The Direct and Enantioselective Organocatalytic α-Oxidation of Aldehydes

The first direct enantioselective catalytic α-oxidation of carbonyls has been accomplished. The use of enamine catalysis has provided a new organocatalytic strategy for the enantioselective oxyamination of aldehydes, to generate α-oxyaldehydes, important chiral synthons for natural product and medicinal agent synthesis. The use of l-proline as the asymmetric catalyst has been found to mediate the oxidation of a large variety of aldehyde substrates with nitrosobenzene serving as the electrophilic oxidant. A diverse spectrum of aldehyde substrates can also be accommodated in this new organocatalytic transformation. While catalyst quantities of 2 mol % were generally employed in this study, successful oxidations conducted using catalyst loadings as low as 0.5 mol % are described

Verification of Item Usage Rules in Product Configuration

In the development of complex products product configuration systems are often used to support the development process. Item Usage Rules (IURs) are conditions for including specific items in products bills of materials based on a high-level product description. Large number of items and significant complexity of IURs make it difficult to maintain and analyze IURs manually. In this paper we present an automated approach for verifying IURs, which guarantees the presence of exactly one item from a predefined set in each product, as well as that an IUR can be reformulated without changing the set of products for which the item was included

Pedicle Screw-Associated Violation of the Adjacent Unfused Facet Joint: Clinical Outcomes and Fusion Rates

STUDY DESIGN: Retrospective review of a prospective randomized trial. OBJECTIVES: To compare outcome scores and fusion rates in patients with and without pedicle screw-associated facet joint violation (FJV) after a single-level lumbar fusion. METHODS: Clinical outcomes data and computed tomography (CT) imaging were reviewed for 157 patients participating in a multicenter prospective trial. Post-operative CT scans at 12-months follow-up were examined for fusion status and FJV. Patient-reported outcomes (PROs) included Oswestry Disability Index (ODI) and Visual Analog Scale (VAS) for leg and low back pain. Chi-square test of independence was used to compare proportions between groups on categorical measures. Two-sample t-test was used to identify differences in mean patient outcome scores. Logistic regression models were performed to determine association between FJV and fusion rates. RESULTS: Of the 157 patients included, there were 18 (11.5%) with FJV (Group A) and 139 (88.5%) without FJV (Group B). Patients with FJV experienced less improvement in ODI (P = .004) and VAS back pain scores (P = .04) vs patients without FJV. There was no difference in mean VAS leg pain (P = .4997). The rate of fusion at 12-months for patients with FJV (27.8%) was lower compared to those without FJV (71.2%) (P = .0002). Patients with FJV were 76% less likely to have a successful fusion at 12-months. CONCLUSION: Pedicle screw-associated violation of the adjacent unfused facet joint during single-level lumbar fusion is associated with less improvement in back pain, back pain-associated disability, and a lower fusion rate at 1-year after surgery

Efficient Certified Resolution Proof Checking

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

A SAT Approach to Clique-Width

Clique-width is a graph invariant that has been widely studied in combinatorics and computer science. However, computing the clique-width of a graph is an intricate problem, the exact clique-width is not known even for very small graphs. We present a new method for computing the clique-width of graphs based on an encoding to propositional satisfiability (SAT) which is then evaluated by a SAT solver. Our encoding is based on a reformulation of clique-width in terms of partitions that utilizes an efficient encoding of cardinality constraints. Our SAT-based method is the first to discover the exact clique-width of various small graphs, including famous graphs from the literature as well as random graphs of various density. With our method we determined the smallest graphs that require a small pre-described clique-width.Comment: proofs in section 3 updated, results remain unchange