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Elliptic Theory for Sets with Higher Co-dimensional Boundaries
Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher
co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields
a notion analogous to that of the harmonic measure, for sets of codimension higher than 1.
To this end, we turn to degenerate
elliptic equations. Let
In another article to appear, we will prove that when
eBook
Price-based investment strategies : how research discoveries reinvented technical analysis
This compelling book examines the price-based revolution in investing, showing how research over recent decades has reinvented technical analysis. The authors discuss the major groups of price-based strategies, considering their theoretical motivation, individual and combined implementation, and back-tested results when applied to investment across country stock markets. Containing a comprehensive sample of performance data, taken from 24 major developed markets around the world and ranging over the last 25 years, the authors construct practical portfolios and display their performance - ensuring the book is not only academically rigorous, but practically applicable too.
Book
Multi-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals
The main purpose of this paper is to establish the theory of the multi-parameter Hardy spaces
More precisely, Street (2014) studied the
eBook
Singular integrals in quantum Euclidean spaces
We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of
noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential calculus for
rotation algebras, thanks to a new form of Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution
kernels. We deduce
eBook
Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting
In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag
setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood–Paley square function
and area integral, Riesz transforms and the atomic decomposition in the multi-parameter flag setting. The novel ingredients in this
paper include (1) establishing appropriate discrete Calderón reproducing formulae in the flag setting and a version of the
Plancherel–Pólya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels
and flag version of harmonic functions; (3) developing an atomic decomposition via the finite speed propagation and area function in
terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the
multi-parameter Hardy space with the flag structure.
eBook
Cytokine clearance with CytoSorb® during cardiac surgery: a pilot randomized controlled trial
Background
Cardiopulmonary bypass (CPB) is often associated with degrees of complex inflammatory response mediated by various cytokines. This response can, in severe cases, lead to systemic hypotension and organ dysfunction. Cytokine removal might therefore improve outcomes of patients undergoing cardiac surgery. CytoSorb® (Cytosorbents, NJ, USA) is a recent device designed to remove cytokine from the blood using haemoadsorption (HA). This trial aims to evaluate the potential of CytoSorb® to decrease peri-operative cytokine levels in cardiac surgery.
Methods
We have conducted a single-centre pilot randomized controlled trial in 30 patients undergoing elective cardiac surgery and deemed at risk of complications. Patients were randomly allocated to either standard of care (
n
= 15) or CytoSorb® HA (
n
= 15) during cardiopulmonary bypass (CPB). Our primary outcome was the difference between the two groups in cytokines levels (IL-1a, IL-1b, IL-2, IL-4, IL-5, IL-6, IL-10, TNF-α, IFN-γ, MCP-1) measured at anaesthesia induction, at the end of CPB, as well as 6 and 24 h post-CPB initiation. In a consecutive subgroup of patients (10 in HA group, 11 in control group), we performed cross-adsorber as well as serial measurements of coagulation factors’ activity (antithrombin, von Willebrand factor, factor II, V, VIII, IX, XI, and XII).
Results
Both groups were similar in terms of baseline and peri-operative characteristics. CytoSorb® HA during CPB was not associated with an increased incidence of adverse event. The procedure did not result in significant coagulation factors’ adsorption but only some signs of coagulation activation. However, the intervention was associated neither with a decrease in pro- or anti-inflammatory cytokine levels nor with any improvement in relevant clinical outcomes.
Conclusions
CytoSorb® HA during CPB was not associated with a decrease in pro- or anti-inflammatory cytokines nor with an improvement in relevant clinical outcomes. The procedure was feasible and safe. Further studies should evaluate the efficacy of CytoSorb® HA in other clinical contexts.
Trial registration
ClinicalTrials.gov
NCT02775123
. Registered 17 May 2016.
Journal Article