Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated.\ud In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called “Q-resolution”, is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs –based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability– corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation

The implementation of effective reasoning tools for deciding the satisfiability of Quantified\ud Boolean Formulas (QBFs) is an important research issue in Artificial Intelligence. Many decision\ud procedures have been proposed in the last few years, most of them based on the Davis, Logemann,\ud Loveland procedure (DLL) for propositional satisfiability (SAT). In this paper we show how it is\ud possible to extend the conflict-directed backjumping schema for SAT to the satisfiability of QBFs:\ud When applicable, conflict-directed backjumping allows search to skip over existentially quantified\ud literals while backtracking. We introduce solution-directed backjumping, which allows the same\ud behavior for universally quantified literals. We show how it is possible to incorporate both conflict-\ud directed and solution-directed backjumping in a DLL-based decision procedure for satisfiability of\ud QBFs. We also implement and test the procedure: The experimental analysis shows that, because of\ud backjumping, significant speed-ups can be obtained.\ud Summing up: We present the first algorithm that applies conflict and solution directed backjumping\ud to QBF, and demonstrate the performance of this algorithm via an empirical study

BackgroundIn the evaluation of Stereo-Electroencephalography (SEEG) signals, the physicist’s workflow involves several operations, including determining the position of individual electrode contacts in terms of both relationship to grey or white matter and location in specific brain regions. These operations are (i) generally carried out manually by experts with limited computer support, (ii) hugely time consuming, and (iii) often inaccurate, incomplete, and prone to errors.ResultsIn this paper we present SEEG Assistant, a set of tools integrated in a single 3DSlicer extension, which aims to assist neurosurgeons in the analysis of post-implant structural data and hence aid the neurophysiologist in the interpretation of SEEG data. SEEG Assistant consists of (i) a module to localize the electrode contact positions using imaging data from a thresholded post-implant CT, (ii) a module to determine the most probable cerebral location of the recorded activity, and (iii) a module to compute the Grey Matter Proximity Index, i.e. the distance of each contact from the cerebral cortex, in order to discriminate between white and grey matter location of contacts. Finally, exploiting 3DSlicer capabilities, SEEG Assistant offers a Graphical User Interface that simplifies the interaction between the user and the tools. SEEG Assistant has been tested on 40 patients segmenting 555 electrodes, and it has been used to identify the neuroanatomical loci and to compute the distance to the nearest cerebral cortex for 9626 contacts. We also performed manual segmentation and compared the results between the proposed tool and gold-standard clinical practice. As a result, the use of SEEG Assistant decreases the post implant processing time by more than 2 orders of magnitude, improves the quality of results and decreases, if not eliminates, errors in post implant processing.ConclusionsThe SEEG Assistant Framework for the first time supports physicists by providing a set of open-source tools for post-implant processing of SEEG data. Furthermore, SEEG Assistant has been integrated into 3D Slicer, a software platform for the analysis and visualization of medical images, overcoming limitations of command-line tools.

BackgroundInvasive monitoring of brain activity by means of intracerebral electrodes is widely practiced to improve pre-surgical seizure onset zone localization in patients with medically refractory seizures. Stereo-Electroencephalography (SEEG) is mainly used to localize the epileptogenic zone and a precise knowledge of the location of the electrodes is expected to facilitate the recordings interpretation and the planning of resective surgery. However, the localization of intracerebral electrodes on post-implant acquisitions is usually time-consuming (i.e., manual segmentation), it requires advanced 3D visualization tools, and it needs the supervision of trained medical doctors in order to minimize the errors. In this paper we propose an automated segmentation algorithm specifically designed to segment SEEG contacts from a thresholded post-implant Cone-Beam CT volume (0.4 mm, 0.4 mm, 0.8 mm). The algorithm relies on the planned position of target and entry points for each electrode as a first estimation of electrode axis. We implemented the proposed algorithm into DEETO, an open source C++ prototype based on ITK library.ResultsWe tested our implementation on a cohort of 28 subjects in total. The experimental analysis, carried out over a subset of 12 subjects (35 multilead electrodes; 200 contacts) manually segmented by experts, show that the algorithm: (i) is faster than manual segmentation (i.e., less than 1s/subject versus a few hours) (ii) is reliable, with an error of 0.5 mm ± 0.06 mm, and (iii) it accurately maps SEEG implants to their anatomical regions improving the interpretability of electrophysiological traces for both clinical and research studies. Moreover, using the 28-subject cohort we show here that the algorithm is also robust (error < 0.005 mm) against deep-brain displacements (< 12 mm) of the implanted electrode shaft from those planned before surgery.ConclusionsOur method represents, to the best of our knowledge, the first automatic algorithm for the segmentation of SEEG electrodes. The method can be used to accurately identify the neuroanatomical loci of SEEG electrode contacts by a non-expert in a fast and reliable manner.

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