Cell movement-for example, during embryogenesis or tumor metastasis-is a complex dynamical process resulting from an intricate interplay of multiple components of the cellular migration machinery. At first sight, the paths of migrating cells resemble those of thermally driven Brownian particles. However, cell migration is an active biological process putting a characterization in terms of normal Brownian motion into question. By analyzing the trajectories of wild-type and mutated epithelial (transformed Madin-Darby canine kidney) cells, we show experimentally that anomalous dynamics characterizes cell migration. A superdiffusive increase of the mean squared displacement, non-Gaussian spatial probability distributions, and power-law decays of the velocity autocorrelations is the basis for this interpretation. Almost all results can be explained with a fractional Klein-Kramers equation allowing the quantitative classification of cell migration by a few parameters. Thereby, it discloses the influence and relative importance of individual components of the cellular migration apparatus to the behavior of the cell as a whole. data analysis ͉ fractional dynamics ͉ non-Brownian motion N early all cells in the human body are mobile at a given time during their life cycle. Embryogenesis, wound-healing, immune defense, and the formation of tumor metastases are well known phenomena that rely on cell migration. Extensive experimental work revealed a precise spatial and temporal coordination of multiple components of the cellular migration machinery such as the actin cytoskeleton, cell-substrate and cell-cell interactions, and the activity of ion channels and transporters (1-4). These findings are the basis for detailed molecular models representing different microscopic aspects of the process of cell migration such as the protrusion of the leading edge of the lamellipodium, or actin dynamics (5). Mathematical continuum models, in contrast, focus on collective properties of the entire cell to explain requirements for the onset of motion and some typical features of cell motility (6). These models are usually limited to small spatiotemporal scales. Therefore, they provide little information about how the integration of protrusion of the lamellipodium, retraction of the rear part, and force transduction onto the extracellular matrix lead to the sustained long-term movement of the entire cell. This process is characterized by alternating phases of directed migration, changes of direction, and polarization. The coordinated interaction of these phases suggests the existence of intermittency (7) and of strong spatiotemporal correlations. It is therefore an important question whether the long-term movement of the entire cell can still be understood as a simple diffusive behavior like usual Brownian motion (8, 9) or whether more advanced concepts of dynamic modeling have to be applied (10, 11). Results and DiscussionWe performed migration experiments and analyzed the trajectories of two migrating transformed renal epithelial MadinDar...

On the basis of Quantum-Monte-Carlo results the evolution of the spectral weight A( k, ω) of the two-dimensional Hubbard model is studied from insulating to metallic behavior. As observed in recent photoemission experiments for cuprates, the electronic excitations display essentially doping-independent features: a quasiparticle-like dispersive narrow band of width of the order of the exchange interaction J and a broad valence-and conduction-band background. The continuous evolution is traced back to one and the same manybody origin: the doping-dependent antiferromagnetic spin-spin correlation.

On the basis of Quantum Monte Carlo simulations of the two-dimensional Hubbard model which cover the doping range from the under-to the over-doped regime, we find that the single-particle spectral weight A( k, ω) qualitatively reproduces both the momentum (d x 2 −y 2 -symmetry) and doping dependence of the pseudogap as found in photoemission experiments. The drastic doping dependence of the spin response χs( q, ω) which is sharp in both q (≈ (π, π)) and ω in the under-doped regime but broad and structureless otherwise, identifies remnants of the antiferromagnetic order as the driving mechanism behind the pseudogap and its evolution with doping.PACS numbers: 75.50.Ee,79.60.Bm Exciting progress in the microscopic understanding of high-T C superconductors has recently come from the observation of a normal-state pseudogap of order of the exchange energy J [1] and a lower energy excitation gap of the order of the superconducting gap [1][2][3][4][5]. Angleresolved photoemission spectroscopy (ARPES) demonstrated that both high-and low-energy gaps are consistent with d x 2 −y 2 -symmetry [1][2][3][4]. In addition, both gaps have a more or less identical doping dependence, which may be a key observation to unlocking the mystery of the cuprates: just below optimal hole concentration, the centroids in the spectral weight A( k, ω) near (π, 0) move to higher binding energy, and a portion of the large Fermi surface seems to disappear. These findings have been interpreted as the opening of a pseudogap with maximal energy J ∼ 200meV near (π, 0) [1]. Simultaneously, a normal-state gap with energy ∼ 20meV , inferred from the leading edge in A( k, ω), opens up in this under-doped regime. Both of these gaps vanish in the over-doped regime, and the superconducting gap also rapidly decreases [5]. This empirical correlation between the disappearance of the order J pseudogap and the decrease of superconducting pairing strength suggests that the high-energy features at (π, 0) are closely related to the pairing interaction [6].In this letter, we address the microscopic mechanism behind the opening of this pseudogap and its evolution from under-doped to over-doped regimes. We present Quantum Monte Carlo (QMC) simulation results on the two-dimensional Hubbard model with on-site interaction U = 8t which demonstrate that the single-particle spectral weight A( k, ω) reproduces the most salient ARPES features as function of doping. In particular, the QMC data reproduce the momentum (d x 2 −y 2 -symmetry) and doping dependence of the pseudogap.Earlier finite-temperature QMC work on the Hubbard model [7,8] has produced results showing a quasiparticle-like band with a dispersion below the Fermi level that is essentially unaffected by doping. On the other hand, groundstate exact diagonalizations [9,10] of the two-dimensional t − J model for small clusters around optimal doping find a signal in the spectral weight corresponding to an insulator-like "shadow" structure; at larger doping this signal vanishes. We present in this work first data of th...

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is inspired and guided by intuition gained from the successful use of ME methods in statistical mechanics. For experiments that cannot be repeated the resulting "entropic prior" is formally identical with the Einstein fluctuation formula. For repeatable experiments, however, the expected value of the entropy of the likelihood turns out to be relevant information that must be included in the analysis. The important case of a Gaussian likelihood is treated in detail.

The chemical erosion of carbon in interaction with a hydrogen plasma has been studied in detail in ion beam experiments, and erosion yield values are available as a function of ion energy and surface temperature. However, the conditions in the ITER divertor cannot be simulated by ion beam experiments, especially as far as ion flux is concerned.Therefore, a joint attempt was made through the EU Task Force on plasma-wall interaction and the international tokamak physics activity involving seven different fusion devices and plasma simulators to clarify the flux dependence. For each data point the local plasma conditions were normalized to an impact energy of 30 eV, care was taken to select data for a surface temperature close to the maximum yield or room temperature and the calibration of the diagnostic was performed in situ. Through this procedure the previous large scatter was significantly reduced, revealing a clear trend for a decreasing yield with increasing ion flux, . After the attribution of an error to each data point a fit using Bayesian probability analysis was performed, yielding a decrease in the erosion yield with −0.54 at high ion fluxes.