Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over compact semi-algebraic sets. In this paper, we show that, for convex polynomial optimization, the Lasserre hierarchy with a slightly extended quadratic module always converges asymptotically even in the face of non-compact semi-algebraic feasible sets. We do this by exploiting a coercivity property of convex polynomials that are bounded below. We further establish that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point (rather than the objective function at each minimizer) guarantees finite convergence of the hierarchy. We obtain finite convergence by first establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets under a saddle-point condition. We finally prove that the existence of a saddle-point of the Lagrangian for a convex polynomial program is also necessary for the hierarchy to have finite convergence.Comment: 17 page

New onset diabetes after transplantation (NODAT): an overview

Although renal transplantation ameliorates cardiovascular risk factors by restoring renal function, it introduces new cardiovascular risks including impaired glucose tolerance or diabetes mellitus, hypertension, and dyslipidemia that are derived, in part, from immunosuppressive medications such as calcineurin inhibitors, corticosteroids, or mammalian target of rapamycin inhibitors. New onset diabetes mellitus after transplantation (NODAT) is a serious and common complication following solid organ transplantation. NODAT has been reported to occur in 2% to 53% of all solid organ transplants. Kidney transplant recipients who develop NODAT have variably been reported to be at increased risk of fatal and nonfatal cardiovascular events and other adverse outcomes including infection, reduced patient survival, graft rejection, and accelerated graft loss compared with those who do not develop diabetes. Identification of high-risk patients and implementation of measures to reduce the development of NODAT may improve long-term patient and graft outcome. The following article presents an overview of the literature on the current diagnostic criteria for NODAT, its incidence after solid organ transplantation, suggested risk factors and potential pathogenic mechanisms. The impact of NODAT on patient and allograft outcomes and suggested guidelines for early identification and management of NODAT will also be discussed

Antithrombotic strategies in patients undergoing percutaneous coronary intervention for acute coronary syndrome

In patients undergoing percutaneous coronary intervention (PCI) for acute coronary syndrome (ACS), both periprocedural acute myocardial infarction and bleeding complications have been shown to be associated with early and late mortality. Current standard antithrombotic therapy after coronary stent implantation consists of lifelong aspirin and clopidogrel for a variable period depending in part on the stent type. Despite its well-established efficacy in reducing cardiac-related death, myocardial infarction, and stroke, dual antiplatelet therapy with aspirin and clopidogrel is not without shortcomings. While clopidogrel may be of little beneficial effect if administered immediately prior to PCI and may even increase major bleeding risk if coronary artery bypass grafting is anticipated, early discontinuation of the drug may result in insufficient antiplatelet coverage with thrombotic complications. Optimal and rapid inhibition of platelet activity to suppress ischemic and thrombotic events while minimizing bleeding complications is an important therapeutic goal in the management of patients undergoing percutaneous coronary intervention. In this article we present an overview of the literature on clinical trials evaluating the different aspects of antithrombotic therapy in patients undergoing PCI and discuss the emerging role of these agents in the contemporary era of early invasive coronary intervention. Clinical trial acronyms and their full names are provided in Table 1

Design of Energy-Efficient Artificial Noise for Physical Layer Security in Visible Light Communications

This paper studies the design of energy-efficient artificial noise (AN) schemes in the context of physical layer security in visible light communications (VLC). Two different transmission schemes termed $\textit{selective AN-aided single-input single-output (SISO)}$ and $\textit{AN-aided multiple-input single-output (MISO)}$ are examined and compared in terms of secrecy energy efficiency (SEE). In the former, the closest LED luminaire to the legitimate user (Bob) is the information-bearing signal's transmitter. At the same time, the rest of the luminaries act as jammers transmitting AN to degrade the channels of eavesdroppers (Eves). In the latter, the information-bearing signal and AN are combined and transmitted by all luminaries. When Eves' CSI is unknown, an indirect design to improve the SEE is formulated by maximizing Bob's channel's energy efficiency. A low-complexity design based on the zero-forcing criterion is also proposed. In the case of known Eves' CSI, we study the design that maximizes the minimum SEE among those corresponding to all eavesdroppers. At their respective optimal SEEs, simulation results reveal that when Eves' CSI is unknown, the selective AN-aided SISO transmission can archive twice better SEE as the AN-aided MISO does. In contrast, when Eves' CSI is known, the AN-aided MISO outperforms by 30%