Generalized modal satisfiability

It is well known that modal satisfiability is PSPACE-complete (Ladner (1977) [21]). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACE-complete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits. We consider both the uni-modal and the multi-modal cases, and study the dual problem of validity as well.     

Hierarchically Structured Poly(alkyl‐p‐xylylene) Nonwovens with Superhydrophobic Properties

Hierarchically structured poly(alkyl‐p‐xylylene) (alkyl‐PPX) nonwovens are prepared by specific parameter variation during the electrospinning process. The investigated parameters are changes in solutions properties and ambient humidity level, which lead to the formation of different fiber architectures and surface morphologies. The characterization of the nonwovens by scanning electron microscopy confirms the formation of hierarchically structured fibers, comprising bead‐on‐string architecture if spun from tetra­hydrofuran (THF) solutions, and porous surfaces at relative humidity (RH) levels > 30% for both chloroform and THF solutions. The wetting properties of nonwovens spun from THF and chloroform solutions are analyzed by water contact angle (CA) measurements, roll‐angle determination, and high speed imaging. PPX‐heptyl and PPX‐butyl fiber mats spun from 2.5 wt% THF and PPX‐heptyl spun from 3 wt% chloroform solutions at RH > 75% show superhydrophobic and self‐cleaning properties with CA > 153° and roll‐off angles of 10–15°. The nonwovens maintain their fiber morphology and water‐repellent properties after thermal and mechanical stress.

     

Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics

We consider large-scale dynamical systems in which both the initial state and some parameters are unknown. These unknown quantities must be estimated from partial state observations over a time window. A data assimilation framework is applied for this purpose. Specifically, we focus on large-scale linear systems with multiplicative parameter-state coupling as they arise in the discretization of parametric linear time-dependent partial differential equations. Another feature of our work is the presence of a quantity of interest different from the unknown parameters, which is to be estimated based on the available data. In this setting, we employ a simplicial decomposition algorithm for an optimal sensor placement and set forth formulae for the efficient evaluation of all required quantities. As a guiding example, we consider a thermo-mechanical PDE system with the temperature constituting the system state and the induced displacement at a certain reference point as the quantity of interest.     

Catalysis of an Essential Step in Vitamin B2 Biosynthesis by a Consortium of Broad Spectrum Hydrolases

An enzyme catalysing the essential dephosphorylation of the riboflavin precursor, 5‐amino‐6‐ribitylamino‐2,4(1H,3H)‐pyrimidinedione 5′‐phosphate ( 6 ), was purified about 800‐fold from a riboflavin‐producing Bacillus subtilis strain, and was assigned as the translation product of the ycsE gene by mass spectrometry. YcsE is a member of the large haloacid dehalogenase (HAD) superfamily. The recombinant protein was expressed in Escherichia coli. It catalyses the hydrolysis of 6 (v_max, 12 μmol mg^?1 min^?1; K_M, 54 μm ) and of FMN (v_max, 25 μmol mg^?1 min^?1; K_M, 135 μm ). A ycsE deletion mutant of B. subtilis was not riboflavin dependent. Two additional proteins (YwtE, YitU) that catalyse the hydrolysis of 6 at appreciable rates were identified by screening 13 putative HAD superfamily members from B. subtilis. The evolutionary processes that have resulted in the handling of an essential step in the biosynthesis of an essential cofactor by a consortium of promiscuous enzymes require further analysis.     

Adsorption and Diffusion of 4d and 5d Transition Metal Adatoms on Graphene/Ru(0001) and the Implications for Cluster Nucleation

To explore the possibility of using the graphene moiré superstructure formed on Ru(0001) (g/Ru(0001)) as a template to self-assemble super-lattices of metal nanoparticles as model catalysts, it is desirable to know the minimum-energy adsorption sites, adsorption energies, and diffusion properties of small metal species on this surface. Toward that end, density functional theory calculations have been carried out to investigate the adsorption and diffusion of 18 4d (Y–Ag) and 5d (La–Au) transition metal adatoms on g/Ru(0001), using small surface models representing different regions of the g/Ru(0001) surface. For each adatom, adsorption is the strongest in the fcc region and the weakest in the mound region of the moiré. Diffusion within the fcc region is facile for most adatoms, but an additional barrier is imposed by the corrugation of the graphene moiré for traversing between neighboring fcc regions. Overall, the earlier 4d and 5d metal adatoms have stronger adsorption energies and higher diffusion barriers on g/Ru(0001) than the later ones. The results are then interpreted to provide a better understanding of the conditions necessary to achieve dense super-lattices of monodisperse metal clusters on g/Ru(0001).