Every set is “symmetric” for some function

Let 〈h _n 〉 denote a sequence of positive real numbers. We show that for every set A ? ? there exists a function f: ? → ω such that A = {x ∈ ?: (∈〈h _n 〉)[h _n ↘ 0 & (? _n ∈ ?)(f(x ? h _n ) = f(x + h _n ) = f(x))]}. This solves a problem of K. Ciesielski, K. Muthuvel and A. Nowik.     

Evaluation of non-selective refocusing pulses for 7 T MRI

There is a continuing need for improved RF pulses that achieve proper refocusing in the context of ultra-high field (≥ 7 T) human MRI. Simple block or sinc pulses are highly susceptible to RF field inhomogeneities, and adiabatic pulses are generally considered too SAR intensive for practical use at 7 T. The performance of the array of pulses falling between these extremes, however, has not been systematically evaluated. The aim of this work was to compare the performances of 21 non-selective refocusing pulses spanning a range of durations and SAR levels. The evaluation was based upon simulations and both phantom and in vivo human brain experiments conducted at 7 T. Tested refocusing designs included block, composite block, BIR-4, hyperbolic secant, and numerically optimized composite waveforms. These pulses were divided into three SAR classes and two duration categories, and, based on signal gain in a 3-D spin echo sequence, practical recommendations on usage are made within each category. All evaluated pulses were found to produce greater volume-averaged signals relative to a 180° block pulse. Although signal gains often come with the price of increased SAR or duration, some pulses were found to result in significant signal enhancement while also adhering to practical constraints. This work demonstrates the signal gains and losses realizable with single-channel refocusing pulse designs and should assist in the selection of suitable refocusing pulses for practical 3-D spin-echo imaging at 7 T. It further establishes a reference against which future pulses and multi-channel designs can be compared.     

Langevin Picture of Lévy Walks and Their Extensions

In this paper we derive Langevin picture of Lévy walks. Applying recent advances in the theory of coupled continuous time random walks we find a limiting process of the properly scaled Lévy walk. Next, we introduce extensions of Levy walks, in which jump sizes are some functions of waiting times. We prove that under proper scaling conditions, such generalized Lévy walks converge in distribution to the appropriate limiting processes. We also derive the corresponding fractional diffusion equations and investigate behavior of the mean square displacements of the limiting processes, showing that different coupling functions lead to various types of anomalous diffusion.     

On the relation between correlation dimension,approximate entropy and sample entropy parameters,and a fast algorithm for their calculation

We explore the relation between correlation dimension, approximate entropy and sample entropy parameters, which are commonly used in nonlinear systems analysis. Using theoretical considerations we identify the points which are shared by all these complexity algorithms and show explicitly that the above parameters are intimately connected and mutually interdependent. A new geometrical interpretation of sample entropy and correlation dimension is provided and the consequences for the interpretation of sample entropy, its relative consistency and some of the algorithms for parameter selection for this quantity are discussed. To get an exact algorithmic relation between the three parameters we construct a very fast algorithm for simultaneous calculations of the above, which uses the full time series as the source of templates, rather than the usual 10%. This algorithm can be used in medical applications of complexity theory, as it can calculate all three parameters for a realistic recording of 10⁴${10}^4$ points within minutes with the use of an average notebook computer.     

Long memory in patterns of mobile phone usage

In this article we show that usage of a mobile phone, i.e. daily series of number of calls made by a customer, exhibits long memory. We use a sample of 4502 postpaid users from a Polish mobile operator and study their two-year billing history. We estimate Hurst exponent by nine estimators: aggregated variance method, differencing the variance, absolute values of the aggregated series, Higuchi’s method, residuals of regression, the R/S method, periodogram method, modified periodogram method and Whittle estimator. We also analyze empirically relations between estimators. Long memory implies an inertial effect in clients’ behavior which may be used by mobile operators to accelerate usage and gain additional profit.     

Mechanical Properties of Poly(dimethylsiloxane)-block-poly(2-methyloxazoline) Polymersomes Probed by Atomic Force Microscopy

Poly(dimethylsiloxane)-block-poly(2-methyloxazoline) (PDMS-b-PMOXA) vesicles were characterized by a combination of dynamic light scattering (DLS), cryogenic transmission electron microscopy (cryo-TEM), and atomic force microscopy imaging and force spectroscopy (AFM). From DLS data, a hydrodynamic radius of ～150 nm was determined, and cryo-TEM micrographs revealed a bilayer thickness of ～16 nm. In AFM experiments on a silicon wafer substrate, adsorption led to a stable spherical caplike conformation of the polymersomes, whereas on mica, adsorption resulted also in vesicle fusion and formation of bilayer patches or multilayer stacks. This indicates a delicate balance between the mechanical stability of PDMS-b-PMOXA polymersomes on one hand and the driving forces for spreading on the other. A Young's modulus of 17 ± 11 MPa and a bending modulus of 7 ± 5 × 10(-18) J were derived from AFM force spectroscopy measurements. Therefore, the elastic response of the PDMS-b-PMOXA polymersomes to external stimuli is much closer to that of lipid vesicles compared to other types of polymersomes, such as polystyrene-block-poly(acrylic acid) (PS-b-PAA).     

Purification and electrophoretic characterization of bovine conglutinin

In this study a two-stage procedure for purification of conglutinin using affinity and ion-exchange chromatography was developed. To isolate conglutinin from bovine serum, its unique ability to bind to complement component iC3b was exploited. Incubation of bovine serum with chromatographic beads (TSK, Toyopearl HW-75 F) at 37 °C allows for iC3b deposition and subsequent binding of conglutinin. A single protein fraction eluted with ethylenediaminetetraacetic acid (EDTA) was then separated on an ion-exchange column in an NaCl gradient. The purification was evaluated by SDS-PAGE and western blotting. Conglutinin analyzed by SDS-PAGE under reducing conditions showed two main bands at 41 and 47 kDa and eight weaker bands. Nonreduced conglutinin appeared as a ladder pattern composed of many fractions ranging from 34 to 630 kDa. The bands at 34, 153, 174, 247, 338 and 387 kDa displayed the highest optical density. In the native conglutinin profile four fractions were observed, and the pI of this protein was below 8.5. The presence of sugar residues in the conglutinin molecule was detected using Schiff's reagent.     

One-step synthesis of reusable, polymer-supported tri-alkyl phosphine ligands. Application in Suzuki-Miyaura and alkoxycarbonylation reactions

A simple, efficient one-step route to polystyrene-supported trialkylphosphine ligands is reported. These polymer-supported alkyl phosphine ligands proved to be highly active for Suzuki-Miyaura reactions and in alkoxycarbonylation reactions. The palladium loaded polymer-supported catalysts can be recycled several times with only minimal loss of catalyst activity.     

Novel thermolabile protecting groups with higher stability at ambient temperature

Novel thermolabile hydroxyl protecting groups of increased thermostability are proposed. The stability of these groups at different temperatures ranges has been determined. The 2-pyridyl-N-(2,4-difluorobenzyl)aminoethyl unit was selected as stable at ambient temperature and very labile at increased temperature. The half-life times for the best groups were established. Application of this chemistry to the protection of different hydroxyl groups of thymidine was also demonstrated.