Expanding the expressive power of Monadic Second-Order logic on restricted graph classes

We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known Monadic Second-Order logic by the addition of cardinality constraints, can be solved in FPT time parameterized by vertex cover. The second meta-theorem shows that the MSO partitioning problems introduced by Rao can also be solved in FPT time with the same parameter. The significance of our contribution stems from the fact that these formalisms can describe problems which are W[1]-hard and even NP-hard on graphs of bounded tree-width. Additionally, our algorithms have only an elementary dependence on the parameter and formula. We also show that both results are easily extended from vertex cover to neighborhood diversity.Comment: Accepted for IWOCA 201

Kinetic Isotope Effect Provides Insight into the Vibrational Relaxation Mechanism of Aromatic Molecules: Application to Cyano-phenylalanine

Varying the reduced mass of an oscillator via isotopic substitution provides a convenient means to alter its vibrational frequency and hence has found wide applications. Herein, we show that this method can also help delineate the vibrational relaxation mechanism, using four isotopomers of the unnatural amino acid <i>p</i>-cyano-phenylalanine (Phe-CN) as models. In water, the nitrile stretching frequencies of these isotopomers, Phe-¹²C¹⁴N (<b>1</b>), Phe-¹²C¹⁵N (<b>2</b>), Phe-¹³C¹⁴N (<b>3</b>), and Phe-¹³C¹⁵N (<b>4</b>), are found to be equally separated by ∼27 cm^–1, whereas their vibrational lifetimes are determined to be 4.0 ± 0.2 (<b>1</b>), 2.2 ± 0.1 (<b>2</b>), 3.4 ± 0.2 (<b>3</b>), and 7.9 ± 0.5 ps (<b>4</b>), respectively. We find that an empirical relationship that considers the effective reduced mass of CN can accurately account for the observed frequency gaps, while the vibrational lifetime distribution, which suggests an intramolecular relaxation mechanism, can be rationalized by the order-specific density of states near the CN stretching frequency