Coding and Counting Arrangements of Pseudolines

Arrangements of lines and pseudolines are important and appealing objects for research in discrete and computational geometry. We show that there are at most 2^{0.657> n2}2^{0.657\> n^{2}} simple arrangements of n pseudolines in the plane. This improves on previous work by Knuth who proved an upper bound of 3^\binomn2 @ 2^{0.792> n2}3^{\binom{n}{2}} \cong 2^{0.792\> n^{2}} in 1992 and the first author, who obtained 2^{0.697> n2}2^{0.697\> n^{2}} in 1997. The argument uses surprisingly little geometry. The main ingredient is a lemma that was already central to the argument given by Knuth.     

Commutability of homogenization and linearization at identity in finite elasticity and applications

We prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization and linearization commute at identity. This generalizes a recent result by S. Müller and the second author by dropping their assumption of periodicity. As a first application, we extend their Γ-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the Γ-closure is local at identity for this class of energy densities.     

A relation-algebraic approach to simple games

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool Rel View after a simple translation into the tool’s programming language. In order to demonstrate the visualization facilities of Rel View we consider an example of the Catalonian Parliament after the 2003 election.     

Pseudodifferential Operators Approach to Singular Integral Operators in Weighted Variable Exponent Lebesgue Spaces on Carleson Curves

The main results of the paper are: (1) The boundedness of singular integral operators in the variable exponent Lebesgue spaces L ^p(·)(Γ, w) on a class of composed Carleson curves Γ where the weights w have a finite set of oscillating singularities. The proof of this result is based on the boundedness of Mellin pseudodifferential operators on the spaces L^p(·)(\mathbbR ₊,dm){L^{p(\cdot )}(\mathbb{R} _{+},d\mu)} where dμ is an invariant measure on multiplicative group ${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}${\mathbb{R}_{+}=\left\{r\in \mathbb{R}:r >0 \right\}}. (2) Criterion of local invertibility of singular integral operators with piecewise slowly oscillating coefficients acting on L ^p(·)(Γ, w) spaces. We obtain this criterion from the corresponding criteria of local invertibility at the point 0 of Mellin pseudodifferential operators on \mathbbR₊{\mathbb{R}_{+}} and local invertibility of singular integral operators on \mathbbR{\mathbb{R}}. (3) Criterion of Fredholmness of singular integral operators in the variable exponent Lebesgue spaces L ^p(·)(Γ, w) where Γ belongs to a class of composed Carleson curves slowly oscillating at the nodes, and the weight w has a finite set of slowly oscillating singularities.     

Continuous Blooming of Convex Polyhedra

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.     

How linker's modification controls swelling properties of highly flexible iron(III) dicarboxylates MIL-88

A series of organically modified iron(III) terephthalate MIL-88B and iron(III) 4,4'-biphenyl dicarboxylate MIL-88D flexible solids have been synthesized and characterized through a combination of X-ray diffraction, IR spectroscopy, and thermal analysis (MIL stands for Material from Institut Lavoisier). The swelling amplitude of the highly flexible MOFs tuned by introducing functional groups onto the phenyl rings shows a clear dependence on the steric hindrance and on the number of groups per aromatic ring. For instance, while the introduction of four methyl groups per spacer in dried MIL-88B results in a large permanent porosity, introducing two or four methyl groups in MIL-88D allows an easier pore opening in the presence of liquids without drastically decreasing the swelling magnitude. The influence of the degree of saturation of the metal center and the nature of the solvent on the swelling is also discussed. Finally, a computationally assisted structure determination has led to a proposal of plausible structures for the closed (dried) and open forms of modified MIL-88B and MIL-88D and to evaluation of their framework energies subject to the nature of the functional groups.     

Core, shell, and surface-optimized dendrimers for blue light-emitting diodes

We present a novel core-shell-surface multifunctional structure for dendrimers using a blue fluorescent pyrene core with triphenylene dendrons and triphenylamine surface groups. We find efficient excitation energy transfer from the triphenylene shell to the pyrene core, substantially enhancing the quantum yield in solution and the solid state (4-fold) compared to dendrimers without a core emitter, while TPA groups facilitate the hole capturing and injection ability in the device applications. With a luminance of up to 1400 cd/m(2), a saturated blue emission CIE(xy) = (0.15, 0.17) and high operational stability, these dendrimers belong to the best reported fluorescence-based blue-emitting organic molecules.     

Structural basis for reductive radical formation and electron recycling in (R)-2-hydroxyisocaproyl-CoA dehydratase

The radical enzyme (R)-2-hydroxyisocaproyl-CoA dehydratase catalyzes the dehydration of (R)-2-hydroxyisocaproyl-CoA in the fermentation of l-leucine by the human pathogenic bacterium Clostridium difficile. In contrast to other radical enzymes, such as bacterial class II ribonucleotide reductase or biotin synthase, the Fe/S cluster containing (R)-2-hydroxyisocaproyl-CoA dehydratase requires no special cofactors such as coenzyme B(12) or S-adenosylmethionine for radical generation. Instead it uses a single high-energy electron that is recycled after each turnover. The catalyzed reaction, an atypical α/β-dehydration, depends on the reductive formation of ketyl radicals on the substrate generated by injection of a single electron from the ATP-dependent activator protein. So far, it is unknown how the active electron is recycled and how unwanted side reactions are prevented, allowing for up to 10,000 turnovers. The crystal structure reveals that the heterodimeric protein contains two [4Fe-4S] clusters at a distance of 12 ?, each coordinated by three cysteines and one terminal ligand. The cluster in the α-subunit is part of the active site. In the absence of substrate, a water/hydroxide ion acts as the fourth ligand. The substrate replaces this ligand and coordinates the cluster via the carbonyl-oxygen of the thioester group. The cluster in the β-subunit has a terminal sulfhydryl/sulfido ligand and can act as a reservoir to protect the electron from unwanted side reactions via a recycling mechanism. The crystal structure of (R)-2-hydroxyisocaproyl-CoA dehydratase serves as a model for the reductively radical-generating metalloenzymes of the (R)-2-hydroxyacyl-CoA dehydratase and benzoyl-CoA reductase families.     

Structural impact of proline-directed pseudophosphorylation at AT8, AT100, and PHF1 epitopes on 441-residue tau

The intrinsically disordered protein tau becomes excessively phosphorylated and aggregates into neurofibrillary tangles in Alzheimer's disease. To obtain insight into the structural consequences of phosphorylation, we characterized a mutant protein of tau in which epitopes recognized by Alzheimer diagnostic antibodies were mimicked by mutation to glutamic acid [AT8 (S199E, S202E, T205E), AT100 (T212E and S214E), and PHF1 (S396E and S404E)]. A large number of distance restraints obtained from NMR paramagnetic relaxation enhancement in combination with ensemble conformer calculations demonstrate that pseudophosphorylation causes an opening of the transient folding of tau. Together with previous studies on the Parkinson-related protein α-synuclein, our data indicate that networks of transient long-range interactions are common properties of intrinsically disordered proteins and that their modulation is important for aggregation.