UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
More information is available at Theses and Dissertations at University of Maryland Libraries.
Browse
5 results
Search Results
Item Dynamics, Networks, and Information: Methods for Nonlinear Interactions in Biological Systems(2021) Milzman, Jesse; Levy, Doron; Lyzinski, Vince; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we investigate complex, non-linear interactions in biological systems.This work is presented as two independent projects. The mathematics and biology in each differ, yet there is a unity in that both frameworks are interested in biological responses that cannot be reduced to linear causal chains, nor can they be expressed as an accumulation of binary interactions. In the first part of this dissertation, we use mathematical modeling to study tumor-immune dynamics at the cellular scale.Recent work suggests that LSD1 inhibition reduces tumor growth, increases T cell tumor infiltration, and complements PD1/PDL1 checkpoint inhibitor therapy. In order to elucidate the immunogenic effects of LSD1 inhibition, we create a delay differential equation model of tumor growth under the influence of the adaptive immune response in order to investigate the anti-tumor cytotoxicity of LSD1-mediated T cell dynamics. We fit our model to the B16 mouse model data from Sheng et al. [DOI:10.1016/j.cell.2018.05.052] Our results suggest that the immunogenic effect of LSD1 inhibition accelerates anti-tumor cytoxicity. However, cytotoxicity does not seem to account for the slower growth observed in LSD1 inhibited tumors, despite evidence suggesting immune-mediation of this effect. In the second part, we consider the partial information decomposition (PID) of response information within networks of interacting nodes, inspired by biomolecular networks.We specifically study the potential of PID synergy as a tool for network inference and edge nomination. We conduct both numeric and analytic investigations of the $\Imin$ and $\Ipm$ PIDs, from [arXiv:1004.2515] and [DOI:10.3390/e20040297], respectively. We find that the $I_\text{PM}$ synergy suffers from issues of non-specificity, while $I_{\text{min}}$ synergy is specific but somewhat insensitive. In the course of our work, we extend the $I_\text{PM}$ and $I_{\text{min}}$ PIDs to continuous variables for a general class of noise-free trivariate systems. The $I_\text{PM}$ PID does not respect conditional independence, while$I_{\text{min}}$ does, as demonstrated through asymptotic analysis of linear and non-linear interaction kernels. The technical results of this chapter relate the analytic and information-theoretic properties of our interactions, by expressing the continuous PID of noise-free interactions in terms of the partial derivatives of the interaction kernel.Item DELAY MINIMIZATION IN ENERGY CONSTRAINED WIRELESS COMMUNICATIONS(2010) Yang, Jing; Ulukus, Sennur; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In wireless communications and networks, especially for many real-time applications, the average delay packets experience is an important quality of service criterion. Therefore, it is imperative to design advanced transmission schemes to jointly address the goals of reliability, high rates and low delay. Achieving these objectives often requires careful allocation of given resources, such as energy, power, rate, among users. It also requires a close collaboration between physical layer, medium access control layer, and upper layers, and yields cross-layer solutions. We first investigate the problem of minimizing the overall transmission delay of packets in a multiple access wireless communication system, where the transmitters have average power constraints. We formulate the problem as a constrained optimization problem, and then transform it into a linear programming problem. We show that the optimal policy has a threshold structure: when the sum of the queue lengths is larger than a threshold, both users should transmit a packet during the current slot; when the sum of the queue lengths is smaller than a threshold, only one of the users, the one with the longer queue, should transmit a packet during the current slot. Then, we study the delay-optimal rate allocation in a multiple access wireless communication system. Our goal is to allocate rates to users, from the multiple access capacity region, based on their current queue lengths, in order to minimize the average delay of the system. We formulate the problem as a Markov decision problem (MDP) with an average cost criterion. We first show that the value function is increasing, symmetric and convex in the queue length vector. Taking advantage of these properties, we show that the optimal rate allocation policy is one which tries to equalize the queue lengths as much as possible in each slot, while working on the dominant face of the capacity region. Next, we extend the delay-optimal rate allocation problem to a communication channel with two transmitters and one receiver, where the underlying rate region is approximated as a general pentagon. We show that the delay-optimal policy has a switch curve structure. For the discounted-cost problem, we prove that the switch curve has a limit along one of the dimensions. The existence of a limit in the switch curve along one of the dimensions implies that, once the queue state is beyond the limit, the system always operates at one of the corner points, implying that the queues can be operated partially distributedly. Next, we shift our focus from the average delay minimization problem to transmission completion time minimization problem in energy harvesting communication systems. We first consider the optimal packet scheduling problem in a single-user energy harvesting wireless communication system. In this system, both the data packets and the harvested energy are modeled to arrive at the source node randomly. Our goal is to adaptively change the transmission rate according to the traffic load and available energy, such that the time by which all packets are delivered is minimized. Under a deterministic system setting, we develop an optimal off-line scheduling policy which minimizes the transmission completion time, under causality constraints on both data and energy arrivals. Then, we investigate the transmission completion time minimization problem in a two-user additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature. We first analyze the structural properties of the optimal transmission policy. We prove that the optimal total transmit power has the same structure as the optimal single-user transmit power. We also prove that there exists a cut-off power level for the stronger user. If the optimal total transmit power is lower than this level, all transmit power is allocated to the stronger user, and when the optimal total transmit power is larger than this level, all transmit power above this level is allocated to the weaker user. Based on these structural properties of the optimal policy, we propose an algorithm that yields the globally optimal off-line scheduling policy. Next, we investigate the transmission completion time minimization problem in a two-user AWGN multiple access channel. We first develop a generalized iterative backward waterfilling algorithm to characterize the maximum departure region of the transmitters for any given deadline. Then, based on the sequence of maximum departure regions at energy arrival epochs, we decompose the transmission completion time minimization problem into a convex optimization problem and solve it efficiently. Finally, we investigate the average delay minimization problem in a single-user communication channel with an energy harvesting transmitter. We consider three different cases. In the first case, both the data packets and the energy to be used to transmit them are assumed to be available at the transmitter at the beginning. In the second case, while the energy is available at the transmitter at the beginning, packets arrive during the transmissions. In the third case, the packets are available at the transmitter at the beginning and the energy arrives during the transmissions, as a result of energy harvesting. In each scenario, we find the structural properties of the optimal solution, and develop iterative algorithms to obtain the solution.Item Capacity Bounds For Multi-User Channels With Feedback, Relaying and Cooperation(2010) Tandon, Ravi; Ulukus, Sennur; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Recent developments in communications are driven by the goal of achieving high data rates for wireless communication devices. To achieve this goal, several new phenomena need to be investigated from an information theoretic perspective. In this dissertation, we focus on three of these phenomena: feedback, relaying and cooperation. We study these phenomena for various multi-user channels from an information theoretic point of view. One of the aims of this dissertation is to study the performance limits of simple wireless networks, for various forms of feedback and cooperation. Consider an uplink communication system, where several users wish to transmit independent data to a base-station. If the base-station can send feedback to the users, one can expect to achieve higher data-rates since feedback can enable cooperation among the users. Another way to improve data-rates is to make use of the broadcast nature of the wireless medium, where the users can overhear each other's transmitted signals. This particular phenomenon has garnered much attention lately, where users can help in increasing each other's data-rates by utilizing the overheard information. This overheard information can be interpreted as a generalized form of feedback. To take these several models of feedback and cooperation into account, we study the two-user multiple access channel and the two-user interference channel with generalized feedback. For all these models, we derive new outer bounds on their capacity regions. We specialize these results for noiseless feedback, additive noisy feedback and user-cooperation models and show strict improvements over the previously known bounds. Next, we study state-dependent channels with rate-limited state information to the receiver or to the transmitter. This state-dependent channel models a practical situation of fading, where the fade information is partially available to the receiver or to the transmitter. We derive new bounds on the capacity of such channels and obtain capacity results for a special sub-class of such channels. We study the effect of relaying by considering the parallel relay network, also known as the diamond channel. The parallel relay network considered in this dissertation comprises of a cascade of a general broadcast channel to the relays and an orthogonal multiple access channel from the relays to the receiver. We characterize the capacity of the diamond channel, when the broadcast channel is deterministic. We also study the diamond channel with partially separated relays, and obtain capacity results when the broadcast channel is either semi-deterministic or physically degraded. Our results also demonstrate that feedback to the relays can strictly increase the capacity of the diamond channel. In several sensor network applications, distributed lossless compression of sources is of considerable interest. The presence of adversarial nodes makes it important to design compression schemes which serve the dual purpose of reliable source transmission to legitimate nodes while minimizing the information leakage to the adversarial nodes. Taking this constraint into account, we consider information theoretic secrecy, where our aim is to limit the information leakage to the eavesdropper. For this purpose, we study a secure source coding problem with coded side information from a helper to the legitimate user. We derive the rate-equivocation region for this problem. We show that the helper node serves the dual purpose of reducing the source transmission rate and increasing the uncertainty at the adversarial node. Next, we considered two different secure source coding models and provide the corresponding rate-equivocation regions.Item A Theory of Cramer-Rao Bounds for Constrained Parametric Models(2010) Moore, Terrence Joseph; Kedem, Benjamin; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A simple expression for the Cram'er-Rao bound (CRB) is presented for the scenario of estimating parameters $\theta$ that are required to satisfy a differentiable constraint function $f(\theta)$. A proof of this constrained CRB (CCRB) is provided using the implicit function theorem, and the encompassing theory of the CCRB is proven in a similar manner. This theory includes connecting the CCRB to notions of identifiability of constrained parameters; the linear model under a linear constraint; the constrained maximum likelihood problem, it's asymptotic properties and the method of scoring with constraints; and hypothesis testing. The value of the tools developed in this theory are then presented in the communications context for the convolutive mixture model and the calibrated array model.Item Finite Mixture Model Specifications Accommodating Treatment Nonresponse in Experimental Research(2009) Wasko, John A.; Hancock, Gregory R; Measurement, Statistics and Evaluation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)For researchers exploring causal inferences with simple two group experimental designs, results are confounded when using common statistical methods and further are unsuitable in cases of treatment nonresponse. In signal processing, researchers have successfully extracted multiple signals from data streams with Gaussian mixture models, where their use is well matched to accommodate researchers in this predicament. While the mathematics underpinning models in either application remains unchanged, there are stark differences. In signal processing, results are definitively evaluated assessing whether extracted signals are interpretable. Such obvious feedback is unavailable to researchers seeking causal inference who instead rely on empirical evidence from inferential statements regarding mean differences, as done in analysis of variance (ANOVA). Two group experimental designs do provide added benefit by anchoring treatment nonrespondents' distributional response properties from the control group. Obtaining empirical evidence supporting treatment nonresponse, however, can be extremely challenging. First, if indeed nonresponse exists, then basic population means, ANOVA or repeated measures tests cannot be used because of a violation of the identical distribution property required for each method. Secondly, the mixing parameter or proportion of nonresponse is bounded between 0 and 1, so does not subscribe to normal distribution theory to enable inference by common methods. This dissertation introduces and evaluates the performance of an information-based methodology as a more extensible and informative alternative to statistical tests of population means while addressing treatment nonresponse. Gaussian distributions are not required under this methodology which simultaneously provides empirical evidence through model selection regarding treatment nonresponse, equality of population means, and equality of variance hypotheses. The use of information criteria measures as an omnibus assessment of a set of mixture and non-mixture models within a maximum likelihood framework eliminates the need for a Newton-Pearson framework of probabilistic inferences on individual parameter estimates. This dissertation assesses performance in recapturing population conditions for hypotheses' conclusions, parameter accuracy, and class membership. More complex extensions addressing multiple treatments, multiple responses within a treatment, a priori consideration of covariates, and multivariate responses within a latent framework are also introduced.