On reconstruction theorems in noncommutative Riemannian geometry

We present a novel account of the theory of commutative spectral triples and their two closest noncommutative generalisations, almost-commutative spectral triples and toric noncommutative manifolds, with a focus on reconstruction theorems, viz, abstract, functional-analytic characterisations of global-analytically defined classes of spectral triples. We begin by reinterpreting Connes's reconstruction theorem for commutative spectral triples as a complete noncommutative-geometric characterisation of Dirac-type operators on compact oriented Riemannian manifolds, and in the process clarify folklore concerning stability of properties of spectral triples under suitable perturbation of the Dirac operator. Next, we apply this reinterpretation of the commutative reconstruction theorem to obtain a reconstruction theorem for almost-commutative spectral triples. In particular, we propose a revised, manifestly global-analytic definition of almost-commutative spectral triple, and, as an application of this global-analytic perspective, obtain a general result relating the spectral action on the total space of a finite normal compact oriented Riemannian cover to that on the base space. Throughout, we discuss the relevant refinements of these definitions and results to the case of real commutative and almost-commutative spectral triples. Finally, we outline progess towards a reconstruction theorem for toric noncommutative manifolds.

Carbon-carbon bond forming reactions from bis(carbene)-platinum(II) complexes and olefin polymerization and oligomerization using group 4 post-metallocene complexes

A long-standing challenge in transition metal catalysis is selective C–C bond coupling of simple feedstocks, such as carbon monoxide, ethylene or propylene, to yield value-added products. This work describes efforts toward selective C–C bond formation using early- and late-transition metals, which may have important implications for the production of fuels and plastics, as well as many other commodity chemicals.

The industrial Fischer-Tropsch (F-T) process converts synthesis gas (syngas, a mixture of CO + H₂) into a complex mixture of hydrocarbons and oxygenates. Well-defined homogeneous catalysts for F-T may provide greater product selectivity for fuel-range liquid hydrocarbons compared to traditional heterogeneous catalysts. The first part of this work involved the preparation of late-transition metal complexes for use in syngas conversion. We investigated C–C bond forming reactions via carbene coupling using bis(carbene)platinum(II) compounds, which are models for putative metal–carbene intermediates in F-T chemistry. It was found that C–C bond formation could be induced by either (1) chemical reduction of or (2) exogenous phosphine coordination to the platinum(II) starting complexes. These two mild methods afforded different products, constitutional isomers, suggesting that at least two different mechanisms are possible for C–C bond formation from carbene intermediates. These results are encouraging for the development of a multicomponent homogeneous catalysis system for the generation of higher hydrocarbons.

A second avenue of research focused on the design and synthesis of post-metallocene catalysts for olefin polymerization. The polymerization chemistry of a new class of group 4 complexes supported by asymmetric anilide(pyridine)phenolate (NNO) pincer ligands was explored. Unlike typical early transition metal polymerization catalysts, NNO-ligated catalysts produce nearly regiorandom polypropylene, with as many as 30-40 mol % of insertions being 2,1-inserted (versus 1,2-inserted), compared to <1 mol % in most metallocene systems. A survey of model Ti polymerization catalysts suggests that catalyst modification pathways that could affect regioselectivity, such as C–H activation of the anilide ring, cleavage of the amine R-group, or monomer insertion into metal–ligand bonds are unlikely. A parallel investigation of a Ti–amido(pyridine)phenolate polymerization catalyst, which features a five- rather than a six-membered Ti–N chelate ring, but maintained a dianionic NNO motif, revealed that simply maintaining this motif was not enough to produce regioirregular polypropylene; in fact, these experiments seem to indicate that only an intact anilide(pyridine)phenolate ligated-complex will lead to regioirregular polypropylene. As yet, the underlying causes for the unique regioselectivity of anilide(pyridine)phenolate polymerization catalysts remains unknown. Further exploration of NNO-ligated polymerization catalysts could lead to the controlled synthesis of new types of polymer architectures.

Finally, we investigated the reactivity of a known Ti–phenoxy(imine) (Ti-FI) catalyst that has been shown to be very active for ethylene homotrimerization in an effort to upgrade simple feedstocks to liquid hydrocarbon fuels through co-oligomerization of heavy and light olefins. We demonstrated that the Ti-FI catalyst can homo-oligomerize 1-hexene to C₁₂ and C₁₈ alkenes through olefin dimerization and trimerization, respectively. Future work will include kinetic studies to determine monomer selectivity by investigating the relative rates of insertion of light olefins (e.g., ethylene) vs. higher α-olefins, as well as a more detailed mechanistic study of olefin trimerization. Our ultimate goal is to exploit this catalyst in a multi-catalyst system for conversion of simple alkenes into hydrocarbon fuels.

Brf1 post-transcriptionally regulates pluripotency and differentiation responses downstream of Erk MAP Kinase

FGF/Erk MAP Kinase Signaling is a central regulator of mouse embryonic stem cell (mESC) self-renewal, pluripotency and differentiation. However, the mechanistic connection between this signaling pathway activity and the gene circuits stabilizing mESCs in vitro remain unclear. Here we show that FGF signaling post-transcriptionally regulates the mESC transcription factor network by controlling the expression of Brf1 (zfp36l1), an AU-rich element mRNA binding protein. Changes in Brf1 level disrupts the expression of core pluripotency-associated genes and attenuates mESC self-renewal without inducing differentiation. These regulatory effects are mediated by rapid and direct destabilization of Brf1 targets, such as Nanog mRNA. Interestingly, enhancing Brf1 expression does not compromise mESC pluripotency, but does preferentially regulate differentiation to mesendoderm by accelerating the expression of primitive streak markers. Together, these studies demonstrate that FGF signals utilize targeted mRNA degradation by Brf1 to enable rapid post-transcriptional control of gene expression.

I. Foehn winds of southern California. II. Foehn wind cyclo-genesis. III. Weather conditions associated with the Akron disaster. IV. The Los Angeles storm of December 30, 1933 to January 1, 1934

I. Foehn winds of southern California.
An investigation of the hot, dry and dust laden winds occurring in the late fall and early winter in the Los Angeles Basin and attributed in the past to the influences of the desert regions to the north revealed that these currents were of a foehn nature. Their properties were found to be entirely due to dynamical heating produced in the descent from the high level areas in the interior to the lower Los Angeles Basin. Any dust associated with the phenomenon was found to be acquired from the Los Angeles area rather than transported from the desert. It was found that the frequency of occurrence of a mild type foehn of this nature during this season was sufficient to warrant its classification as a winter monsoon. This results from the topography of the Los Angeles region which allows an easy entrance to the air from the interior by virtue of the low level mountain passes north of the area. This monsoon provides the mild winter climate of southern California since temperatures associated with the foehn currents are far higher than those experienced when maritime air from the adjacent Pacific Ocean occupies the region.

II. Foehn wind cyclo-genesis.
Intense anticyclones frequently build up over the high level regions of the Great Basin and Columbia Plateau which lie between the Sierra Nevada and Cascade Mountains to the west and the Rocky Mountains to the east. The outflow from these anticyclones produce extensive foehns east of the Rockies in the comparatively low level areas of the middle west and the Canadian provinces of Alberta and Saskatchewan. Normally at this season of the year very cold polar continental air masses are present over this territory and with the occurrence of these foehns marked discontinuity surfaces arise between the warm foehn current, which is obliged to slide over a colder mass, and the Pc air to the east. Cyclones are easily produced from this phenomenon and take the form of unstable waves which propagate along the discontinuity surface between the two dissimilar masses. A continual series of such cyclones was found to occur as long as the Great Basin anticyclone is maintained with undiminished intensity.

III. Weather conditions associated with the Akron disaster.
This situation illustrates the speedy development and propagation of young disturbances in the eastern United States during the spring of the year under the influence of the conditionally unstable tropical maritime air masses which characterise the region. It also furnishes an excellent example of the superiority of air mass and frontal methods of weather prediction for aircraft operation over the older methods based upon pressure distribution.

IV. The Los Angeles storm of December 30, 1933 to January 1, 1934.
This discussion points out some of the fundamental interactions occurring between air masses of the North Pacific Ocean in connection with Pacific Coast storms and the value of topographic and aerological considerations in predicting them. Estimates of rainfall intensity and duration from analyses of this type may be made and would prove very valuable in the Los Angeles area in connection with flood control problems.