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

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

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

Anatomical characteristics of the lingual foramen in ancient skulls: a cone beam computed tomography study in an Anatolian population

Background: The purpose of this study is to evaluate the anatomical features of lingual foramina and their bony canals in Anatolian ancient mandibles (9–10th century) by using cone beam computed tomography (CBCT). Materials and methods: Fifty-eight ancient dry mandibles were scanned with CBCT. Lingual foramina were grouped into midline, paramedian, posterior foramina and combination of these groups. Midline group was also classified according to internal surface of the mandible (gonial tubercles [GTs]). The incidence, vertical distance and diameter of lingual foramina were measured according to age groups and gender. Results: The incidence of the lingual foramen was 96.6%. Midline of the symphysis had the highest incidence (34.4%) of foramina (p &lt; 0.05), followed by both midline and paramedian type (32.8%; p &lt; 0.05). Classification in terms of GT represented class 3 as the most encountered group (28.6%). Number of foramina observed in the mandibles ranged from 0 to 6 with the incidence of 3.4% and 32.8%, respectively. The male and &lt; 35 years groups presented larger measurement values in midline region (p &lt; 0.05). Conclusions: Mandibular lingual foramina and bony canals are frequently present in ancient mandibles. When compared with modern subjects, similar findings are observed according to published literatures. CBCT is also proved to be an effective imaging modality in the detection of lingual foramina and canals in anthropological studies

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

Lithium-mediated downregulation of PKB/Akt and cyclin E with growth inhibition in hepatocellular carcinoma cells

We studied in vitro effects of glycogen synthase kinase 3β (GSK3β)-inhibitor lithium on the growth of hepatocellular carcinoma (HCC) cells. Lithium induced strong growth inhibition (&gt;70%) in 75% (n = 9 of 12) of cell lines, apparently independent from the status of major genes that are mutated in HCC including p53, p16INK4a, β-catenin and Axin1. Comparative studies with a growth-sensitive Huh7 and growth-resistant Hep40 cell lines showed that lithium induces growth arrest in Huh7 cells but not in Hep40 cells. Lithium induced the accumulation of N-terminally phosphorylated inactive form of GSK3β with concomitant increase in β-catenin and β-catenin/TCF transcriptional activity in both cell lines. This suggests that lithium-mediated HCC growth inhibition is independent of its well-known stimulatory effect on Wnt-β-catenin signaling. The main differences between Huh7 and Hep40 responses to lithium treatment were observed at the levels PKB/Akt and cyclin E proteins. Lithium induced depletion of both proteins in growth-sensitive Huh7, but not in growth-resistant Hep40 cells. PKB/Akt and Cyclin E are 2 major proteins that are known to be constitutively active in HCC. The targeting of both proteins with lithium may be the main reason why most HCC cells are responsive to lithium-mediated growth inhibition, independent of their p53, retinoblastoma and Wnt-β-catenin pathways. The exploration of molecular mechanisms involved in lithium-mediated growth inhibition in relation with PKB/Akt and cyclin E downregulation may provide new insights for therapy of liver tumors. © 2005 Wiley-Liss, Inc

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

Symmetrized mean-field description of magnetic instabilities in k-(BEDT-TTF)_2Cu[N(CN)]_2 Y salts

We present a novel and convenient mean-field method, and apply it to study the metallic/antiferromagnetic interface of k-(BEDT-TTF)_2Cu[N(CN)]_2 Y organic superconductors (BEDT_TTF is bis-ethylen-dithio-tetrathiafulvalene, Y=Cl, Br). The method, which fully exploits the crystal symmetry, allows one to obtain the mean-field solution of the 2D Hubbard model for very large lattices, up to 6x10^5 sites, yielding a reliable description of the phase boundary in a wide region of the parameter space. The metal/antiferromagnet transtion appears to be second order, except for a narrow region of the parameter space, where the transition is very sharp and possibly first order. The cohexistence of metallic and antiferromagnetic properties is only observed for the transient state in the case of smooth second order transitions. The relevance of the present resaults to the complex experimental behavior of centrosymmetric k-phase BEDT-TTF salts is discussed.Comment: 9 pages in PS format, 7 figures (included in PS), 1 tabl