Drawing Disconnected Graphs on the Klein Bottle

We prove that two disjoint graphs must always be drawn separately on the Klein bottle in order to minimize the crossing number of the whole drawing.     

The High‐Pressure Phase of MgB2C2

A high‐pressure modification of MgB₂C₂ was synthesized and structurally characterized. The compound crystallizes in the orthorhombic space group Pnnm, with the lattice parameters a = 7.19633(3) Å, b = 4.61791(13) Å and c = 2.77714(8) Å. The compound contains heterographene B–C nets, isoelectronic to graphite, just like the ambient pressure modification. The layers are intercalated by magnesium atoms, which are arranged in a chain‐like manner. According to Density Functional Theory (DFT) calculations, the high‐pressure form of MgB₂C₂ is a semiconductor with a band gap of 1.02 eV. The compound does not undergo a superconducting transition down to 2 K.     

An NHC-Mediated Metal-Free Approach towards an NHC-Coordinated Endocyclic Disilene

A convenient metal-free approach towards an N-heterocyclic carbene (NHC)-coordinated disilene 2 is described. Compound 2 , featuring the disilene incorporated in cyclopolysilane framework, was obtained in good yield and characterized using NMR spectroscopy and X-ray crystallography. Density functional theory (DFT) calculations of the reaction mechanism provide a rationale for the observed reactivity and give detailed information on the bonding situation of the base-stabilized disilene. Compound 2 undergoes thermal or light- induced (λ=456 nm) NHC loss, and a dimerization process to give a corresponding dimer with a Si₁₀ skeleton. In order to shed light on the dimerization mechanism, DFT calculations were performed. Moreover, the reactivity of 2 was examined with selected examples of transition metal carbonyl compounds.     

Spatial Distribution of Intracellular Ion Concentrations in Aggregate-Forming HeLa Cells Analyzed by μ-XRF Imaging

Protein aggregation is a hallmark of several severe neurodegenerative disorders such as Huntington's, Parkinson's, or Alzheimer's disease. Metal ions play a profound role in protein aggregation and altered metal-ion homeostasis is associated with disease progression. Here we utilize μ-X-ray fluorescence imaging in combination with rapid freezing to resolve the elemental distribution of phosphorus, sulfur, potassium, and zinc in huntingtin exon-1-mYFP expressing HeLa cells. Using quantitative XRF analysis, we find a threefold increase in zinc and a 10-fold enrichment of potassium that can be attributed to cellular stress response. While the averaged intracellular ion areal masses are significantly different in aggregate-containing cells, a local intracellular analysis shows no different ion content at the location of intracellular inclusion bodies. The results are compared to corresponding experiments on HeLa cells forming pseudoisocyanine chloride aggregates. As those show similar results, changes in ion concentrations are not exclusively linked to huntingtin exon-1 amyloid formation.     

Microstructured Hydrogel Templates for the Formation of Conductive Gold Nanowire Arrays

Microstructured hydrogel allows for a new template‐guided method to obtain conductive nanowire arrays on a large scale. To generate the template, an imprinting process is used in order to synthesize the hydrogel directly into the grooves of wrinkled polydimethylsiloxane (PDMS). The resulting poly(N‐vinylimidazole)‐based hydrogel is defined by the PDMS stamp in pattern and size. Subsequently, tetrachloroaurate(III) ions from aqueous solution are coordinated within the humps of the N‐vinylimidazole‐containing polymer template and reduced by air plasma. After reduction and development of the gold, to achieve conductive wires, the extension perpendicular to the long axis (width) of the gold strings is considerably reduced compared to the dimension of the parental hydrogel wrinkles (from ≈1 μm down to 200–300 nm). At the same time, the wire‐to‐wire distance and the overall length of the wires is preserved. The PDMS templates and hydrogel structures are analyzed with scanning force microscopy (SFM) and the gold structures via scanning electron microscopy (SEM) and energy‐dispersive X‐ray spectroscopy. The conductivity measurements of the gold nanowires are performed in situ in the SEM, showing highly conductive gold leads. Hence, this method can be regarded as a facile nonlithographic top‐down approach from micrometer‐sized structures to nanometer‐sized features.

     

Insider behavior under different market structures: experimental evidence on trading patterns,manipulation, and profitability

Central European Journal of Operations Research - We conduct laboratory experiments incorporating different market structures and insiders who compete with imperfectly informed traders. The...     

Inverse multi-objective combinatorial optimization

Inverse multi-objective combinatorial optimization consists of finding a minimal adjustment of the objective functions coefficients such that a given set of feasible solutions becomes efficient. An algorithm is proposed for rendering a given feasible solution into an efficient one. This is a simplified version of the inverse problem when the cardinality of the set is equal to one. The adjustment is measured by the Chebyshev distance. It is shown how to build an optimal adjustment in linear time based on this distance, and why it is right to perform a binary search for determining the optimal distance. These results led us to develop an approach based on the resolution of mixed-integer linear programs. A second approach based on a branch-and-bound is proposed to handle any distance function that can be linearized. Finally, the initial inverse problem is solved by a cutting plane algorithm.     

Scaling relationship between the copositive cone and Parrilo’s first level approximation

We investigate the relation between the cone ${\mathcal{C}^{n}}$ of n × n copositive matrices and the approximating cone ${\mathcal{K}_{n}^{1}}$ introduced by Parrilo. While these cones are known to be equal for n ≤ 4, we show that for n ≥ 5 they are not equal. This result is based on the fact that ${\mathcal{K}_{n}^{1}}$ is not invariant under diagonal scaling. We show that for any copositive matrix which is not the sum of a nonnegative and a positive semidefinite matrix we can find a scaling which is not in ${\mathcal{K}_{n}^{1}}$ . In fact, we show that if all scaled versions of a matrix are contained in ${\mathcal{K}_{n}^{r}}$ for some fixed r, then the matrix must be in ${\mathcal{K}_{n}^{0}}$ . For the 5 × 5 case, we show the more surprising result that we can scale any copositive matrix X into ${\mathcal{K}_{5}^{1}}$ and in fact that any scaling D such that ${(DXD)_{ii} \in \{0,1\}}$ for all i yields ${DXD \in \mathcal{K}_{5}^{1}}$ . From this we are able to use the cone ${\mathcal{K}_{5}^{1}}$ to check if any order 5 matrix is copositive. Another consequence of this is a complete characterisation of ${\mathcal{C}^{5}}$ in terms of ${\mathcal{K}_{5}^{1}}$ . We end the paper by formulating several conjectures.