Approval-Based Shortlisting

Shortlisting is the task of reducing a long list of alternatives to a (smaller) set of best or most suitable alternatives from which a final winner will be chosen. Shortlisting is often used in the nomination process of awards or in recommender systems to display featured objects. In this paper, we analyze shortlisting methods that are based on approval data, a common type of preferences. Furthermore, we assume that the size of the shortlist, i.e., the number of best or most suitable alternatives, is not fixed but determined by the shortlisting method. We axiomatically analyze established and new shortlisting methods and complement this analysis with an experimental evaluation based on biased voters and noisy quality estimates. Our results lead to recommendations which shortlisting methods to use, depending on the desired properties

An Analog of the Neumann Problem for the 11-Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability

We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincar\'e inequality. We show that solutions exist under certain regularity assumptions on the domain, but are generally nonunique. We also show that solutions can be taken to be differences of two characteristic functions, and that they are regular up to the boundary when the boundary is of positive mean curvature. By regular up to the boundary we mean that if the boundary data is $1$ in a neighborhood of a point on the boundary of the domain, then the solution is $-1$ in the intersection of the domain with a possibly smaller neighborhood of that point. Finally, we consider the stability of solutions with respect to boundary data.Comment: 8 figure

Extensibility and limitations of FDDI

Recently two standards for Metropolitan Area Networks (MANs), Fiber Distributed Data Interface (FDDI) and Distributed Queue Dual Bus (DQDB), have emerged as the primary competitors for the MAN arena. Great interest exists in building higher speed networks which support large numbers of node and greater distance, and it is not clear what types of protocols are needed for this type of environment. There is some question as to whether or not these MAN standards can be extended to such environments. The extensibility of FDDI to the Gbps range and a long distance environment is investigated. Specification parameters which affect performance are shown and a measure is provided for predicting utilization of FDDI. A comparison of FDDI at 100 Mbps and 1 Gbps is presented. Some specific problems with FDDI are addressed and modifications which improve the viability of FDDI in such high speed networks are investigated

Performance of gigabit FDDI

Great interest exists in developing high speed protocols which will be able to support data rates at gigabit speeds. Hardware currently exists which can experimentally transmit at data rates exceeding a gigabit per second, but it is not clear as to what types of protocols will provide the best performance. One possibility is to examine current protocols and their extensibility to these speeds. Scaling of Fiber Distributed Data Interface (FDDI) to gigabit speeds is studied. More specifically, delay statistics are included to provide insight as to which parameters (network length, packet length or number of nodes) have the greatest effect on performance

Short Coherence Length Superconductivity: A Generalization of BCS Theory for the Underdoped Cuprates

On the basis of the observed short coherence lengths in the cuprates we argue that a BCS-Bose-Einstein condensation (BEC) crossover approach is an appropriate starting point for correcting the mean field approach of BCS and, thereby, for addressing pseudogap phenomena in these materials. Our version of the BCS-BEC approach is based on a particular Greens' function decoupling scheme which should be differentiated from others in the literature, and which yields (i) the Leggett crossover ground state (for all coupling constants g, at T=0) and (ii) BCS theory (for all $T \leq T_c$ over a range of small g). In this paper we provide a simple physical picture of the pseudogap phase above and below $T_c$, and review the quantitative and qualitative implications of this theory, which, for the most part have been published in a series of recent papers.Comment: M2S-HTSC-VI conference paper, (4 pages, 1 figure), using Elsevier style espcrc2.st

Synthesis, Properties, and Solid-State Structures of a Series of 6,13-Dicyanoheteropentacene Analogues: Towards New Liquid Crystalline Materials

The focus of this thesis is the synthesis of novel heterocyclic pentacene analogs and the investigation of their self-organization for the development of new materials for organic electronics. The thesis consists of two interrelated projects: the first being development of an improved synthesis of a series of liquid crystalline dicyanotetraoxapentacenes (DCTOPs) while the second entails the exploratory synthesis of several novel dicyanoheteropentacene analogues and a preliminary investigation of their photophysical properties and solid-state structures. Both of these projects centre around the use of nucleophilic aromatic substitution reactions on tetrafluoroterephthalonitrile. Soluble, tetrakis(bis(alkoxy)phenyl)-substituted DCTOPs were originally synthesised via a short synthesis complicated by a tedious purification required in the last step. Despite this, derivatives bearing long alkyl chains were prepared which displayed liquid crystalline properties in addition to aggregation-induced emission. Building upon this success, but with the goal of achieving DCTOPs in an efficient synthetic manner for this thesis, changes were made which eliminated the troublesome fourfold Suzuki coupling by changing the order of reactions, which in turn required a protection-deprotection sequence. Purification in the new synthesis was greatly simplified and the target tetraaryl-DCTOPs were accessed in good overall yields and purities. The synthesis and solid state structures of these DCTOPs are discussed in Chapter 2. Building on the methods developed in Chapter 2, several novel pentacene analogues containing combinations of nitrogen, oxygen, and sulfur atoms installed within the pentacene core were also synthesised. These compounds were prepared in good yields, and preliminary photophysical studies show that all the compounds displayed luminescence in solution and the solid state. It was also shown that replacement of O with N leads to a red shift in absorption and emission spectra. The X-ray crystal structures show that several of these compounds exhibit π−stacking in the solid state, which is an important design element for applications in organic electronics. The synthesis, photophysical properties, and solid-state organization of these novel 6,13-dicyanoheteropentacene analogues are discussed in Chapter 3

Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient

We study the geometry of domains in complete metric measure spaces equipped with a doubling measure supporting a $1$-Poincar\'e inequality. We propose a notion of \emph{domain with boundary of positive mean curvature} and prove that, for such domains, there is always a solution to the Dirichlet problem for least gradients with continuous boundary data. Here \emph{least gradient} is defined as minimizing total variation (in the sense of BV functions) and boundary conditions are satisfied in the sense that the \emph{boundary trace} of the solution exists and agrees with the given boundary data. This extends the result of Sternberg, Williams and Ziemer to the non-smooth setting. Via counterexamples we also show that uniqueness of solutions and existence of \emph{continuous} solutions can fail, even in the weighted Euclidean setting with Lipschitz weights