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The author considers the heat equation in dimension one with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous w.r.t. the Lebesgue measure, neither in space nor in time. Under some assumptions the author gives statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions.

Three cDNAs encoding purple acid phosphatase (PAP) were cloned from potato (Solanum tuberosum L. cv. Desiree) and expression of the corresponding genes was characterised. StPAP1 encodes a low-molecular weight PAP clustering with mammalian, cyanobacterial, and other plant PAPs. It was highly expressed in stem and root and its expression did not change in response to phosphorus (P) deprivation. StIPAP2 and StPAP3 code for high-molecular weight PAPs typical for plants. Corresponding gene expression was shown to be responsive to the level of P supply, with transcripts of StPAP2 and StPAP3 being most abundant in P-deprived roots or both stem and roots, respectively. Root colonisation by arbuscular mycorrhizal fungi had no effect on the expression of any of the three PAP genes. StIPAP1 mRNA is easily detectable along the root axis, including root hairs, but is barely detectable in root tips. In contrast, both StPAP2 and StPAP3 transcripts are abundant along the root axis, but absent in root hairs, and are most abundant in the root tip. All three PAPs described contain a predicted N-terminal secretion signal and could play a role in extracellular P scavenging, P mobilisation from the rhizosphere, or cell wall regeneration

A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems

We propose two methods that reduce the post-nonlinear blind source separation problem (PNL-BSS) to a linear BSS problem. The first method is based on the concept of maximal correlation: we apply the alternating conditional expectation (ACE) algorithm-a powerful technique from nonparametric statistics-to approximately invert the componentwise nonlinear functions. The second method is a Gaussianizing transformation, which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately Gaussian distributed. This heuristic, but simple and efficient procedure works as good as the ACE method. Using the framework provided by ACE, convergence can be proven. The optimal transformations obtained by ACE coincide with the sought-after inverse functions of the nonlinearitics. After equalizing the nonlinearities, temporal decorrelation separation (TDSEP) allows us to recover the source signals. Numerical simulations testing "ACE-TD" and "Gauss-TD" on realistic examples are performed with excellent results

We discuss the role of gravitational excitons/radions in different cosmological scenarios. Gravitational excitons are massive moduli fields which describe conformal excitations of the internal spaces and which, due to their Planck-scale suppressed coupling to matter fields, are WIMPs. It is demonstrated that, depending on the concrete scenario, observational cosmological data set strong restrictions on the allowed masses and initial oscillation amplitudes of these particles

We investigate noise-controlled resonant response of active media to weak periodic forcing, both in excitable and oscillatory regimes. In the excitable regime, we find that noise-induced irregular wave structures can be reorganized into frequency-locked resonant patterns by weak signals with suitable frequencies. The resonance occurs due to a matching condition between the signal frequency and the noise-induced inherent time scale of the media. m:1 resonant regions similar to the Arnold tongues in frequency locking of self-sustained oscillatory media are observed. In the self-sustained oscillatory regime, noise also controls the oscillation frequency and reshapes significantly the Arnold tongues. The combination of noise and weak signal thus could provide an efficient tool to manipulate active extended systems in experiments

The optical, structural, and electrical properties of thin layers made from poly(3-hexylthiophene) (P3HT) samples of different molecular weights are presented. As reported in a previous paper by Kline et al., Adv. Mater 2003, 15, 1519, the mobilities of these layers are a strong function of the molecular weight, with the largest mobility found for the largest molecular weight. Atomic force microscopy studies reveal a complex polycrystalline morphology which changes considerably upon annealing. X-ray studies show the occurrence of a layered phase for all P3HT fractions, especially after annealing at 1.50 degreesC . However, there is no clear correlation between the differences in the transport properties and the data from structural investigations. In order to reveal the processes limiting the mobility in these layers, the transistor properties were investigated as a function of temperature. The mobility decreases continuously with increasing temperatures; with the same trend pronounced thermochromic effects of the P3HT films occur. Apparently, the polymer chains adopt a more twisted, disordered conformation at higher temperatures, leading to interchain transport barriers. We conclude that the backbone conformation of the majority of the bulk material rather than the crystallinity of the layer is the most crucial parameter controlling the charge transport in these P3HT layers. This interpretation is supported by the significant blue-shift of the solid-state absorption spectra with decreasing molecular weight, which is indicative of a larger distortion of the P3HT backbone in the low-molecular weight P3HT layers

Stofftransport in einem Lösseinzugsgebiet: Experimentelle Evidenz und numerische Modellierung.
(2004)

Predictability of hydrologic response at the plot and catchment scales: Role of initial conditions
(2004)

This paper examines the effect of uncertain initial soil moisture on hydrologic response at the plot scale (1 m2) and the catchment scale (3.6 km2) in the presence of threshold transitions between matrix and preferential flow. We adopt the concepts of microstates and macrostates from statistical mechanics. The microstates are the detailed patterns of initial soil moisture that are inherently unknown, while the macrostates are specified by the statistical distributions of initial soil moisture that can be derived from the measurements typically available in field experiments. We use a physically based model and ensure that it closely represents the processes in the Weiherbach catchment, Germany. We then use the model to generate hydrologic response to hypothetical irrigation events and rainfall events for multiple realizations of initial soil moisture microstates that are all consistent with the same macrostate. As the measures of uncertainty at the plot scale we use the coefficient of variation and the scaled range of simulated vertical bromide transport distances between realizations. At the catchment scale we use similar statistics derived from simulated flood peak discharges. The simulations indicate that at both scales the predictability depends on the average initial soil moisture state and is at a minimum around the soil moisture value where the transition from matrix to macropore flow occurs. The predictability increases with rainfall intensity. The predictability increases with scale with maximum absolute errors of 90 and 32% at the plot scale and the catchment scale, respectively. It is argued that even if we assume perfect knowledge on the processes, the level of detail with which one can measure the initial conditions along with the nonlinearity of the system will set limits to the repeatability of experiments and limits to the predictability of models at the plot and catchment scales.

[1] This paper examines the effect of uncertain initial soil moisture on hydrologic response at the plot scale (1 m(2)) and the catchment scale (3.6 km(2)) in the presence of threshold transitions between matrix and preferential flow. We adopt the concepts of microstates and macrostates from statistical mechanics. The microstates are the detailed patterns of initial soil moisture that are inherently unknown, while the macrostates are specified by the statistical distributions of initial soil moisture that can be derived from the measurements typically available in field experiments. We use a physically based model and ensure that it closely represents the processes in the Weiherbach catchment, Germany. We then use the model to generate hydrologic response to hypothetical irrigation events and rainfall events for multiple realizations of initial soil moisture microstates that are all consistent with the same macrostate. As the measures of uncertainty at the plot scale we use the coefficient of variation and the scaled range of simulated vertical bromide transport distances between realizations. At the catchment scale we use similar statistics derived from simulated flood peak discharges. The simulations indicate that at both scales the predictability depends on the average initial soil moisture state and is at a minimum around the soil moisture value where the transition from matrix to macropore flow occurs. The predictability increases with rainfall intensity. The predictability increases with scale with maximum absolute errors of 90 and 32% at the plot scale and the catchment scale, respectively. It is argued that even if we assume perfect knowledge on the processes, the level of detail with which one can measure the initial conditions along with the nonlinearity of the system will set limits to the repeatability of experiments and limits to the predictability of models at the plot and catchment scales

A statistical model describing the propensity for protein aggregation is presented. Only amino-acid hydrophobicity values and calculated net charge are used for the model. The combined effects of hydrophobic patterns as computed by the signal analysis technique, recurrence quantification, plus calculated net charge were included in a function emphasizing the effect of singular hydrophobic patches which were found to be statistically significant for predicting aggregation propensity as quantified by fluorescence studies obtained from the literature. These results suggest preliminary evidence for a mesoscopic principle for protein folding/aggregation. (C) 2004 Elsevier B.V. All rights reserved

The presence of partially folded intermediates along the folding funnel of proteins has been suggested to be a signature of potentially aggregating systems. Many studies have concluded that metastable, highly flexible intermediates are the basic elements of the aggregation process. In a previous paper, we demonstrated how the choice between aggregation and folding behavior was influenced by hydrophobicity distribution patterning along the sequence, as quantified by recurrence quantification analysis (RQA) of the Myiazawa-Jernigan coded primary structures. In the present paper, we tried to unify the "partially folded intermediate" and "hydrophobicity/charge" models of protein aggregation verifying the ability of an empirical relation, developed for rationalizing the effect of different mutations on aggregation propensity of acyl-phosphatase and based on the combination of hydrophobicity RQA and charge descriptors, to discriminate in a statistically significant way two different protein populations: (a) proteins that fold by a process passing by partially folded intermediates and (b) proteins that do not present partially folded intermediates

The article starts with an overview of modernization theories, its history of ups and downs as well as its present status. This first part is followed by an analysis of basic social structure distributions and trends in human development in selected countries. One major focal point of the paper is the Non-Western world and the Arab countries, in particular. The author looks at modernization and modernity in that region and comes to the conclusion that the Western world can no longer expect to be able to simply export its own values and its way of life to the rest of the world.