Fractional variational calculus for nondifferentiable functions

We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free boundary conditions is considered, as well as problems with isoperimetric and holonomic constraints.Comment: Submitted 13-Aug-2010; revised 24-Nov-2010; accepted 28-March-2011; for publication in Computers and Mathematics with Application

Isoperimetric problems of the calculus of variations with fractional derivatives

In this paper we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.Comment: Submitted 02-Oct-2009; revised 30-Jun-2010; accepted 10-May-2011; for publication in the journal Acta Mathematica Scienti

Higher-order Hahn's quantum variational calculus

We prove a necessary optimality condition of Euler-Lagrange type for quantum variational problems involving Hahn's derivatives of higher-order. (C) 2011 Elsevier Ltd. All rights reserved

Duality for the left and right fractional derivatives

We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operators is useful to obtain results for the left operators from analogous results on the right operators and vice versa. We illustrate the usefulness of our duality theory by proving a fractional integration by parts formula for the right Caputo derivative and by proving a Tonelli-type theorem that ensures the existence of minimizer for fractional variational problems with right fractional operators. (C) 2014 Elsevier B.V. All rights reserved

Which outcomes are most important to measure in patients with COVID-19 and how and when should these be measured? Development of an international standard set of outcomes measures for clinical use in patients with COVID-19: a report of the International Consortium for Health Outcomes Measurement (ICHOM) COVID-19 Working Group

Objectives: The COVID-19 pandemic has resulted in widespread morbidity and mortality with the consequences expected to be felt for many years. Significant variation exists in the care even of similar patients with COVID-19, including treatment practices within and between institutions. Outcome measures vary among clinical trials on the same therapies. Understanding which therapies are of most value is not possible unless consensus can be reached on which outcomes are most important to measure. Furthermore, consensus on the most important outcomes may enable patients to monitor and track their care, and may help providers to improve the care they offer through quality improvement. To develop a standardised minimum set of outcomes for clinical care, the International Consortium for Health Outcomes Measurement (ICHOM) assembled a working group (WG) of 28 volunteers, including health professionals, patients and patient representatives. Design: A list of outcomes important to patients and professionals was generated from a systematic review of the published literature using the MEDLINE database, from review of outcomes being measured in ongoing clinical trials, from a survey distributed to patients and patient networks, and from previously published ICHOM standard sets in other disease areas. Using an online-modified Delphi process, the WG selected outcomes of greatest importance. Results: The outcomes considered by the WG to be most important were selected and categorised into five domains: (1) functional status and quality of life, (2) mental functioning, (3) social functioning, (4) clinical outcomes and (5) symptoms. The WG identified demographic and clinical variables for use as case-mix risk adjusters. These included baseline demographics, clinical factors and treatment-related factors. Conclusion: Implementation of these consensus recommendations could help institutions to monitor, compare and improve the quality and delivery of care to patients with COVID-19. Their consistent definition and collection could also broaden the implementation of more patient-centric clinical outcomes research

Pileup mitigation at CMS in 13 TeV data

With increasing instantaneous luminosity at the LHC come additional reconstruction challenges. At high luminosity, many collisions occur simultaneously within one proton-proton bunch crossing. The isolation of an interesting collision from the additional "pileup" collisions is needed for effective physics performance. In the CMS Collaboration, several techniques capable of mitigating the impact of these pileup collisions have been developed. Such methods include charged-hadron subtraction, pileup jet identification, isospin-based neutral particle "δβ" correction, and, most recently, pileup per particle identification. This paper surveys the performance of these techniques for jet and missing transverse momentum reconstruction, as well as muon isolation. The analysis makes use of data corresponding to 35.9 fb$^{-1}$ collected with the CMS experiment in 2016 at a center-of-mass energy of 13 TeV. The performance of each algorithm is discussed for up to 70 simultaneous collisions per bunch crossing. Significant improvements are found in the identification of pileup jets, the jet energy, mass, and angular resolution, missing transverse momentum resolution, and muon isolation when using pileup per particle identification

Identification of heavy, energetic, hadronically decaying particles using machine-learning techniques

Machine-learning (ML) techniques are explored to identify and classify hadronic decays of highly Lorentz-boosted W/Z/Higgs bosons and top quarks. Techniques without ML have also been evaluated and are included for comparison. The identification performances of a variety of algorithms are characterized in simulated events and directly compared with data. The algorithms are validated using proton-proton collision data at √s = 13TeV, corresponding to an integrated luminosity of 35.9 fb−1. Systematic uncertainties are assessed by comparing the results obtained using simulation and collision data. The new techniques studied in this paper provide significant performance improvements over non-ML techniques, reducing the background rate by up to an order of magnitude at the same signal efficiency