BACKGROUND Catheter navigation and 3-dimensional (3D) cardiac mapping are essential components of minimally invasive electrophysiological procedures. OBJECTIVE The purpose of this study was to develop a novel 3D mapping system (KODEX-EPD, EPD Solutions, Best, The Netherlands) that measures changing electric field gradients induced on intracardiac electrodes to enable catheter localization and real-time 3D cardiac mapping. METHODS We first validated the accuracy of the system's measurement and localization capabilities by comparing known and KODEX-EPD-measured distances and locations at 12 anatomical landmarks in both the atria and ventricles of 4 swine. Next, in vivo images of 3D porcine cardiac anatomy generated by KODEX-EPD and widely used CARTO 3 system (Biosense Webster, Inc., Diamond Bar, CA) were compared with gold standard computed tomography images acquired from the same animals. Finally, 3D maps of atrial anatomy were created for 22 patients with paroxysmal atrial fibrillation (Dielectric Unravelling of Radiofrequency ABLation Effectiveness trial). RESULTS First, the mean error between known and measured distances was 1.08 6 0.11 mm (P , .01) and the overall standard deviation between known and measured locations in 12 areas of the porcine heart was 0.35 mm (P , .01). Second, an expert comparison of 3D image quality revealed that KODEX-EPD is noninferior to CARTO 3. Third, the system enabled 3D imaging of atrial anatomy in humans, provided real-time images of atrioventricular valves, and detected important anatomical variations in a subset of patients. CONCLUSION The KODEX-EPD system is a novel 3D mapping system that accurately detects catheter location and can generate high-resolution images without the need for preacquired imaging, specialty catheters, or a point-by-point mapping procedure.

We consider learning problems in which the learner is supplied with partial information derived from randomly drawn examples. We generalize the known learning models by incorpo-tribution, and the efficient learnability, under a product distribution, of claases of subsets of Rfi which are defined by mild surfaces.

No abstract

In this paper, we prove various results about PAC learning in the presence of malicious noise. Our main interest is the sample size behavior of learning algorithms. We prove the first nontrivial sample complexity lower bound in this model by showing that order of ⑀/⌬ 2 ϩ d/⌬ (up to logarithmic factors) examples are necessary for PAC learning any target class of {0, 1}-valued functions of VC dimension d, where ⑀ is the desired accuracy and ϭ ⑀/(1 ϩ ⑀) Ϫ ⌬ the malicious noise rate (it is well known that any nontrivial target class cannot be PAC learned with accuracy ⑀ and malicious noise rate Ն ⑀/(1 ϩ ⑀), this irrespective to sample complexity). We also show that this result cannot be significantly improved in general by presenting efficient learning algorithms for the class of all subsets of d elements and the class of unions of at most d intervals on the real line. This is especially interesting as we can also show that the popular minimum disagreement strategy needs samples of size d⑀/⌬ 2 , hence is not optimal with respect to sample size. We then discuss the use of randomized hypotheses. For these the bound ⑀/(1 ϩ ⑀) on the noise rate is no longer true and is replaced by 2⑀/(1 ϩ 2⑀). In fact, we present a generic algorithm using randomized hypotheses that can tolerate noise rates slightly larger than ⑀/(1 ϩ ⑀) while using samples of size d/⑀ as in the noise-free case. Again one observes a quadratic powerlaw (in this case d⑀/⌬ 2 , ⌬ ϭ 2⑀/(1 ϩ 2⑀) Ϫ ) as ⌬ goes to zero. We show upper and lower bounds of this order.

We consider learning tasks in which the learner faces restrictions on the amount of information he can extract from each example he encounters. We introduce a formal framework for the analysis of such scenarios. We call this framework RFA (restricted focus of attention) learning. Although it is a natural refinement of the PAC learning model, some of the fundamental PAC-learning results and techniques fail in the RFA paradigm; learnability in the RFA model is no longer characterized by the VC dimension, and many PAC learning algorithms are not applicable in the RFA setting. Hence, the RFA formulation reflects the need for new techniques and tools to cope with some fundamental constraints of realistic learning problems. In this work we also present some paradigms and algorithms that may serve as a first step toward answering this need.Two main types of restrictions are considered here: In the more stringent one, called k-RFA, only k of the n attributes of each example are revealed to the learner, while in the more permissive one, called k-wRFA, the restriction is made on the size of each observation (k bits), and no restriction is made on how the observations are extracted from the examples.For the k-RFA restriction we develop a general technique for composing efficient k-RFA algorithms and apply it to deduce, for instance, the efficient k-RFA learnability of k-DNF formulas and the efficient 1-RFA learnability of axis-aligned rectangles in the Euclidean space R n . We also prove the k-RFA learnability of richer classes of Boolean functions (such as k-decision lists) with respect to a given distribution and the efficient (n&1)-RFA learnability (for fixed n), under product distributions, of classes of subsets of R n which are defined by mild surfaces.For the k-wRFA restriction, we show that for k=O(log n), efficient k-wRFA learning is robust against classification noise. As a straightforward application, we obtain a new simple noise-tolerant algorithm for the class of k-decision lists by constructing an intuitive k-wRFA algorithm for this task.1998 Academic Press