The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

Artificial pancreas using a personalized rule-based controller achieves overnight normoglycemia in patients with type 1 diabetes

Objective: This study assessed the efficacy of a closed-loop (CL) system consisting of a predictive rule-based algorithm (pRBA) on achieving nocturnal and postprandial normoglycemia in patients with type 1 diabetes mellitus (T1DM). The algorithm is personalized for each patient’s data using two different strategies to control nocturnal and postprandial periods. Research Design and Methods: We performed a randomized crossover clinical study in which 10 T1DM patients treated with continuous subcutaneous insulin infusion (CSII) spent two nonconsecutive nights in the research facility: one with their usual CSII pattern (open-loop [OL]) and one controlled by the pRBA (CL). The CL period lasted from 10 p.m. to 10 a.m., including overnight control, and control of breakfast. Venous samples for blood glucose (BG) measurement were collected every 20 min. Results: Time spent in normoglycemia (BG, 3.9–8.0 mmol/L) during the nocturnal period (12 a.m.–8 a.m.), expressed as median (interquartile range), increased from 66.6% (8.3–75%) with OL to 95.8% (73–100%) using the CL algorithm (P<0.05). Median time in hypoglycemia (BG, <3.9 mmol/L) was reduced from 4.2% (0–21%) in the OL night to 0.0% (0.0–0.0%) in the CL night (P<0.05). Nine hypoglycemic events (<3.9 mmol/L) were recorded with OL compared with one using CL. The postprandial glycemic excursion was not lower when the CL system was used in comparison with conventional preprandial bolus: time in target (3.9–10.0 mmol/L) 58.3% (29.1–87.5%) versus 50.0% (50–100%). Conclusions: A highly precise personalized pRBA obtains nocturnal normoglycemia, without significant hypoglycemia, in T1DM patients. There appears to be no clear benefit of CL over prandial bolus on the postprandial glycemia

Personalized rule-based closed-loop control algorithm for type 1 diabetes

Type 1 diabetes-mellitus implies a life-threatening absolute insulin deficiency. Artificial pancreas (CGM sensor, insulin pump and control algorithm) is promising to outperform current open-loop therapies.

Translocation and Functional Analysis of Pseudomonas savastanoi pv. savastanoi NCPPB 3335 Type III Secretion System Effectors Reveals Two Novel Effector Families of the Pseudomonas syringae Complex

Pseudomonas savastanoi pv. savastanoi NCPPB 3335 causes olive knot disease and is a model pathogen for exploring bacterial infection of woody hosts. The type III secretion system (T3SS) effector repertoire of this strain includes 31 effector candidates plus two novel candidates identified in this study which have not been reported to translocate into plant cells. In this work, we demonstrate the delivery of seven NCPPB 3335 effectors into Nicotiana tabacum leaves, including three proteins from two novel families of the P. syringae complex effector super-repertoire (HopBK and HopBL), one of which comprises two proteins (HopBL1 and HopBL2) that harbor a SUMO protease domain. When delivered by P. fluorescens heterologously expressing a P. syringae T3SS, all seven effectors were found to suppress the production of defense-associated reactive oxygen species. Moreover, six of these effectors, including the truncated versions of HopAA1 and HopAZ1 encoded by NCPPB 3335, suppressed callose deposition. The expression of HopAZ1 and HopBL1 by functionally effectorless P. syringae pv. tomato DC3000D28E inhibited the hypersensitive response in tobacco and, additionally, expression of HopBL2 by this strain significantly increased its competitiveness in N. benthamiana. DNA sequences encoding HopBL1 and HopBL2 were uniquely detected in a collection of 31 P. savastanoi pv. savastanoi strains and other P. syringae strains isolated from woody hosts, suggesting a relevant role of these two effectors in bacterial interactions with olive and other woody plants.