Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.

Properties of the Bellman Gamma Distribution

2000 Mathematics Subject Classification: 62H10.

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

The Shapley value for shortest path games

In this paper shortest path games are considered. The transportation of a good in a network has costs and benet too. The problem is to divide the prot of the transportation among the players. Fragnelli et al (2000) introduce the class of shortest path games, which coincides with the class of monotone games. They also give a characterization of the Shapley value on this class of games. In this paper we consider further four characterizations of the Shapley value (Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s axiomatizations), and conclude that all the mentioned axiomatizations are valid for shortest path games. Fragnelli et al (2000)'s axioms are based on the graph behind the problem, in this paper we do not consider graph specic axioms, we take TU axioms only, that is, we consider all shortest path problems and we take the view of abstract decision maker who focuses rather on the abstract problem than on the concrete situations.

The Shapley value for shortest path games

In this paper shortest path games are considered. The transportation of a good in a network has costs and benet too. The problem is to divide the prot of the transportation among the players. Fragnelli et al (2000) introduce the class of shortest path games, which coincides with the class of monotone games. They also give a characterization of the Shapley value on this class of games. In this paper we consider further four characterizations of the Shapley value (Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s axiomatizations), and conclude that all the mentioned axiomatizations are valid for shortest path games. Fragnelli et al (2000)'s axioms are based on the graph behind the problem, in this paper we do not consider graph specic axioms, we take TU axioms only, that is, we consider all shortest path problems and we take the view of abstract decision maker who focuses rather on the abstract problem than on the concrete situations.

Stable sets in one-seller assignment games

We consider von Neumann -- Morgenstern stable sets in assignment games with one seller and many buyers. We prove that a set of imputations is a stable set if and only if it is the graph of a certain type of continuous and monotone function. This characterization enables us to interpret the standards of behavior encompassed by the various stable sets as possible outcomes of well-known auction procedures when groups of buyers may form bidder rings. We also show that the union of all stable sets can be described as the union of convex polytopes all of whose vertices are marginal contribution payoff vectors. Consequently, each stable set is contained in the Weber set. The Shapley value, however, typically falls outside the union of all stable sets.

Leap Aided Modelling (LAM) in Blender

L'evoluzione tecnologica e l'utilizzo crescente della computer grafica in diversi settori stanno suscitando l'interesse di sempre più persone verso il mondo della modellazione 3D. I software di modellazione, tuttavia, si presentano spesso inadeguati all'utilizzo da parte di utenti senza esperienza, soprattutto a causa dei comandi di navigazione e modellazione poco intuitivi. Dal punto di vista dell'interazione uomo-computer, questi software devono infatti affrontare un grande ostacolo: il rapporto tra dispositivi di input 2D (come il mouse) e la manipolazione di una scena 3D. Il progetto presentato in questa tesi è un addon per Blender che consente di utilizzare il dispositivo Leap Motion come ausilio alla modellazione di superfici in computer grafica. L'obiettivo di questa tesi è stato quello di progettare e realizzare un'interfaccia user-friendly tra Leap e Blender, in modo da potere utilizzare i sensori del primo per facilitare ed estendere i comandi di navigazione e modellazione del secondo. L'addon realizzato per Blender implementa il concetto di LAM (Leap Aided Modelling: modellazione assistita da Leap), consentendo quindi di estendere le feature di Blender riguardanti la selezione, lo spostamento e la modifica degli oggetti in scena, la manipolazione della vista utente e la modellazione di curve e superfici Non Uniform Rational B-Splines (NURBS). Queste estensioni sono state create per rendere più veloci e semplici le operazioni altrimenti guidate esclusivamente da mouse e tastiera.

Weighted nucleoli and dually essential coalitions

We consider linearly weighted versions of the least core and the (pre)nucleolus and investigate the reduction possibilities in their computation. We slightly extend some well-known related results and establish their counterparts by using the dual game. Our main results imply, for example, that if the core of the game is not empty, all dually inessential coalitions (which can be weakly minorized by a partition in the dual game) can be ignored when we compute the per-capita least core and the per-capita (pre)nucleolus from the dual game. This could lead to the design of polynomial time algorithms for the per-capita (and other monotone nondecreasingly weighted versions of the) least core and the (pre)nucleolus in specific classes of balanced games with polynomial many dually esential coalitions.

Feature recognition & tool path generation for 5 axis step-nc machining of free form / irregular contoured surfaces

This research paper presents a five step algorithm to generate tool paths for machining Free form / Irregular Contoured Surface(s) (FICS) by adopting STEP-NC (AP-238) format. In the first step, a parametrized CAD model with FICS is created or imported in UG-NX6.0 CAD package. The second step recognizes the features and calculates a Closeness Index (CI) by comparing them with the B-Splines / Bezier surfaces. The third step utilizes the CI and extracts the necessary data to formulate the blending functions for identified features. In the fourth step Z-level 5 axis tool paths are generated by adopting flat and ball end mill cutters. Finally, in the fifth step, tool paths are integrated with STEP-NC format and validated. All these steps are discussed and explained through a validated industrial component.

Integration of cad/ tool path data for 5-axis step-nc machining of free form / irrregular contoured surfaces

This research paper presents the work on feature recognition, tool path data generation and integration with STEP-NC (AP-238 format) for features having Free form / Irregular Contoured Surface(s) (FICS). Initially, the FICS features are modelled / imported in UG CAD package and a closeness index is generated. This is done by comparing the FICS features with basic B-Splines / Bezier curves / surfaces. Then blending functions are caculated by adopting convolution theorem. Based on the blending functions, contour offsett tool paths are generated and simulated for 5 axis milling environment. Finally, the tool path (CL) data is integrated with STEP-NC (AP-238) format. The tool path algorithm and STEP- NC data is tested with various industrial parts through an automated UFUNC plugin.

Improvement of Mineral and Bone Metabolism Markers Is Associated with Better Survival in Haemodialysis Patients: the COSMOS Study

BACKGROUND: Abnormalities in serum phosphorus, calcium and parathyroid hormone (PTH) have been associated with poor survival in haemodialysis patients. This COSMOS (Current management Of Secondary hyperparathyroidism: a Multicentre Observational Study) analysis assesses the association of high and low serum phosphorus, calcium and PTH with a relative risk of mortality. Furthermore, the impact of changes in these parameters on the relative risk of mortality throughout the 3-year follow-up has been investigated. METHODS:COSMOS is a 3-year, multicentre, open-cohort, prospective study carried out in 6797 adult chronic haemodialysis patients randomly selected from 20 European countries. RESULTS:Using Cox proportional hazard regression models and penalized splines analysis, it was found that both high and low serum phosphorus, calcium and PTH were associated with a higher risk of mortality. The serum values associated with the minimum relative risk of mortality were 4.4 mg/dL for serum phosphorus, 8.8 mg/dL for serum calcium and 398 pg/mL for serum PTH. The lowest mortality risk ranges obtained using as base the previous values were 3.6-5.2 mg/dL for serum phosphorus, 7.9-9.5 mg/dL for serum calcium and 168-674 pg/mL for serum PTH. Decreases in serum phosphorus and calcium and increases in serum PTH in patients with baseline values of >5.2 mg/dL (phosphorus), >9.5 mg/dL (calcium) and <168 pg/mL (PTH), respectively, were associated with improved survival. CONCLUSIONS:COSMOS provides evidence of the association of serum phosphorus, calcium and PTH and mortality, and suggests survival benefits of controlling chronic kidney disease-mineral and bone disorder biochemical parameters in CKD5D patients.

A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

SYSTEMS OF DIFFERENTIAL EQUATIONSTHAT ARE COMPETITIVE OR COOPERATIVE II:CONVERGENCE ALMOST EVERYWHERE*MORRIS W. HIRSCH

A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all of the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative). The main results in this article are the following. A cooperative system cannot have nonconstant attracting periodic solutions. In a cooperative system whose Jacobian matrices are irreducible the forward orbit converges for almost every point having compact forward orbit closure. In a cooperative system in 2 dimensions, every solution is eventually monotone.  Applications are made to generalizations of positive feedback loops.

Development of a Real-Time Hierarchical 3D Path Planning Algorithm for Unmanned Aerial Vehicles

Unmanned aerial vehicles (UAVs) frequently operate in partially or entirely unknown environments. As the vehicle traverses the environment and detects new obstacles, rapid path replanning is essential to avoid collisions. This thesis presents a new algorithm called Hierarchical D* Lite (HD*), which combines the incremental algorithm D* Lite with a novel hierarchical path planning approach to replan paths sufficiently fast for real-time operation. Unlike current hierarchical planning algorithms, HD* does not require map corrections before planning a new path. Directional cost scale factors, path smoothing, and Catmull-Rom splines are used to ensure the resulting paths are feasible. HD* sacrifices optimality for real-time performance. Its computation time and path quality are dependent on the map size, obstacle density, sensor range, and any restrictions on planning time. For the most complex scenarios tested, HD* found paths within 10% of optimal in under 35 milliseconds.

Some results on open-edge and open mobile guarding of polygons and triangulations

This paper focuses on a variation of the Art Gallery problem that considers open-edge guards and open mobile-guards. A mobile guard can be placed on edges and diagonals of a polygon, and the ‘open’ prefix means that the endpoints of such an edge or diagonal are not taken into account for visibility purposes. This paper studies the number of guards that are sufficient and sometimes necessary to guard some classes of simple polygons for both open-edge and open mobile-guards. A wide range of polygons is studied, which include orthogonal polygons with or without holes, spirals, orthogonal spirals and monotone polygons. Moreover, this problem is also considered for planar triangulation graphs using open-edge guards.