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.     

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.     

On problems of multicomponent system maintenance modelling

We present an overview of some recent developments in the area of mathematical modeling of maintenance decisions for multi-unit systems. The emphasis is on three main groups of multicomponent maintenance optimization models： the block replacement models, group maintenance models, and opportunistic maintenance models. Moreover, an example of a two-unit system maintenance process is provided in order to compare various maintenance policies.     

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.     

Biofunctionalized upconverting CaF<Subscript>2</Subscript>:Yb,Tm nanoparticles for <Emphasis Type="Italic">Candida albicans</Emphasis> detection and imaging

Versatile optimization of the synthesis method and composition of Yb3+ and Tm3+ co-doped CaF2 nanoparticles as well as a novel biofunctionalization method were developed and evaluated.Through multistep synthesis,the luminescence intensity of the Tm3+ activator was enhanced by more than 10-fold compared to standard one-step synthesis.The proposed methods were used to homogenously distribute the doping ions within the nanoparticle's volume and thus reduce luminescence quenching.Optimization of dopant ions concentration led to the selection of the most efficient visible and near-infrared up-converting nanoparticles,which were CaF2 doped with 10％ Yb3+ 0.05％ Tm3+ and 20％ Yb3+ 0.5％ Tm3+,respectively.To illustrate the suitability of the synthesized nanoparticles as bio-labels,a dedicated biofunctionalization method was used,and the nanoparticles were applied for labeling and imaging of Candida albicans cells.This method shows great promise because of extremely low background and high specificity because of the presence of the attached molecules.     

Controlling patterns of geospatial phenomena

Modeling spatially distributed phenomena in terms of its controlling factors is a recurring problem in geoscience. Most efforts concentrate on predicting the value of response variable in terms of controlling variables either through a physical model or a regression model. However, many geospatial systems comprises complex, nonlinear, and spatially non-uniform relationships, making it difficult to even formulate a viable model. This paper focuses on spatial partitioning of controlling variables that are attributed to a particular range of a response variable. Thus, the presented method surveys spatially distributed relationships between predictors and response. The method is based on association analysis technique of identifying emerging patterns, which are extended in order to be applied more effectively to geospatial data sets. The outcome of the method is a list of spatial footprints, each characterized by a unique “controlling pattern”—a list of specific values of predictors that locally correlate with a specified value of response variable. Mapping the controlling footprints reveals geographic regionalization of relationship between predictors and response. The data mining underpinnings of the method are given and its application to a real world problem is demonstrated using an expository example focusing on determining variety of environmental associations of high vegetation density across the continental United States.     

Michell cantilevers constructed within a half strip. Tabulation of selected benchmark results

The paper delivers the benchmark results for the Michell cantilevers constructed within a half strip, for selected values of the σ _T /σ _C ratio, σ _T , σ _C being the admissible stresses in tension and compression, respectively.     

TSV constraints related to temperature excursion, pressure during molding, materials used and handling loads

The current paper focuses on several mechanical aspects of a waferlevel packaging approach using a direct face-to-face Chip-to-Wafer (C2W) bonding of a MEMS device on an ASIC substrate wafer. Requirements of minimized inherent stress from packaging and good decoupling from forces applied in manufacturing and application are discussed with particular attention to the presence of through-silicon vias (TSV) in the substrate wafer. The paper deals with FEM analysis of temperature excursion, pressure during molding, materials used and handling load influence on mechanical stress within the TSV system and on wafer level, which can be large enough to disintegrate the system.