Steady stokes flow with long-range correlations,fractal fourier spectrum,and anomalous transport

We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law, and the Fourier spectrum is neither discrete nor absolutely continuous. We demonstrate that spreading of the droplet of tracers in such flows is anomalously fast. Since the flow is equivalent to the integrable Hamiltonian system with 1 degree of freedom, this provides an example of integrable dynamics with long-range correlations, fractal power spectrum, and anomalous transport properties.     

Synthesis of rosefuran from citral

Conclusions The action of pyridinesulfotrioxide causes the conversion of the morpholine derivative of citral to rosefuran.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2614–2615, November, 1982.     

Updating kernel methods in spectral decomposition by affinity perturbations

Many machine learning based algorithms contain a training step that is done once. The training step is usually computational expensive since it involves processing of huge matrices. If the training profile is extracted from an evolving dynamic dataset, it has to be updated as some features of the training dataset are changed. This paper proposes a solution how to update this profile efficiently. Therefore, we investigate how to update the training profile when the data is constantly evolving. We assume that the data is modeled by a kernel method and processed by a spectral decomposition. In many algorithms for clustering and classification, a low dimensional representation of the affinity (kernel) graph of the embedded training dataset is computed. Then, it is used for classifying newly arrived data points. We present methods for updating such embeddings of the training datasets in an incremental way without the need to perform the entire computation upon the occurrences of changes in a small number of the training samples. Efficient computation of such an algorithm is critical in many web based applications.     

Whole-Object Fluorescence Lifetime Setup for Efficient Non-Imaging Quantitative Intracellular Fluorophore Measurements

In the present study we introduce a Whole-Object Fluorescence Life Time (wo-FLT) measurement approach for ease and a relatively inexpensive method of tracing alterations in intracellular fluorophore distribution and in the physical-chemical features of the microenvironments hosting the fluorophore. Two common fluorophores, Rhodamine 123 and Acridine Orange, were used to stain U937 cells which were incubated, with and without either Carbonyl cyanide 3-chlorphenylhydrazon or the apoptosis inducer H₂O₂. The wo-FLT, which is a non-imaging quantitative measurement, was able to detect several fluorescence decay components and corresponding weights in a single cell resolution. Following cell treatment, both decay time and weight were altered. Results suggest that the prominent factor responsible for these alterations and in some cases to a shift in emission spectrum as well, is the intracellular fluorophore local concentration. In this study it was demonstrated that the proposed wo-FLT method is superior to color fluorescence based imaging in cases where the emission spectrum of a fluorophore remains unchanged during the investigated process. The proposed wo-FLT approach may be of particular importance when direct imaging is impossible.     

Quantitative structure-activity relationship analysis of β-amyloid aggregation inhibitors

Inhibiting the aggregation process of the β-amyloid peptide is a promising strategy in treating Alzheimer’s disease. In this work, we have collected a dataset of 80 small molecules with known inhibition levels and utilized them to develop two comprehensive quantitative structure–activity relationship models: a Bayesian model and a decision tree model. These models have exhibited high predictive accuracy: 87% of the training and test sets using the Bayesian model and 89 and 93% of the training and test sets, respectively, by the decision tree model. Subsequently these models were used to predict the activities of several new potential β-amyloid aggregation inhibitors and these predictions were indeed validated by in vitro experiments. Key chemical features correlated with the inhibition ability were identified. These include the electro-topological state of carbonyl groups, AlogP and the number of hydrogen bond donor groups. The results demonstrate the feasibility of the developed models as tools for rapid screening, which could help in the design of novel potential drug candidates for Alzheimer’s disease.     

Radially symmetric minimizers for a p-Ginzburg Landau type energy in {\mathbb R^2}

We consider the minimization of a p-Ginzburg-Landau energy functional over the class of radially symmetric functions of degree one. We prove the existence of a unique minimizer in this class, and show that its modulus is monotone increasing and concave. We also study the asymptotic limit of the minimizers as p ?? ??. Finally, we prove that the radially symmetric solution is locally stable for 2?<?p????4.     

Global Stability of the Normal State of Superconductors in the Presence of a Strong Electric Current

We consider the time-dependent Ginzburg–Landau model of superconductivity in the presence of an electric current flowing through a two-dimensional wire. We show that when the current is sufficiently strong the solution converges in the long-time limit to the normal state. We provide two types of upper bounds for the critical current where such global stability is achieved: by using the principal eigenvalue of the magnetic Laplacian associated with the normal magnetic field, and through the norm of the resolvent of the linearized steady-state operator. In the latter case we estimate the resolvent norm in large domains by the norms of approximate operators defined on the plane and the half-plane. We also obtain a lower bound, in large domains, for the above critical current by obtaining the current for which the normal state looses its local stability.