The combinatorial game Nofil played on Steiner triple systems

We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions.     

Synthesis of stable and cell-type selective analogues of cyclic ADP-ribose, a Ca(2+)-mobilizing second messenger. Structure--activity relationship of the N1-ribose moiety

We previously developed cyclic ADP-carbocyclic ribose (cADPcR, 2) as a stable mimic of cyclic ADP-ribose (cADPR, 1), a Ca(2+)-mobilizing second messenger. A series of the N1-ribose modified cADPcR analogues, designed as novel stable mimics of cADPR, which were the 2"-deoxy analogue 3, the 3"-deoxy analogue 4, the 3"-deoxy-2"-O-(methoxymethyl) analogue 5, the 3"-O-methyl analogue 6, the 2",3"-dideoxy analogue 7, and the 2",3"-dideoxydidehydro analogue 8, were successfully synthesized using the key intramolecular condensation reaction with phenylthiophosphate-type substrates. We investigated the conformations of these analogues and of cADPR and found that steric repulsion between both the adenine and N9-ribose moieties and between the adenine and N1-ribose moieties was a determinant of the conformation. The Ca(2+)-mobilizing effects were evaluated systematically using three different biological systems, i.e., sea urchin eggs, NG108-15 neuronal cells, and Jurkat T-lymphocytes. The relative potency of Ca(2+)-mobilization by these cADPR analogues varies depending on the cell-type used: e.g., 3"-deoxy-cADPcR (4) > cADPcR (2) > cADPR (1) in sea urchin eggs; cADPR (1) > cADPcR (2) approximately 3"-deoxy-cADPcR (4) in T-cells; and cADPcR (2) > cADPR (1) > 3"-deoxy-cADPcR (4) in neuronal cells, respectively. These indicated that the target proteins and/or the mechanism of action of cADPR in sea urchin eggs, T-cells, and neuronal cells are different. Thus, this study represents an entry to cell-type selective cADPR analogues, which can be used as biological tools and/or novel drug leads.     

Matrix-valued radial basis functions: stability estimates and applications

Radial basis functions (RBFs) have found important applications in areas such as signal processing, medical imaging, and neural networks since the early 1980s. Several applications require that certain physical properties are satisfied by the interpolant, for example, being divergence-free in case of incompressible data. In this paper we consider a class of customized (e.g., divergence-free) RBFs that are matrix-valued and have compact support; these are matrix-valued analogues of the well-known Wendland functions. We obtain stability estimates for a wide class of interpolants based on matrix-valued RBFs, also taking into account the size of the compact support of the generating RBF. We conclude with an application based on an incompressible Navier–Stokes equation, namely the driven-cavity problem, where we use divergence-free RBFs to solve the underlying partial differential equation numerically. We discuss the impact of the size of the support of the basis function on the stability of the solution. AMS subject classification 65D05