An algorithm to analyze stability of gene-expression patterns

Many problems in the field of computational biology consist of the analysis of so-called gene-expression data. The successful application of approximation and optimization techniques, dynamical systems, algorithms and the utilization of the underlying combinatorial structures lead to a better understanding in that field. For the concrete example of gene-expression data we extend an algorithm, which exploits discrete information. This is lying in extremal points of polyhedra, which grow step by step, up to a possible stopping. We study gene-expression data in time, mathematically model it by a time-continuous system, and time-discretize this system. By our algorithm we compute the regions of stability and instability. We give an motivating introduction from genetics, present biological and mathematical interpretations of (in)stability, point out structural frontiers and give an outlook to future research

Tracking Coordination Environment and Reaction Intermediates in Homo- and Heterogeneous Epoxidation Catalysts via Ti L2,3-edge NEXAFS

Ti-based molecules and materials are ubiquitous, and play a major role in both homogeneous and heterogeneous catalytic processes. Understanding the electronic structures of their active sites (oxidation state, local symmetry and ligand environment) is key to developing molecular-level structure-property relationships. In that context, X-ray absorption spectroscopy (XAS) offers a unique combination of element selectivity and sensitivity to local symmetry. Commonly, for early transition metals such as Ti, K-edge XAS is applied for in situ characterization and subsequent structural analysis with high sensitivity towards tetrahedral species. Ti L2,3-edge spectroscopy is in principle complementary and offers specific opportunities to interrogate the electronic structure of five-and six-coordinated species. It is, however, much more rarely implemented, because the use of soft X-rays implies ultra-high vacuum conditions. Furthermore, the interpretation of the data can be challenging. Here, we show how Ti L2,3-edge spectroscopy can help to obtain unique information about both homogenous and heterogeneous epoxidation catalysts and to develop a molecular-level relationship between spectroscopic signatures and electronic structures. Towards this goal, we first establish a spectral library of molecular Ti reference compounds, comprising various coordination environments with mono- and dimeric Ti species having O, N and Cl-ligands. We next implemented a computational methodology based on multiplet ligand field theory and maximally localized Wannier orbitals benchmarked on our library to understand Ti L2,3-edge spectroscopic signatures. We finally used this approach to track and predict spectra of catalytically relevant intermediates, focusing on Ti-based olefin epoxidation catalysts

Role and dynamics of transition metal carbides in methane coupling

Transition metal carbides have numerous applications and are known to excel in terms of hardness, thermal stability and conductivity. In particular, the Pt-like behavior of Mo and W carbides has led to the popularization of metal carbides in catalysis, ranging from electrochemically-driven reactions to thermal methane coupling. Herein, we show the active participation of carbidic carbon in the formation of C2 products during methane coupling at high temperature that is associated with the dynamics of Mo and W carbides. A detailed mechanistic study reveals that the catalyst performance of these metal carbides can be traced back to its carbon diffusivity and exchange capability upon interaction with methane (gas phase carbon). A stable C2 selectivity over time on stream for Mo carbide (Mo2C) can be rationalized by fast carbon diffusion dynamics, while W carbide (WC) shows loss of selectivity due to slow diffusion leading to surface carbon depletion. This finding showcases that the bulk carbidic carbon of the catalyst plays a crucial role and that the metal carbide is not only responsible for methyl radical formation. Overall, this study evidences the presence of a carbon equivalent to the Mars–Van Krevelen type mechanism for non-oxidative coupling of methane.ISSN:2041-6520ISSN:2041-653

Role and Dynamics of Transition Metal Carbides in Methane Coupling

Transition metal carbides have numerous applications and are known to excel in terms of hardness, thermal stability and conductivity. In particular, the Pt-like behavior of Mo and W carbides has led to a popularization of metal carbides in catalysis, ranging from electrochemically-driven reactions to thermal methane coupling. Herein, we show the dynamics of Mo and W carbides and the active participation of carbidic carbon in the formation of C2 products during methane coupling. A detailed mechanistic study reveals that the catalyst performance of these metal carbides can be traced back to its carbon diffusivity and exchange capability upon interaction with gas phase carbon (methane). A stable C2 selectivity over time on stream for Mo carbide (Mo2C) can be rationalized by fast carbon diffusion dynamics, while W carbide (WC) shows loss of selectivity due to slow diffusion leading to surface carbon depletion. This finding showcases that the bulk carbidic carbon of the catalyst plays a crucial role and that the metal carbide is not only responsible for methyl radical formation. Overall, this study supports the presence of a carbon equivalent to the Mars-Van Krevelen type mechanism for non-oxidative coupling of methane, thus introducing guiding principles to design and develop associated catalysts