Models and algorithms for transient queueing congestion at a hub airport

Includes bibliographical references (p. 35-37).Supported by a grant from Draper Laboratory and a National Science Foundation Graduate Fellowship.Dimitris Bertsimas, Michael D. Peterson and Amedeo R. Odoni

Twistor interpretation of slice regular functions

Given a slice regular function $f:\Omega\subset\mathbb{H}\to \mathbb{H}$, with $\Omega\cap\mathbb{R}\neq \emptyset$, it is possible to lift it to a surface in the twistor space $\mathbb{CP}^{3}$ of $\mathbb{S}^4\simeq \mathbb{H}\cup \{\infty\}$ (see~\cite{gensalsto}). In this paper we show that the same result is true if one removes the hypothesis $\Omega\cap\mathbb{R}\neq \emptyset$ on the domain of the function $f$. Moreover we find that if a surface $\mathcal{S}\subset\mathbb{CP}^{3}$ contains the image of the twistor lift of a slice regular function, then $\mathcal{S}$ has to be ruled by lines. Starting from these results we find all the projective classes of algebraic surfaces up to degree 3 in $\mathbb{CP}^{3}$ that contain the lift of a slice regular function. In addition we extend and further explore the so-called twistor transform, that is a curve in $\mathbb{G}r_2(\mathbb{C}^4)$ which, given a slice regular function, returns the arrangement of lines whose lift carries on. With the explicit expression of the twistor lift and of the twistor transform of a slice regular function we exhibit the set of slice regular functions whose twistor transform describes a rational line inside $\mathbb{G}r_2(\mathbb{C}^4)$, showing the role of slice regular functions not defined on $\mathbb{R}$. At the end we study the twistor lift of a particular slice regular function not defined over the reals. This example shows the effectiveness of our approach and opens some questions.Comment: 29 page

On the real differential of a slice regular function

In this paper we show that the real differential of any injective slice regular function is everywhere invertible. The result is a generalization of a theorem proved by G. Gentili, S. Salamon and C. Stoppato, and it is obtained thanks, in particular, to some new information regarding the first coefficients of a certain polynomial expansion for slice regular functions (called \textit{spherical expansion}), and to a new general result which says that the slice derivative of any injective slice regular function is different from zero. A useful tool proven in this paper is a new formula that relates slice and spherical derivatives of a slice regular function. Given a slice regular function, part of its singular set is described as the union of surfaces on which it results to be constant.Comment: 23 pages, some adjustment in the structure of the sections, some typos removed, last example reviewe

Greenways and Ecological Networks: Concepts, Differences, Similarities

In recent decades green infrastructure (GI) frameworks have been widely used for developing theoretical and practical models of sustainable land reorganization. Although there is still much confusion regarding various aspects of green infrastructure, since many differing perspectives have generated different definitions that emphasise the complexity of the green infrastructure concept, it is possible to find important differences and common points

Maori & Psychology Research Unit annual report 2006

Annual report of the Maori and Psychology Research Unit (MPRU) 2006. The unit was established in August of 1997. The unit is designed to provide a catalyst and support network for enhancing research concerning the psychological needs, aspirations, and priorities of Maori people. The MPRU is well situated to draw together skilled and experienced interdisciplinary research groups by networking and establishing working relationships with staff and students within the Faculty of Arts and Social Sciences, the University, and the wider community

On mining complex sequential data by means of FCA and pattern structures

Nowadays data sets are available in very complex and heterogeneous ways. Mining of such data collections is essential to support many real-world applications ranging from healthcare to marketing. In this work, we focus on the analysis of "complex" sequential data by means of interesting sequential patterns. We approach the problem using the elegant mathematical framework of Formal Concept Analysis (FCA) and its extension based on "pattern structures". Pattern structures are used for mining complex data (such as sequences or graphs) and are based on a subsumption operation, which in our case is defined with respect to the partial order on sequences. We show how pattern structures along with projections (i.e., a data reduction of sequential structures), are able to enumerate more meaningful patterns and increase the computing efficiency of the approach. Finally, we show the applicability of the presented method for discovering and analyzing interesting patient patterns from a French healthcare data set on cancer. The quantitative and qualitative results (with annotations and analysis from a physician) are reported in this use case which is the main motivation for this work. Keywords: data mining; formal concept analysis; pattern structures; projections; sequences; sequential data.Comment: An accepted publication in International Journal of General Systems. The paper is created in the wake of the conference on Concept Lattice and their Applications (CLA'2013). 27 pages, 9 figures, 3 table