Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Optimization of the Neutron Detector Design Based on the 6LiF/ZnS(Ag) Scintillation Screens for the GAMMA-400 Space Observatory

AbstractThe Neutron Detector (ND) is a new detector sub-system for the future GAMMA-400 space observatory. It aims to complement the instrument's GAMMA-400 electromagnetic calorimeter (CsI(Tl), total depth is 25.0 X0) in identifying cosmic-ray electrons from ∼ 100 MeV up to 3 TeV. Such electrons are of significant scientific interest, but their identification is complicated by the overwhelmingly more abundant hadronic cosmic rays, hence making significant hadronic rejection power of paramount importance. Particle showers initiated by nuclei in the GAMMA-400 calorimeter have a profile different from an electron-induced electromagnetic cascade, and the hadron rejection power deriving from this difference can be significantly enhanced by making use of the thermal neutron activity at late (>100ns) times relative to the start of the shower. Indeed hadron-induced showers tend to be accompanied by significantly more neutron activity than electromagnetic showers. In the described ND for capturing thermalized neutrons applied isotope 6Li, which is part of the scintillation screen 6LiF/ZnS(Ag). ND placed are under the electromagnetic calorimeter. The results GEANT4 simulation of the ND shows that ND has high neutron detection efficiency

Supplementary Material for: International Multi-Specialty Delphi Survey: Identification of Diagnostic Criteria for Hepatic and Renal Cyst Infection

Background: Cyst infection is one of the complications of autosomal dominant polycystic kidney disease and polycystic liver disease. The diagnosis is typically made on a mix of clinical, laboratory and imaging abnormalities but the importance of individual items is uncertain. We aimed to perform a Delphi survey amongst physicians to achieve consensus on diagnostic criteria. Methods: We retrieved diagnostic items from the literature and conducted physician and patient interviews. All items were combined to create the online questionnaire. Participants rated each item during 3 consecutive rounds. Items were rated for diagnostic helpfulness for hepatic and renal cyst infection on a 9-point scale with anchors, from extremely unimportant (n = 1) to extremely important (n = 9). We determined consensus with the disagreement index. The median rating of each item was calculated and categorized into inappropriate (≤3.4), uncertain (3.5-6.4) or appropriate (≥6.5). By combining all items that reached an appropriate consensus rating, we developed a diagnostic algorithm based on expert consensus. Results: We invited 58 physicians to participate in the survey. In total, 35 (60%) responded to round 1 of which 91% (n = 32) and 86% (n = 30) responded to round 2 and 3, respectively. The final panel included 23 nephrologists, 5 hepatologists, a nuclear medicine specialist and an infectious disease physician from 11 countries (male 67%, mean age 47 ± 11 years, median clinical experience 21 years). The panel rated the diagnostic helpfulness of 59 potential items. Ultimately, 22 hepatic and 26 renal items were rated appropriate, including positive blood cultures and fluorodeoxyglucose positron-emission CT imaging. Ultrasonography and absence of intracystic bleeding were amongst those deemed uncertain or inappropriate. Subsequently, by combining items rated appropriate, we developed a clinical tool to diagnose hepatic and renal cyst infection.Conclusions: We identified diagnostic items for hepatic and renal cyst infection and developed an expert-based diagnostic algorithm, which may aid physicians in the diagnostic work-up. A prospective study is necessary to validate this algorithm