Group judgement with ties. A position-based approach

A system for defining the positions taken by alternatives under preference orders proposed by Cook and Seiford is discussed. This makes it possible to apply some positional methods of group judgement to the case of ties in experts’ opinions, as well as in group judgements. Numerical examples are presented.tied alternatives in experts’ opinions, tied alternatives in group judgement, positional methods of making a group judgement

Ordering Events in Minkowski Space

We are given k points (events) in (n+1)-dimensional Minkowski space. Using the theory of hyperplane arrangments and chromatic polynomials, we obtain information the number of different orders in which the events can occur in different reference frames if the events are sufficiently generic. We consider the question of what sets of orderings of the points are possible and show a connection with sphere orders and the allowable sequences of Goodman and Pollack.Comment: 17 page

Proportional Approval Voting, Harmonic k-median, and Negative Association

We study a generic framework that provides a unified view on two important classes of problems: (i) extensions of the k-median problem where clients are interested in having multiple facilities in their vicinity (e.g., due to the fact that, with some small probability, the closest facility might be malfunctioning and so might not be available for using), and (ii) finding winners according to some appealing multiwinner election rules, i.e., election system aimed for choosing representatives bodies, such as parliaments, based on preferences of a population of voters over individual candidates. Each problem in our framework is associated with a vector of weights: we show that the approximability of the problem depends on structural properties of these vectors. We specifically focus on the harmonic sequence of weights, since it results in particularly appealing properties of the considered problem. In particular, the objective function interpreted in a multiwinner election setup reflects to the well-known Proportional Approval Voting (PAV) rule. Our main result is that, due to the specific (harmonic) structure of weights, the problem allows constant factor approximation. This is surprising since the problem can be interpreted as a variant of the k-median problem where we do not assume that the connection costs satisfy the triangle inequality. To the best of our knowledge this is the first constant factor approximation algorithm for a variant of k-median that does not require this assumption. The algorithm we propose is based on dependent rounding [Srinivasan, FOCS\u2701] applied to the solution of a natural LP-relaxation of the problem. The rounding process is well known to produce distributions over integral solutions satisfying Negative Correlation (NC), which is usually sufficient for the analysis of approximation guarantees offered by rounding procedures. In our analysis, however, we need to use the fact that the carefully implemented rounding process satisfies a stronger property, called Negative Association (NA), which allows us to apply standard concentration bounds for conditional random variables

Use of Enumerative Combinatorics for proving the applicability of an asymptotic stability result on discrete-time SIS epidemics in complex networks

In this paper, we justify by the use of Enumerative Combinatorics, that the results obtained in \cite{Alarcon1}, where is analysed the complex dynamics of an epidemic model to identify the nodes that contribute the most to the propagation process and because of that are good candidates to be controlled in the network in order to stabilize the network to reach the extinction state, is applicable in almost all the cases. The model analysed was proposed in \cite{Gomez1} %et al. [Phys.Rev.E 84, 036105(2011)] and results obtained in \cite{Alarcon1} implies that it is not necessary to control all nodes, but only a minimal set of nodes if the topology of the network is not regular. This result could be important in the spirit of considering policies of isolation or quarantine of those nodes to be controlled. Simulation results were presented in \cite{Alarcon1} for large free-scale and regular networks, that corroborate the theoretical findings. In this article we justify the applicability of the controllability result obtained in \cite{Alarcon1} in almost all the cases by means of the use of Combinatorics. {\em Mathematics Subjects Classification}: 05A16,34H20,58E25 {\em Keywords}: Asymptotic Graph Enumeration Problems; Network control; virus spreading

Optimization and validation of automated hippocampal subfield segmentation across the lifespan

Automated segmentation of hippocampal (HC) subfields from magnetic resonance imaging (MRI) is gaining popularity, but automated procedures that afford high speed and reproducibility have yet to be extensively validated against the standard, manual morphometry. We evaluated the concurrent validity of an automated method for hippocampal subfields segmentation (automated segmentation of hippocampal subfields, ASHS; Yushkevich et al.,2015b) using a customized atlas of the HC body, with manual morphometry as a standard. We built a series of customized atlases comprising the entorhinal cortex (ERC) and subfields of the HC body from manually segmented images, and evaluated the correspondence of automated segmentations with manual morphometry. In samples with age ranges of 6–24 and 62–79 years, 20 participants each, we obtained validity coefficients (intraclass correlations, ICC) and spatial overlap measures (dice similarity coefficient) that varied substantially across subfields. Anterior and posterior HC body evidenced the greatest discrepancies between automated and manual segmentations. Adding anterior and posterior slices for atlas creation and truncating automated output to the ranges manually defined by multiple neuroanatomical landmarks substantially improved the validity of automated segmentation, yielding ICC above 0.90 for all subfields and alleviating systematic bias. We cross-validated the developed atlas on an independent sample of 30 healthy adults (age 31–84) and obtained good to excellent agreement: ICC (2) = 0.70–0.92. Thus, with described customization steps implemented by experts trained in MRI neuroanatomy, ASHS shows excellent concurrent validity, and can become a promising method for studying age-related changes in HC subfield volumes

Ensemble classification and signal image processing for genus Gyrodactylus (Monogenea)

This thesis presents an investigation into Gyrodactylus species recognition, making use of machine learning classification and feature selection techniques, and explores image feature extraction to demonstrate proof of concept for an envisaged rapid, consistent and secure initial identification of pathogens by field workers and non-expert users. The design of the proposed cognitively inspired framework is able to provide confident discrimination recognition from its non-pathogenic congeners, which is sought in order to assist diagnostics during periods of a suspected outbreak. Accurate identification of pathogens is a key to their control in an aquaculture context and the monogenean worm genus Gyrodactylus provides an ideal test-bed for the selected techniques. In the proposed algorithm, the concept of classification using a single model is extended to include more than one model. In classifying multiple species of Gyrodactylus, experiments using 557 specimens of nine different species, two classifiers and three feature sets were performed. To combine these models, an ensemble based majority voting approach has been adopted. Experimental results with a database of Gyrodactylus species show the superior performance of the ensemble system. Comparison with single classification approaches indicates that the proposed framework produces a marked improvement in classification performance. The second contribution of this thesis is the exploration of image processing techniques. Active Shape Model (ASM) and Complex Network methods are applied to images of the attachment hooks of several species of Gyrodactylus to classify each species according to their true species type. ASM is used to provide landmark points to segment the contour of the image, while the Complex Network model is used to extract the information from the contour of an image. The current system aims to confidently classify species, which is notifiable pathogen of Atlantic salmon, to their true class with high degree of accuracy. Finally, some concluding remarks are made along with proposal for future work