69 research outputs found
Robust, Non-stationary, and Adaptive Fractionation in Radiotherapy
No full textThesis (Ph.D.)--University of Washington, 2017In external beam radiotherapy for cancer, high-energy radiation is passed through the pa- tient’s body from an outside source to kill tumor cells. The challenge is that radiation also damages healthy tissue and organs-at-risk (OAR) in its path. The objective therefore is to devise treatment plans that maximize tumor-damage while protecting healthy anatomies. Treatment planners attempt two separate methods to attain this goal: spatial and biological. The spatial side focuses on the geometry and physics of the problem. The key consider- ation here is the location of the tumor relative to the nearby healthy regions as seen in an anatomical image, and the dose (energy absorbed per unit mass) deposition properties of the radiation beam. The treatment planner prescribes a high dose to the tumor and puts upper limits on the doses delivered to the healthy regions. Intensity Modulated Radiation Therapy (IMRT) technology is then employed to tune the profile (fluence-map) of the radiation beam to administer a dose that is as close as possible to this tumor-conforming prescription. Sev- eral mathematical optimization models and solution algorithms for this problem have been developed and embedded into treatment planning systems. The biological side of planning exploits the difference between the dose-response charac- teristics of tumors and healthy anatomies. For example, healthy cells are believed to possess better damage repair capabilities than tumor cells. Thus, treatment is delivered over mul- tiple sessions to give healthy tissue some time to recover between sessions. This is called fractionation. Fractionation also gives the tumor some time to re-oxygenate, which increases its sensitivity to radiation. Tumors, however, proliferate during the treatment course, and hence, too long a treatment course may not be ideal. One key question on this biological side is to determine the optimal number of treatment sessions. This is called the fraction- ation problem. Existing optimization research on the fractionation problem relies on the linear-quadratic (LQ) model of dose-response with tumor- and OAR-specific parameters to approximately capture the behavior of the complex biological system involved. Recent studies have suggested that an integrated approach that simultaneously tackles the spatial and biological sides of the problem may lead to a higher tumor-damage as com- pared to tackling the two aspects separately. The goal in such integrated formulations is to simultaneously find the fluence-map and the number of sessions that maximize tumor- damage while limiting toxic effects of dose on the healthy anatomies. Emerging advances in quantitative functional imaging technologies are enabling planners to observe the tumor’s actual dose-response over the treatment course. This provides additional opportunities for better-utilizing the LQ model by dynamically adapting treatment plans to further improve outcomes. The challenge, however, is that spatiobiologically integrated formulations based on the LQ model typically yield nonconvex quadratically constrained quadratic programming problems, which are computationally difficult to solve exactly. The research objective of this dissertation is to develop efficient convex, robust, and dynamic optimization methods to formulate and approximately solve different nonadaptive and adaptive versions of the spatiobiologically integrated fractionation problem within the LQ framework. Chapter 1 briefly describes state-of-the-art literature on spatiobiologically integrated fractionation. Each subsequent chapter is motivated by a distinct limitation of an existing formulation of the spatiobiologically integrated fractionation problem from this literature. Chapter 2: The solutions offered by existing formulations of the fractionation problem crucially depend on the assumed values of the dose-response parameters of the LQ model. Unfortunately, “true” values of these parameters are unknown. Consequently, a solution of the fractionation problem may not be feasible in practice. This concern is addressed in Chapter 2 via a robust formulation, whose solution remains feasible as long as the dose- response parameters belong to an interval. An efficient solution method rooted in a convex, finite-dimensional reformulation of the resulting infinite-dimensional problem is proposed. The price of robustness and feasibility properties of the robust solution are quantified via numerical experiments. Chapter 3: Existing spatiobiologically integrated formulations of the fractionation problem assume that the fluence-map is not changed across treatment sessions. From a computational viewpoint, this simplifies the problem significantly. Chapter 3 relaxes this assumption, and proposes an efficient solution method that allows the fluence-maps to vary across sessions. The quality of the time-variant solutions produced by this method is compared against traditional time-invariant solutions via numerical experiments. Chapter 4: Adaptive spatiobiologically integrated fractionation attempts to alter fluence- maps according to the observed evolution of tumor cell density in functional images. Chapter 4 proposes a formulation and solution method that also determine the length of the remaining treatment course adaptively. Potential benefits of such adaptive treatment-length planning are investigated through numerical experiments. Chapter 5: Adaptive fluence-map planning methods assume that the treatment planner knows the probability distribution of the uncertainty in the tumor’s dose-response parame- ters. In contrast to this “clairvoyant” approach, Chapter 5 proposes an alternative formula- tion, where the treatment planner learns this distribution from tumor-response information observed in functional images over the treatment course while also adaptively optimizing fluence-maps. This yields a Bayesian stochastic control formulation whose exact solution is impossible to derive. The chapter proposes a simple approximate solution method rooted in certainty equivalent control, and compares its performance agains a clairvoyant certainty equivalent control scheme and a “no learning” approach via numerical experiments. Finally, Chapter 6 outlines limitations of this dissertation work and describes two direc- tions for future research
A model predictive control approach for discovering nonstationary fluence-maps in cancer radiotherapy fractionation
No full textDynamical Networks (miniporject) Effect of Topology of the Reservoir on Performance of Echo State Networks
No full textInformation Processing and Structure of Dynamical Networks
No full textNetworks are everywhere and we are confronted with many networks in our daily life. Networks such as Internet, World Wide Web, social, biological and economical networks have been subject to extensive studies in the last decade. The volume of publications and investments are sharply increasing and the applications are spreading widely over various disciplines. One of the most important problems in this context, which is the subject of interest of this thesis, is how the information is processed in a dynamical network and how a dynamical network can be exploited to solve information processing tasks. To study the problem more systematically, the information processing dynamical networks (IPDNs) are divided into two sub categories namely, (i) autonomous IPDNs in which the input information is static and is given as the initial state of the network and (ii) non-autonomous IPDNs in which the input information is injected by an input signal. In this thesis, synchronizability of dynamical networks, community detection on dynamical networks and skill acquisition in reinforcement learning (RL) using dynamical networks have been considered as the problems for the category of autonomous IPDNs. Furthermore, adaptation of the internal weights of a special type of recurrent neural networks, so called reservoir-based RNN (RRNN), and multi tasking in RRNNs have been investigated in the non-autonomous IPDNs category. First, we discuss the interplay between the structure of a complex network and its dynamical behavior and in particular the synchronizability of the network. There are several interpretations of synchronizability in the literature which are categorized in four main groups that do not coincide in general. One of these interpretations uses the second smallest eigenvalue of the graph Laplacian, the so called algebraic connectivity, which is an important measure for various applications in dynamical networks. We introduce a new lower bound for the algebraic connectivity and prove that it is always larger or equal to the previously published lower bounds. In addition, the proposed bound helps to explain the most effective parameters for the synchronizability of the network from the algebraic connectivity point of view. Having found the most influential parameters, we propose two algorithms for enhancing synchronizability of a given network by efficient rewiring of the links and by assigning proper weights to the links, respectively. The rewiring algorithm converts an arbitrary graph, irrespective of the topology, to a class of networks, so called super democratic networks that are identified by their homogenous degree and load distribution and their very low average path length. On the other hand, the weighting algorithm utilizes a novel graph theoretic measure, the so called neighboring graph to determine the proper weights of the links. The optimality of the weighting algorithm is proved and it is shown by numerical simulation on the benchmark networks that it outperforms the previously published approaches. In addition, introducing an iterated map that is associated with each node of the network, we propose a general algorithm for the community detection problem on the complex networks. We prove that there is a direct relation between the global optimum of a general energy function and the asymptotically stable fixed points of the system of the coupled iterated maps. Interestingly, we show that the optimization of this energy function can be reduced to well-known community detection algorithms when the parameters of the energy function are set through appropriate heuristics. The proposed algorithm is very fast, i.e. linear in the size of the network for sparse networks, and very accurate. Furthermore, it is capable of discovering overlapping communities. Next, we develop a new algorithm for automatically skill acquisition of an intelligent agent that learns a task using the Reinforcement Learning approach in a partially observable environment. Mapping the agent's transition history to a graph, one can utilize the complex network framework to solve the problem. Introducing a new betweenness centrality measure, the so called node connection graph stability centrality, the bottlenecks of the corresponding graph, under some conditions, can be interpreted as sub-goals of the agent in the environment which facilitates and accelerates its exploration. Eliminating redundant sup-goals and injecting useful prior information about the environment, the agent that performs the proposed algorithm, is significantly faster in learning the optimal strategy. For the case of non-autonomous IPDNs, we focus on reservoir-based recurrent neural networks. In this class of RNNs, considering a random, large and sparse network as the hidden layer, called reservoir, only the weights of the output layer are trained. Although the weights of the reservoir in RRNNs are usually assumed fixed, it turns out that adapting the hidden layer can enhance the performance significantly. Accordingly, we show how the structural properties of the reservoir can be exploited to enhance the performance of a task on RRNNs. One can create a large weight matrix of the reservoir using iterative Kronecker products of small size matrices. In this way, the number of parameters of the reservoir decreases significantly and allows for optimization by adjusting the elements of the small size matrices. Although the space of Kronecker-based weight matrices is much smaller than the space of the unconstrained random matrices, it is shown through numerical simulations on benchmark tasks that the corresponding space of Kronecker-based matrices is still useful to find "good enough" reservoirs with much lower complexity. Furthermore, the problem of learning multiple tasks that share the same input in reservoir computing methods was investigated. To this end, a special reservoir architecture that consist of two layers, namely, the general workspace (GW) and the task specific (TS) layers, is proposed. The shared inputs are fed into the GW layer and the reservoirs of the TS layer are driven by the outputs of the GW. Any task-specific configuration, e.g. transfer function, training parameters, and additional inputs should be implemented in the corresponding reservoirs of the TSlayer. The presence of two separate layers makes it possible to apply different and independent adaptation methods; more precisely, unsupervised training was applied to the GW to maximize the relevant information passing to the TS layer and supervised training of the reservoirs of the TS layer to minimize the output error of the corresponding task. By considering a two-task problem, it is shown that the layered model outperforms two other approaches, namely the one with a single reservoir and the other with two separate reservoirs, one for each task.LANOSLTH
Rewirings based on the eigenvectors of the Laplacian matrix for enhancing synchronizability of dynamical networks
No full textComment on Rewiring networks for synchronization
No full textThis is a comment on a recent paper by A. Hagberg and D. A. Schult [Chaos 18, 037105 (2008)]. By taking the eigenratio of the Laplacian of an undirected and unweighted network as its synchronizability measure, they proposed a greedy rewiring algorithm for enhancing the synchronizability of the network. The algorithm is not capable of avoiding local minima, and as a consequence, for each initial network, different optimized networks with different synchronizabilities are obtained. Here, we show that by employing a simulated annealing based optimization method, it is possible to further enhance the synchronizability of the network. Moreover, using this approach, the optimized network is not biased by the initial network and regardless of the initial networks, the final optimized networks have similar synchronization propertiesLANO
Synchronizability of dynamical networks: different measures and coincidence
No full textIn this paper, we list four different interpretations of synchronizability, study their profile in different network structures and give evidence that they do not coincide, in general. By changing the network topological properties, their behavior is tracked and compared with each other. It is shown that their trend goes in different directions in heterogeneous networks such as scale-free ones, whereas in homogeneous ones such as random networks they go hand in hand, as networks’ structural parameters change. We also consider networks whose synchronization properties are enhanced through proper weighting or rewiring. The weighting procedure considers information on the node-degrees, node and edges betweenness centralities to assign proper weights for the links. In this way, an undirected and unweighted graph is changed to a weighted and directed one and with enhanced synchronizability. The rewiring algorithm uses information on the eigenvectors corresponding to the second smallest and the largest eigenvalues of the Laplacian matrix to perform efficient rewirings to enhance the synchronizability. It is shown that in these networks (weighted or rewired), different synchronizability interpretations have the same trend as the network structural parameter changes.LANO
The Relation of Epistemology and Society in the View of Dr. Ali Shariati
No full textThe research aims to present the viewpoint of Shariati on the relation of epistemology and Society. Thus, the following generalities will be reviewed: introduction, problem exposition, questions, assumptions, background and theoretical framework based on the following five factors: depth of determination, degree of determination, level of determination, the dominant factor on determination and subject of determination. The research concludes with an evaluation of the reviewed subjects
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