Prognostic significance of 25‐hydroxivitamin D entirely explained by a higher comorbidity burden: Experience from a South‐Eastern European Dialysis Cohort

Vitamin D deficiency is still a common problem particularly in the elderly and in individuals with various degrees of renal impairment. The present study aimed to evaluate the association between plasma concentrations of 25(OH)D and death in a large cohort of prevalent patients on hemodialysis (HD) from south‐east Romania, a typical Balkan region. This is an observational prospective study that included a total of 570 patients on maintenance HD. Study patients were classified into three groups by baseline 25(OH)D levels: (1) sufficient 25(OH)D—i.e., >30 ng/mL; (2) insufficient 25(OH)D—i.e., between 10 and 29 ng/mL; and (3) deficient 25(OH)D—i.e., <10 ng/mL. During the follow‐up period of 14 months, 68 patients (11.9%) died, the Kaplan–Meier analysis showing significant differences in all‐cause mortality for chronic kidney disease patients in different 25(OH)D groups (P = 0.002). Unadjusted Cox regression analysis also showed significant differences in survival. The multivariate Cox regression model showed no significant differences in survival according to vitamin D levels. Hazard ratio for death in the “<10 ng/mL” group was 1.619 (P = 0.190) and in the “10–30 ng/mL” group was 0.837 (P = 0.609). In our dialysis population with a high comorbidity burden, low 25(OH)D concentration was not associated with mortality in the adjusted Cox model, suggesting that vitamin D deficiency could represent only a non‐specific marker for a poor health status, with less impact on mortality.     

Joint beamforming and power control in downlink multiuser multiple‐input multiple‐output systems

In this paper, we study joint beamforming and power control for downlink multiple‐input multiple‐output systems with multiple users and target values for signal‐to‐interference plus noise ratios (SINRs). We formulate this as a constrained optimization problem of minimizing total interference subject to constraints on the beamforming vector norms, target SINRs, and total transmit power. Necessary and sufficient conditions satisfied by the optimal beamformer and power allocation are presented, and a new algorithm for joint beamforming and power control is proposed. This adapts the beamforming vectors and transmit powers incrementally, and it stops when the specified SINR targets are achieved with minimum powers. The proposed algorithm is illustrated with numerical results obtained from simulations, which study its convergence and compare it with other similar algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

On Closure Under Stuttering

For over a decade, researchers in formal methods have tried to create formalisms that permit natural specification of systems and allow mathematical reasoning about their correctness. The availability of fully automated reasoning tools enables non-experts to use formal methods effectively—their responsibility reduces to specifying the model and expressing the desired properties. Thus, it is essential that these properties be represented in a language that is easy to use, sufficiently expressive and succinct. Linear-time temporal logic (LTL) is a formalism that has been used extensively by researchers for program specification and verification. One of the desired properties of LTL formulas is closure under stuttering. That is, we do not want the interpretation of formulas to change over traces where some states are repeated. This property is important from both practical and theoretical prospectives; all properties which are closed under stuttering can be expressed in LTL_–X—a fragment of LTL without the next operator. However, it is often difficult to express properties in this fragment of LTL. Further, determining whether a given LTL property is closed under stuttering is PSPACE-complete. In this paper, we introduce a notion of edges of LTL formulas and present a formal theory of closure under stuttering. Edges allow natural modelling of systems with events. Our theory enables syntactic reasoning about whether the resulting properties are closed under stuttering. Finally, we apply the theory to the pattern-based approach of specifying temporal formulas.     

The remainder in the approximation by a generalized Bernstein operator: a representation by a convex combination of second-order divided differences

We investigate the remainder of the approximation formula of a function f∈C[0,1] by means of a generalized Bernstein operator (1.3), depending on two nonnegative integer parameters, introduced by the author in 1984 in the paper [11]. The remainder is expressed in (2.1)–(2.2) by a formula generalizing the author's earlier representation (1.2) of the remainder in Bernstein's classical approximation formula. In (2.13)–(2.14) an expression is given for the remainder involving a linear functional (2.14) which is a convex combination of second-order divided differences. Received: March 1996 / Accepted: April 1996