A finiteness result for Heegaard splittings

In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of 3g−3 disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition.     

Combinatorics of n-color cyclic compositions

Integer compositions and related enumeration problems have been of interest to combinatorialists and number theorists for a long time. The cyclic and colored analogues of this concept, although interesting, have not been extensively studied. In this paper we explore the combinatorics of $n$-color cyclic compositions, presenting generating functions, bijections, asymptotic formulas related to the number of such compositions, the number of parts, and the number of restricted parts.     

Heegaard splittings of twisted torus knots

Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are known to have a unique minimal genus splitting. Here we demonstrate that an infinite class of hyperbolic knot exteriors, namely exteriors of certain “twisted torus knots” originally studied by Morimoto, Sakuma and Yokota, have a unique minimal genus Heegaard splitting of genus two. We also conjecture that these manifolds possess irreducible yet weakly reducible splittings of genus three. There are no known examples of such Heegaard splittings.     

Closed incompressible surfaces in knot complements

In this paper we show that given a knot or link in a -plat projection with and , where is the length of the plat, if the twist coefficients all satisfy then has at least nonisotopic essential meridional planar surfaces. In particular if is a knot then contains closed incompressible surfaces. In this case the closed surfaces remain incompressible after all surgeries except perhaps along a ray of surgery coefficients in .

     

Vanadium bromoperoxidase from Delisea pulchra: enzyme-catalyzed formation of bromofuranone and attendant disruption of quorum sensing

Vanadium bromoperoxidase was isolated and cloned from the marine red alga Delisea pulchra. This enzyme catalyzes the bromolactonization of 4-pentynoic acid forming 5E-bromo-methylidenetetrahydro-2-furanone, a compound which is shown herein to inhibit quorum sensing in the engineered reporter strain, Agrobacterium tumefaciens NTL4.     

Electrochemical characterization of 17β-estradiol with fast-scan cyclic voltammetry

We have developed a sensitive and stable electrochemical method for 17β-estradiol (E2) detection using fast-scan cyclic voltammetry (FSCV). Recently, E2 was proposed to function as a rapid synaptocrine signaling molecule in the brain; however, methods to directly monitor subsecond fluctuations in E2 are currently unavailable, limiting our understanding of the dynamics and mechanism of rapid E2 release. FSCV at carbon-fiber microelectrodes enables subsecond detection of electroactive neurochemicals directly in tissues like the brain. Here, we have electrochemically characterized E2 using FSCV for use in a tissue matrix. The limit of detection of E2 is 31.2±2.5 nM with FSCV, which will enable low nanomolar fluctuations in extracellular E2 to be monitored with hundred millisecond temporal resolution. We also identify specific parameters for waveform modification to improve future detection. This method will significantly improve E2 sensing capabilities and will have far-reaching impacts on improving our understanding of dynamic E2 signaling in the brain.     

Non-tame automorphisms of extensions of periodic groups

LetF be a free group andR≤F a characteristic subgroup. Automorphisms ofF/R which are induced by automorphisms ofF are called tame. In this paper we use theN-torsion invariant discovered by the first author and M. Lustig [LM] to show the existence of non-tame automorphisms of free central extensions and free nilpotent extensions of Burnside groups. Partially supported by the German Israel Foundation for Research and Development (G. I. F.). Supported by a grant from the Israel Planning and Budgeting Committee.     

Reconstructing Nonparametric Productivity Networks

Network models provide a general representation of inter-connected system dynamics. This ability to connect systems has led to a proliferation of network models for economic productivity analysis, primarily estimated non-parametrically using Data Envelopment Analysis (DEA). While network DEA models can be used to measure system performance, they lack a statistical framework for inference, due in part to the complex structure of network processes. We fill this gap by developing a general framework to infer the network structure in a Bayesian sense, in order to better understand the underlying relationships driving system performance. Our approach draws on recent advances in information science, machine learning and statistical inference from the physics of complex systems to estimate unobserved network linkages. To illustrate, we apply our framework to analyze the production of knowledge, via own and cross-disciplinary research, for a world-country panel of bibliometric data. We find significant interactions between related disciplinary research output, both in terms of quantity and quality. In the context of research productivity, our results on cross-disciplinary linkages could be used to better target research funding across disciplines and institutions. More generally, our framework for inferring the underlying network production technology could be applied to both public and private settings which entail spillovers, including intra- and inter-firm managerial decisions and public agency coordination. This framework also provides a systematic approach to model selection when the underlying network structure is unknown.