Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Multicystic Changes of Juvenile Nasopharyngeal Angiofibroma: The First Case Report in the Literature

Multicystic changes of juvenile nasopharyngeal angiofibroma: the first case report in the literature. Otolaryngologists, pathologists, and radiologists had better pay attention to this infrequent incidence

You can't see what you can't see: Experimental evidence for how much relevant information may be missed due to Google's Web search personalisation

The influence of Web search personalisation on professional knowledge work is an understudied area. Here we investigate how public sector officials self-assess their dependency on the Google Web search engine, whether they are aware of the potential impact of algorithmic biases on their ability to retrieve all relevant information, and how much relevant information may actually be missed due to Web search personalisation. We find that the majority of participants in our experimental study are neither aware that there is a potential problem nor do they have a strategy to mitigate the risk of missing relevant information when performing online searches. Most significantly, we provide empirical evidence that up to 20% of relevant information may be missed due to Web search personalisation. This work has significant implications for Web research by public sector professionals, who should be provided with training about the potential algorithmic biases that may affect their judgments and decision making, as well as clear guidelines how to minimise the risk of missing relevant information.Comment: paper submitted to the 11th Intl. Conf. on Social Informatics; revision corrects error in interpretation of parameter Psi/p in RBO resulting from discrepancy between the documentation of the implementation in R (https://rdrr.io/bioc/gespeR/man/rbo.html) and the original definition (https://dl.acm.org/citation.cfm?id=1852106) as per 20/05/201

Dual-responsive supramolecular colloidal microcapsules from cucurbit[8]uril molecular recognition in microfluidic droplets

The macrocyclic host, cucurbit[8]uril, is used to facilitate cross-linking of colloidal particles and polymers in microdroplets resulting in thermo- and photo-responsive supramolecular colloidal microcapsules. Methyl viologen-bearing colloidal particles were prepared using template polymerisation and combined with cucurbit[8]uril and an azobenzene-functionalised polymer within microfluidic droplets. The colloidal particles self-assembled at the droplet interface, whereupon polymeric cross-links formed $\textit{via}$ ternary host-guest complexation with cucurbit[8]uril. The resultant supramolecular colloidal microcapsules were uniform in size and were able to retain a macromolecular cargo. It is shown that the capsule skin porosity, and consequently the rate of release of encapsulated cargo, can be remotely controlled $\textit{via}$ either temperature or light triggers. This simple and versatile method could be extended to other polymer or colloidal derivatives for the fabrication of nano- and microcapsules with dual stimuli response for controlled release.Engineering and Physical Sciences Research Council (Grant IDs: EP/K503496/1, EP/H046593/1), CSC Cambridge Scholarshi

A multiple exp-function method for nonlinear differential equations and its application

A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure which generalizes Hirota's perturbation scheme. With help of Maple, an application of the approach to the $3+1$ dimensional potential-Yu-Toda-Sasa-Fukuyama equation yields exact explicit 1-wave and 2-wave and 3-wave solutions, which include 1-soliton, 2-soliton and 3-soliton type solutions. Two cases with specific values of the involved parameters are plotted for each of 2-wave and 3-wave solutions.Comment: 12 pages, 16 figure

Behavior of Steel Moment Frames using Top-and-Seat Angle Connections under Various Column Removal Scenarios

Top-and-seat angle connection is a conventional type of steel moment connection. However, its capacity in accommodating columns loss is rarely studied. In this study, five multi-story steel moment sub-frames using top-and-seat angle connection were fabricated and tested to investigate their performance subjected to various column removal scenarios including: (a) a middle column loss; (b) a penultimate column loss; and (c) a corner column loss. Moreover, the effects of the thickness of steel angle on load resistance were quantified. The test results indicated that load resisting capacity increased significantly with the increase of angle thickness. In both middle column and penultimate column removal scenarios, catenary action was developed in the frames. It is also noticed that, flexural action dominated the load resisting mechanism of the frames under a corner column loss scenario. For beams in different stories, similar flexural resistance was developed. However, the beams in the first story are able to develop larger catenary action than that in the second story. It worth noting that, for a corner column missing scenario, Vierendeel action helps to enhance the flexural action significantly

Effects of Steel Braces on Robustness of Steel Frames against Progressive Collapse

External installation of steel braces is one of the effective approaches to increase the lateral load resistance of the steel moment-resisting frames. However, the effects of existence of steel braces on the robustness of steel moment-resisting frames to resist progressive collapse is still not clear as little study has been carried out. To fill this gap, in this paper, six multi-story steel moment-resisting sub frames (three bare frames and three braced frames) were fabricated and tested. Test results indicated that the specimen with reduced beam section in the connection zone performed best among three types of connections, due to the guaranteed formation of plastic hinges at the location of reduced section and avoiding brittle fracture of weld at the connection. Experimental results proved that steel braces could increase the load resisting capacity by 45.1% and 83.9% of the frame with weld connection and end plate connection, respectively. As the gusset plate restricted the rotation of the plastic hinges in the second story of the braced frames with V-shaped bracing, which decreased its deformation capacity and degraded its catenary action capacity. Actually, the ultimate load of the braced frames with V shaped bracing is only 87.5% of that of the counterpart without any braces. As the compressive braces were severe buckled before the displacement reached 0.4% of the beam span, it has little effects on yield load but increases the initial stiffness of the bare frames. Thus, majority of the benefits of the bracing system were attributed into the tensile braces. Moreover, the analytical results evaluated the differences in load resistance and development of load resisting mechanisms in different stories. Furthermore, the contribution of compressive and tensile braces was de-composed individually by analytical analysis