Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Response of CO₂ and CH₄ emissions from Arctic tundra soils to a multifactorial manipulation of water table, temperature and thaw depth

Significant uncertainties persist concerning how Arctic soil tundra carbon emission responds to environmental changes. In this study, 24 cores were sampled from drier (high centre polygons and rims) and wetter (low centre polygons and troughs) permafrost tundra ecosystems. We examined how soil CO2 and CH4 fluxes responded to laboratory-based manipulations of soil temperature (and associated thaw depth) and water table depth, representing current and projected conditions in the Arctic. Similar soil CO2 respiration rates occurred in both the drier and the wetter sites, suggesting that a significant proportion of soil CO2 emission occurs via anaerobic respiration under water-saturated conditions in these Arctic tundra ecosystems. In the absence of vegetation, soil CO2 respiration rates decreased sharply within the first 7 weeks of the experiment, while CH4 emissions remained stable for the entire 26 weeks of the experiment. These patterns suggest that soil CO2 emission is more related to plant input than CH4 production and emission. The stable and substantial CH4 emission observed over the entire course of the experiment suggests that temperature limitations, rather than labile carbon limitations, play a predominant role in CH4 production in deeper soil layers. This is likely due to the presence of a substantial source of labile carbon in these carbon-rich soils. The small soil temperature difference (a median difference of 1 ◦C) and a more substantial thaw depth difference (a median difference of 6 cm) between the high and low temperature treatments resulted in a non-significant difference between soil CO2 and CH4 emissions. Although hydrology continued to be the primary factor influencing CH4 emissions, these emissions remained low in the drier ecosystem, even with a water table at the surface. This result suggests the potential absence of a methanogenic microbial community in high-centre polygon and rim ecosystems. Overall, our results suggest that the temperature increases reported for these Arctic regions are not responsible for increases in carbon losses. Instead, it is the changes in hydrology that exert significant control over soil CO2 and CH4 emissions

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than classical computers.Comment: 11 pages, 13 figure

Perturbations of nuclear C*-algebras

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, and we obtain embeddings from certain near inclusions involving separable nuclear C*-algebras. At the end of the paper we demonstrate how our methods lead to improved characterisations of some of the types of algebras that are of current interest in the classification programme.Comment: 45 page

Supersymmetry in the shadow of photini

Additional neutral gauge fermions -- "photini" -- arise in string compactifications as superpartners of U(1) gauge fields. Unlike their vector counterparts, the photini can acquire weak-scale masses from soft SUSY breaking and lead to observable signatures at the LHC through mass mixing with the bino. In this work we investigate the collider consequences of adding photini to the neutralino sector of the MSSM. Relatively large mixing of one or more photini with the bino can lead to prompt decays of the lightest ordinary supersymmetric particle; these extra cascades transfer most of the energy of SUSY decay chains into Standard Model particles, diminishing the power of missing energy as an experimental handle for signal discrimination. We demonstrate that the missing energy in SUSY events with photini is reduced dramatically for supersymmetric spectra with MSSM neutralinos near the weak scale, and study the effects on limits set by the leading hadronic SUSY searches at ATLAS and CMS. We find that in the presence of even one light photino the limits on squark masses from hadronic searches can be reduced by 400 GeV, with comparable (though more modest) reduction of gluino mass limits. We also consider potential discovery channels such as dilepton and multilepton searches, which remain sensitive to SUSY spectra with photini and can provide an unexpected route to the discovery of supersymmetry. Although presented in the context of photini, our results apply in general to theories in which additional light neutral fermions mix with MSSM gauginos.Comment: 23 pages, 8 figures, references adde

Sequencing the genome of the Atlantic salmon (Salmo salar)

The International Collaboration to Sequence the Atlantic Salmon Genome (ICSASG) will produce a genome sequence that identifies and physically maps all genes in the Atlantic salmon genome and acts as a reference sequence for other salmonids

In-cell NMR characterization of the secondary structure populations of a disordered conformation of α-Synuclein within E. coli cells

α-Synuclein is a small protein strongly implicated in the pathogenesis of Parkinson’s disease and related neurodegenerative disorders. We report here the use of in-cell NMR spectroscopy to observe directly the structure and dynamics of this protein within E. coli cells. To improve the accuracy in the measurement of backbone chemical shifts within crowded in-cell NMR spectra, we have developed a deconvolution method to reduce inhomogeneous line broadening within cellular samples. The resulting chemical shift values were then used to evaluate the distribution of secondary structure populations which, in the absence of stable tertiary contacts, are a most effective way to describe the conformational fluctuations of disordered proteins. The results indicate that, at least within the bacterial cytosol, α-synuclein populates a highly dynamic state that, despite the highly crowded environment, has the same characteristics as the disordered monomeric form observed in aqueous solution

Observations of bedforms on a dissipative macrotidal beach

NERC NE/H004262/1 and NE/H02543X/1 DRIB