Liberal Arts and Sciences, College of
http://hdl.handle.net/10027/9
UIC College of Liberal Arts and Sciences2019-04-17T18:26:39ZMOST BOSON QUANTUM STATES ARE ALMOST MAXIMALLY ENTANGLED
http://hdl.handle.net/10027/23378
MOST BOSON QUANTUM STATES ARE ALMOST MAXIMALLY ENTANGLED
Friedland, Shmuel; Kemp, Todd
The geometric measure E of entanglement of an m qubit quantum state takes maximal possible value m. In previous work of Gross, Flammia, and Eisert, it was shown that E ≥ m − O(log m) with high probability as m → ∞. They show, as a consequence, that the vast majority of states are too entangled to be computationally useful. In this paper, we show that for m qubit Boson quantum states (those that are actually available in current designs for quantum computers), the maximal possible geometric measure of entanglement is log2 m, opening the door to many computationally universal states. We further show the corresponding concentration result that E ≥ log2 m − O(log log m) with high probability as m → ∞. We extend these results also to m-mode n-bit Boson quantum states.
Copyright @ American Mathematical Society
2018-09-04T00:00:00ZON THE COMPARISON OF STABLE AND UNSTABLE p-COMPLETION
http://hdl.handle.net/10027/23374
ON THE COMPARISON OF STABLE AND UNSTABLE p-COMPLETION
Barthel, Tobias; Bousfield, A.K.
In this note we show that a p-complete nilpotent space X has a p-complete suspension spectrum if and only if its homotopy groups pi X-* are bounded p-torsion. In contrast, if pi X-* is not all bounded p-torsion, we locate uncountable rational vector spaces in the integral homology and in the stable homotopy groups of X. To prove this, we establish a homological criterion for p-completeness of connective spectra. Moreover, we illustrate our results by studying the stable homotopy groups of K(Z(p), n) via Goodwillie calculus.
2019-02-01T00:00:00ZDoes God roll dice? Neutrality and determinism in evolutionary ecology
http://hdl.handle.net/10027/23364
Does God roll dice? Neutrality and determinism in evolutionary ecology
Ale, Som, B.; Halloway, Abdel; Mitchell, William, A.; Whelan, Christopher, J.
A tension between perspectives that emphasize deterministic versus stochastic processes has sparked controversy in ecology since pre-Darwinian times. The most recent manifestation of the contrasting perspectives arose with Hubbell’s proposed “neutral theory”, which hypothesizes a paramount role for stochasticity in ecological community composition. Here we shall refer to the deterministic and the stochastic perspectives as the niche-based and neutral-based research programs, respectively. Our goal is to represent these perspectives in the context of Lakatos’ notion of a scientific research program. We argue that the niche-based program exhibits all the characteristics of a robust, progressive research program, including the ability to deal with disconfirming data by generating new testable predictions within the program. In contrast, the neutral-based program succeeds as a mathematical tool to capture, as epiphenomena, broad-scale patterns of ecological communities but appears to handle disconfirming data by incorporating hypotheses and assumptions from outside the program, specifically, from the niche-based program. We conclude that the neutral research program fits the Lakatosian characterization of a degenerate research program.
Post print version of article may differ from published version. The final publication is available at springerlink.com; DOI:10.1007/s10539-018-9657-8
2019-02-01T00:00:00ZBenzimidazoles as Metal-Free and Recyclable Hydrides for CO2 Reduction to Formate
http://hdl.handle.net/10027/23360
Benzimidazoles as Metal-Free and Recyclable Hydrides for CO2 Reduction to Formate
Lim, Chern-Hooi; Ilic, Stefan; Alherz, Abdulaziz; Worrell, Brady T.; Bacon, Samuel S.; Hynes, James T.; Glusac, Ksenija D.; Musgrave, Charles B.
We report a novel metal-free chemical reduction of CO2 by a recyclable benzimidazole-based organo-hydride, whose choice was guided by quantum chemical calculations. Notably, benzimidazole-based hydride donors rival the hydride-donating abilities of noble metal-based hydrides such as [Ru(tpy)(bpy)H]+ and [Pt(depe)2H]+. Chemical CO2 reduction to the formate anion (HCOO) was carried out in the absence of biological enzymes, a sacrificial Lewis acid, or a base to activate the substrate or reductant. 13CO2 experiments confirmed the formation of H13COO by CO2 reduction with the formate product characterized by 1H-NMR and 13C-NMR spectroscopies, and ESI-MS. The highest formate yield of 66% was obtained in the presence of potassium tetrafluoroborate under mild conditions. The likely role of exogenous salt additives in this reaction is to stabilize and shift the equilibrium towards the ionic products. After CO2 reduction, the benzimidazole-based hydride donor was quantitatively oxidized to its aromatic benzimidazolium cation, establishing its recyclability. In addition, we electrochemically reduced the benzimidazolium cation to its organo-hydride form in quantitative yield, demonstrating its potential for electrocatalytic CO2 reduction. These results serve as a proof of concept for the electrocatalytic reduction of CO2 by sustainable, recyclable and metal-free organo-hydrides.
Copyright @ American Chemical Society.
2018-11-27T00:00:00Z