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]

An efficient algorithm for learning with semi-bandit feedback

We consider the problem of online combinatorial optimization under semi-bandit feedback. The goal of the learner is to sequentially select its actions from a combinatorial decision set so as to minimize its cumulative loss. We propose a learning algorithm for this problem based on combining the Follow-the-Perturbed-Leader (FPL) prediction method with a novel loss estimation procedure called Geometric Resampling (GR). Contrary to previous solutions, the resulting algorithm can be efficiently implemented for any decision set where efficient offline combinatorial optimization is possible at all. Assuming that the elements of the decision set can be described with d-dimensional binary vectors with at most m non-zero entries, we show that the expected regret of our algorithm after T rounds is O(m sqrt(dT log d)). As a side result, we also improve the best known regret bounds for FPL in the full information setting to O(m^(3/2) sqrt(T log d)), gaining a factor of sqrt(d/m) over previous bounds for this algorithm.Comment: submitted to ALT 201

Syndrome de détresse respiratoire aiguë secondaire à une infection à Toxocara cati

Human toxocarosis is a helminthozoonosis due to the migration of toxocara species larvae throughout the human body. Lung manifestations vary and range from asymptomatic infection to severe disease. Dry cough and chest discomfort are the most common respiratory symptoms. Clinical manifestations include a transient form of Loeffler\u27s syndrome or an eosinophilic pneumonia. We report a case of bilateral pneumonia in an 80 year old caucasian man who developed very rapidly an acute respiratory distress syndrome, with a PaO2/FiO2 ratio of 55, requiring mechanical ventilation and adrenergic support. There was an increased eosinophilia in both blood and bronchoalveolar lavage fluid. Positive toxocara serology and the clinical picture confirmed the diagnosis of the "visceral larva migrans" syndrome. Intravenous corticosteroid therapy produced a rapid rise in PaO2/FiO2 before the administration of specific treatment. A few cases of acute pneumonia requiring mechanical ventilation due to toxocara have been published but this is, to our knowledge, is the first reported case of ARDS with multi-organ failure

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

An expression signature of the angiogenic response in gastrointestinal neuroendocrine tumours: correlation with tumour phenotype and survival outcomes.

BACKGROUND: Gastroenteropancreatic neuroendocrine tumours (GEP-NETs) are heterogeneous with respect to biological behaviour and prognosis. As angiogenesis is a renowned pathogenic hallmark as well as a therapeutic target, we aimed to investigate the prognostic and clinico-pathological role of tissue markers of hypoxia and angiogenesis in GEP-NETs. METHODS: Tissue microarray (TMA) blocks were constructed with 86 tumours diagnosed from 1988 to 2010. Tissue microarray sections were immunostained for hypoxia inducible factor 1α (Hif-1α), vascular endothelial growth factor-A (VEGF-A), carbonic anhydrase IX (Ca-IX) and somatostatin receptors (SSTR) 1–5, Ki-67 and CD31. Biomarker expression was correlated with clinico-pathological variables and tested for survival prediction using Kaplan–Meier and Cox regression methods. RESULTS: Eighty-six consecutive cases were included: 51% male, median age 51 (range 16–82), 68% presenting with a pancreatic primary, 95% well differentiated, 51% metastatic. Higher grading (P=0.03), advanced stage (P<0.001), high Hif-1α and low SSTR-2 expression (P=0.03) predicted for shorter overall survival (OS) on univariate analyses. Stage, SSTR-2 and Hif-1α expression were confirmed as multivariate predictors of OS. Median OS for patients with SSTR-2+/Hif-1α-tumours was not reached after median follow up of 8.8 years, whereas SSTR-2-/Hif-1α+ GEP-NETs had a median survival of only 4.2 years (P=0.006). CONCLUSION: We have identified a coherent expression signature by immunohistochemistry that can be used for patient stratification and to optimise treatment decisions in GEP-NETs independently from stage and grading. Tumours with preserved SSTR-2 and low Hif-1α expression have an indolent phenotype and may be offered less aggressive management and less stringent follow up

Sequential decision making with vector outcomes

We study a multi-round optimization setting in which in each round a player may select one of several actions, and each action produces an outcome vector, not observable to the player until the round ends. The final payoff for the player is computed by applying some known function f to the sum of all outcome vectors (e.g., the minimum of all coordinates of the sum). We show that standard notions of performance measure (such as comparison to the best single action) used in related expert and bandit settings (in which the payoff in each round is scalar) are not useful in our vector setting. Instead, we propose a different performance measure, and design algorithms that have vanishing regret with respect to our new measure