Matching Items (42)
Description
A tiling is a collection of vertex disjoint subgraphs called tiles. If the tiles are all isomorphic to a graph $H$ then the tiling is an $H$-tiling. If a graph $G$ has an $H$-tiling which covers all of the vertices of $G$ then the $H$-tiling is a perfect $H$-tiling or an $H$-factor. A goal of this study is to extend theorems on sufficient minimum degree conditions for perfect tilings in graphs to directed graphs. Corrádi and Hajnal proved that every graph $G$ on $3k$ vertices with minimum degree $delta(G)ge2k$ has a $K_3$-factor, where $K_s$ is the complete graph on $s$ vertices. The following theorem extends this result to directed graphs: If $D$ is a directed graph on $3k$ vertices with minimum total degree $delta(D)ge4k-1$ then $D$ can be partitioned into $k$ parts each of size $3$ so that all of parts contain a transitive triangle and $k-1$ of the parts also contain a cyclic triangle. The total degree of a vertex $v$ is the sum of $d^-(v)$ the in-degree and $d^+(v)$ the out-degree of $v$. Note that both orientations of $C_3$ are considered: the transitive triangle and the cyclic triangle. The theorem is best possible in that there are digraphs that meet the minimum degree requirement but have no cyclic triangle factor. The possibility of added a connectivity requirement to ensure a cycle triangle factor is also explored. Hajnal and Szemerédi proved that if $G$ is a graph on $sk$ vertices and $delta(G)ge(s-1)k$ then $G$ contains a $K_s$-factor. As a possible extension of this celebrated theorem to directed graphs it is proved that if $D$ is a directed graph on $sk$ vertices with $delta(D)ge2(s-1)k-1$ then $D$ contains $k$ disjoint transitive tournaments on $s$ vertices. We also discuss tiling directed graph with other tournaments. This study also explores minimum total degree conditions for perfect directed cycle tilings and sufficient semi-degree conditions for a directed graph to contain an anti-directed Hamilton cycle. The semi-degree of a vertex $v$ is $min{d^+(v), d^-(v)}$ and an anti-directed Hamilton cycle is a spanning cycle in which no pair of consecutive edges form a directed path.
ContributorsMolla, Theodore (Author) / Kierstead, Henry A (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Spielberg, Jack (Committee member) / Arizona State University (Publisher)
Created2013
Description
Biological systems are complex in many dimensions as endless transportation and communication networks all function simultaneously. Our ability to intervene within both healthy and diseased systems is tied directly to our ability to understand and model core functionality. The progress in increasingly accurate and thorough high-throughput measurement technologies has provided a deluge of data from which we may attempt to infer a representation of the true genetic regulatory system. A gene regulatory network model, if accurate enough, may allow us to perform hypothesis testing in the form of computational experiments. Of great importance to modeling accuracy is the acknowledgment of biological contexts within the models -- i.e. recognizing the heterogeneous nature of the true biological system and the data it generates. This marriage of engineering, mathematics and computer science with systems biology creates a cycle of progress between computer simulation and lab experimentation, rapidly translating interventions and treatments for patients from the bench to the bedside. This dissertation will first discuss the landscape for modeling the biological system, explore the identification of targets for intervention in Boolean network models of biological interactions, and explore context specificity both in new graphical depictions of models embodying context-specific genomic regulation and in novel analysis approaches designed to reveal embedded contextual information. Overall, the dissertation will explore a spectrum of biological modeling with a goal towards therapeutic intervention, with both formal and informal notions of biological context, in such a way that will enable future work to have an even greater impact in terms of direct patient benefit on an individualized level.
ContributorsVerdicchio, Michael (Author) / Kim, Seungchan (Thesis advisor) / Baral, Chitta (Committee member) / Stolovitzky, Gustavo (Committee member) / Collofello, James (Committee member) / Arizona State University (Publisher)
Created2013
Description
Well-established model systems exist in four out of the seven major classes of vertebrates. These include the mouse, chicken, frog and zebrafish. Noticeably missing from this list is a reptilian model organism for comparative studies between the vertebrates and for studies of biological processes unique to reptiles. To help fill in this gap the green anole lizard, Anolis carolinensis, is being adapted as a model organism. Despite the recent release of the complete genomic sequence of the A. carolinensis, the lizard lacks some resources to aid researchers in their studies. Particularly, the lack of transcriptomic resources for lizard has made it difficult to identify genes complete with alternative splice forms and untranslated regions (UTRs). As part of this work the genome annotation for A. carolinensis was improved through next generation sequencing and assembly of the transcriptomes from 14 different adult and embryonic tissues. This revised annotation of the lizard will improve comparative studies between vertebrates, as well as studies within A. carolinensis itself, by providing more accurate gene models, which provide the bases for molecular studies. To demonstrate the utility of the improved annotations and reptilian model organism, the developmental process of somitogenesis in the lizard was analyzed and compared with other vertebrates. This study identified several key features both divergent and convergent between the vertebrates, which was not previously known before analysis of a reptilian model organism. The improved genome annotations have also allowed for molecular studies of tail regeneration in the lizard. With the annotation of 3' UTR sequences and next generation sequencing, it is now possible to do expressional studies of miRNA and predict their mRNA target transcripts at genomic scale. Through next generation small RNA sequencing and subsequent analysis, several differentially expressed miRNAs were identified in the regenerating tail, suggesting miRNA may play a key role in regulating this process in lizards. Through miRNA target prediction several key biological pathways were identified as potentially under the regulation of miRNAs during tail regeneration. In total, this work has both helped advance A. carolinensis as model system and displayed the utility of a reptilian model system.
ContributorsEckalbar, Walter L (Author) / Kusumi, Kenro (Thesis advisor) / Huentelman, Matthew (Committee member) / Rawls, Jeffery (Committee member) / Wilson-Rawls, Norma (Committee member) / Arizona State University (Publisher)
Created2012
Description
A central concept of combinatorics is partitioning structures with given constraints. Partitions of on-line posets and on-line graphs, which are dynamic versions of the more familiar static structures posets and graphs, are examined. In the on-line setting, vertices are continually added to a poset or graph while a chain partition or coloring (respectively) is maintained. %The optima of the static cases cannot be achieved in the on-line setting. Both upper and lower bounds for the optimum of the number of chains needed to partition a width $w$ on-line poset exist. Kierstead's upper bound of $\frac{5^w-1}{4}$ was improved to $w^{14 \lg w}$ by Bosek and Krawczyk. This is improved to $w^{3+6.5 \lg w}$ by employing the First-Fit algorithm on a family of restricted posets (expanding on the work of Bosek and Krawczyk) . Namely, the family of ladder-free posets where the $m$-ladder is the transitive closure of the union of two incomparable chains $x_1\le\dots\le x_m$, $y_1\le\dots\le y_m$ and the set of comparabilities $\{x_1\le y_1,\dots, x_m\le y_m\}$. No upper bound on the number of colors needed to color a general on-line graph exists. To lay this fact plain, the performance of on-line coloring of trees is shown to be particularly problematic. There are trees that require $n$ colors to color on-line for any positive integer $n$. Furthermore, there are trees that usually require many colors to color on-line even if they are presented without any particular strategy. For restricted families of graphs, upper and lower bounds for the optimum number of colors needed to maintain an on-line coloring exist. In particular, circular arc graphs can be colored on-line using less than 8 times the optimum number from the static case. This follows from the work of Pemmaraju, Raman, and Varadarajan in on-line coloring of interval graphs.
ContributorsSmith, Matthew Earl (Author) / Kierstead, Henry A (Thesis advisor) / Colbourn, Charles (Committee member) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2012
Description
The primary function of the medium access control (MAC) protocol is managing access to a shared communication channel. From the viewpoint of transmitters, the MAC protocol determines each transmitter's persistence, the fraction of time it is permitted to spend transmitting. Schedule-based schemes implement stable persistences, achieving low variation in delay and throughput, and sometimes bounding maximum delay. However, they adapt slowly, if at all, to changes in the network. Contention-based schemes are agile, adapting quickly to changes in perceived contention, but suffer from short-term unfairness, large variations in packet delay, and poor performance at high load. The perfect MAC protocol, it seems, embodies the strengths of both contention- and schedule-based approaches while avoiding their weaknesses. This thesis culminates in the design of a Variable-Weight and Adaptive Topology Transparent (VWATT) MAC protocol. The design of VWATT first required answers for two questions: (1) If a node is equipped with schedules of different weights, which weight should it employ? (2) How is the node to compute the desired weight in a network lacking centralized control? The first question is answered by the Topology- and Load-Aware (TLA) allocation which defines target persistences that conform to both network topology and traffic load. Simulations show the TLA allocation to outperform IEEE 802.11, improving on the expectation and variation of delay, throughput, and drop rate. The second question is answered in the design of an Adaptive Topology- and Load-Aware Scheduled (ATLAS) MAC that computes the TLA allocation in a decentralized and adaptive manner. Simulation results show that ATLAS converges quickly on the TLA allocation, supporting highly dynamic networks. With these questions answered, a construction based on transversal designs is given for a variable-weight topology transparent schedule that allows nodes to dynamically and independently select weights to accommodate local topology and traffic load. The schedule maintains a guarantee on maximum delay when the maximum neighbourhood size is not too large. The schedule is integrated with the distributed computation of ATLAS to create VWATT. Simulations indicate that VWATT offers the stable performance characteristics of a scheduled MAC while adapting quickly to changes in topology and traffic load.
ContributorsLutz, Jonathan (Author) / Colbourn, Charles J (Thesis advisor) / Syrotiuk, Violet R. (Thesis advisor) / Konjevod, Goran (Committee member) / Lloyd, Errol L. (Committee member) / Arizona State University (Publisher)
Created2013
Description
Given the process of tumorigenesis, biological signaling pathways have become of interest in the field of oncology. Many of the regulatory mechanisms that are altered in cancer are directly related to signal transduction and cellular communication. Thus, identifying signaling pathways that have become deregulated may provide useful information to better understanding altered regulatory mechanisms within cancer. Many methods that have been created to measure the distinct activity of signaling pathways have relied strictly upon transcription profiles. With advancements in comparative genomic hybridization techniques, copy number data has become extremely useful in providing valuable information pertaining to the genomic landscape of cancer. The purpose of this thesis is to develop a methodology that incorporates both gene expression and copy number data to identify signaling pathways that have become deregulated in cancer. The central idea is that copy number data may significantly assist in identifying signaling pathway deregulation by justifying the aberrant activity being measured in gene expression profiles. This method was then applied to four different subtypes of breast cancer resulting in the identification of signaling pathways associated with distinct functionalities for each of the breast cancer subtypes.
ContributorsTrevino, Robert (Author) / Kim, Seungchan (Thesis advisor) / Ringner, Markus (Committee member) / Liu, Huan (Committee member) / Arizona State University (Publisher)
Created2011
Description
In many classication problems data samples cannot be collected easily, example in drug trials, biological experiments and study on cancer patients. In many situations the data set size is small and there are many outliers. When classifying such data, example cancer vs normal patients the consequences of mis-classication are probably more important than any other data type, because the data point could be a cancer patient or the classication decision could help determine what gene might be over expressed and perhaps a cause of cancer. These mis-classications are typically higher in the presence of outlier data points. The aim of this thesis is to develop a maximum margin classier that is suited to address the lack of robustness of discriminant based classiers (like the Support Vector Machine (SVM)) to noise and outliers. The underlying notion is to adopt and develop a natural loss function that is more robust to outliers and more representative of the true loss function of the data. It is demonstrated experimentally that SVM's are indeed susceptible to outliers and that the new classier developed, here coined as Robust-SVM (RSVM), is superior to all studied classier on the synthetic datasets. It is superior to the SVM in both the synthetic and experimental data from biomedical studies and is competent to a classier derived on similar lines when real life data examples are considered.
ContributorsGupta, Sidharth (Author) / Kim, Seungchan (Thesis advisor) / Welfert, Bruno (Committee member) / Li, Baoxin (Committee member) / Arizona State University (Publisher)
Created2011
Description
Semiconductor scaling technology has led to a sharp growth in transistor counts. This has resulted in an exponential increase on both power dissipation and heat flux (or power density) in modern microprocessors. These microprocessors are integrated as the major components in many modern embedded devices, which offer richer features and attain higher performance than ever before. Therefore, power and thermal management have become the significant design considerations for modern embedded devices. Dynamic voltage/frequency scaling (DVFS) and dynamic power management (DPM) are two well-known hardware capabilities offered by modern embedded processors. However, the power or thermal aware performance optimization is not fully explored for the mainstream embedded processors with discrete DVFS and DPM capabilities. Many key problems have not been answered yet. What is the maximum performance that an embedded processor can achieve under power or thermal constraint for a periodic application? Does there exist an efficient algorithm for the power or thermal management problems with guaranteed quality bound? These questions are hard to be answered because the discrete settings of DVFS and DPM enhance the complexity of many power and thermal management problems, which are generally NP-hard. The dissertation presents a comprehensive study on these NP-hard power and thermal management problems for embedded processors with discrete DVFS and DPM capabilities. In the domain of power management, the dissertation addresses the power minimization problem for real-time schedules, the energy-constrained make-span minimization problem on homogeneous and heterogeneous chip multiprocessors (CMP) architectures, and the battery aware energy management problem with nonlinear battery discharging model. In the domain of thermal management, the work addresses several thermal-constrained performance maximization problems for periodic embedded applications. All the addressed problems are proved to be NP-hard or strongly NP-hard in the study. Then the work focuses on the design of the off-line optimal or polynomial time approximation algorithms as solutions in the problem design space. Several addressed NP-hard problems are tackled by dynamic programming with optimal solutions and pseudo-polynomial run time complexity. Because the optimal algorithms are not efficient in worst case, the fully polynomial time approximation algorithms are provided as more efficient solutions. Some efficient heuristic algorithms are also presented as solutions to several addressed problems. The comprehensive study answers the key questions in order to fully explore the power and thermal management potentials on embedded processors with discrete DVFS and DPM capabilities. The provided solutions enable the theoretical analysis of the maximum performance for periodic embedded applications under power or thermal constraints.
ContributorsZhang, Sushu (Author) / Chatha, Karam S (Thesis advisor) / Cao, Yu (Committee member) / Konjevod, Goran (Committee member) / Vrudhula, Sarma (Committee member) / Xue, Guoliang (Committee member) / Arizona State University (Publisher)
Created2012
Description
This dissertation studies routing in small-world networks such as grids plus long-range edges and real networks. Kleinberg showed that geography-based greedy routing in a grid-based network takes an expected number of steps polylogarithmic in the network size, thus justifying empirical efficiency observed beginning with Milgram. A counterpart for the grid-based model is provided; it creates all edges deterministically and shows an asymptotically matching upper bound on the route length. The main goal is to improve greedy routing through a decentralized machine learning process. Two considered methods are based on weighted majority and an algorithm of de Farias and Megiddo, both learning from feedback using ensembles of experts. Tests are run on both artificial and real networks, with decentralized spectral graph embedding supplying geometric information for real networks where it is not intrinsically available. An important measure analyzed in this work is overpayment, the difference between the cost of the method and that of the shortest path. Adaptive routing overtakes greedy after about a hundred or fewer searches per node, consistently across different network sizes and types. Learning stabilizes, typically at overpayment of a third to a half of that by greedy. The problem is made more difficult by eliminating the knowledge of neighbors' locations or by introducing uncooperative nodes. Even under these conditions, the learned routes are usually better than the greedy routes. The second part of the dissertation is related to the community structure of unannotated networks. A modularity-based algorithm of Newman is extended to work with overlapping communities (including considerably overlapping communities), where each node locally makes decisions to which potential communities it belongs. To measure quality of a cover of overlapping communities, a notion of a node contribution to modularity is introduced, and subsequently the notion of modularity is extended from partitions to covers. The final part considers a problem of network anonymization, mostly by the means of edge deletion. The point of interest is utility preservation. It is shown that a concentration on the preservation of routing abilities might damage the preservation of community structure, and vice versa.
ContributorsBakun, Oleg (Author) / Konjevod, Goran (Thesis advisor) / Richa, Andrea (Thesis advisor) / Syrotiuk, Violet R. (Committee member) / Czygrinow, Andrzej (Committee member) / Arizona State University (Publisher)
Created2011
Description
Finding the optimal solution to a problem with an enormous search space can be challenging. Unless a combinatorial construction technique is found that also guarantees the optimality of the resulting solution, this could be an infeasible task. If such a technique is unavailable, different heuristic methods are generally used to improve the upper bound on the size of the optimal solution. This dissertation presents an alternative method which can be used to improve a solution to a problem rather than construct a solution from scratch. Necessity analysis, which is the key to this approach, is the process of analyzing the necessity of each element in a solution. The post-optimization algorithm presented here utilizes the result of the necessity analysis to improve the quality of the solution by eliminating unnecessary objects from the solution. While this technique could potentially be applied to different domains, this dissertation focuses on k-restriction problems, where a solution to the problem can be presented as an array. A scalable post-optimization algorithm for covering arrays is described, which starts from a valid solution and performs necessity analysis to iteratively improve the quality of the solution. It is shown that not only can this technique improve upon the previously best known results, it can also be added as a refinement step to any construction technique and in most cases further improvements are expected. The post-optimization algorithm is then modified to accommodate every k-restriction problem; and this generic algorithm can be used as a starting point to create a reasonable sized solution for any such problem. This generic algorithm is then further refined for hash family problems, by adding a conflict graph analysis to the necessity analysis phase. By recoloring the conflict graphs a new degree of flexibility is explored, which can further improve the quality of the solution.
ContributorsNayeri, Peyman (Author) / Colbourn, Charles (Thesis advisor) / Konjevod, Goran (Thesis advisor) / Sen, Arunabha (Committee member) / Stanzione Jr, Daniel (Committee member) / Arizona State University (Publisher)
Created2011