<p>Distributed real-time system consists of many tasks on different processors communicating with</p><p>each other. The communication between these tasks must occur in bounded time. In our thesis we</p><p>are considering a holistic approach to estimate the end-to-end delays between two processors</p><p>communicating with each other. For both tasks scheduled by fixed priority and dynamic priority,</p><p>the system model considered is time token passing ring. The method is described to calculate</p><p>worst-case communication delay of the message sent by certain tasks over the network. Once the</p><p>worst-case communication delay of the message is obtained, and all required parameters are</p><p>provided i.e. deadline of the message, transmission time of the packet etc, one can figure out how</p><p>many messages will successfully meet their deadline. Thus this will enable us to select</p><p>appropriate algorithm according to system requirement.</p>

Distributed real-time system consists of many tasks on different processors communicating with each other. The communication between these tasks must occur in bounded time. In our thesis we are considering a holistic approach to estimate the end-to-end delays between two processors communicating with each other. For both tasks scheduled by fixed priority and dynamic priority, the system model considered is time token passing ring. The method is described to calculate worst-case communication delay of the message sent by certain tasks over the network. Once the worst-case communication delay of the message is obtained, and all required parameters are provided i.e. deadline of the message, transmission time of the packet etc, one can figure out how many messages will successfully meet their deadline. Thus this will enable us to select appropriate algorithm according to system requirement.

Diss. Uppsala : Univ., 2002.

Downlink power control and beamforming designs in wireless system have been a recent research focus. To achieve reliable and efficient designs, good estimation of wireless channel knowledge is desired. However, the presence of uncertain channel knowledge due to constant changing radio environment will cause performance degradation in system designs. Thus the mismatches between the actual and presumed channel state information (CSI) may frequently occur in practical situations. Robust power control and beamforming were introduced considering the channel uncertainty. In this thesis, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach explicitly models uncertainties in the downlink channel correlation (DCC) matrices, uses worst-case performance optimization and guarantees that the quality of service (QoS) constraints are satisfied for all users using minimum amount of power. An iterative algorithm to find the optimum power allocation is proposed. The key in the iteration is the step to solve an originally non-convex problem to obtain worst-case uncertainty matrices. When the uncertainty is small enough to guarantee that the DCC matrices are positive semidefinite, we obtain a closed-form solution of this problem. When the uncertainty is large, we transform this intractable problem into a convex problem. Simulation results show that our proposed robust downlink power control using the approach of worst-case performance optimization converges in a few iterations and reduces the transmission power effectively under imperfect knowledge of the channel condition. / Thesis / Master of Applied Science (MASc)

In our bachelor thesis, we described an implicit data structure that, given a way to maintain an implicit representation of polylogarithmic buckets, could implement all the dynamic ordered dictionary operations in logarithmic time. We now fulfill our obligation and provide a corresponding construction of implicit buckets. 1

In some recent papers, the weight based statistical bounds have arguably explained time complexity better than the count based mathematical bounds. This is definitely true for average case where for an arbitrary code it is difficult to identify the pivotal operation or pivotal region in the code for taking the expectation and/or when the probability distribution, over which expectation is taken, becomes unrealistic over the problem domain. In worst case, it can certify whether a mathematical bound is conservative or not. Here we revisit the results on Bubble sort in sequential mode and make an independent study of the same algorithm in parallel mode using statistical bound

This thesis is made up of three parts: i) the development of a comprehensive computational model of the pulmonary (patho)physiology of healthy and diseased lungs, ii) the application of a novel optimisation-based approach to validate this computational model, and iii) the use of this model to optimise mechanical ventilator settings for patients with diseased lungs. The model described in this thesis is an extended implementation of the Nottingham Physiological Simulator (NPS) in MATLAB. An iterative multi-compartmental modelling approach is adopted, and modifications (based on physiological mechanisms) are proposed to characterise healthy as well as diseased states. In the second part of the thesis, an optimisation-based approach is employed to validate the robustness of this model. The model is subjected to simultaneous variations in the values of multiple physiologically relevant uncertain parameters with respect to a set of specified performance criteria, based on expected levels of variation in arterial blood gas values found in the patient population. Performance criteria are evaluated using computer simulations. Local and global optimisation algorithms are employed to search for the worst-case parameter combination that could cause the model outputs to deviate from their expected range of operation, i.e. violate the specified model performance criteria. The optimisation-based analysis is proposed as a useful complement to current statistical model validation techniques, which are reliant on matching data from in vitro and in vivo studies. The last section of the thesis considers the problem of optimising settings of mechanical ventilation in an Intensive Therapy Unit (ITU) for patients with diseased lungs. This is a challenging task for physicians who have to select appropriate mechanical ventilator settings to satisfy multiple, sometimes conflicting, objectives including i) maintaining adequate oxygenation, ii) maintaining adequate carbon dioxide clearance and iii) minimising the risks of ventilator associated lung injury (VALI). Currently, physicians are reliant on guidelines based on previous experience and recommendations from a very limited number of in vivo studies which, by their very nature, cannot form the basis of personalised, disease-specific treatment protocols. This thesis formulates the choice of ventilator settings as a constrained multi-objective optimisation problem, which is solved using a hybrid optimisation algorithm and a validated physiological simulation model, to optimise the settings of mechanical ventilation for a healthy lung and for several pulmonary disease cases. The optimal settings are shown to satisfy the conflicting clinical objectives, to improve the ventilation perfusion matching within the lung, and, crucially, to be disease-specific.

<p>In Black-Scholes model, the parameters -a volatility and an interest rate were assumed as constants. In this thesis we concentrate on behaviour of the volatility as</p><p>a function and we find more realistic models for the volatility, which elimate a risk</p><p>connected with behaviour of the volatility of an underlying asset. That is</p><p>the reason why we will study the Uncertain Volatility Model. In Chapter</p><p>1 we will make some theoretical introduction to the Uncertain Volatility Model</p><p>introduced by Avellaneda, Levy and Paras and study how it behaves in the different scenarios. In</p><p>Chapter 2 we choose one of the scenarios. We also introduce the BSB equation</p><p>and try to make some modification to narrow the uncertainty bands using</p><p>the idea of a static hedging. In Chapter 3 we try to construct the proper</p><p>portfolio for the static hedging and compare the theoretical results with the real</p><p>market data from the Stockholm Stock Exchange.</p>

We consider the survivable network design problem - the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worstcase analyses of two heuristics for the survivable network design problem.

In Black-Scholes model, the parameters -a volatility and an interest rate were assumed as constants. In this thesis we concentrate on behaviour of the volatility as a function and we find more realistic models for the volatility, which elimate a risk connected with behaviour of the volatility of an underlying asset. That is the reason why we will study the Uncertain Volatility Model. In Chapter 1 we will make some theoretical introduction to the Uncertain Volatility Model introduced by Avellaneda, Levy and Paras and study how it behaves in the different scenarios. In Chapter 2 we choose one of the scenarios. We also introduce the BSB equation and try to make some modification to narrow the uncertainty bands using the idea of a static hedging. In Chapter 3 we try to construct the proper portfolio for the static hedging and compare the theoretical results with the real market data from the Stockholm Stock Exchange.