Optimization of transit transfer times: A system-wide approach

This dissertation presents a system-wide approach, based on genetic algorithms, for the optimization of transfer times for an entire bus transit system. Optimization of transfer times in a transit system is a complicated problem because of the large set of binary and discrete values involved. The combinatorial nature of the problem imposes a computational burden and makes it difficult to solve by classical mathematical programming methods. ^ The genetic algorithm proposed in this research attempts to find an optimal solution for the transfer time optimization problem by searching for a combination of adjustments to the timetable for all the routes in the system. It makes use of existing scheduled timetables, ridership demand at all transfer locations, and takes into consideration the randomness of bus arrivals. ^ Data from Broward County Transit are used to compute total transfer times. The proposed genetic algorithm-based approach proves to be capable of producing substantial time savings compared to the existing transfer times in a reasonable amount of time. ^ The dissertation also addresses the issues related to spatial and temporal modeling, variability in bus arrival and departure times, walking time, as well as the integration of scheduling and ridership data. ^

Abstractions to support dynamic adaptation of communication frameworks for user-centric communication

The convergence of data, audio and video on IP networks is changing the way individuals, groups and organizations communicate. This diversity of communication media presents opportunities for creating synergistic collaborative communications. This form of collaborative communication is however not without its challenges. The increasing number of communication service providers coupled with a combinatorial mix of offered services, varying Quality-of-Service and oscillating pricing of services increases the complexity for the user to manage and maintain ‘always best’ priced or performance services. Consumers have to manually manage and adapt their communication in line with differences in services across devices, networks and media while ensuring that the usage remain consistent with their intended goals. This dissertation proposes a novel user-centric approach to address this problem. The proposed approach aims to reduce the aforementioned complexity to the user by (1) providing high-level abstractions and a policy based methodology for automated selection of the communication services guided by high-level user policies and (2) providing services through the seamless integration of multiple communication service providers and providing an extensible framework to support the integration of multiple communication service providers. The approach was implemented in the Communication Virtual Machine (CVM), a model-driven technology for realizing communication applications. The CVM includes the Network Communication Broker, the layer responsible for providing a network-independent API to the upper layers of CVM. The initial prototype for the NCB supported only a single communication framework which limited the number, quality and types of services available. Experimental evaluation of the approach show the additional overhead of the approach is minimal compared to the individual communication services frameworks. Additionally the automated approach proposed out performed the individual communication services frameworks for cross framework switching.

Analysis of key predistribution schemes in wireless sensor networks

Combinatorial designs are used for designing key predistribution schemes that are applied to wireless sensor networks in communications. This helps in building a secure channel. Private-key cryptography helps to determine a common key between a pair of nodes in sensor networks. Wireless sensor networks using key predistribution schemes have many useful applications in military and civil operations. When designs are efficiently implemented on sensor networks, blocks with unique keys will be the result. One such implementation is a transversal design which follows the principle of simple key establishment. Analysis of designs and modeling the key schemes are the subjects of this project.

Protein and Drug Design Algorithms Using Improved Biophysical Modeling

This thesis focuses on the development of algorithms that will allow protein design calculations to incorporate more realistic modeling assumptions. Protein design algorithms search large sequence spaces for protein sequences that are biologically and medically useful. Better modeling could improve the chance of success in designs and expand the range of problems to which these algorithms are applied. I have developed algorithms to improve modeling of backbone flexibility (DEEPer) and of more extensive continuous flexibility in general (EPIC and LUTE). I’ve also developed algorithms to perform multistate designs, which account for effects like specificity, with provable guarantees of accuracy (COMETS), and to accommodate a wider range of energy functions in design (EPIC and LUTE).

Petri Net Siphon Analysis and Network Centrality Measures for Identifying Combination Therapies in Signaling Pathways

Aberrant behavior of biological signaling pathways has been implicated in diseases such as cancers. Therapies have been developed to target proteins in these networks in the hope of curing the illness or bringing about remission. However, identifying targets for drug inhibition that exhibit good therapeutic index has proven to be challenging since signaling pathways have a large number of components and many interconnections such as feedback, crosstalk, and divergence. Unfortunately, some characteristics of these pathways such as redundancy, feedback, and drug resistance reduce the efficacy of single drug target therapy and necessitate the employment of more than one drug to target multiple nodes in the system. However, choosing multiple targets with high therapeutic index poses more challenges since the combinatorial search space could be huge. To cope with the complexity of these systems, computational tools such as ordinary differential equations have been used to successfully model some of these pathways. Regrettably, for building these models, experimentally-measured initial concentrations of the components and rates of reactions are needed which are difficult to obtain, and in very large networks, they may not be available at the moment. Fortunately, there exist other modeling tools, though not as powerful as ordinary differential equations, which do not need the rates and initial conditions to model signaling pathways. Petri net and graph theory are among these tools. In this thesis, we introduce a methodology based on Petri net siphon analysis and graph network centrality measures for identifying prospective targets for single and multiple drug therapies. In this methodology, first, potential targets are identified in the Petri net model of a signaling pathway using siphon analysis. Then, the graph-theoretic centrality measures are employed to prioritize the candidate targets. Also, an algorithm is developed to check whether the candidate targets are able to disable the intended outputs in the graph model of the system or not. We implement structural and dynamical models of ErbB1-Ras-MAPK pathways and use them to assess and evaluate this methodology. The identified drug-targets, single and multiple, correspond to clinically relevant drugs. Overall, the results suggest that this methodology, using siphons and centrality measures, shows promise in identifying and ranking drugs. Since this methodology only uses the structural information of the signaling pathways and does not need initial conditions and dynamical rates, it can be utilized in larger networks.

Personalized cancer medicine: molecular diagnostics, predictive biomarkers, and drug resistance.

The progressive elucidation of the molecular pathogenesis of cancer has fueled the rational development of targeted drugs for patient populations stratified by genetic characteristics. Here we discuss general challenges relating to molecular diagnostics and describe predictive biomarkers for personalized cancer medicine. We also highlight resistance mechanisms for epidermal growth factor receptor (EGFR) kinase inhibitors in lung cancer. We envisage a future requiring the use of longitudinal genome sequencing and other omics technologies alongside combinatorial treatment to overcome cellular and molecular heterogeneity and prevent resistance caused by clonal evolution.

Three dimensional Sklyanin algebras and Gröbner bases

We consider Sklyanin algebras $S$ with 3 generators, which are quadratic algebras over a field $\K$ with $3$ generators $x,y,z$ given by $3$ relations $pxy+qyx+rzz=0$, $pyz+qzy+rxx=0$ and $pzx+qxz+ryy=0$, where $p,q,r\in\K$. this class of algebras has enjoyed much attention. In particular, using tools from algebraic geometry, Feigin, Odesskii \cite{odf}, and Artin, Tate and Van Den Bergh, showed that if at least two of the parameters $p$, $q$ and $r$ are non-zero and at least two of three numbers $p^3$, $q^3$ and $r^3$ are distinct, then $S$ is Artin--Schelter regular. More specifically, $S$ is Koszul and has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates (PHS). It has became commonly accepted that it is impossible to achieve the same objective by purely algebraic and combinatorial means like the Groebner basis technique. The main purpose of this paper is to trace the combinatorial meaning of the properties of Sklyanin algebras, such as Koszulity, PBW, PHS, Calabi-Yau, and to give a new constructive proof of the above facts due to Artin, Tate and Van Den Bergh. Further, we study a wider class of Sklyanin algebras, namely
the situation when all parameters of relations could be different. We call them generalized Sklyanin algebras. We classify up to isomorphism all generalized Sklyanin algebras with the same Hilbert series as commutative polynomials on
3 variables. We show that generalized Sklyanin algebras in general position have a Golod–Shafarevich Hilbert series (with exception of the case of field with two elements).

Multi-stage scheduling problems with precedence constraints

Abstract not available

On f-vectors of polytopes and matroids

Thesis (Ph.D.)--University of Washington, 2016-08

Dual stimulation of antigen presenting cells using carbon nanotube-based vaccine delivery system for cancer immunotherapy

Although anti−cancer immuno−based combinatorial therapeutic approaches have shown promising results, efficient tumour eradication demands further intensification of anti−tumour immune response. With the emerging field of nanovaccinology, multi−walled carbon nanotubes (MWNTs) have manifested prominent potentials as tumour antigen nanocarriers. Nevertheless, the utilization of MWNTs in co−delivering antigen along with different types of immunoadjuvants to antigen presenting cells (APCs) has not been investigated yet. We hypothesized that harnessing MWNT for concurrent delivery of cytosine−phosphate−guanine oligodeoxynucleotide (CpG) and anti-CD40 Ig (αCD40), as immunoadjuvants, along with the model antigen ovalbumin (OVA) could potentiate immune response induced against OVA−expressing tumour cells. We initially investigated the effective method to co−deliver OVA and CpG using MWNT to the APC. Covalent conjugation of OVA and CpG prior to loading onto MWNTs markedly augmented the CpG−mediated adjuvanticity, as demonstrated by the significantly increased OVA−specific T cell responses in vitro and in C57BL/6 mice. αCD40 was then included as a second immunoadjuvant to further intensify the immune response. Immune response elicited in vitro and in vivo by OVA, CpG and αCD40 was significantly potentiated by their co−incorporation onto the MWNTs. Furthermore, MWNT remarkably improved the ability of co−loaded OVA, CpG and αCD40 in inhibiting the growth of OVA−expressing B16F10 melanoma cells in subcutaneous or lung pseudo−metastatic tumour models. Therefore, this study suggests that the utilization of MWNTs for the co−delivery of tumour−derived antigen, CpG and αCD40 could be a competent approach for efficient tumours eradication.

Asymmetric polygons with maximum area

We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given n diameters of a circle and a positive integer k < n, this paper addresses the problem of computing a maximum area asymmetric k-gon having as vertices k < n endpoints of the given diameters. The study of this type of polygons is motivated by ethnomusiciological applications.

A signaling visualization toolkit to support rational design of combination therapies and biomarker discovery: SiViT

Targeted cancer therapy aims to disrupt aberrant cellular signalling pathways. Biomarkers are surrogates of pathway state, but there is limited success in translating candidate biomarkers to clinical practice due to the intrinsic complexity of pathway networks. Systems biology approaches afford better understanding of complex, dynamical interactions in signalling pathways targeted by anticancer drugs. However, adoption of dynamical modelling by clinicians and biologists is impeded by model inaccessibility. Drawing on computer games technology, we present a novel visualisation toolkit, SiViT, that converts systems biology models of cancer cell signalling into interactive simulations that can be used without specialist computational expertise. SiViT allows clinicians and biologists to directly introduce for example loss of function mutations and specific inhibitors. SiViT animates the effects of these introductions on pathway dynamics, suggesting further experiments and assessing candidate biomarker effectiveness. In a systems biology model of Her2 signalling we experimentally validated predictions using SiViT, revealing the dynamics of biomarkers of drug resistance and highlighting the role of pathway crosstalk. No model is ever complete: the iteration of real data and simulation facilitates continued evolution of more accurate, useful models. SiViT will make accessible libraries of models to support preclinical research, combinatorial strategy design and biomarker discovery.

State sum models for quantum gravity

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.

A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

Dynamic Resource Allocation in Wireless Heterogeneous Networks

Deployment of low power basestations within cellular networks can potentially increase both capacity and coverage. However, such deployments require efficient resource allocation schemes for managing interference from the low power and macro basestations that are located within each other’s transmission range. In this dissertation, we propose novel and efficient dynamic resource allocation algorithms in the frequency, time and space domains. We show that the proposed algorithms perform better than the current state-of-art resource management algorithms. In the first part of the dissertation, we propose an interference management solution in the frequency domain. We introduce a distributed frequency allocation scheme that shares frequencies between macro and low power pico basestations, and guarantees a minimum average throughput to users. The scheme seeks to minimize the total number of frequencies needed to honor the minimum throughput requirements. We evaluate our scheme using detailed simulations and show that it performs on par with the centralized optimum allocation. Moreover, our proposed scheme outperforms a static frequency reuse scheme and the centralized optimal partitioning between the macro and picos. In the second part of the dissertation, we propose a time domain solution to the interference problem. We consider the problem of maximizing the alpha-fairness utility over heterogeneous wireless networks (HetNets) by jointly optimizing user association, wherein each user is associated to any one transmission point (TP) in the network, and activation fractions of all TPs. Activation fraction of a TP is the fraction of the frame duration for which it is active, and together these fractions influence the interference seen in the network. To address this joint optimization problem which we show is NP-hard, we propose an alternating optimization based approach wherein the activation fractions and the user association are optimized in an alternating manner. The subproblem of determining the optimal activation fractions is solved using a provably convergent auxiliary function method. On the other hand, the subproblem of determining the user association is solved via a simple combinatorial algorithm. Meaningful performance guarantees are derived in either case. Simulation results over a practical HetNet topology reveal the superior performance of the proposed algorithms and underscore the significant benefits of the joint optimization. In the final part of the dissertation, we propose a space domain solution to the interference problem. We consider the problem of maximizing system utility by optimizing over the set of user and TP pairs in each subframe, where each user can be served by multiple TPs. To address this optimization problem which is NP-hard, we propose a solution scheme based on difference of submodular function optimization approach. We evaluate our scheme using detailed simulations and show that it performs on par with a much more computationally demanding difference of convex function optimization scheme. Moreover, the proposed scheme performs within a reasonable percentage of the optimal solution. We further demonstrate the advantage of the proposed scheme by studying its performance with variation in different network topology parameters.