Volume Fractions of the Kinematic "Near-Critical" Sets of the Quantum Ensemble Control Landscape

An estimate is derived for the volume fraction of a subset $C_{\epsilon}^{P} = \{U : ||grad J(U)|\leq {\epsilon}\}\subset\mathrm{U}(N)$ in the neighborhood of the critical set $C^{P}\simeq\mathrm{U}(\mathbf{n})P\mathrm{U}(\mathbf{m})$ of the kinematic quantum ensemble control landscape J(U) = Tr(U\rho U' O), where $U$ represents the unitary time evolution operator, {\rho} is the initial density matrix of the ensemble, and O is an observable operator. This estimate is based on the Hilbert-Schmidt geometry for the unitary group and a first-order approximation of $||grad J(U)||^2$. An upper bound on these near-critical volumes is conjectured and supported by numerical simulation, leading to an asymptotic analysis as the dimension $N$ of the quantum system rises in which the volume fractions of these "near-critical" sets decrease to zero as $N$ increases. This result helps explain the apparent lack of influence exerted by the many saddles of $J$ over the gradient flow.Comment: 27 pages, 1 figur

Mapping nanoscale electrostatic field fluctuations around graphene dislocation cores using four-dimensional scanning transmission electron microscopy (4D-STEM)

Defects in crystalline lattices cause modulation of the atomic density, and this leads to variations in the associated electrostatics at the nanoscale. Mapping these spatially varying charge fluctuations using transmission electron microscopy has typically been challenging due to complicated contrast transfer inherent to conventional phase contrast imaging. To overcome this, we used four-dimensional scanning transmission electron microscopy (4D-STEM) to measure electrostatic fields near point dislocations in a monolayer. The asymmetry of the atomic density in a (1,0) edge dislocation core in graphene yields a local enhancement of the electric field in part of the dislocation core. Through experiment and simulation, the increased electric field magnitude is shown to arise from "long-range" interactions from beyond the nearest atomic neighbor. These results provide insights into the use of 4D-STEM to quantify electrostatics in thin materials and map out the lateral potential variations that are important for molecular and atomic bonding through Coulombic interactions

Haemodynamics and oxygenation improvement induced by high frequency percussive ventilation in a patient with hypoxia following cardiac surgery: a case report

<p>Abstract</p> <p>Introduction</p> <p>High frequency percussive ventilation is a ventilatory technique that delivers small bursts of high flow respiratory gas into the lungs at high rates. It is classified as a pneumatically powered, pressure-regulated, time-cycled, high-frequency flow interrupter modality of ventilation. High frequency percussive ventilation improves the arterial partial pressure of oxygen with the same positive end expiratory pressure and fractional inspiratory oxygen level as conventional ventilation using a minor mean airway pressure in an open circuit. It reduces the barotraumatic events in a hypoxic patient who has low lung-compliance. To the best of our knowledge, there have been no papers published about this ventilation modality in patients with severe hypoxaemia after cardiac surgery.</p> <p>Case presentation</p> <p>A 75-year-old Caucasian man with an ejection fraction of 27 percent, developed a lung infection with severe hypoxaemia [partial pressure of oxygen/fractional inspiratory oxygen of 90] ten days after cardiac surgery. Conventional ventilation did not improve the gas exchange. He was treated with high frequency percussive ventilation for 12 hours with a low conventional respiratory rate (five per minute). His cardiac output and systemic and pulmonary pressures were monitored.</p> <p>Compared to conventional ventilation, high frequency percussive ventilation gives an improvement of the partial pressure of oxygen from 90 to 190 mmHg with the same fractional inspiratory oxygen and positive end expiratory pressure level. His right ventricular stroke work index was lowered from 19 to seven g-m/m²/beat; his pulmonary vascular resistance index from 267 to 190 dynes•seconds/cm⁵/m²; left ventricular stroke work index from 28 to 16 gm-m/m²/beat; and his pulmonary arterial wedge pressure was lowered from 32 to 24 mmHg with a lower mean airway pressure compared to conventional ventilation. His cardiac index (2.7 L/min/m²) and ejection fraction (27 percent) did not change.</p> <p>Conclusion</p> <p>Although the high frequency percussive ventilation was started ten days after the conventional ventilation, it still improved the gas exchange. The reduction of right ventricular stroke work index, left ventricular stroke work index, pulmonary vascular resistance index and pulmonary arterial wedge pressure is directly related to the lower respiratory mean airway pressure and the consequent afterload reduction.</p

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Assessment of Surface Water Contamination from Coalbed Methane Fracturing-Derived Volatile Contaminants in Sullivan County, Indiana, USA

There is a growing concern over the contamination of surface water and the associated environmental and public health consequences from the recent proliferation in hydraulic fracturing in the USA. Petroleum hydrocarbon-derived contaminants of concern [benzene, toluene, ethylbenzene, and xylene (BTEX)] and various dissolved cations and anions were spatially determined in surface waters around 14 coalbed methane fracking wells in Sullivan County, IN, USA. At least one BTEX was detected in 69% of sampling sites (n=13) and 23% of sampling sites were found to be contaminated with all of the BTEX. Toluene was the most common BTEX compound detected across all sites, both upstream and downstream from coalbed methane fracking sites. The calcium (~60 ppm) and sulfates (~175 ppm) were the dominant cations and anions, respectively, in surface water around the fracking sites. This study represents the first report of BTEX contamination in surface water from coalbed methane hydraulic fracturing wells

Ecological and evolutionary consequences of alternative sex-change pathways in fish

Sequentially hermaphroditic fish change sex from male to female (protandry) or vice versa (protogyny), increasing their fitness by becoming highly fecund females or large dominant males, respectively. These life-history strategies present different social organizations and reproductive modes, from near-random mating in protandry, to aggregate- and harem-spawning in protogyny. Using a combination of theoretical and molecular approaches, we compared variance in reproductive success (V k*) and effective population sizes (N e) in several species of sex-changing fish. We observed that, regardless of the direction of sex change, individuals conform to the same overall strategy, producing more offspring and exhibiting greater V k* in the second sex. However, protogynous species show greater V k*, especially pronounced in haremic species, resulting in an overall reduction of N e compared to protandrous species. Collectively and independently, our results demonstrate that the direction of sex change is a pivotal variable in predicting demographic changes and resilience in sex-changing fish, many of which sustain highly valued and vulnerable fisheries worldwide

The Journal of Microelectronic Research 2005

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