Noncrossing partitions and the shard intersection order

We define a new lattice structure \((W,\preceq)\) on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC?(W) as a sublattice. The new construction of NC?(W) yields a new proof that NC?(W) is a lattice. The shard intersection order is graded and its rank generating function is the W-Eulerian polynomial. Many order-theoretic properties of \((W,\preceq)\), like Möbius number, number of maximal chains, etc., are exactly analogous to the corresponding properties of NC?(W). There is a natural dimension-preserving bijection between simplices in the order complex of \((W,\preceq)\) (i.e. chains in \((W,\preceq)\)) and simplices in a certain pulling triangulation of the W-permutohedron. Restricting the bijection to the order complex of NC?(W) yields a bijection to simplices in a pulling triangulation of the W-associahedron.The lattice \((W,\preceq)\) is defined indirectly via the polyhedral geometry of the reflecting hyperplanes of W. Indeed, most of the results of the paper are proven in the more general setting of simplicial hyperplane arrangements.     

Generic transient memory formation in disordered systems with noise

Out-of-equilibrium disordered systems may form memories of external driving in a remarkable fashion. The system "remembers" multiple values from a series of training inputs yet "forgets" nearly all of them at long times despite the inputs being continually repeated. Here, learning and forgetting are inseparable aspects of a single process. The memory loss may be prevented by the addition of noise. We identify a class of systems with this behavior, giving as an example a model of non-Brownian suspensions under cyclic shear.     

Continuation of periodic solutions in the waveguide array mode-locked laser

We apply the adjoint continuation method to construct highly accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle-node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models.     

X-ray photoelectron spectroscopic analysis of the surface chemistry of silica nanowires

A thorough analysis of the surface chemistry of silica nanowires has been performed by X-ray photoelectron spectroscopy to investigate unexpected surface changes. Examination of the Si 2p, O 1s, and C 1s core level states before and after exposure of the nanowires to various liquid media showed that silica nanowires are capable of much higher surface hydroxyl concentrations than planar native oxides. It is further demonstrated that the nanowire surface hydroxyl concentration corresponds to the pH of the aqueous media to which the nanowires are exposed. Spectral feature changes due to water exposure similar to those observed for fibronectin binding suggests that fibronectin binding is competitively inhibited by slow changes in surface chemistry resulting from water exposure.     

Inhibition of 2-oxoglutarate dependent oxygenases

2-Oxoglutarate (2OG) dependent oxygenases are ubiquitous iron enzymes that couple substrate oxidation to the conversion of 2OG to succinate and carbon dioxide. In humans their roles include collagen biosynthesis, fatty acid metabolism, DNA repair, RNA and chromatin modifications, and hypoxic sensing. Commercial applications of 2OG oxygenase inhibitors began with plant growth retardants, and now extend to a clinically used pharmaceutical compound for cardioprotection. Several 2OG oxygenases are now being targeted for therapeutic intervention for diseases including anaemia, inflammation and cancer. In this critical review, we describe studies on the inhibition of 2OG oxygenases, focusing on small molecules, and discuss the potential of 2OG oxygenases as therapeutic targets (295 references).     

Phosphonic acid functionalized asymmetric phthalocyanines: synthesis, modification of indium tin oxide, and charge transfer

Metalated and free-base A(3)B-type asymmetric phthalocyanines (Pcs) bearing, in the asymmetric quadrant, a flexible alkyl linker of varying chain lengths terminating in a phosphonic acid (PA) group have been synthesized. Two parallel series of asymmetric Pc derivatives bearing aryloxy and arylthio substituents are reported, and their synthesis and characterization through NMR, combustion analysis, and MALDI-MS are described. We also demonstrate the modification of indium tin oxide (ITO) substrates using the PA functionalized asymmetric Pc derivatives and monitoring their electrochemistry. The PA functionalized asymmetric Pcs were anchored to the ITO surface through chemisorption and their electrochemical properties characterized using cyclic voltammetry to investigate the effects of PA structure on the thermodynamics and kinetics of charge transfer. Ionization energies of the modified ITO surfaces were measured using ultraviolet photoemission spectroscopy.     

Solvent-based assembly of CdSe nanorods in solution

We demonstrate a purely solvent-based approach to assembling CdSe nanorods into vertically aligned, hexagonally packed monolayers in solution. Nanorods were dispersed in a mixture of good solvent with high vapor pressure and bad solvent with low vapor pressure, and preferential evaporation of the good solvent led to ordered assembly under conditions of continuously decreasing solvent quality. No applied external bias, extensive control of drying conditions, exceptionally monodisperse nanoparticles, or high concentrations of additives were required. This clean and facile method yielded ordered nanorod sheets of up to 7.5 μm wide with potential use as active materials in unique applications.     

Stable multivariate W-Eulerian polynomials

We prove a multivariate strengthening of Brenti?s result that every root of the Eulerian polynomial of type B is real. Our proof combines a refinement of the descent statistic for signed permutations with the notion of real stability—a generalization of real-rootedness to polynomials in multiple variables. The key is that our refined multivariate Eulerian polynomials satisfy a recurrence given by a stability-preserving linear operator.Our results extend naturally to colored permutations, and we also give stable generalizations of recent real-rootedness results due to Dilks, Petersen, and Stembridge on affine Eulerian polynomials of types A and C. Finally, although we are not able to settle Brenti?s real-rootedness conjecture for Eulerian polynomials of type D, nor prove a companion conjecture of Dilks, Petersen, and Stembridge for affine Eulerian polynomials of types B and D, we indicate some methods of attack and pose some related open problems.     

Delta Sets of Numerical Monoids Using Nonminimal Sets of Generators

Several recent articles have studied the structure of the delta set of a numerical monoid. We continue this work with the assumption that the generating set S chosen for the numerical monoid M is not necessarily minimal. We show that for certain choices of S, the resulting delta set can be made (in terms of cardinality) arbitrarily large or small. We close with a close analysis of the case where M =?n ₁, n ₂, in ₁ + jn ₂?for non-negative i and j.