6,056 research outputs found

    The hydrogen atom in an electric field: Closed-orbit theory with bifurcating orbits

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    Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent simplicity, a semiclassical quantization of this system by means of closed-orbit theory has not been achieved so far. It is the aim of this paper to close that gap. We first present a detailed analytic study of the closed classical orbits and their bifurcations. We then derive a simple form of the uniform semiclassical approximation for the bifurcations that is suitable for an inclusion into a closed-orbit summation. By means of a generalized version of the semiclassical quantization by harmonic inversion, we succeed in calculating high-quality semiclassical spectra for the hydrogen atom in an electric field

    Properties of cage rearrangements observed near the colloidal glass transition

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    We use confocal microscopy to study the motions of particles in concentrated colloidal systems. Near the glass transition, diffusive motion is inhibited, as particles spend time trapped in transient ``cages'' formed by neighboring particles. We measure the cage sizes and lifetimes, which respectively shrink and grow as the glass transition approaches. Cage rearrangements are more prevalent in regions with lower local concentrations and higher disorder. Neighboring rearranging particles typically move in parallel directions, although a nontrivial fraction move in anti-parallel directions, usually from pairs of particles with initial separations corresponding to the local maxima and minima of the pair correlation function g(r)g(r), respectively.Comment: 5 pages, 4 figures; text & figures revised in v

    Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis

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    We investigate how extreme loss of data affects the scaling behavior of long-range power-law correlated and anti-correlated signals applying the DFA method. We introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of correlations. These surrogate signals are characterized by: (i) the DFA scaling exponent α\alpha of the original correlated signal, (ii) the percentage pp of the data removed, (iii) the average length μ\mu of the removed (or remaining) data segments, and (iv) the functional form of the distribution of the length of the removed (or remaining) data segments. We find that the {\it global} scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90%. In contrast, the global scaling of anti-correlated signals changes to uncorrelated behavior even when a very small fraction of the data is lost. These observations are confirmed on the examples of human gait and commodity price fluctuations. We systematically study the {\it local} scaling behavior of signals with missing data to reveal deviations across scales. We find that for anti-correlated signals even 10% of data loss leads to deviations in the local scaling at large scales from the original anti-correlated towards uncorrelated behavior. In contrast, positively correlated signals show no observable changes in the local scaling for up to 65% of data loss, while for larger percentage, the local scaling shows overestimated regions (with higher local exponent) at small scales, followed by underestimated regions (with lower local exponent) at large scales. Finally, we investigate how the scaling is affected by the statistics of the remaining data segments in comparison to the removed segments

    Crossover behavior and multi-step relaxation in a schematic model of the cut-off glass transition

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    We study a schematic mode-coupling model in which the ideal glass transition is cut off by a decay of the quadratic coupling constant in the memory function. (Such a decay, on a time scale tau_I, has been suggested as the likely consequence of activated processes.) If this decay is complete, so that only a linear coupling remains at late times, then the alpha relaxation shows a temporal crossover from a relaxation typical of the unmodified schematic model to a final strongly slower-than-exponential relaxation. This crossover, which differs somewhat in form from previous schematic models of the cut-off glass transition, resembles light-scattering experiments on colloidal systems, and can exhibit a `slower-than-alpha' relaxation feature hinted at there. We also consider what happens when a similar but incomplete decay occurs, so that a significant level of quadratic coupling remains for t>>tau_I. In this case the correlator acquires a third, weaker relaxation mode at intermediate times. This empirically resembles the beta process seen in many molecular glass formers. It disappears when the initial as well as the final quadratic coupling lies on the liquid side of the glass transition, but remains present even when the final coupling is only just inside the liquid (so that the alpha relaxation time is finite, but too long to measure). Our results are suggestive of how, in a cut-off glass, the underlying `ideal' glass transition predicted by mode-coupling theory can remain detectable through qualitative features in dynamics.Comment: 14 pages revtex inc 10 figs; submitted to pr

    How to pass the false-belief task before your fourth birthday.

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    The experimental record of the last three decades shows that children under 4 years old fail all sorts of variations on the standard false-belief task, whereas more recent studies have revealed that infants are able to pass nonverbal versions of the task. We argue that these paradoxical results are an artifact of the type of false-belief tasks that have been used to test infants and children: Nonverbal designs allow infants to keep track of a protagonist's perspective over a course of events, whereas verbal designs tend to disrupt the perspective-tracking process in various ways, which makes it too hard for younger children to demonstrate their capacity for perspective tracking. We report three experiments that confirm this hypothesis by showing that 3-year-olds can pass a suitably streamlined version of the verbal false-belief task. We conclude that young children can pass the verbal false-belief task provided that they are allowed to keep track of the protagonist's perspective without too much disruption

    Higher order glass-transition singularities in colloidal systems with attractive interactions

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    The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line, and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third order bifurcation point, i.e. in a A_3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth order A_4 (swallow-tail) singularity at a critical well width. Close to the A_3 and A_4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.Comment: 19 pages, 12 figures, Phys. Rev. E, in prin

    Comparative simulation study of colloidal gels and glasses

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    Using computer simulations, we identify the mechanisms causing aggregation and structural arrest of colloidal suspensions interacting with a short-ranged attraction at moderate and high densities. Two different non-ergodicity transitions are observed. As the density is increased, a glass transition takes place, driven by excluded volume effects. In contrast, at moderate densities, gelation is approached as the strength of the attraction increases. At high density and interaction strength, both transitions merge, and a logarithmic decay in the correlation function is observed. All of these features are correctly predicted by mode coupling theory

    Separated cross sections in \pi^0 electroproduction at threshold at Q^2 = 0.05 GeV^2/c^2

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    The differential cross sections \sigma_0=\sigma_T+\epsilon \sigma_L, \sigma_{LT}, and \sigma_{TT} of \pi^0 electroproduction from the proton were measured from threshold up to an additional center of mass energy of 40 MeV, at a value of the photon four-momentum transfer of Q^2= 0.05 GeV^2/c^2 and a center of mass angle of \theta=90^\circ. By an additional out-of-plane measurement with polarized electrons \sigma_{LT'} was determined. This showed for the first time the cusp effect above the \pi^+ threshold in the imaginary part of the s-wave. The predictions of Heavy Baryon Chiral Perturbation Theory are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.Comment: 6 pages, 4 figure

    Metastable Dynamics of the Hard-Sphere System

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    The reformulation of the mode-coupling theory (MCT) of the liquid-glass transition which incorporates the element of metastability is applied to the hard-sphere system. It is shown that the glass transition in this system is not a sharp one at the special value of the density or the packing fraction, which is in contrast to the prediction by the conventional MCT. Instead we find that the slowing down of the dynamics occurs over a range of values of the packing fraction. Consequently, the exponents governing the sequence of time relaxations in the intermediate time regime are given as functions of packing fraction with one additional parameter which describes the overall scale of the metastable potential energy for defects in the hard-sphere system. Implications of the present model on the recent experiments on colloidal systems are also discussed.Comment: 21 pages, 5 figures (available upon request), RevTEX3.0, JFI Preprint

    Proteomics biomarker discovery for individualized prevention of familial pancreatic cancer using statistical learning

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    BACKGROUND: The low five-year survival rate of pancreatic ductal adenocarcinoma (PDAC) and the low diagnostic rate of early-stage PDAC via imaging highlight the need to discover novel biomarkers and improve the current screening procedures for early diagnosis. Familial pancreatic cancer (FPC) describes the cases of PDAC that are present in two or more individuals within a circle of first-degree relatives. Using innovative high-throughput proteomics, we were able to quantify the protein profiles of individuals at risk from FPC families in different potential pre-cancer stages. However, the high-dimensional proteomics data structure challenges the use of traditional statistical analysis tools. Hence, we applied advanced statistical learning methods to enhance the analysis and improve the results’ interpretability. METHODS: We applied model-based gradient boosting and adaptive lasso to deal with the small, unbalanced study design via simultaneous variable selection and model fitting. In addition, we used stability selection to identify a stable subset of selected biomarkers and, as a result, obtain even more interpretable results. In each step, we compared the performance of the different analytical pipelines and validated our approaches via simulation scenarios. RESULTS: In the simulation study, model-based gradient boosting showed a more accurate prediction performance in the small, unbalanced, and high-dimensional datasets than adaptive lasso and could identify more relevant variables. Furthermore, using model-based gradient boosting, we discovered a subset of promising serum biomarkers that may potentially improve the current screening procedure of FPC. CONCLUSION: Advanced statistical learning methods helped us overcome the shortcomings of an unbalanced study design in a valuable clinical dataset. The discovered serum biomarkers provide us with a clear direction for further investigations and more precise clinical hypotheses regarding the development of FPC and optimal strategies for its early detection
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