The Directional Distance Function and Measurement of Super-Efficiency: An Application to Airlines Data

Lovell and Rouse (LR) have recently proposed a modification of the standard DEA model that overcomes the infeasibility problem often encountered in computing super-efficiency. In the LR procedure one appropriately scales up the observed input vector (scale down the output vector) of the relevant super-efficient firm thereby usually creating its inefficient surrogate. An alternative procedure proposed in this paper uses the directional distance function introduced by Chambers, Chung, and Färe and the resulting Nerlove-Luenberger (NL) measure of super-efficiency. The fact that the directional distance function combines features of both an input-oriented and an output-oriented model, generally leads to a more complete ranking of the observations than either of the oriented models. An added advantage of this approach is that the NL super-efficiency measure is unique and does not depend on any arbitrary choice of a scaling parameter. A data set on international airlines from Coelli, Perelman, and Griffel-Tatje (2002) is utilized in an illustrative empirical application.

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

New glimpses on convex infinite optimization duality

Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that inf(P)=max(D), inf(P)=max(Q), and inf(P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing min(P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described.

On the completion of Latin rectangles to symmetric Latin squares

We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n - 1)-edge colouring of K-n (n even), and for an n-edge colouring of K-n (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.

Using the Amazon metric to construct an image database based on what people do, not what they say

Current image database metadata schemas require users to adopt a specific text-based vocabulary. Text-based metadata is good for searching but not for browsing. Existing image-based search facilities, on the other hand, are highly specialised and so suffer similar problems. Wexelblat's semantic dimensional spatial visualisation schemas go some way towards addressing this problem by making both searching and browsing more accessible to the user in a single interface. But the question of how and what initial metadata to enter a database remains. Different people see different things in an image and will organise a collection in equally diverse ways. However, we can find some similarity across groups of users regardless of their reasoning. For example, a search on Amazon.com returns other products also, based on an averaging of how users navigate the database. In this paper, we report on applying this concept to a set of images for which we have visualised them using traditional methods and the Amazon.com method. We report on the findings of this comparative investigation in a case study setting involving a group of randomly selected participants. We conclude with the recommendation that in combination, the traditional and averaging methods would provide an enhancement to current database visualisation, searching, and browsing facilities.

On-line learning of unrealizable tasks

The dynamics of on-line learning is investigated for structurally unrealizable tasks in the context of two-layer neural networks with an arbitrary number of hidden neurons. Within a statistical mechanics framework, a closed set of differential equations describing the learning dynamics can be derived, for the general case of unrealizable isotropic tasks. In the asymptotic regime one can solve the dynamics analytically in the limit of large number of hidden neurons, providing an analytical expression for the residual generalization error, the optimal and critical asymptotic training parameters, and the corresponding prefactor of the generalization error decay.

Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission

We propose and analyze a first-order optical differentiator based on a fiber Bragg grating (FBG) in transmission. It is shown in the examples that a simple uniform-period FBG in a very strong coupling regime (maximum reflectivity very close to 100%) can perform close to ideal temporal differentiation of the complex envelope of an arbitrary-input optical signal.

Identifying candidate subunit vaccines using an alignment-independent method based on principal amino acid properties

Subunit vaccine discovery is an accepted clinical priority. The empirical approach is time- and labor-consuming and can often end in failure. Rational information-driven approaches can overcome these limitations in a fast and efficient manner. However, informatics solutions require reliable algorithms for antigen identification. All known algorithms use sequence similarity to identify antigens. However, antigenicity may be encoded subtly in a sequence and may not be directly identifiable by sequence alignment. We propose a new alignment-independent method for antigen recognition based on the principal chemical properties of protein amino acid sequences. The method is tested by cross-validation on a training set of bacterial antigens and external validation on a test set of known antigens. The prediction accuracy is 83% for the cross-validation and 80% for the external test set. Our approach is accurate and robust, and provides a potent tool for the in silico discovery of medically relevant subunit vaccines.

On Typical Compact Convex Sets in Hilbert Spaces

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

Radon Measures on Banach Spaces with their Weak Topologies

The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.

Recent Results on Stability Analysis of an Optimal Assembly Line Balance

Two assembly line balancing problems are addressed. The first problem (called SALBP-1) is to minimize number of linearly ordered stations for processing n partially ordered operations V = {1, 2, ..., n} within the fixed cycle time c. The second problem (called SALBP-2) is to minimize cycle time for processing partially ordered operations V on the fixed set of m linearly ordered stations. The processing time ti of each operation i ∈V is known before solving problems SALBP-1 and SALBP-2. However, during the life cycle of the assembly line the values ti are definitely fixed only for the subset of automated operations V\V . Another subset V ⊆ V includes manual operations, for which it is impossible to fix exact processing times during the whole life cycle of the assembly line. If j ∈V , then operation times tj can differ for different cycles of the production process. For the optimal line balance b of the assembly line with operation times t1, t2, ..., tn, we investigate stability of its optimality with respect to possible variations of the processing times tj of the manual operations j ∈ V .

The economic well -being of low -income immigrants in the U.S.: An examination of the impact of the 1996 welfare reform on immigrants

The 1996 welfare reform, for the first time in U.S. history, set a five-year residence requirement for immigrants to be eligible for federal welfare benefits. This dissertation assessed the impact of the 1996 welfare reform, specifically the immigrant provisions, on the economic well-being of low-income immigrants. This dissertation also explored the roles that migration selection theory and social capital theory play in the economic well-being of low-income immigrants. ^ This dissertation was based on an analysis of the March 1995, March 2002, and March 2006 Annual Demographic Supplement Files of the Current Population Survey (CPS). Both logistic regression and multiple regression were used to analyze economic well-being, comparing low-income immigrants with low-income citizens. Economic well-being was measured in the current survey year and the year before on the following variables: employment status, full-time status (35 or more hours per week), the number of weeks worked, and the total annual wage or salary.^ The major findings reported in this dissertation were that low-income immigrants had advantages over low-income citizens in the labor market. This may be due to immigrants' stronger motivation to obtain success, consistent with migration selection theory. Also, this research suggested that immigrant provisions had not ameliorated employment outcomes of low-income immigrants as policymakers may have expected.^ The study also confirmed the role of social capital in advancing the economic well-being of qualified immigrants. Ultimately, this dissertation contributed to our understanding of low-income immigrants in the U.S. The study questioned the claim that immigrants are attracted to the U.S. by welfare benefits. This dissertation suggested that immigrants come to the U.S., to a large extent, to pursue the goal of upward mobility. Consequently, immigrants may employ greater initiative and work harder than native-born Americans.^

On surfaces with prescribed shape operator

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. I show that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimension of realizability is achieved are analyzed and it is found that there are two such families of shape operators, one depending essentially on three arbitrary functions of one variable and another depending essentially on two arbitrary functions of one variable. The space of realizations is discussed in each case, along with some of their remarkable geometric properties. Several explicit examples are constructed.

Port decoupling for small arrays by means of an eigenmode feed network

An alternative approach to port decoupling and matching of arrays with tightly coupled elements is proposed. The method is based on the inherent decoupling effect obtained by feeding the orthogonal eigenmodes of the array. For this purpose, a modal feed network is connected to the array. The decoupled external ports of the feed network may then be matched independently by using conventional matching circuits. Such a system may be used in digital beam forming applications with good signal-to-noise performance. The theory is applicable to arrays with an arbitrary number of elements, but implementation is only practical for smaller arrays. The principle is illustrated by means of two examples.

Effect of section geometry on the lateral distortional buckling of LiteSteel beams

The LiteSteel Beam (LSB) is a new hollow flange section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming technologies. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. It has found increasing popularity in residential, industrial and commercial buildings as flexural members. The LSB is considerably lighter than traditional hot-rolled steel beams and provides both structural and construction efficiencies. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their member moment capacities. Unlike the commonly observed lateral torsional buckling of steel beams, the lateral distortional buckling of LSBs is characterised by simultaneous lateral defection, twist and cross sectional change due to web distortion. The current design rules in AS/NZS 4600 (SA, 2005) for flexural members subject to lateral distortional buckling were found to be conservative by about 8% in the inelastic buckling region. Therefore, a new design rule was developed for LSBs subject to lateral distortional buckling based on finite element analyses of LSBs. The effect of section geometry was then considered and several geometrical parameters were used to develop an advanced set of design rules. This paper presents the details of the finite element analyses and the design curve development for hollow flange sections subject to lateral distortional buckling.