Using generative models for handwritten digit recognition

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques.

Flow patterns and performance of distillation trays

It is known that distillation tray efficiency depends on the liquid flow pattern, particularly for large diameter trays. Scale·up failures due to liquid channelling have occurred, and it is known that fitting flow control devices to trays sometirr.es improves tray efficiency. Several theoretical models which explain these observations have been published. Further progress in understanding is at present blocked by lack of experimental measurements of the pattern of liquid concentration over the tray. Flow pattern effects are expected to be significant only on commercial size trays of a large diameter and the lack of data is a result of the costs, risks and difficulty of making these measurements on full scale production columns. This work presents a new experiment which simulates distillation by water cooling. and provides a means of testing commercial size trays in the laboratory. Hot water is fed on to the tray and cooled by air forced through the perforations. The analogy between heat and mass transfer shows that the water temperature at any point is analogous to liquid concentration and the enthalpy of the air is analogous to vapour concentration. The effect of the liquid flow pattern on mass transfer is revealed by the temperature field on the tray. The experiment was implemented and evaluated in a column of 1.2 m. dia. The water temperatures were measured by thennocouples interfaced to an electronic computerised data logging system. The "best surface" through the experimental temperature measurements was obtained by the mathematical technique of B. splines, and presented in tenos of lines of constant temperature. The results revealed that in general liquid channelling is more imponant in the bubbly "mixed" regime than in the spray regime. However, it was observed that severe channelling also occurred for intense spray at incipient flood conditions. This is an unexpected result. A computer program was written to calculate point efficiency as well as tray efficiency, and the results were compared with distillation efficiencies for similar loadings. The theoretical model of Porter and Lockett for predicting distillation was modified to predict water cooling and the theoretical predictions were shown to be similar to the experimental temperature profiles. A comparison of the repeatability of the experiments with an errors analysis revealed that accurate tray efficiency measurements require temperature measurements to better than ± 0.1 °c which is achievable with conventional techniques. This was not achieved in this work, and resulted in considerable scatter in the efficiency results. Nevertheless it is concluded that the new experiment is a valuable tool for investigating the effect of the liquid flow pattern on tray mass transfer.

Computer aided design and manufacture for three dimensional milling

Advances in both computer technology and the necessary mathematical models capable of capturing the geometry of arbitarily shaped objects has led to the development in this thesis of a surface generation package called 'IBSCURF' aimed at providing a more economically viable solution to free-form surface manufacture. A suit of computer programs written in FORTRAN 77 has been developed to provide computer aids for every aspect of work in designing and machining free-form surfaces. A vector-valued parametric method was used for shape description and a lofting technique employed for the construction of the surface. The development of the package 'IBSCURF' consists of two phases. The first deals with CAD. The design process commences in defining the cross-sections which are represented by uniform B-spline curves as approximations to give polygons. The order of the curve and the position and number of the polygon vertices can be used as parameters for the modification to achieve the required curves. When the definitions of the sectional curves is complete, the surface is interpolated over them by cubic cardinal splines. To use the CAD function of the package to design a mould for a plastic handle, a mathematical model was developed. To facilitate the integration of design and machining using the mathematical representation of the surface, the second phase of the package is concerned with CAM which enables the generation of tool offset positions for ball-nosed cutters and a general post-processor has been developed which automatically generates NC tape programs for any CNC milling machine. The two phases of these programs have been successfully implemented, as a CAD/CAM package for free-form surfaces on the VAX 11/750 super-minicomputer with graphics facilities for displaying drawings interactively on the terminal screen. The development of this package has been beneficial in all aspects of design and machining of free form surfaces.

Penalized Least Squares Fitting

* Supported by the Army Research Office under grant DAAD-19-02-10059.

Detection of foveation windows and analysis of foveation sequences in congenital nystagmus

Congenital nystagmus (CN) is an ocular-motor disorder characterised by involuntary, conjugated ocular oscillations, that can arise since the first months of life. Pathogenesis of congenital nystagmus is still under investigation. In general, CN patients show a considerable decrease of their visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations, mainly horizontal. However, image stabilisation is still achieved during the short periods in which eye velocity slows down while the target image is placed onto the fovea (called foveation intervals). To quantify the extent of nystagmus, eye movement recording are routinely employed, allowing physicians to extract and analyse nystagmus main features such as shape, amplitude and frequency. Using eye movement recording, it is also possible to compute estimated visual acuity predictors: analytical functions which estimates expected visual acuity using signal features such as foveation time and foveation position variability. Use of those functions add information to typical visual acuity measurement (e.g. Landolt C test) and could be a support for therapy planning or monitoring. This study focus on robust detection of CN patients' foveations. Specifically, it proposes a method to recognize the exact signal tracts in which a subject foveates, This paper also analyses foveation sequences. About 50 eyemovement recordings, either infrared-oculographic or electrooculographic, from different CN subjects were acquired. Results suggest that an exponential interpolation for the slow phases of nystagmus could improve foveation time computing and reduce influence of breaking saccades and data noise. Moreover a concise description of foveation sequence variability can be achieved using non-fitting splines. © 2009 Springer Berlin Heidelberg.

Application of MARS for the Construction of Nonparametric Models

2000 Mathematics Subject Classification: 62G08, 62P30.

Monte Carlo Method for Reconstruction of Densities

2000 Mathematics Subject Classification: 65C05

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.

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.

Towards a performance based design of shear walls based on damage criteria = Vers un dimensionnement performanciel des murs de refend basé sur des critères d'endommagement

Le dimensionnement basé sur la performance (DBP), dans une approche déterministe, caractérise les objectifs de performance par rapport aux niveaux de performance souhaités. Les objectifs de performance sont alors associés à l'état d'endommagement et au niveau de risque sismique établis. Malgré cette approche rationnelle, son application est encore difficile. De ce fait, des outils fiables pour la capture de l'évolution, de la distribution et de la quantification de l'endommagement sont nécessaires. De plus, tous les phénomènes liés à la non-linéarité (matériaux et déformations) doivent également être pris en considération. Ainsi, cette recherche montre comment la mécanique de l'endommagement pourrait contribuer à résoudre cette problématique avec une adaptation de la théorie du champ de compression modifiée et d'autres théories complémentaires. La formulation proposée adaptée pour des charges monotones, cycliques et de type pushover permet de considérer les effets non linéaires liés au cisaillement couplé avec les mécanismes de flexion et de charge axiale. Cette formulation est spécialement appliquée à l'analyse non linéaire des éléments structuraux en béton soumis aux effets de cisaillement non égligeables. Cette nouvelle approche mise en œuvre dans EfiCoS (programme d'éléments finis basé sur la mécanique de l'endommagement), y compris les critères de modélisation, sont également présentés ici. Des calibrations de cette nouvelle approche en comparant les prédictions avec des données expérimentales ont été réalisées pour les murs de refend en béton armé ainsi que pour des poutres et des piliers de pont où les effets de cisaillement doivent être pris en considération. Cette nouvelle version améliorée du logiciel EFiCoS a démontrée être capable d'évaluer avec précision les paramètres associés à la performance globale tels que les déplacements, la résistance du système, les effets liés à la réponse cyclique et la quantification, l'évolution et la distribution de l'endommagement. Des résultats remarquables ont également été obtenus en référence à la détection appropriée des états limites d'ingénierie tels que la fissuration, les déformations unitaires, l'éclatement de l'enrobage, l'écrasement du noyau, la plastification locale des barres d'armature et la dégradation du système, entre autres. Comme un outil pratique d'application du DBP, des relations entre les indices d'endommagement prédits et les niveaux de performance ont été obtenus et exprimés sous forme de graphiques et de tableaux. Ces graphiques ont été développés en fonction du déplacement relatif et de la ductilité de déplacement. Un tableau particulier a été développé pour relier les états limites d'ingénierie, l'endommagement, le déplacement relatif et les niveaux de performance traditionnels. Les résultats ont démontré une excellente correspondance avec les données expérimentales, faisant de la formulation proposée et de la nouvelle version d'EfiCoS des outils puissants pour l'application de la méthodologie du DBP, dans une approche déterministe.

Incomplete information games of conflict and collective action

My thesis consists of three essays that investigate strategic interactions between individuals engaging in risky collective action in uncertain environments. The first essay analyzes a broad class of incomplete information coordination games with a wide range of applications in economics and politics. The second essay draws from the general model developed in the first essay to study decisions by individuals of whether to engage in protest/revolution/coup/strike. The final essay explicitly integrates state response to the analysis. The first essay, Coordination Games with Strategic Delegation of Pivotality, exhaustively analyzes a class of binary action, two-player coordination games in which players receive stochastic payoffs only if both players take a ``stochastic-coordination action''. Players receive conditionally-independent noisy private signals about the normally distributed stochastic payoffs. With this structure, each player can exploit the information contained in the other player's action only when he takes the “pivotalizing action”. This feature has two consequences: (1) When the fear of miscoordination is not too large, in order to utilize the other player's information, each player takes the “pivotalizing action” more often than he would based solely on his private information, and (2) best responses feature both strategic complementarities and strategic substitutes, implying that the game is not supermodular nor a typical global game. This class of games has applications in a wide range of economic and political phenomena, including war and peace, protest/revolution/coup/ strike, interest groups lobbying, international trade, and adoption of a new technology. My second essay, Collective Action with Uncertain Payoffs, studies the decision problem of citizens who must decide whether to submit to the status quo or mount a revolution. If they coordinate, they can overthrow the status quo. Otherwise, the status quo is preserved and participants in a failed revolution are punished. Citizens face two types of uncertainty. (a) non-strategic: they are uncertain about the relative payoffs of the status quo and revolution, (b) strategic: they are uncertain about each other's assessments of the relative payoff. I draw on the existing literature and historical evidence to argue that the uncertainty in the payoffs of status quo and revolution is intrinsic in politics. Several counter-intuitive findings emerge: (1) Better communication between citizens can lower the likelihood of revolution. In fact, when the punishment for failed protest is not too harsh and citizens' private knowledge is accurate, then further communication reduces incentives to revolt. (2) Increasing strategic uncertainty can increase the likelihood of revolution attempts, and even the likelihood of successful revolution. In particular, revolt may be more likely when citizens privately obtain information than when they receive information from a common media source. (3) Two dilemmas arise concerning the intensity and frequency of punishment (repression), and the frequency of protest. Punishment Dilemma 1: harsher punishments may increase the probability that punishment is materialized. That is, as the state increases the punishment for dissent, it might also have to punish more dissidents. It is only when the punishment is sufficiently harsh, that harsher punishment reduces the frequency of its application. Punishment Dilemma 1 leads to Punishment Dilemma 2: the frequencies of repression and protest can be positively or negatively correlated depending on the intensity of repression. My third essay, The Repression Puzzle, investigates the relationship between the intensity of grievances and the likelihood of repression. First, I make the observation that the occurrence of state repression is a puzzle. If repression is to succeed, dissidents should not rebel. If it is to fail, the state should concede in order to save the costs of unsuccessful repression. I then propose an explanation for the “repression puzzle” that hinges on information asymmetries between the state and dissidents about the costs of repression to the state, and hence the likelihood of its application by the state. I present a formal model that combines the insights of grievance-based and political process theories to investigate the consequences of this information asymmetry for the dissidents' contentious actions and for the relationship between the magnitude of grievances (formulated here as the extent of inequality) and the likelihood of repression. The main contribution of the paper is to show that this relationship is non-monotone. That is, as the magnitude of grievances increases, the likelihood of repression might decrease. I investigate the relationship between inequality and the likelihood of repression in all country-years from 1981 to 1999. To mitigate specification problem, I estimate the probability of repression using a generalized additive model with thin-plate splines (GAM-TPS). This technique allows for flexible relationship between inequality, the proxy for the costs of repression and revolutions (income per capita), and the likelihood of repression. The empirical evidence support my prediction that the relationship between the magnitude of grievances and the likelihood of repression is non-monotone.

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.

Triangular mesh parameterization with trimmed surfaces

Given a 2manifold triangular mesh \(M \subset {\mathbb {R}}^3\), with border, a parameterization of \(M\) is a FACE or trimmed surface \(F=\{S,L_0,\ldots, L_m\}\) -- \(F\) is a connected subset or region of a parametric surface \(S\), bounded by a set of LOOPs \(L_0,\ldots ,L_m\) such that each \(L_i \subset S\) is a closed 1manifold having no intersection with the other \(L_j\) LOOPs -- The parametric surface \(S\) is a statistical fit of the mesh \(M\) -- \(L_0\) is the outermost LOOP bounding \(F\) and \(L_i\) is the LOOP of the ith hole in \(F\) (if any) -- The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc -- Stateofart mesh procedures parameterize a rectangular mesh \(M\) -- To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes \(M\) presenting holes and concavities -- We synthesize a parametric surface \(S \subset {\mathbb {R}}^3\) which approximates a superset of the mesh \(M\) -- Then, we compute a set of LOOPs trimming \(S\), and therefore completing the FACE \(F=\ {S,L_0,\ldots ,L_m\}\) -- Our algorithm gives satisfactory results for \(M\) having low Gaussian curvature (i.e., \(M\) being quasi-developable or developable) -- This assumption is a reasonable one, since \(M\) is the product of manifold segmentation preprocessing -- Our algorithm computes: (1) a manifold learning mapping \(\phi : M \rightarrow U \subset {\mathbb {R}}^2\), (2) an inverse mapping \(S: W \subset {\mathbb {R}}^2 \rightarrow {\mathbb {R}}^3\), with \ (W\) being a rectangular grid containing and surpassing \(U\) -- To compute \(\phi\) we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE) -- For the back mapping (NURBS) \(S\) the crucial step is to find a control polyhedron \(P\), which is an extrapolation of \(M\) -- We calculate \(P\) by extrapolating radial basis functions that interpolate points inside \(\phi (M)\) -- We successfully test our implementation with several datasets presenting concavities, holes, and are extremely nondevelopable -- Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization