Regular Languages of Thin Trees

An infinite tree is called thin if it contains only countably many infinite branches. Thin trees can be seen as intermediate structures between infinite words and infinite trees. In this work we investigate properties of regular languages of thin trees. Our main tool is an algebra suitable for thin trees. Using this framework we characterize various classes of regular languages: commutative, open in the standard topology, and definable in weak MSO logic among all trees. We also show that in various meanings thin trees are not as rich as all infinite trees. In particular we observe a collapse of the parity index to the level (1, 3) and a collapse of the topological complexity to co-analytic sets. Moreover, a gap property is shown: a regular language of thin trees is either weak MSO-definable among all trees or co-analytic-complete.     

Hydrophilic polycarbonate chips for generation of oil-in-water (O/W) and water-in-oil-in-water (W/O/W) emulsions

Modification of the surfaces of polycarbonate (PC) with the use of a solution of tin (II) chloride renders them hydrophilic. The surface draping is stable against exposure to water and to alcohols. Exposure to alkanes reduces but does not diminish the effect. The method is compatible—in using the same solvent and temperature—with the hydrophobic modification of PC (Jankowski et al. in Lab Chip 11:1151–1156, 2011). The combination of these methods makes it possible to generate single and multiple monodisperse emulsions with the use of flow-focusing junctions in systems made in PC—a material that is suitable for fabrication of multilayer, high-throughput microfluidic devices.     

Hydrophilic polycarbonate chips for generation of oil-in-water (O/W) and water-in-oil-in-water (W/O/W) emulsions

Modification of the surfaces of polycarbonate (PC) with the use of a solution of tin (II) chloride renders them hydrophilic. The surface draping is stable against exposure to water and to alcohols. Exposure to alkanes reduces but does not diminish the effect. The method is compatible—in using the same solvent and temperature—with the hydrophobic modification of PC Jankowski et al. ( Lab Chip 11:748–752, 2011). The combination of these methods makes it possible to generate single and multiple monodisperse emulsions with the use of flow-focusing junctions in systems made in PC—material that is suitable for fabrication of multilayer, high throughput microfluidic devices.     

Low-latency atomic broadcast in the presence of contention

The Atomic Broadcast algorithm described in this paper can deliver messages in two communication steps, even if multiple processes broadcast at the same time. It tags all broadcast messages with the local real time, and delivers all messages in the order of these timestamps. Both positive and negative statements are used: “m broadcast at time 51” vs. “no messages broadcast between times 31 and 51”. To prevent crashed processes from blocking the system, the -elected leader broadcasts negative statements on behalf of the processes it suspects () to have crashed. A new cheap Generic Broadcast algorithm is used to ensure consistency between conflicting statements. It requires only a majority of correct processes (n > 2f) and, in failure-free runs, delivers all non-conflicting messages in two steps. The main algorithm satisfies several new lower bounds, which are proved in this paper.     

Computing all efficient solutions of the biobjective minimum spanning tree problem

A common way of computing all efficient (Pareto optimal) solutions for a biobjective combinatorial optimisation problem is to compute first the extreme efficient solutions and then the remaining, non-extreme solutions. The second phase, the computation of non-extreme solutions, can be based on a “k-best” algorithm for the single-objective version of the problem or on the branch-and-bound method. A k-best algorithm computes the k-best solutions in order of their objective values. We compare the performance of these two approaches applied to the biobjective minimum spanning tree problem. Our extensive computational experiments indicate the overwhelming superiority of the k-best approach. We propose heuristic enhancements to this approach which further improve its performance.     

A Y-channel design for improving zeta potential and surface conductivity measurements using the current monitoring method

This study presents a new Y-channel design for measuring the zeta potential and surface conductance of a solid-liquid pairing using the current monitoring technique. The new design improves the throughput and reliability of the testing apparatus since the displacement between two solutions can be repeated many times without interfering with the experiments. It also increases the accuracy of the measurement by producing sharper start and end transitions for the current–time plot of the solution displacement process. In this design, efforts have been made to minimize the effects of electrolysis, Joule heating and undesired pressure driven flow on the measurements. An improvement on the current–time slope analysis is also presented. The Y-channel design was validated by comparing zeta potential measurements to published results. The zeta potential of several biological buffers relevant to the microfluidic community in plasma treated PDMS/PDMS and PDMS/Glass microchannels are presented. Preliminary studies of surface conductivity measurements using the Y-channel design were also conducted and are briefly discussed.     

On the robust control of nonlinear systems

In this paper we consider robust stabilization of the class of nonlinear plants of the form $$\dot x = f(x) + \sum\limits_{i = 1}^m {g_i } (x)u_i (t),$$ which are equivalent, under smooth state space coordinate transformations and nonlinear state feedback, to controllable systems. This approach is very sensitive for unknown parameters' values. Parameter adaptation may be used as a technique to robustify minimum-phase systems [3]. We give an example of a locally stable adaptive tracking system in which the last assumption is weakened. The minimum-phase plant considered in the paper is a current-controlled squirrel cage induction motor.     

Casein kinase 2 down-regulation and activation by polybasic peptides are mediated by acidic residues in the 55-64 region of the beta-subunit. A study with calmodulin as phosphorylatable substrate

The noncatalytic beta-subunit is responsible for the latency of casein kinase 2 (CK2) activity toward calmodulin. Twenty-one mutants of the beta-subunit bearing either deletions or Ala substitutions for charged residues in the 5-6, 55-70, and 171-178 sequences have been assayed for their ability to substitute for wild-type beta-subunit as a suppressor of activity toward calmodulin. The only mutations that reduced the ability of the beta-subunit to suppress calmodulin phosphorylation activity, though being compatible with normal reconstitution of CK2 holoenzyme, were those affecting Asp55, Glu57 and the whole triplet Glu59-Asp-Glu61. The activity of CK2 holoenzyme, either native or reconstituted, toward calmodulin can be elicited by a variety of polybasic effectors, including polylysine, polyarginine, salmine, and histones H4, H3, and, to a lesser extent, H2a and H2b. Histone H1 and polyamines are conversely ineffective. The latent "calmodulin kinase" activity of CK2 can also be specifically unmasked by a peptide (alpha[66-86]) reproducing a basic insert of the catalytic subunit. This effect is reversed by equimolar addition of a peptide (beta[55-71]) including the 55-64 acidic stretch of the beta-subunit. Comparable polylysine stimulation was observed with the holoenzymes reconstituted with either beta wt or the beta mutants capable of assembling with the alpha-subunit, with the notable exception of those bearing Ala substitutions for acidic residues at positions 55, 57, and 59-61. These were nearly insensitive to 42 nM polylysine, which conversely promotes a more than 10-fold increase of calmodulin phosphorylation with wild-type beta.(ABSTRACT TRUNCATED AT 250 WORDS)     

Optimization of output power in hollow-waveguide lasers

We present an approximate analysis of the nonlinear operation of the hollow-waveguide laser, including gain saturation and longitudinal- as well as transverse-field distribution of the laser mode. The model presented is general and can be applied to the study of an arbitrary configuration of the waveguide laser. The laser characteristics obtained reveal that the optimal position of the output mirror (which provides maximal power efficiency of the laser system with the other parameters constant) depends on the output-power level and the mirror-reflectivity coefficient. Moreover, it has been shown that when an addition device is introduced into the cavity, the power efficiency also depends on which end of the laser the light power is extracted from.