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We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly(More)
We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. The presented method requires O(M<sup>2</sup> N&#x221A;log N/&#x03B5;) to provide an(More)
The use of cw-Doppler sonography and digital subtraction angiography (DSA) for diagnosis of cerebro-vascular insufficiency (CVI) was evaluated in a retrospective study. 113 findings obtained by DSA and 315 findings obtained by cw-Doppler sonography were compared to the corresponding intraoperative finding. Furthermore, we examined the incidence of(More)
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the(More)
We propose an iterative method for efficiently approximating the capacity of discrete memoryless channels, possibly having additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To find an &#x03B5;-approximation of the capacity, in case of no additional input(More)
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal process given the full set of observations. This, in particular, leads to systematic approximations of the smoothing(More)
We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite-dimensional output under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To provide an additive &#x03B5;-close estimate(More)
Medullary thyroid carcinoma (MTC) is a rare thyroid malignancy. About 75% are sporadic (sMTC) while the remaining 25% are hereditary (hMTC). The treatment of choice for both sMTC and hMTC is surgery. An adequate initial operation provides the best chance of cure. Hence, the diagnosis of MTC should be made preoperatively. In sMTC, ultrasound,(More)