The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés- Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view

A Mathematical Approach to Paint Production Process Optimization

As the global paint market steadily grows, finding the most effective processing model to increase production capacity will be the best way to enhance competitiveness. Therefore, this study proposes two production environments commonly used in the paint industry: build-to-order (BTO) and the variation of a configuration-to-order (CTO), called group production, to schedule paint production. Mixed-Integer Linear Program (MILP) was solved using genetic algorithms (GA) to analyze two production environments with various products, different set-up times, and different average demand for each product. The models determine the number of batches, the size and product of each batch, and the batch sequence such that the makespan is minimized. Several numerical instances are presented to analyze the proposed models. The experimental results show that BTO production completes products faster than group production when products are simple (low variety). However, group production is more applicable to manufacturing diverse products (high variety) and mass production (high volume). Finally, the number of colors has the most significant impact on the two models, followed by the number of product types, and finally the average demand

Математические модели нечеткой случайной величины: сравнительное изучение

В статье проведено сравнительное изучение основных подходов к определению нечеткой случайной величины и ее числовых характеристик. Рассматриваются примеры выполнения и невыполнения свойств, характерных для обычных случайных величин при различных определениях нечетких случайных величин. Предлагаются методы идентификации ожидаемого значения нечетких случайных величи

Estimation of Fourier Transform Using Alias-free Hybrid-Stratified Sampling

This paper proposes a novel method of estimating the Fourier Transform (FT) of deterministic, continuous-time signals, from a finite number \u1d441 of their samples taken from a fixed-length observation window. It uses alias-free hybrid-stratified sampling to probe the processed signal at a mixture of deterministic and random time instants. The FT estimator, specifically designed to work with this sampling scheme, is unbiased, consistent and fast converging. It is shown that if the processed signal has continuous third derivative, then the estimator's rate of uniform convergence in mean square is \u1d441^−5. Therefore, in terms of frequency-independent upper bounds on the FT estimation error, the proposed approach significantly outperforms existing estimators that utilize alias-free sampling, such as total random, stratified sampling, and antithetical stratified whose rate of uniform convergence is \u1d441^−1. It is proven here that \u1d441^−1 is a guaranteed minimum rate for all stratified-sampling-based estimators satisfying four weak conditions formulated in this paper. Owing to the alias-free nature of the sampling scheme, no constraints are imposed on the spectral support of the processed signal or the frequency ranges for which the Fourier Transform is estimated

Channel assembling and resource allocation in multichannel spectrum sharing wireless networks

Submitted in fulfilment of the academic requirements for the degree of Doctor of Philosophy (Ph.D.) in Engineering, in the School of Electrical and Information Engineering, Faculty of Engineering and the Built Environment, at the University of the Witwatersrand, Johannesburg, South Africa, 2017The continuous evolution of wireless communications technologies has increasingly imposed a burden on the use of radio spectrum. Due to the proliferation of new wireless networks applications and services, the radio spectrum is getting saturated and becoming a limited resource. To a large extent, spectrum scarcity may be a result of deficient spectrum allocation and management policies, rather than of the physical shortage of radio frequencies. The conventional static spectrum allocation has been found to be ineffective, leading to overcrowding and inefficient use. Cognitive radio (CR) has therefore emerged as an enabling technology that facilitates dynamic spectrum access (DSA), with a great potential to address the issue of spectrum scarcity and inefficient use. However, provisioning of reliable and robust communication with seamless operation in cognitive radio networks (CRNs) is a challenging task. The underlying challenges include development of non-intrusive dynamic resource allocation (DRA) and optimization techniques. The main focus of this thesis is development of adaptive channel assembling (ChA) and DRA schemes, with the aim to maximize performance of secondary user (SU) nodes in CRNs, without degrading performance of primary user (PU) nodes in a primary network (PN). The key objectives are therefore four-fold. Firstly, to optimize ChA and DRA schemes in overlay CRNs. Secondly, to develop analytical models for quantifying performance of ChA schemes over fading channels in overlay CRNs. Thirdly, to extend the overlay ChA schemes into hybrid overlay and underlay architectures, subject to power control and interference mitigation; and finally, to extend the adaptive ChA and DRA schemes for multiuser multichannel access CRNs. Performance analysis and evaluation of the developed ChA and DRA is presented, mainly through extensive simulations and analytical models. Further, the cross validation has been performed between simulations and analytical results to confirm the accuracy and preciseness of the novel analytical models developed in this thesis. In general, the presented results demonstrate improved performance of SU nodes in terms of capacity, collision probability, outage probability and forced termination probability when employing the adaptive ChA and DRA in CRNs.CK201

Adaptive and learning-based formation control of swarm robots

Autonomous aerial and wheeled mobile robots play a major role in tasks such as search and rescue, transportation, monitoring, and inspection. However, these operations are faced with a few open challenges including robust autonomy, and adaptive coordination based on the environment and operating conditions, particularly in swarm robots with limited communication and perception capabilities. Furthermore, the computational complexity increases exponentially with the number of robots in the swarm. This thesis examines two different aspects of the formation control problem. On the one hand, we investigate how formation could be performed by swarm robots with limited communication and perception (e.g., Crazyflie nano quadrotor). On the other hand, we explore human-swarm interaction (HSI) and different shared-control mechanisms between human and swarm robots (e.g., BristleBot) for artistic creation. In particular, we combine bio-inspired (i.e., flocking, foraging) techniques with learning-based control strategies (using artificial neural networks) for adaptive control of multi- robots. We first review how learning-based control and networked dynamical systems can be used to assign distributed and decentralized policies to individual robots such that the desired formation emerges from their collective behavior. We proceed by presenting a novel flocking control for UAV swarm using deep reinforcement learning. We formulate the flocking formation problem as a partially observable Markov decision process (POMDP), and consider a leader-follower configuration, where consensus among all UAVs is used to train a shared control policy, and each UAV performs actions based on the local information it collects. In addition, to avoid collision among UAVs and guarantee flocking and navigation, a reward function is added with the global flocking maintenance, mutual reward, and a collision penalty. We adapt deep deterministic policy gradient (DDPG) with centralized training and decentralized execution to obtain the flocking control policy using actor-critic networks and a global state space matrix. In the context of swarm robotics in arts, we investigate how the formation paradigm can serve as an interaction modality for artists to aesthetically utilize swarms. In particular, we explore particle swarm optimization (PSO) and random walk to control the communication between a team of robots with swarming behavior for musical creation

Registration of prostate surfaces for image-guided robotic surgery via the da Vinci System

Organ-confined prostate cancer represents a commonly diagnosed cancer among men rendering an early diagnosis and screening a necessity. The prostate laparoscopic surgery using the da Vinci system is a minimally invasive, computer assisted and image-guided surgery application that provides surgeons with (i) navigational assistance by displaying targeting lesions of the intraoperative prostate anatomy onto aligned preoperative high-field magnetic resonance imaging (MRI) scans of the pelvis; and (ii) an effective clinical management of intra-abdominal cancers in real time. Such an image guidance system can improve both functional and oncological outcomes as well as augment the learning curve of the process increasing simultaneously the eligibility of patients for surgical resection. By segmenting MRI scans into 3D models of intraprostatic anatomy preoperatively, and overlaying them onto 3D stereoendoscopic images acquired intraoperatively using the da Vinci surgical system, a graphical representation of intraoperative anatomy can be provided for surgical navigation. The preoperative MRI surfaces are full 3D models and the stereoendoscopic images represent partial 3D views of the prostate due to occlusion. Hence achieving an accurate non-rigid image registration of full prostate surfaces onto occluded ones in real time becomes of critical importance, especially for use intraoperatively with the stereoendoscopic and MRI imaging modalities. This work exploits the registration accuracy that can be achieved from the application of selected state-of-the-art non-rigid registration algorithms and in doing so identifies the most accurate technique(s) for registration of full prostate surfaces onto occluded ones; a series of rigorous computational registration experiments is performed on synthetic target prostate data, which are aligned manually onto the MRI prostate models before registration is initiated. This effort extends to using real target prostate data leading to visually acceptable non-rigid registration results. A great deal of emphasis is placed on examining the capacity of the selected non-rigid algorithms to recover the deformation of the intraoperative prostate surfaces; the deformation of prostate can become pronounced during the surgical intervention due to surgical-induced anatomical deformities and pathological or other factors. The warping accuracy of the non-rigid registration algorithms is measured within the space of common overlap (established between the full MRI model and the target scene) and beyond. From the results of the registrations to occluded and deformed prostate surfaces (in the space beyond common overlap) it is concluded that the modified versions of the Kernel Correlation/Thin-plane Spline (KC/TPS) and Gaussian Mixture Model/Thin-plane Spline (GMM/TPS) methodologies can provide the clinical accuracy required for image-guided prostate surgery procedures (performed by the da Vinci system) as long as the size of the target scene is greater than ca. 30% of the full MRI surface. For the modified KC/TPS and GMM/TPS non-rigid registration techniques to be clinically acceptable when the measurement noise is also included in the simulations: (i) the size of the target model must be greater than ca. 38% of the full MRI surface; (ii) the standard deviation σ of the contributing Gaussian noise must be less than 0.345 for μ=0; and (iii) the observed deformation must not be characterized by excessively increased complexity. Otherwise the contribution of Gaussian noise must be explicitly parameterized in the objective cost functions of these non-rigid algorithms. The Expectation Maximization/Thin-plane Spline (EM/TPS) non-rigid registration algorithm cannot recover the prostate surface deformation accurately in full-model-to-occluded-model registrations due to the way that the correspondences are estimated. However, EM/TPS is more accurate than KC+TPS and GMM+TPS in recovering the deformation of the prostate surface in full-model-to-full-model registrations