Learning probability distributions generated by finite-state machines

We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft

Dupilumab efficacy in uncontrolled, moderate-to-severe asthma with self-reported chronic rhinosinusitis

BACKGROUND: Dupilumab, a fully human monoclonal antibody, blocks the shared receptor component for IL-4 and IL-13 signaling, key drivers of type 2 inflammation. In the phase 3 study (NCT02414854), add-on dupilumab 200 mg/300 mg every 2 weeks, versus placebo, significantly reduced severe asthma exacerbations and improved pre-bronchodilator forced expiratory volume in 1 second (FEV OBJECTIVE: To assess the efficacy and safety of dupilumab in patients with uncontrolled, moderate-to-severe asthma with or without self-reported comorbid chronic rhinosinusitis (CRS or non-CRS). METHODS: Comorbid CRS was self-reported by patients using an e-diary. Annualized severe exacerbation rates, changes from baseline in pre- and post-bronchodilator FEV RESULTS: CRS was self-reported by 382 of 1902 (20.1%) patients. Dupilumab 200 mg/300 mg reduced annualized severe exacerbation rates by 63%/61%, respectively, in patients with CRS, and by 42%/40% in patients without CRS (all P \u3c .001 vs placebo). Dupilumab also improved lung function and patient-reported asthma control and quality of life, and suppressed type 2 biomarkers versus placebo in both subgroups. Clinical responses were rapid, with near-maximal responses observed at the earliest measured time points and sustained at week 52. Improvements observed in the CRS subgroup were similar to or numerically greater than those in the non-CRS subgroup. CONCLUSION: Dupilumab showed efficacy and was generally well tolerated in patients with uncontrolled, moderate-to-severe asthma with or without CRS

Calder\'on-Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.Comment: 21 page

UMD Banach spaces and the maximal regularity for the square root of several operators

In this paper we prove that the maximal $L^p$-regularity property on the interval $(0,T)$, $T>0$, for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre type operators on $L^2(\Omega, d\mu; X),$ characterizes the UMD property for the Banach space $X$.Comment: 23 pages. To appear in Semigroup Foru