: latest science cases and simulations

The Thirty Meter Telescope (TMT) first light instrument IRIS (Infrared Imaging Spectrograph) will complete its preliminary design phase in 2016. The IRIS instrument design includes a near-infrared (0.85 - 2.4 micron) integral field spectrograph (IFS) and imager that are able to conduct simultaneous diffraction-limited observations behind the advanced adaptive optics system NFIRAOS. The IRIS science cases have continued to be developed and new science studies have been investigated to aid in technical performance and design requirements. In this development phase, the IRIS science team has paid particular attention to the selection of filters, gratings, sensitivities of the entire system, and science cases that will benefit from the parallel mode of the IFS and imaging camera. We present new science cases for IRIS using the latest end-to-end data simulator on the following topics: Solar System bodies, the Galactic center, active galactic nuclei (AGN), and distant gravitationally-lensed galaxies. We then briefly discuss the necessity of an advanced data management system and data reduction pipeline.Comment: 15 pages, 7 figures, SPIE (2016) 9909-0

Dispersal syndromes in challenging environments: A cross‐species experiment

Dispersal is a central biological process tightly integrated into life-histories, morphology, physiology and behaviour. Such associations, or syndromes, are anticipated to impact the eco-evolutionary dynamics of spatially structured populations, and cascade into ecosystem processes. As for dispersal on its own, these syndromes are likely neither fixed nor random, but conditional on the experienced environment. We experimentally studied how dispersal propensity varies with individuals' phenotype and local environmental harshness using 15 species ranging from protists to vertebrates. We reveal a general phenotypic dispersal syndrome across studied species, with dispersers being larger, more active and having a marked locomotion-oriented morphology and a strengthening of the link between dispersal and some phenotypic traits with environmental harshness. Our proof-of-concept metacommunity model further reveals cascading effects of context-dependent syndromes on the local and regional organisation of functional diversity. Our study opens new avenues to advance our understanding of the functioning of spatially structured populations, communities and ecosystems. Keywords: context-dependent dispersal; dispersal strategy; distributed experiment; predation risk; resource limitatio

Catching Element Formation In The Act

Gamma-ray astronomy explores the most energetic photons in nature to address some of the most pressing puzzles in contemporary astrophysics. It encompasses a wide range of objects and phenomena: stars, supernovae, novae, neutron stars, stellar-mass black holes, nucleosynthesis, the interstellar medium, cosmic rays and relativistic-particle acceleration, and the evolution of galaxies. MeV gamma-rays provide a unique probe of nuclear processes in astronomy, directly measuring radioactive decay, nuclear de-excitation, and positron annihilation. The substantial information carried by gamma-ray photons allows us to see deeper into these objects, the bulk of the power is often emitted at gamma-ray energies, and radioactivity provides a natural physical clock that adds unique information. New science will be driven by time-domain population studies at gamma-ray energies. This science is enabled by next-generation gamma-ray instruments with one to two orders of magnitude better sensitivity, larger sky coverage, and faster cadence than all previous gamma-ray instruments. This transformative capability permits: (a) the accurate identification of the gamma-ray emitting objects and correlations with observations taken at other wavelengths and with other messengers; (b) construction of new gamma-ray maps of the Milky Way and other nearby galaxies where extended regions are distinguished from point sources; and (c) considerable serendipitous science of scarce events -- nearby neutron star mergers, for example. Advances in technology push the performance of new gamma-ray instruments to address a wide set of astrophysical questions.Comment: 14 pages including 3 figure

Catching Element Formation In The Act

Gamma-ray astronomy explores the most energetic photons in nature to address some of the most pressing puzzles in contemporary astrophysics. It encompasses a wide range of objects and phenomena: stars, supernovae, novae, neutron stars, stellar-mass black holes, nucleosynthesis, the interstellar medium, cosmic rays and relativistic-particle acceleration, and the evolution of galaxies. MeV gamma-rays provide a unique probe of nuclear processes in astronomy, directly measuring radioactive decay, nuclear de-excitation, and positron annihilation. The substantial information carried by gamma-ray photons allows us to see deeper into these objects, the bulk of the power is often emitted at gamma-ray energies, and radioactivity provides a natural physical clock that adds unique information. New science will be driven by time-domain population studies at gamma-ray energies. This science is enabled by next-generation gamma-ray instruments with one to two orders of magnitude better sensitivity, larger sky coverage, and faster cadence than all previous gamma-ray instruments. This transformative capability permits: (a) the accurate identification of the gamma-ray emitting objects and correlations with observations taken at other wavelengths and with other messengers; (b) construction of new gamma-ray maps of the Milky Way and other nearby galaxies where extended regions are distinguished from point sources; and (c) considerable serendipitous science of scarce events -- nearby neutron star mergers, for example. Advances in technology push the performance of new gamma-ray instruments to address a wide set of astrophysical questions

Catching element formation in the act

Gamma-ray astronomy explores the most energetic photons in nature to address some of the most pressing puzzles in contemporary astrophysics. It encompasses a wide range of objects and phenomena: stars, supernovae, novae, neutron stars, stellar-mass black holes, nucleosynthesis, the interstellar medium, cosmic rays and relativistic-particle acceleration, and the evolution of galaxies. MeV gamma-rays provide a unique probe of nuclear processes in astronomy, directly measuring radioactive decay, nuclear de-excitation, and positron annihilation. The substantial information carried by gamma-ray photons allows us to see deeper into these objects, the bulk of the power is often emitted at gamma-ray energies, and radioactivity provides a natural physical clock that adds unique information. New science will be driven by time-domain population studies at gamma-ray energies. This science is enabled by next-generation gamma-ray instruments with one to two orders of magnitude better sensitivity, larger sky coverage, and faster cadence than all previous gamma-ray instruments. This transformative capability permits: (a) the accurate identification of the gamma-ray emitting objects and correlations with observations taken at other wavelengths and with other messengers; (b) construction of new gamma-ray maps of the Milky Way and other nearby galaxies where extended regions are distinguished from point sources; and (c) considerable serendipitous science of scarce events -- nearby neutron star mergers, for example. Advances in technology push the performance of new gamma-ray instruments to address a wide set of astrophysical questions

NOVEL GENERALIZATIONS AND ALGORITHMS FOR THE MAX-k-COVERAGE PROBLEM

In this thesis we consider the fundamental optimization problem known as the Max-k- Coverage problem and its generalizations. We first discuss the well-studied generalization to the problem of maximizing a monotone submodular function subject to a cardinality constraint and introduce a new primal-dual algorithm which achieves the optimal approximation factor of (1 − 1/e). While greedy algorithms have been known to achieve this approximation factor, our algorithms also provide a dual certificate which upper bounds the optimum value of an instance. This certificate may be used in practice to provide much stronger guarantees than the worst-case (1 − 1/e) approximation factor. We then introduce a novel generalization of the Max-k-Coverage problem known as the Monotone Coverage Utility Maximization (mcum) problem. Here, we are given a set of clients C and a set of facilities F in a metric space (F ∪ C, d), a positive integer k, and a radius parameter r. Each client v ∈ C is associated with a non-decreasing utility function fv : N → R≥0, and the objective is to locate centers S ⊆ F with |S| = k so as to maximize ∑v∈C fv(S ∩ Bv(r)), where Bv(r) is the ball of radius r around v. This general problem reduces to the special case Threshold Utility Maximization (thrum), where the fv’s are threshold step functions, that is, fv(a) = wv if a ≥ ℓv for some positive integer ℓv, and 0 otherwise. thrum, in turn, generalizes Max-k-Coverage problem by putting ℓv = 1 for all clients. On the other hand, even when all ℓv’s are 2, the problem is as hard as Densest-k- Subgraph. We circumvent this hardness by addressing the “soft” version of the problem, where the same center can be opened multiple times. In this realm, we give a 1 2 -approximation in the uniform case where all ℓv’s equal ℓ, which readily implies a Θ(1/ log k) approximation for the general problem. We also describe matching integrality gaps for the natural LP relaxations for both problems. Furthermore, we consider the thrum problem from a radius-dilation perspective. Here, we want to obtain a utility of opt, but allow the algorithm’s neighborhood to be dilated to αr for α ≥ 1, with α as small as possible. This problem becomes equivalent to the Fault- tolerant k-Supplier with Outliers (FkSO) problem. Our main result is a 3-approximation for FkSO in the uniform case where all ℓv = ℓ, which improves upon an 11-approximation described by Inamdar and Varadarajan in 2020