Quantum moment maps and invariants for G-invariant star products

We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under $G$-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of $G$-invariant star products.Comment: 20 page

On subshift presentations

We consider partitioned graphs, by which we mean finite strongly connected directed graphs with a partitioned edge set ${\mathcal E} ={\mathcal E}^- \cup{\mathcal E}^+$. With additionally given a relation $\mathcal R$ between the edges in ${\mathcal E}^-$ and the edges in $\mathcal E^+$, and denoting the vertex set of the graph by ${\frak P}$, we speak of an an ${\mathcal R}$-graph ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^+)$. From ${\mathcal R}$-graphs ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^+)$ we construct semigroups (with zero) ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-,{\mathcal E}^+)$ that we call ${\mathcal R}$-graph semigroups. We describe a method of presenting subshifts by means of suitably structured labelled directed graphs $({\mathcal V}, \Sigma,\lambda)$ with vertex set ${\mathcal V}$, edge set $\Sigma$, and a label map that asigns to the edges in $\Sigma$ labels in an ${\mathcal R}$-graph semigroup ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-, {\mathcal E}^-)$. We call the presented subshift an ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-, {\mathcal E}^-)$-presentation. We introduce a Property $(B)$ and a Property (c), tof subshifts, and we introduce a notion of strong instantaneity. Under an assumption on the structure of the ${\mathcal R}$-graphs ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-, {\mathcal E}^-)$ we show for strongly instantaneous subshifts with Property $(A)$ and associated semigroup ${\mathcal S}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^-)$, that Properties $(B)$ and (c) are necessary and sufficient for the existence of an ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-,{\mathcal E}^-)$-presentation, to which the subshift is topologically conjugate,Comment: 33 page

On Certain Subshifts and their Associated Monoids

Within a subclass of monoids (with zero) a structural characterization is given of those that are associated to topologically transitive subshifts with Property (A).Comment: 11 page

Exploratory analysis of high-resolution power interruption data reveals spatial and temporal heterogeneity in electric grid reliability

Modern grid monitoring equipment enables utilities to collect detailed records of power interruptions. These data are aggregated to compute publicly reported metrics describing high-level characteristics of grid performance. The current work explores the depth of insights that can be gained from public data, and the implications of losing visibility into heterogeneity in grid performance through aggregation. We present an exploratory analysis examining three years of high-resolution power interruption data collected by archiving information posted in real-time on the public-facing website of a utility in the Western United States. We report on the size, frequency and duration of individual power interruptions, and on spatio-temporal variability in aggregate reliability metrics. Our results show that metrics of grid performance can vary spatially and temporally by orders of magnitude, revealing heterogeneity that is not evidenced in publicly reported metrics. We show that limited access to granular information presents a substantive barrier to conducting detailed policy analysis, and discuss how more widespread data access could help to answer questions that remain unanswered in the literature to date. Given open questions about whether grid performance is adequate to support societal needs, we recommend establishing pathways to make high-resolution power interruption data available to support policy research.Comment: Journal submission (in review), 22 pages, 8 figures, 1 tabl

Chemical labelling for visualizing native AMPA receptors in live neurons

The location and number of neurotransmitter receptors are dynamically regulated at postsynaptic sites. However, currently available methods for visualizing receptor trafficking require the introduction of genetically engineered receptors into neurons, which can disrupt the normal functioning and processing of the original receptor. Here we report a powerful method for visualizing native α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)-type glutamate receptors (AMPARs) which are essential for cognitive functions without any genetic manipulation. This is based on a covalent chemical labelling strategy driven by selective ligand-protein recognition to tether small fluorophores to AMPARs using chemical AMPAR modification (CAM) reagents. The high penetrability of CAM reagents enables visualization of native AMPARs deep in brain tissues without affecting receptor function. Moreover, CAM reagents are used to characterize the diffusion dynamics of endogenous AMPARs in both cultured neurons and hippocampal slices. This method will help clarify the involvement of AMPAR trafficking in various neuropsychiatric and neurodevelopmental disorders

Control Over Cadmium Chalcogenide Nanocrystal Heterostructures via Precursor Conversion Kinetics

Semiconductor nanocrystals have immense potential to make an impact in consumer products due to their narrow, tunable emission linewidths. One factor limiting their use is the ease and reproducibility of core/shell nanocrystal syntheses. This thesis aims to address this issue by providing chemical control over the formation of core/shell nanostructures by replacing engineering controls with kinetic controls. Chapter 1 contextualizes our study on nanoparticle synthesis with a brief discussion on the physics of quantum confinement and the importance of narrow size dispersities, core/shell band alignments, and low lattice mismatches and strain at core/shell nanocrystal interfaces. Next, the evolution of cadmium chalcogenide nanocrystal reagents is described, ranging from the original organometallic reagents used in the 1980s to modern approaches involving cadmium phosphonates and carboxylates. This is followed by a description of chalcogen precursors, highlighting the recent introduction of molecules whose well-controlled and tunable reaction rates allow for the size tuning of nanocrystals at 100% yield, and accompanying theories on nanocrystal nucleation. Chapter 2 covers work to expand the library of available sulfur precursors to a wider range of molecules relevant for the synthesis of cadmium sulfide nanocrystals. Using thioureas alone, only very fast or very slow precursor conversion rates can be accessed. This limits the accessible sizes of cadmium sulfide nanocrystals using a single hot injection of precursor at standardized reaction conditions. We observe that thiocarbonate and thiocarbamate precursors with varying electronic substituents allow access to intermediate precursor conversion rates and cadmium sulfide nanocrystal sizes. Interestingly, we note that these new precursor classes nucleate particles with higher monodispersity than ones synthesized from thioureas. These results indicate that in addition to precursor structure controlling precursor conversion rate, precursor structure additionally impacts nanocrystal monodispersity. Chapter 3 expands the library of sulfur and selenium precursors to include cyclic thiones and selenones which extends chemical control of precursor conversion kinetics to cover five orders of magnitude. This unprecedented breadth of rate control allows for the simultaneous hot injection of multiple precursors to generate core/shell or alloyed nanoparticles using precursor reactivity. Using this new synthetic strategy, we observe that kinetic control runs into several issues which we partially attribute to differences in cadmium sulfide and cadmium selenide critical concentrations and growth rates. Nevertheless, combined with a syringe pump shelling method, we are able to access core/shell and alloyed nanocrystals with photoluminescence quantum yields of 67-81%. Chapter 4 applies the concept of nanostructure control via precursor conversion kinetics to a better model system: two-dimensional nanoplatelets. Cadmium chalcogenide nanoplatelets are highly desirable materials due to their exceptionally narrow emission full width half max (FWHM) values which make them pure emitters relative to quantum dots or organic dyes. We synthesize 3 monolayer thick nanoplatelets whose lateral dimensions vary from 10 nm x 10 nm to 186 x 100 nm and demonstrate compositional control on the smallest platelet sizes with STEM EELS

Precursor reaction kinetics control compositional grading and size of CdSe1-xSx nanocrystal heterostructures

We report a method to control the composition and microstructure of CdSe1-xSx nanocrystals by the simultaneous injection of sulfide and selenide precursors into a solution of cadmium oleate and oleic acid at 240 degrees C. Pairs of substituted thio- and selenoureas were selected from a library of compounds with conversion reaction reactivity exponents (k(E)) spanning 1.3 x 10(-5) s(-1) to 2.0 x 10(-1) s(-1). Depending on the relative reactivity (k(Se)/k(S)), core/shell and alloyed architectures were obtained. Growth of a thick outer CdS shell using a syringe pump method provides gram quantities of brightly photoluminescent quantum dots (PLQY = 67 to 90%) in a single reaction vessel. Kinetics simulations predict that relative precursor reactivity ratios of less than 10 result in alloyed compositions, while larger reactivity differences lead to abrupt interfaces. CdSe1-xSx alloys (k(Se)/k(S) = 2.4) display two longitudinal optical phonon modes with composition dependent frequencies characteristic of the alloy microstructure. When one precursor is more reactive than the other, its conversion reactivity and mole fraction control the number of nuclei, the final nanocrystal size at full conversion, and the elemental composition. The utility of controlled reactivity for adjusting alloy microstructure is discussed