A Pathfinding Problem for Fork-Join Directed Acyclic Graphs with Unknown Edge Length

In a previous paper by the author, a pathfinding problem for directed trees is studied under the following situation: each edge has a nonnegative integer length, but the length is unknown in advance and should be found by a procedure whose computational cost becomes exponentially larger as the length increases. In this paper, the same problem is studied for a more general class of graphs called fork-join directed acyclic graphs. The problem for the new class of graphs contains the previous one. In addition, the optimality criterion used in this paper is stronger than that in the previous paper and is more appropriate for real applications.

The optimization process leading to the tessellation of the first geodesic dome structure, the first Planetarium of Jena

The tessellation of the first built geodesic dome structure (the first planetarium of Jena, designed by Walther Bauersfeld, built 1922–23) has been unknown until recently. While original documentation of the tessellation has been published, the concept behind it has not been uncovered. This article presents the evolution of the final tessellation based on Bauersfeld’s hand-written notes found in the Zeiss Archives in Jena. Bauersfeld contemplated various methods of subdivision and performed detailed calculations and optimality analysis on them—preceding the theoretical studies on the tessellation of geodesic domes by almost 30 years. His key findings, relevant and comparable with later studies are highlighted. The concept of the presumably final tessellation is revealed to be the equal-area triangulation of the sphere—which has to the author’s knowledge not been considered ever since for geodesic domes. The remarkably simple algorithm applied did not result in a theoretically exact solution (well known to Bauersfeld), but as shown in this article in engineering terms it got sufficiently close. Moreover, it is concluded that the resulting tessellation excels in terms of important parameters (e.g. edge length ratio, number of different edges) compared to existing practical and theoretical solutions.

Physical-Chemical Properties of Compressible Clathrates: A Natural Pressure Shift by Extending the van der Waals and Platteeuw Model

We have developed a new model for compressible clathrates that extends the well-known van der Waals and Platteeuw model. The new model is derived by dispensing with the assumption of constant cages radii in the partition function level, resulting in new thermodynamically consistent expressions relating thermodynamic properties of the hydrate phase and the empty lattice isochoric reference. One set of additional parameters to the clathrate modeling framework is introduced, consisting of a scaling factor for each cage radius relative to the edge length of the unit cell. No additional guest-dependent empirical parameters are required. The model exhibits two features not previously reported in the literature: (i) a pressure shift between the clathrate being described and the empty lattice isochoric reference, and (ii) differences in the edge length of the unit cell and in the cages radii for different guest species at the same temperature and pressure, as a consequence of the sorption of guests. We also propose a test for thermodynamic consistency at high pressure, based on the multicomponent and multiphase Clapeyron equation. Using this test, we show that the proposed model solves an inconsistency issue observed in phase equilibrium calculations with some of the compressible clathrate models currently in use. We have performed parameter optimization for methane, ethane, and xenon in sI hydrates. Two sets of results are presented: 3-phase equilibrium conditions; and lattice size versus temperature or pressure for each of these substances, along with available experimental data.

DOX-loaded silver nanotriangles and photothermal therapy exert a synergistic antibreast cancer effect via ROS/ERK1/2 signaling pathway

The combination of multiple therapies has been proved to be more effective than a single therapy for many cancers. This study aimed to investigate the synergistic antibreast cancer effect of doxorubicin-loaded silver nanotriangles (DOX-AgNTs) combined with near-infrared (NIR) irradiation and explore the underlying mechanism. AgNTs were prepared by a chemical method and DOX was loaded via electrostatic adsorption. Characterization was performed by transmission electron microscopy, ultraviolet-visible spectroscopy and dynamic light scattering. The viability of MDA-MB-231 cells was detected by using MTT assay to evaluate the synergistic anticancer effect of DOX-AgNTs combined with NIR irradiation. The intracellular reactive oxygen species (ROS) level and cell apoptosis were analyzed by flow cytometry. Mitochondrial membrane potential (MMP) was measured with fluorescence microscopy. The mechanism was further investigated with ROS scavenger N-acetylcysteine and specific inhibitors of extracellular signal-regulated kinase 1/2 (ERK1/2), C-jun N-terminal kinase and p38 pathways. Characterization results revealed that the prepared AgNTs were mostly triangular and the mean edge length was about 126 nm. The combination of DOX-AgNTs and NIR exhibited a superior synergistic anticancer effect over single DOX-AgNTs or photothermal therapy. N-acetylcysteine and ERK1/2 inhibitor U0126 were found to significantly rescue the decreased cell viability, declined MMP and increased apoptosis induced by the combined treatment. Our results suggested that DOX-AgNTs combined with photothermal therapy performed a synergistic antibreast cancer effect. The synergy might be closely associated with the excessive production of ROS, changed MMP and the activation of ERK1/2 signaling pathway. These findings might provide a new perspective for the development of breast cancer treatments with excellent efficacy.

Better tired than lost: Turtle ant trail networks favor coherence over short edges

Creating a routing backbone is a fundamental problem in both biology and engineering. The routing backbone of the trail networks of arboreal turtle ants (Cephalotes goniodontus) connects many nests and food sources using trail pheromone deposited by ants as they walk. Unlike species that forage on the ground, the trail networks of arboreal ants are constrained by the vegetation. We examined what objectives the trail networks meet by comparing the observed ant trail networks with networks of random, hypothetical trail networks in the same surrounding vegetation and with trails optimized for four objectives: minimizing path length, minimizing average edge length, minimizing number of nodes, and minimizing opportunities to get lost. The ants’ trails minimized path length by minimizing the number of nodes traversed rather than choosing short edges. In addition, the ants’ trails reduced the opportunity for ants to get lost at each node, favoring nodes with 3D configurations most likely to be reinforced by pheromone. Thus, rather than finding the shortest edges, turtle ant trail networks take advantage of natural variation in the environment to favor coherence, keeping the ants together on the trails.

Rapid Prototyping of Moulds for PDMS-based Microfluidic Chips

To shorten the production time for PDMS-moulds by additive manufacturing (AM) several 3D printers have been investigated in comparison to standard micro-milling by producing benchmark structures. These are evaluated regarding their shape accuracy, the transparency of the casted PDMS which is linked to the surface quality of the mould, and the production time until the moulds are ready to use. Even though the additively manufactured moulds showed significantly better surface quality and shorter production time, the necessary shape accuracy for non-square-structures or structures with < 250 μm edge length could not be achieved due to limiting factors like nozzle diameter, size of the digital micromirror device or spot size of the LCD-panel.

Fiber statistics of nonwoven materials by SEM images - influence of number of images

Electrospun nonwovens are widely applied in biomedicine and various other fields. For control of the manufacturing process and quality assurance Scanning electron microscopy (SEM) imaging is one standard practice. In this study, statistical datasets of 60 SEM images of three nonwoven samples were evaluated using Gaussian fit to obtain numerical results of their fiber diameter distributions. The question of how much effort is required for acceptable imaging and processing is being discussed. As determined here, for reliable statistics, a minimum surface area of the nonwoven has to be evaluated. The fiber diameter should be in a range of approximately 2 - 3% of the edge length of the square equivalent of the evaluated image area, using sufficiently magnified SEM images, in which the fiber diameter is imaged over at least 30 pixels.