Classifying Cantor Sets by their Fractal Dimensions

In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences.Comment: 10 pages, revised version. To appear in Proceedings of the AMS

Orientation of optically trapped nonspherical birefringent particles

While the alignment and rotation of microparticles in optical traps have received increased attention recently, one of the earliest examples has been almost totally neglected the alignment of particles relative to the beam axis, as opposed to about the beam axis. However, since the alignment torques determine how particles align in a trap, they are directly relevant to practical applications. Lysozyme crystals are an ideal model system to study factors determining the orientation of nonspherical birefringent particles in a trap. Both their size and their aspect ratio can be controlled by the growth parameters, and their regular shape makes computational modeling feasible. We show that both external shape and internal birefringence anisotropy contribute to the alignment torque. Three-dimensionally trapped elongated objects either align with their long axis parallel or perpendicular to the beam axis depending on their size. The shape-dependent torque can exceed the torque due to birefringence, and can align negative uniaxial particles with their optic axis parallel to the electric field, allowing an application of optical torque about the beam axis.Comment: 5 pages, 5 figure

Current Status and Evolution of Preclinical Drug Development Models of Epithelial Ovarian Cancer

Epithelial ovarian cancer (EOC) is the most lethal gynecologic malignancy and the fifth most common cause of female cancer death in the United States. Although important advances in surgical and chemotherapeutic strategies over the last three decades have significantly improved the median survival of EOC patients, the plateau of the survival curve has not changed appreciably. Given that EOC is a genetically and biologically heterogeneous disease, identification of specific molecular abnormalities that can be targeted in each individual ovarian cancer on the basis of predictive biomarkers promises to be an effective strategy to improve outcome in this disease. However, for this promise to materialize, appropriate preclinical experimental platforms that recapitulate the complexity of these neoplasms and reliably predict antitumor activity in the clinic are critically important. In this review, we will present the current status and evolution of preclinical models of EOC, including cell lines, immortalized normal cells, xenograft models, patient-derived xenografts, and animal models, and will discuss their potential for oncology drug development

Emergence of hidden phases of methylammonium lead-iodide (CH3_3NH3_3PbI3_3) upon compression

We perform a thorough structural search with the minima hopping method (MHM) to explore low-energy structures of methylammonium lead iodide. By combining the MHM with a forcefield, we efficiently screen vast portions of the configurational space with large simulation cells containing up to 96 atoms. Our search reveals two structures of methylammonium iodide perovskite (MAPI) that are substantially lower in energy than the well-studied experimentally observed low-temperature $Pnma$ orthorhombic phase according to density functional calculations. Both structures have not yet been reported in the literature for MAPI, but our results show that they could emerge as thermodynamically stable phases via compression at low temperatures. In terms of the electronic properties, the two phases exhibit larger band gaps than the standard perovskite-type structures. Hence, pressure induced phase selection at technologically achievable pressures (i.e., via thin-film strain) is a route towards the synthesis of several MAPI polymorph with variable band gaps

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

School-based Understanding of Human Rights in Four Countries: A Commonwealth Study

Teaching/Communication/Extension/Profession,