We develop a class of models to represent the dynamics of a virus spreading in a cellphone network, employing a taxonomy that includes five key characteristics. Based on the resulting dynamics governing the spread, we present optimization models to rapidly detect the virus, subject to resource limitations. We consider two goals, maximizing the probability of detecting a virus by a time threshold and minimizing the expected time to detection, which can be applied to all spread models we consider. We establish a submodularity result for these two objective functions that ensures that a greedy heuristic yields a well-known constant-factor (63%) approximation. We relate the latter optimization problem, under a specific virus-spread mechanism from our class of models, to a classic facility-location model. Using data from a large carrier, we build several base cellphone contact networks of different scale. We then rescale these base networks using the so-called c-core decomposition that removes vertices of low degree in a recursive way. We further show that this down-sampling strategy preserves, in general, the topological properties of the base networks, based on testing several measures. For the objective that maximizes the probability that we detect a virus by a time threshold, we provide a sample-average optimization model that yields an asymptotically-optimal design for locating the detection devices, as the number of samples grows large. To choose a relevant time threshold, we perform a simulation for some spread models. We then test the performance of our proposed solution methods by solving the presented optimization models for some spread dynamics using some of the contact networks built after the c-core decomposition. The computational results show that the greedy algorithm is an efficient way to solve the corresponding sample-average approximation model, and the greedy solutions outperform some other simple solution approaches. / text

The Successive Approximation Register (SAR) Analog to Digital Converter (ADC) is power efficient and operates at moderate resolution. However, the conversion speed is limited by settling time and control logic constraints. This report investigates a flip-flop bypass technique to reduce the required conversion time. A conventional design and flip-flop bypass design are simulated using a 0.18[micrometer] CMOS process. Background and design of the control logic, comparator, capacitive array, and switches for implementing the SAR ADCs is presented with the emphasis on optimizing for conversion speed. / text

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In the conventional approach to geophysical fluid dynamics, only the horizontal components of the Coriolis force due to horizontal motions of the fluid are taken into account. All the other components of the Coriolis force, which are called the non-traditional (NT) terms, are considered to be small second order quantities and are usually dropped. This effectively simplifies the system and the nice and clean quasi-geostrophic (QG) equation can be obtained, which is widely used in analytical studies of climate systems. Interest has been drawn to the dropped terms in recent studies. It is shown that in some special cases these second order terms actually have a noticeable influence on the dynamics of the system. However, a full picture of these terms in the dynamics of the real ocean is still lacking. Here, we will start from the fundamental equations of fluid dynamics, and through careful scaling analysis conduct a detailed study of the governing equations of geophysical fluid dynamics while keeping the NT terms. We will specifically investigate the influence of these NT terms on equatorial waves, since near the equator the NT components of the Coriolis force are the most significant. / text

Value of information is one of the key features of decision analysis. This work deals with providing a consistent and functional methodology to determine VOI on proposed well tests in the presence of uncertainties. This method strives to show that VOI analysis with the help of discretized versions of continuous probability distributions with conventional decision trees can be very accurate if the optimal method of discrete approximation is chosen rather than opting for methods such as Monte Carlo simulation to determine the VOI. This need not necessarily mean loss of accuracy at the cost of simplifying probability calculations. Both the prior and posterior probability distributions are assumed to be continuous and are discretized to find the VOI. This results in two steps of discretizations in the decision tree. Another interesting feature is that there lies a level of decision making between the two discrete approximations in the decision tree. This sets it apart from conventional discretized models since the accuracy in this case does not follow the rules and conventions that normal discrete models follow because of the decision between the two discrete approximations. The initial part of the work deals with varying the number of points chosen in the discrete model to test their accuracy against different correlation coefficients between the information and the actual values. The latter part deals more with comparing different methods of existing discretization methods and establishing conditions under which each is optimal. The problem is comprehensively dealt with in the cases of both a risk neutral and a risk averse decision maker. / text

published_or_final_version / abstract / Computer Science / Master / Master of Philosophy

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

The intricate dependency of networking protocols upon the performance of the wireless channel motivates the investigation of network channel approximations for fading channels. Wireless networking protocols are increasingly being designed and evaluated with the assistance of networking simulators. While evaluating networking protocols such as medium access control, routing, and reliable transport, the network channel model, and its associated capacity, will drastically impact the achievable network throughput. Researcher relying upon simulation results must therefore use extreme caution to ensure the use of similar channel models when performing protocol comparisons. Some channel approximations have been created to mimic the behavior of a fading environment, however there exists little to no justification for these channel approximations. This dissertation addresses the need for a computationally efficient fading channel approximation for use in network simulations. A rigorous flat fading channel model was developed for use in accuracy measurements of channel approximations. The popular two-state Markov model channel approximation is analyzed and shown to perform poorly for low to moderate signal-to-noise ratios (SNR). Three novel channel approximations are derived, with multiple methods of parameter estimation. Each model is analyzed for both statistical performance and network performance. The final model is shown to achieve very accurate network throughput performance by achieving a very close matching of the frame run distributions. This work provides a rigorous evaluation of the popular two-state Markov model, and three novel low complexity channel models in both statistical accuracy and network throughput performance. The novel models are formed through attempts to match key statistical parameters of frame error run and good frame run statistics. It is shown that only matching key parameters is insufficient to achieve an acceptable channel approximation and that it is necessary to approximate the distribution of frame error duration and good frame run duration. The final novel channel approximation, the three-state run-length model, is shown to achieve a good approximation of the desired distributions when some key statistical parameters are matched.

Sudaryta ir išbandyta Matchad‘o programiniu paketu Gauso funkcijų splino programa glodinanti didelio matavimo skaičiaus eksperimentinį masyvą. Glodinimo funkciją sudaro polinomų ir Gauso funkcijų sandaugos suma. Glodinimo procedūra suvedama į algebrinių lygčių sistemą neapibrėžtiems koeficientams Cn,l rasti. Sudaryta Matchad‘o programa, kuri panaudojus suglodintą funkciją apruoksimuoja ją tik teigiamų Gauso funkcijų suma.Šis uždavinys realizuotas programa, kuri remiasi didžiausio nuolydžio metodu. Glodinimo ir aproksimavimo rezultatai tenkina eksperimentatorių reikalavimus. / Formed and, used MathCad software, tested Gauss function spline program, which smoothes big measure number experimental array. Smoothing function contains polynomial and Gauss functions multiplication sum. Smoothing procedure is reduced to algebraic equation system to find indeterminate coefficients Cn,l. Created MathCad program, which, by using smoothed function, approximates it to positive Gauss functions sum. This task was solved with program, which refers to biggest pitch method. Smoothing and approximation results fit experimenters’ requirements.

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