Sparse computation for large-scale binary classification

Well-known data mining algorithms rely on inputs in the form of pairwise similarities between objects. For large datasets it is computationally impossible to perform all pairwise comparisons. We therefore propose a novel approach that uses approximate Principal Component Analysis to efficiently identify groups of similar objects. The effectiveness of the approach is demonstrated in the context of binary classification using the supervised normalized cut as a classifier. For large datasets from the UCI repository, the approach significantly improves run times with minimal loss in accuracy.

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

Unfolding Feasible Arithmetic and Weak Truth

In this paper we continue Feferman’s unfolding program initiated in (Feferman, vol. 6 of Lecture Notes in Logic, 1996) which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm (Ann Pure Appl Log, 104(1–3):75–96, 2000) and for a system FA (with and without Bar rule) in Feferman and Strahm (Rev Symb Log, 3(4):665–689, 2010). The present contribution elucidates the concept of unfolding for a basic schematic system FEA of feasible arithmetic. Apart from the operational unfolding U0(FEA) of FEA, we study two full unfolding notions, namely the predicate unfolding U(FEA) and a more general truth unfolding UT(FEA) of FEA, the latter making use of a truth predicate added to the language of the operational unfolding. The main results obtained are that the provably convergent functions on binary words for all three unfolding systems are precisely those being computable in polynomial time. The upper bound computations make essential use of a specific theory of truth TPT over combinatory logic, which has recently been introduced in Eberhard and Strahm (Bull Symb Log, 18(3):474–475, 2012) and Eberhard (A feasible theory of truth over combinatory logic, 2014) and whose involved proof-theoretic analysis is due to Eberhard (A feasible theory of truth over combinatory logic, 2014). The results of this paper were first announced in (Eberhard and Strahm, Bull Symb Log 18(3):474–475, 2012).

First steps towards probabilistic justification logic

In this article, we introduce the probabilistic justification logic PJ, a logic in which we can reason about the probability of justification statements. We present its syntax and semantics, and establish a strong completeness theorem. Moreover, we investigate the relationship between PJ and the logic of uncertain justifications.

Searching the hearts of graphene-like molecules for simplicity, sensitivity and logic

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons (PAHs) could be isolated and manipulated, then a significant step towards realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers.

Reconsidering the logic of World Federation of Neurosurgical Societies grading in patients with severe subarachnoid hemorrhage.

OBJECT Current data show a favorable outcome in up to 50% of patients with World Federation of Neurosurgical Societies (WFNS) Grade V subarachnoid hemorrhage (SAH) and a rather poor prediction of worst cases. Thus, the usefulness of the current WFNS grading system for identifying the worst scenarios for clinical studies and for making treatment decisions is limited. One reason for this lack of differentiation is the use of "negative" or "silent" diagnostic signs as part of the WFNS Grade V definition. The authors therefore reevaluated the WFNS scale by using "positive" clinical signs and the logic of the Glasgow Coma Scale as a progressive herniation score. METHODS The authors performed a retrospective analysis of 182 patients with SAH who had poor grades on the WFNS scale. Patients were graded according to the original WFNS scale and additionally according to a modified classification, the WFNS herniation (hWFNS) scale (Grade IV, no clinical signs of herniation; Grade V, clinical signs of herniation). The prediction of poor outcome was compared between these two grading systems. RESULTS The positive predictive values of Grade V for poor outcome were 74.3% (OR 3.79, 95% CI 1.94-7.54) for WFNS Grade V and 85.7% (OR 8.27, 95% CI 3.78-19.47) for hWFNS Grade V. With respect to mortality, the positive predictive values were 68.3% (OR 3.9, 95% CI 2.01-7.69) for WFNS Grade V and 77.9% (OR 6.22, 95% CI 3.07-13.14) for hWFNS Grade V. CONCLUSIONS Limiting WFNS Grade V to the positive clinical signs of the Glasgow Coma Scale such as flexion, extension, and pupillary abnormalities instead of including "no motor response" increases the prediction of mortality and poor outcome in patients with severe SAH.

Index Tracking Using Data-Mining Techniques and Mixed-Binary Linear Programming

Index tracking has become one of the most common strategies in asset management. The index-tracking problem consists of constructing a portfolio that replicates the future performance of an index by including only a subset of the index constituents in the portfolio. Finding the most representative subset is challenging when the number of stocks in the index is large. We introduce a new three-stage approach that at first identifies promising subsets by employing data-mining techniques, then determines the stock weights in the subsets using mixed-binary linear programming, and finally evaluates the subsets based on cross validation. The best subset is returned as the tracking portfolio. Our approach outperforms state-of-the-art methods in terms of out-of-sample performance and running times.