Browsing by Subject "Stochastic modeling"
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item Aggregation, dissemination and filtering : controlling complex information flows in networks(2013-08) Banerjee, Siddhartha; Sanghavi, Sujay Rajendra, 1979-; Shakkottai, SanjayModern day networks, both physical and virtual, are designed to support increasingly sophisticated applications based on complex manipulation of information flows. On the flip side, the ever-growing scale of the underlying networks necessitate the use of low-complexity algorithms. Exploring this tension needs an understanding of the relation between these flows and the network structure. In this thesis, we undertake a study of three such processes: aggregation, dissemination and filtering. In each case, we characterize how the network topology imposes limits on these processes, and how one can use knowledge of the topology to design simple yet efficient control algorithms. Aggregation: We study data-aggregation in sensor networks via in-network computation, i.e., via combining packets at intermediate nodes. In particular, we are interested in maximizing the refresh-rate of repeated/streaming aggregation. For a particular class of functions, we characterize the maximum achievable refresh-rate in terms of the underlying graph structure; furthermore we develop optimal algorithms for general networks, and also a simple distributed algorithm for acyclic wired networks. Dissemination: We consider dissemination processes on networks via intrinsic peer-to-peer transmissions aided by external agents: sources with bounded spreading power, but unconstrained by the network. Such a model captures many static (e.g. long-range links) and dynamic/controlled (e.g. mobile nodes, broadcasting) models for long-range dissemination. We explore the effect of external sources for two dissemination models: spreading processes, wherein nodes once infected remain so forever, and epidemic process, in which nodes can recover from the infection. The main takeaways from our results demonstrate: (i) the role of graph structure, and (ii) the power of random strategies. In spreading processes, we show that external agents dramatically reduce the spreading time in networks that are spatially constrained; furthermore random policies are order-wise optimal. In epidemic processes, we show that for causing long-lasting epidemics, external sources must scale with the number of nodes -- however the strategies can be random. Filtering: A common phenomena in modern recommendation systems is the use of user-feedback to infer the 'value' of an item to other users, resulting in an exploration vs. exploitation trade-off. We study this in a simple natural model, where an 'access-graph' constrains which user is allowed to see which item, and the number of items and the number of item-views are of the same order. We want algorithms that recommend relevant content in an online manner (i.e., instantaneously on user arrival). To this end, we consider both finite-population (i.e., with a fixed set of users and items) and infinite-horizon settings (i.e., with user/item arrivals and departures) -- in each case, we design algorithms with guarantees on the competitive ratio for any arbitrary user. Conversely, we also present upper bounds on the competitive ratio, which show that in many settings our algorithms are orderwise optimal.Item Deterministic and stochastic nonlinear age-structured models(Texas Tech University, 1998-12) Block, Garry L.The Leslie age-structured population model is reviewed, as well as its stochastic analogue. Nonlinear adjustments in the form of the Ricker and Beverton-Holt densitydependent factors are made to these models. The deterministic density-dependent nonlinear models are discussed and compared to their stochastic nonlinear analogs.Item Modeling of point bar geology using a grid transformation scheme and geostatistics(2015-12) Li, Henry; Sepehrnoori, Kamy, 1951-; Srinivasan, SanjayPoint bars, the convex inner banks of meandering rivers, exhibit distinct heterogeneities. Modeling these heterogeneities is essential because of the presence of mud/silt layers in point bars impede the flow of fluids in processes strongly controlled by buoyancy or gravity such as the steam chamber rise during Steam-Assisted Gravity Drainage (SAGD). This thesis details the modeling of point bars using geological trends and well data to supplement geostatistical simulation. The modeling processes in this thesis capture the internal geometry of the accretion layers as well as geological trends. Curvilinear grids are constructed between major erosional surfaces where a grid transformation scheme is used to transform the curvilinear coordinates into orthogonal coordinates for geostatistical simulation. The grid transformation allows flexibility in performing statistical simulation in rectangular coordinate while honoring the curvilinear geometry of the point bar. An entire point bar model contains a series of accreting curviplanar grids. Geological modeling is done independently for each grid. The geology captures key trends that make up the heterogeneities in the model. The point bar model created is based on a modern point bar in the Brazos River. Data from thirty-three wells are used in creating the reservoir model. Several distinct trends are observed. There is an upward decrease in sediment size in the point bar. An overall fining downstream trend is observed in the vertical slices of the point bar. Heterolithic bedding is observed where frequent layers of silt extend from the top to near the base analogous to outcrops. Mud and silt dominate the upward regions of the point bar while conglomerate and cobble are mainly present at the base. The flow simulation model investigated the effect of mud drapes and fining heterogeneities on the development of steam chamber in SAGD recovery. The mud drapes impeded the steam chamber rise. The steam chambers were initially divided into pockets based on the flow barriers present. After 1 years of production, the steam chamber reaches the top of the reservoir but continued to be separated by the mud/silt barriers. Comparing to the homogeneous case, the point bar model exhibited lower oil recovery.Item Stochastic models for the time to the most recent common ancestor(Texas Tech University, 1999-05) Stinnett, Sarah DianneA new area of recent research is inferring ancestral history from samples of DNA [11]. Most of this research has focused on the evolution of mitochondrial DNA. These molecules have a very high mutation rate, thereby allowing one to see differences in the DNA samples of two closely related individuals [11]. Mitochondria are maternally inherited which allows one to trace back female lineages. Also, male lineages can be traced back by using a specific locations on the Y chromosome. Estimates of the time to the origin of modern humans. Homo-sapiens, have been made by tracing back female lineages (referred to "the time to Mitochondria Eve") and by tracing back male lineages (referred to as "the time to Y-Adam") [1, 2. 4. 11. 13]. In theory, it is possible to trace back lineages for any species with information about mitochondrial DNA, population size, and mutation rates. Our research will be concerned with development of mathematical models and numerical techniques so that inferences can be made about the time to the most recent common ancestor (or TMRCA) given a data set from DNA samples taken from a population. Due to the fact that there is really no way of knowing the exact ancestral history from a given sample of DNA sequences we will use a probabilistic approach by developing a stochastic model for the TMRCA. We will generate a probability distribution for TMRCA from which we can calculate means, variances, or other summary statistics.