Generalized roof duality

The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems. It works by constructing the tightest possible lower-bounding submodular function, and instead of minimizing the original objective function, the relaxation is minimized. However, for higher-order problems the technique has been less successful. A standard technique is to first reduce the problem into a quadratic one by introducing auxiliary variables and then apply the quadratic roof dual bound, but this may lead to loose bounds.We generalize the roof duality technique to higher-order optimization problems. Similarly to the quadratic case, optimal relaxations are defined to be the ones that give the maximum lower bound. We show how submodular relaxations can efficiently be constructed in order to compute the generalized roof dual bound for general cubic and quartic pseudo-boolean functions. Further, we prove that important properties such as persistency still hold, which allows us to determine optimal values for some of the variables. From a practical point of view, we experimentally demonstrate that the technique outperforms the state of the art for a wide range of applications, both in terms of lower bounds and in the number of assigned variables.     

Health-based pharmaceutical pay-for-performance risk-sharing agreements

Many new drugs, such as biologics and cancer drugs, are very costly. However, their effectiveness outside of clinical trial settings is often uncertain at the time they gain market approval. This uncertainty may reflect a lack of real-world outcomes data, as opposed to clinical trials data, for a typical patient population. A risk-sharing agreement is a contract between a drug manufacturer and a healthcare payer to help manage uncertainties regarding the cost and effectiveness of those drugs. In this paper, we model a risk-sharing agreement in which a proportion of total sales is rebated. We model disease progression using a continuous time Markov chain with uncertain transition rates. We examine the performance of this risk-sharing agreement from the manufacturer’s perspective and investigate the conditions under which the manufacturer will make a profit. We illustrate with a numerical model parameterized using data from a Phase 2 clinical trial of an oncology drug that was subjected to a risk-sharing agreement in the UK.     

Asymmetric synthesis of 1,3-oxathiolan-5-one derivatives through dynamic covalent kinetic resolution

The asymmetric synthesis of 1,3-oxathiolan-5-one derivatives through an enzyme-catalyzed, dynamic covalent kinetic resolution strategy is presented. Dynamic hemithioacetal formation combined with intramolecular, lipase-catalyzed lactonization resulted in good conversions with moderate to good enantiomeric excess (ee) for the final products. The process was evaluated for different lipase preparations, solvents, bases, and reaction temperatures, where lipase B from Candida antarctica (CAL-B) proved most efficient. The substrate scope was furthermore explored for a range of aldehyde structures, together with the potential access to nucleoside analog inhibitor core structures.     

Cone motion viscosity and optical second harmonic generation of ferroelectric liquid crystalline dendrimers

We report second harmonic generation in a ferroelectric liquid crystalline trimer and ferroelectric liquid crystalline dendrimers of first, second and third generation. Thin cells were filled with the compounds by capillary forces at elevated temperature, and cooled from the surface stabilized ferroelectric state to below the glass transition temperature, while kept in an electric field. The cone motion viscosity and the threshold electric field for unwinding of the helix axis of the chiral tilted smectic mesophases were studied separately at elevated temperature, and these data were used to optimize the preparation of the films. The measured response time was between 0.3 and 3ms, which corresponds to a cone motion viscosity between 0.5 and 50 Pa s. Second harmonic generation was studied both at elevated temperature with an electric field and at room temperature with and without electric field. The first generation dendrimer exhibited a strong increase in the second order non-linear optical response with time at room temperature. The d ₂₃-coefficient of this dendrimer was approximately four times larger than for the other macromolecules and was 0.045 pm V^-1. The relatively large d-coefficient of the first generation dendrimer is ascribed to crystallization, which improved the orientation of the molecular dipoles.     

Synthesis of S-Glycosyl Xanthates by Phase Transfer Catalyzed Substitution of Glycosyl Halides

Abstract

Peracetylated glycosyl- and glycobiosyl bromides and chlorides 1-4 including acetochloroneuraminic acid 5 were stereoselectively transformed into their corresponding S-glycosyl xanthates 6-10 in high yield (91-98%) under phase transfer catalyzed conditions. The reactions occurred at room temperature using tetrabutylammonium hydrogen sulfate as the catalyst. The substitutions gave complete inversion of configuration and thus proceeded by an S_N2 type mechanism. Changing the organic solvent from methylene chloride to ethyl acetate had no detrimental effect on the outcome of the reactions but avoided an undesirable side reaction between the xanthate anion and methylene chloride.