Quantum control and the Strocchi map

Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite real inner product which provides a geometrical interpretation of the measurement process. Together they endow the quantum Hilbert space with the structure of a K\"{a}ller manifold. Quantum control is discussed in this setting. Quantum time-evolution corresponds to smooth Hamiltonian dynamics and measurements to jumps in the phase space. This adds additional power to quantum control, non unitarily controllable systems becoming controllable by ``measurement plus evolution''. A picture of quantum evolution as Hamiltonian dynamics in a classical-like phase-space is the appropriate setting to carry over techniques from classical to quantum control. This is illustrated by a discussion of optimal control and sliding mode techniques.Comment: 16 pages Late

A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.Comment: Revtex, 29 pages (incl. figures

Concentrations of Polychlorinated Biphenyls (PCB’s), Chlorinated Pesticides, and Heavy Metals and Other Elements in Tissues of Belugas, Delphinapterus leucas, from Cook Inlet

Tissues from Cook Inlet beluga whales, Delphinapterus leucas, that were collected as part of the Alaska Marine Mammal Tissue Archival Project were analyzed for polychlorinated biphenyls (PCB’s), chlorinated pesticides, and heavy metals and other elements. Concentrations of total PCB’s (ΣPCB’s), total DDT (ΣDDT), chlordane compounds, hexachlorobenzene (HCB), dieldrin, mirex, toxaphene, and hexachlorocyclohexane (HCH) measured in Cook Inlet beluga blubber were compared with those reported for belugas from two Arctic Alaska locations (Point Hope and Point Lay), Greenland, Arctic Canada, and the highly contaminated stock from the St. Lawrence estuary in eastern Canada. The Arctic and Cook Inlet belugas had much lower concentrations (ΣPCB’s and ΣDDT were an order of magnitude lower) than those found in animals from the St. Lawrence estuary. The Cook Inlet belugas had the lowest concentrations of all (ΣPCB’s aver-aged 1.49 ± 0.70 and 0.79 ± 0.56 mg/kg wet mass, and ΣDDT averaged 1.35 ± 0.73 and 0.59 ± 0.45 mg/kg in males and females, respectively). Concentrations in the blubber of the Cook Inlet males were significantly lower than those found in the males of the Arctic Alaska belugas (ΣPCB’s and ΣDDT were about half). The lower levels in the Cook Inlet animals might be due to differences in contaminant sources, food web differences, or different age distributions among the animals sampled. Cook Inlet males had higher mean and median concentrations than did females, a result attributable to the transfer of these compounds from mother to calf during pregnancy and during lactation. Liver concentrations of cadmium and mercury were lower in the Cook Inlet belugas (most cadmium values were <1 mg/kg and mercury values were 0.704–11.42 mg/kg wet mass), but copper levels were significantly higher in the Cook Inlet animals (3.97–123.8 mg/kg wet mass) than in Arctic Alaska animals and similar to those reported for belugas from Hudson Bay. Although total mercury levels were the lowest in the Cook Inlet population, methylmercury concentrations were similar among all three groups of the Alaska animals examined (0.34–2.11 mg/kg wet mass). As has been reported for the Point Hope and Point Lay belugas, hepatic concentrations of silver were r

Cracking the code of oscillatory activity

Neural oscillations are ubiquitous measurements of cognitive processes and dynamic routing and gating of information. The fundamental and so far unresolved problem for neuroscience remains to understand how oscillatory activity in the brain codes information for human cognition. In a biologically relevant cognitive task, we instructed six human observers to categorize facial expressions of emotion while we measured the observers' EEG. We combined state-of-the-art stimulus control with statistical information theory analysis to quantify how the three parameters of oscillations (i.e., power, phase, and frequency) code the visual information relevant for behavior in a cognitive task. We make three points: First, we demonstrate that phase codes considerably more information (2.4 times) relating to the cognitive task than power. Second, we show that the conjunction of power and phase coding reflects detailed visual features relevant for behavioral response-that is, features of facial expressions predicted by behavior. Third, we demonstrate, in analogy to communication technology, that oscillatory frequencies in the brain multiplex the coding of visual features, increasing coding capacity. Together, our findings about the fundamental coding properties of neural oscillations will redirect the research agenda in neuroscience by establishing the differential role of frequency, phase, and amplitude in coding behaviorally relevant information in the brai

Stochastic Resonance of Ensemble Neurons for Transient Spike Trains: A Wavelet Analysis

By using the wavelet transformation (WT), we have analyzed the response of an ensemble of $N$ (=1, 10, 100 and 500) Hodgkin-Huxley (HH) neurons to {\it transient} $M$-pulse spike trains ($M=1-3$) with independent Gaussian noises. The cross-correlation between the input and output signals is expressed in terms of the WT expansion coefficients. The signal-to-noise ratio (SNR) is evaluated by using the {\it denoising} method within the WT, by which the noise contribution is extracted from output signals. Although the response of a single (N=1) neuron to sub-threshold transient signals with noises is quite unreliable, the transmission fidelity assessed by the cross-correlation and SNR is shown to be much improved by increasing the value of $N$: a population of neurons play an indispensable role in the stochastic resonance (SR) for transient spike inputs. It is also shown that in a large-scale ensemble, the transmission fidelity for supra-threshold transient spikes is not significantly degraded by a weak noise which is responsible to SR for sub-threshold inputs.Comment: 20 pages, 4 figure

Optimal Control of Molecular Motion Expressed Through Quantum Fluid Dynamics

A quantum fluid dynamic control formulation is presented for optimally manipulating atomic and molecular systems. In quantum fluid dynamic the control quantum system is expressed in terms of the probability density and the quantum current. This choice of variables is motivated by the generally expected slowly varying spatial-temporal dependence of the fluid dynamical variables. The quantum fluid dynamic approach is illustrated for manipulation of the ground electronic state dynamics of HCl induced by an external electric field.Comment: 18 pages, latex, 3 figure

Learning causal networks from systems biology time course data: an effective model selection procedure for the vector autoregressive process

Background: Causal networks based on the vector autoregressive (VAR) process are a promising statistical tool for modeling regulatory interactions in a cell. However, learning these networks is challenging due to the low sample size and high dimensionality of genomic data. Results: We present a novel and highly efficient approach to estimate a VAR network. This proceeds in two steps: (i) improved estimation of VAR regression coefficients using an analytic shrinkage approach, and (ii) subsequent model selection by testing the associated partial correlations. In simulations this approach outperformed for small sample size all other considered approaches in terms of true discovery rate (number of correctly identified edges relative to the significant edges). Moreover, the analysis of expression time series data from Arabidopsis thaliana resulted in a biologically sensible network. Conclusion: Statistical learning of large-scale VAR causal models can be done efficiently by the proposed procedure, even in the difficult data situations prevalent in genomics and proteomics. Availability: The method is implemented in R code that is available from the authors on request

Risk Factors for and Prediction of Post-Intubation Hypotension in Critically Ill Adults: A Multicenter Prospective Cohort Study

OBJECTIVE: Hypotension following endotracheal intubation in the ICU is associated with poor outcomes. There is no formal prediction tool to help estimate the onset of this hemodynamic compromise. Our objective was to derive and validate a prediction model for immediate hypotension following endotracheal intubation. METHODS: A multicenter, prospective, cohort study enrolling 934 adults who underwent endotracheal intubation across 16 medical/surgical ICUs in the United States from July 2015-January 2017 was conducted to derive and validate a prediction model for immediate hypotension following endotracheal intubation. We defined hypotension as: 1) mean arterial pressure \u3c 65 mmHg; 2) systolic blood pressure \u3c 80 mmHg and/or decrease in systolic blood pressure of 40% from baseline; 3) or the initiation or increase in any vasopressor in the 30 minutes following endotracheal intubation. RESULTS: Post-intubation hypotension developed in 344 (36.8%) patients. In the full cohort, 11 variables were independently associated with hypotension: increasing illness severity; increasing age; sepsis diagnosis; endotracheal intubation in the setting of cardiac arrest, mean arterial pressure \u3c 65 mmHg, and acute respiratory failure; diuretic use 24 hours preceding endotracheal intubation; decreasing systolic blood pressure from 130 mmHg; catecholamine and phenylephrine use immediately prior to endotracheal intubation; and use of etomidate during endotracheal intubation. A model excluding unstable patients’ pre-intubation (those receiving catecholamine vasopressors and/or who were intubated in the setting of cardiac arrest) was also developed and included the above variables with the exception of sepsis and etomidate. In the full cohort, the 11 variable model had a C-statistic of 0.75 (95% CI 0.72, 0.78). In the stable cohort, the 7 variable model C-statistic was 0.71 (95% CI 0.67, 0.75). In both cohorts, a clinical risk score was developed stratifying patients’ risk of hypotension. CONCLUSIONS: A novel multivariable risk score predicted post-intubation hypotension with accuracy in both unstable and stable critically ill patients. STUDY REGISTRATION: Clinicaltrials.gov identifier: NCT02508948 and Registered Report Identifier: RR2-10.2196/11101