Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates

In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $\Omega(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\varepsilon})$. The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices. This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [SS11] via the application of matrix multiplicative weight updates (MWU) [CHS11, Vis14]. In this paper, we explain how matrix MWU naturally arises as an instance of the Follow-the-Regularized-Leader framework and generalize this approach to yield a larger class of updates. This new class allows us to accelerate the construction of linear-sized spectral sparsifiers, and give novel insights on the motivation behind Batson, Spielman and Srivastava [BSS14]

Functional Sequential Treatment Allocation

Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present paper we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies

PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control the risk of the latter. These results allow to bound the risk of very general estimation procedures, as well as to perform model selection

Master Equation Study of Hydrogen Relaxation Using Complete Sets of State-to-state Transition Rates

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97096/1/AIAA2012-362.pd

Multi-phase characterization of AGN winds in 5 local type-2 quasars

We present MEGARA (Multi-Espectr\'ografo en GTC de Alta Resoluci\'on para Astronom\'ia) Integral Field Unit (IFU) observations of 5 local type-2 quasars (QSO2s, z $\sim 0.1$) from the Quasar Feedback (QSOFEED) sample. These active galactic nuclei (AGN) have bolometric luminosities of 10$^{45.5-46}$ erg/s and stellar masses of $\sim$10$^{11}$ M$_{\odot}$. We explore the kinematics of the ionized gas through the [O~III]$\lambda$5007 $\r{A}$ emission line. The nuclear spectra of the 5 QSO2s, extracted in a circular aperture of $\sim$ 1.2" ($\sim$ 2.2 kpc) in diameter, show signatures of high velocity winds in the form of broad (full width at half maximum; 1300$\leq$FWHM$\leq$2240 km/s and blueshifted components. We find that 4 out of the 5 QSO2s present outflows that we can resolve with our seeing-limited data, and they have radii ranging from 3.1 to 12.6 kpc. In the case of the two QSO2s with extended radio emission, we find that it is well-aligned with the outflows, suggesting that low-power jets might be compressing and accelerating the ionized gas in these radio-quiet QSO2s. In the four QSO2s with spatially resolved outflows, we measure ionized mass outflow rates of 3.3-6.5 Msun/yr when we use [S~II]-based densities, and of 0.7-1.6 Msun/yr when trans-auroral line-based densities are considered instead. We compare them with the corresponding molecular mass outflow rates (8 - 16 Msun/yr), derived from CO(2-1) ALMA observations at 0.2" resolution. Both phases show lower outflow mass rates than those expected from observational scaling relations where uniform assumptions on the outflow properties were adopted. This might be indicating that the AGN luminosity is not the only driver of massive outflows and/or that these relations need to be re-scaled using accurate outflow properties. We do not find a significant impact of the outflows on the global star formation rates.Comment: 24 pages, 13 figures and 4 tables. Accepted for publication in A&A; A&A 665, A55 (2023); doi: 10.1051/0004-6361/20234771

Multiphase characterization of AGN winds in five local type-2 quasars

SWe present MEGARA integral field unit (IFU) observations of five local type-2 quasars (QSO2s, z 0:1) from the Quasar Feedback (QSOFEED) sample. These active galactic nuclei (AGN) have bolometric luminosities of 045:546 erg s1 and stellar masses of 1011 M. The LR-V grating of MEGARA allows us to explore the kinematics of the ionized gas through the [O III]5007Å emission line. The nuclear spectra of the five QSO2s, extracted in a circular aperture of 1:200 (2.2 kpc) in diameter, matching the resolution of these seeing-limited observations, show signatures of high velocity winds in the form of broad (full width at half maximum, 1300 FWHM 2240 km s1) and blueshifted components. We found that four out of the five QSO2s present outflows that we can resolve with our seeing-limited data, and they have radii ranging from 3.1 to 12.6 kpc. In the case of the two QSO2s with extended radio emission, we found that it is well aligned with the outflows, suggesting that low-power jets might be compressing and accelerating the ionized gas in these radio-quiet QSO2s. In the four QSO2s with spatially resolved outflows, we measured ionized mass outflow rates of 3.3–6.5 M yr1 when we used [S II]-based densities, and of 0.7–1.6 M yr1 when trans-auroral line-based densities were considered instead. We compared them with the corresponding molecular mass outflow rates (8–16 M yr1), derived from CO(2–1) ALMA observations at 0.200 resolution. The cold molecular outflows carry more mass than their ionized counterparts. However, both phases show lower outflow mass rates than those expected from observational scaling relations where uniform assumptions on the outflow properties were adopted. This might be indicating that the AGN luminosity is not the only driver of massive outflows and/or that these relations need to be rescaled using accurate outflow properties (i.e., electron density and radius).We did not find a significant impact of the outflows on the global star formation rates when considering the energy budget of the molecular and ionized outflows together. However, spatially resolved measurements of recent star formation in these targets are needed in order to evaluate this fairly, considering the dynamical timescales of the outflows, of 3–20 Myr for the ionized gas and 1–10 Myr for the molecular gas

ALMA captures feeding and feedback from the active galactic nucleus in NGC 613

We report ALMA observations of CO(3-2) emission in the Seyfert/nuclear starburst galaxy NGC 613, at a spatial resolution of 17 pc, as part of our NUclei of GAlaxies (NUGA) sample. Our aim is to investigate the morphology and dynamics of the gas inside the central kiloparsec, and to probe nuclear fueling and feedback phenomena. The morphology of CO(3-2) line emission reveals a two-arm trailing nuclear spiral at r≤ 100 pc and a circumnuclear ring at a radius of ∼350 pc that is coincident with the star-forming ring seen in the optical images. Also, we find evidence for a filamentary structure connecting the ring and the nuclear spiral. The ring reveals two breaks into two winding spiral arms corresponding to the dust lanes in the optical images. The molecular gas in the galaxy disk is in a remarkably regular rotation, however the kinematics in the nuclear region are very skewed. The nuclear spectrum of CO and dense gas tracers HCN(4-3), HCO+(4-3), and CS(7-6) show broad wings up to \ub1300 km s-1, associated with a molecular outflow emanating from the nucleus (r ∼ 25 pc). We derive a molecular outflow mass Mout=2 7 106 M⊙ and a mass outflow rate of M out = 27 M⊙ yr-1. The molecular outflow energetics exceed the values predicted by AGN feedback models: the kinetic power of the outflow corresponds to PK, out=20%LAGN and the momentum rate is M outv ∼400LAGN/c. The outflow is mainly boosted by the AGN through entrainment by the radio jet, but given the weak nuclear activity of NGC 613, we might be witnessing a fossil outflow resulting from a previously strong AGN that has now faded. Furthermore, the nuclear trailing spiral observed in CO emission is inside the inner Lindblad resonance ring of the bar. We compute the gravitational torques exerted in the gas to estimate the efficiency of the angular momentum exchange. The gravity torques are negative from 25 to 100 pc and the gas loses its angular momentum in a rotation period, providing evidence for a highly efficient inflow towards the center. This phenomenon shows that the massive central black hole has significant dynamical influence on the gas, triggering the inflowing of molecular gas to feed the black hole

Notch and Prospero Repress Proliferation following Cyclin E Overexpression in the Drosophila Bristle Lineage

Understanding the mechanisms that coordinate cell proliferation, cell cycle arrest, and cell differentiation is essential to address the problem of how “normal” versus pathological developmental processes take place. In the bristle lineage of the adult fly, we have tested the capacity of post-mitotic cells to re-enter the cell cycle in response to the overexpression of cyclin E. We show that only terminal cells in which the identity is independent of Notch pathway undergo extra divisions after CycE overexpression. Our analysis shows that the responsiveness of cells to forced proliferation depends on both Prospero, a fate determinant, and on the level of Notch pathway activity. Our results demonstrate that the terminal quiescent state and differentiation are regulated by two parallel mechanisms acting simultaneously on fate acquisition and cell cycle progression