Malmquist-type indices in the presence of negative data:an application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.

Accessibility indices and linked trips: a case study of the elderly

The confusion over the concept of accessibility in transport planning and the deficiencies of existing accessibility indices are examined by developing a conceptual framework of accessibility with a fundamental distinction being drawn between the, often conflicting, theoretical and practical dimensions. The theoretical validity of alternative indices is assessed with reference to the problems and assumptions implicit in defining, measuring, valuing and aggregating the variables and components comprising accessibility. The major deficiencies of existing indices are identified as the inability of indices to take account of the potential to link trips between more than one activity location and the level of assumptions implicit in valuing and aggregating accessibility information. In this context, it is argued that accessibility information is more appropriately expressed on a comparative basis in the form of a profile rather than as a composite single-unit index and that the present confines of accessibility measurement must be extended in line with current developments in disaggregate travel and activity modelling. The sensitivity of accessibility levels to the use of alternative value judgements, alternative forms and levels of aggregation and the inclusion of information on the potential to link trips is examined by undertaking a case study. Accessibility profiles are developed for 23 zones in the London Borough of Hammersmith and Fulham showing the accessibility of the elderly to post offices and grocers. In a practical context, the profiles assist in identifying areas and individuals with relatively poor accessibility. The incidence and nature of linked trip-making and its significance and implications for accessibility measurement are explored further by analysing the results of a survey of the elderly's travel patterns. It is concluded that future accessibility analysis should be undertaken at a disaggregate level, taking account of the potential opportunity available from nonhome as well as home origins.

Complexity and chirality indices for molecular informatics::differential geometry approach

Novel molecular complexity measures are designed based on the quantum molecular kinematics. The Hamiltonian matrix constructed in a quasi-topological approximation describes the temporal evolution of the modelled electronic system and determined the time derivatives for the dynamic quantities. This allows to define the average quantum kinematic characteristics closely related to the curvatures of the electron paths, particularly, the torsion reflecting the chirality of the dynamic system. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

Visual field severity indices demonstrate dose-dependent visual loss from Vigabatrin therapy

Purpose: The aims of this study were to develop an algorithm to accurately quantify Vigabatrin (VGB)-induced central visual field loss and to investigate the relationship between visual field loss and maximum daily dose, cumulative dose and duration of dose. Methods: The sample comprised 31 patients (mean age 37.9 years; SD 14.4 years) diagnosed with epilepsy and exposed to VGB. Each participant underwent standard automated static visual field examination of the central visual field. Central visual field loss was determined using continuous scales quantifying severity in terms of area and depth of defect and additionally by symmetry of defect between the two eyes. A simultaneous multiple regression model was used to explore the relationship between these visual field parameters and the drug predictor variables. Results: The regression model indicated that maximum VGB dose was the only factor to be significantly correlated with individual eye severity (right eye: p = 0.020; left eye: p = 0.012) and symmetry of visual field defect (p = 0.024). Conclusions: Maximum daily dose was the single most reliable indicator of those patients likely to exhibit visual field defects due to VGB. These findings suggest that high maximum dose is more likely to result in visual field defects than high cumulative doses or those of long duration.

Modeling the peptide-T cell receptor interaction by the comparative molecular similarity indices analysis-soft independent modeling of class analogy technique

A set of 38 epitopes and 183 non-epitopes, which bind to alleles of the HLA-A3 supertype, was subjected to a combination of comparative molecular similarity indices analysis (CoMSIA) and soft independent modeling of class analogy (SIMCA). During the process of T cell recognition, T cell receptors (TCR) interact with the central section of the bound nonamer peptide; thus only positions 4−8 were considered in the study. The derived model distinguished 82% of the epitopes and 73% of the non-epitopes after cross-validation in five groups. The overall preference from the model is for polar amino acids with high electron density and the ability to form hydrogen bonds. These so-called “aggressive” amino acids are flanked by small-sized residues, which enable such residues to protrude from the binding cleft and take an active role in TCR-mediated T cell recognition. Combinations of “aggressive” and “passive” amino acids in the middle part of epitopes constitute a putative TCR binding motif

A comparative molecular similarity indices (CoMSIA) study of peptide binding to the HLA-A3 superfamily

Epitope identification is the basis of modern vaccine design. The present paper studied the supermotif of the HLA-A3 superfamily, using comparative molecular similarity indices analysis (CoMSIA). Four alleles with high phenotype frequencies were used: A*1101, A*0301, A*3101 and A*6801. Five physicochemical properties—steric bulk, electrostatic potential, local hydro-phobicity, hydrogen-bond donor and acceptor abilities—were considered and ‘all fields’ models were produced for each of the alleles. The models have a moderate level of predictivity and there is a good correlation between the data. A revised HLA-A3 supermotif was defined based on the comparison of favoured and disfavoured properties for each position of the MHC bound peptide. The present study demonstrated that CoMSIA is an effective tool for studying peptide–MHC interactions.

Procedure of Formalization of the Indices of Banks’ Stable Functioning in Comparative Estimates of Their Development

The advisability of analyzing the banks liquidity and profitability as the key factor when building the comparative estimate of their functioning is considered. The procedure of formal description of the bank stable functioning indices is substantiated. Fuzzy interpretation of the bank management efficiency estimation is offered. The possibility to formalize the bank functioning estimates on the basis of the corresponding fuzzy set levels hierarchy is analyzed. The comparative estimate of different bank systems functioning is given.

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs

Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM Computing Classification System (1998): G.2.2, G.2.3.

Distance-based accessibility indices

The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at least as accessible. We argue for the need of eliminating the independence property in certain applications. Therefore generalized distance sum, a family of accessibility indices, will be suggested. It is linear, considers the accessibility of vertices besides their distances and depends on a parameter in order to control its deviation from distance sum. Generalized distance sum is anonymous and satisfies dominance preservation if its parameter meets a sufficient condition. Two detailed examples demonstrate its ability to reflect the vulnerability of accessibility to link disruptions.

A multi-method approach for the assessment of composite indices and rankings

There is growing popularity in the use of composite indices and rankings for cross-organizational benchmarking. However, little attention has been paid to alternative methods and procedures for the computation of these indices and how the use of such methods may impact the resulting indices and rankings. This dissertation developed an approach for assessing composite indices and rankings based on the integration of a number of methods for aggregation, data transformation and attribute weighting involved in their computation. The integrated model developed is based on the simulation of composite indices using methods and procedures proposed in the area of multi-criteria decision making (MCDM) and knowledge discovery in databases (KDD). The approach developed in this dissertation was automated through an IT artifact that was designed, developed and evaluated based on the framework and guidelines of the design science paradigm of information systems research. This artifact dynamically generates multiple versions of indices and rankings by considering different methodological scenarios according to user specified parameters. The computerized implementation was done in Visual Basic for Excel 2007. Using different performance measures, the artifact produces a number of excel outputs for the comparison and assessment of the indices and rankings. In order to evaluate the efficacy of the artifact and its underlying approach, a full empirical analysis was conducted using the World Bank's Doing Business database for the year 2010, which includes ten sub-indices (each corresponding to different areas of the business environment and regulation) for 183 countries. The output results, which were obtained using 115 methodological scenarios for the assessment of this index and its ten sub-indices, indicated that the variability of the component indicators considered in each case influenced the sensitivity of the rankings to the methodological choices. Overall, the results of our multi-method assessment were consistent with the World Bank rankings except in cases where the indices involved cost indicators measured in per capita income which yielded more sensitive results. Low income level countries exhibited more sensitivity in their rankings and less agreement between the benchmark rankings and our multi-method based rankings than higher income country groups.

Derivation of lake mixing and stratification indices from high-resolution lake buoy data

Lake Analyzer is a numerical code coupled with supporting visualization tools for determining indices of mixing and stratification that are critical to the biogeochemical cycles of lakes and reservoirs. Stability indices, including Lake Number, Wedderburn Number, Schmidt Stability, and thermocline depth are calculated according to established literature definitions and returned to the user in a time series format. The program was created for the analysis of high-frequency data collected from instrumented lake buoys, in support of the emerging field of aquatic sensor network science. Available outputs for the Lake Analyzer program are: water temperature (error-checked and/or down-sampled), wind speed (error-checked and/or down-sampled), metalimnion extent (top and bottom), thermocline depth, friction velocity, Lake Number, Wedderburn Number, Schmidt Stability, mode-1 vertical seiche period, and Brunt-Väisälä buoyancy frequency. Secondary outputs for several of these indices delineate the parent thermocline depth (seasonal thermocline) from the shallower secondary or diurnal thermocline. Lake Analyzer provides a program suite and best practices for the comparison of mixing and stratification indices in lakes across gradients of climate, hydro-physiography, and time, and enables a more detailed understanding of the resulting biogeochemical transformations at different spatial and temporal scales.