Inferential stability in systems biology

The modern biological sciences are fraught with statistical difficulties. Biomolecular stochasticity, experimental noise, and the “large p, small n” problem all contribute to the challenge of data analysis. Nevertheless, we routinely seek to draw robust, meaningful conclusions from observations. In this thesis, we explore methods for assessing the effects of data variability upon downstream inference, in an attempt to quantify and promote the stability of the inferences we make. We start with a review of existing methods for addressing this problem, focusing upon the bootstrap and similar methods. The key requirement for all such approaches is a statistical model that approximates the data generating process. We move on to consider biomarker discovery problems. We present a novel algorithm for proposing putative biomarkers on the strength of both their predictive ability and the stability with which they are selected. In a simulation study, we find our approach to perform favourably in comparison to strategies that select on the basis of predictive performance alone. We then consider the real problem of identifying protein peak biomarkers for HAM/TSP, an inflammatory condition of the central nervous system caused by HTLV-1 infection. We apply our algorithm to a set of SELDI mass spectral data, and identify a number of putative biomarkers. Additional experimental work, together with known results from the literature, provides corroborating evidence for the validity of these putative biomarkers. Having focused on static observations, we then make the natural progression to time course data sets. We propose a (Bayesian) bootstrap approach for such data, and then apply our method in the context of gene network inference and the estimation of parameters in ordinary differential equation models. We find that the inferred gene networks are relatively unstable, and demonstrate the importance of finding distributions of ODE parameter estimates, rather than single point estimates

Neural Connectivity with Hidden Gaussian Graphical State-Model

The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural space. Nevertheless, what we observe at the sensor space is a superposition of projected fields, from the whole gray-matter. This is the reason for a major pitfall of noninvasive Electrophysiology methods: distorted reconstruction of neural activity and its connectivity or leakage. It has been proven that current methods produce incorrect connectomes. Somewhat related to the incorrect connectivity modelling, they disregard either Systems Theory and Bayesian Information Theory. We introduce a new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is equivalent to a frequency domain Linear State Space Model (LSSM) but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human Steady State Visual Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey. Open source packages are freely available online, to reproduce the results presented in this paper and to analyze external MEEG databases

Generic Error Bounds for the Generalized Lasso with Sub-Exponential Data

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore what conclusions are still valid when going beyond. While many statistical features of the generalized Lasso remain unaffected (e.g., consistency), the key difference becomes manifested in the way how the complexity of the hypothesis set is measured. It turns out that the estimation error can be controlled by means of two complexity parameters that arise naturally from a generic-chaining-based proof strategy. The output model can be non-realizable, while the only requirement for the input vector is a generic concentration inequality of Bernstein-type, which can be implemented for a variety of sub-exponential distributions. This abstract approach allows us to reproduce, unify, and extend previously known guarantees for the generalized Lasso. In particular, we present applications to semi-parametric output models and phase retrieval via the lifted Lasso. Moreover, our findings are discussed in the context of sparse recovery and high-dimensional estimation problems

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Microscopic Theory for Coupled Atomistic Magnetization and Lattice Dynamics

A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known inter-atomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double anti-ferromagnetic materials, as well as, charge density waves induced by a non-uniform spin structure are given. In the final parts, a set of coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and damped driven mechanical oscillator for the ...Comment: 22 pages, including 7 pages of Appendix and references, 6 figure

Radio Resource Management in LTE-Advanced Systems with Carrier Aggregation

In order to meet the ever-increasing demand for wireless broadband services from fast growing mobile users, the Long Term Evolution -Advanced (LTE-A) standard has been proposed to effectively improve the system capacity and the spectral efficiency for the fourth-generation (4G) wireless mobile communications. Many advanced techniques are incorporated in LTE-A systems to jointly ameliorate system performance, among which Carrier Aggregation (CA) is considered as one of the most promising improvements that has profound significance even in the upcoming 5G era. Component carriers (CCs) from various portions of the spectrum are logically concatenated to form a much larger virtual band, resulting in remarkable boosted system capacity and user data throughput. However, the unique features of CA have posed many emerging challenges as well as span-new opportunities on the Radio Resource Management (RRM) in the LTE-A systems. First, although multi-CC transmission can bring higher throughput, it may incur more intensive interference for each CC and more power consumption for users. Thus the performance gain of CA under different conditions needs fully evaluating. Besides, as CA offers flexible CC selection and cross-CC load balancing and scheduling, enhanced RRM strategies should be designed to further optimize the overall resource utilization. In addition, CA enables the frequency reuse on a CC resolution, adding another dimension to inter-cell interference management in heterogeneous networks (HetNets). New interference management mechanisms should be designed to take the advantage of CA. Last but not least, CA empowers the LTE-A systems to aggregate the licensed spectrum with the unlicensed spectrum, thus offering a capacity surge. Yet how to balance the traffic between licensed and unlicensed spectrum and how to achieve a harmony coexistence with other unlicensed systems are still open issues. To this end, the dissertation emphasizes on the new functionalities introduced by CA to optimize the RRM performance in LTE-A systems. The main objectives are four-fold: 1) to fully evaluate the benefits of CA from different perspectives under different conditions via both theoretical analysis and simulations; 2) to design cross-layer CC selection, packet scheduling and power control strategies to optimize the target performance; 3) to analytically model the interference of HetNets with CA and propose dynamic interference mitigation strategies in a CA scenario; and 4) to investigate the impact of LTE transmissions on other unlicensed systems and develop enhanced RRM mechanisms for harmony coexistence. To achieve these objectives, we first analyze the benefits of CA via investigating the user accommodation capabilities of the system in the downlink admission control process. The LTE-A users with CA capabilities and the legacy LTE users are considered. Analytical models are developed to derive the maximum number of users that can be admitted into the system given the user QoS requirements and traffic features. The results show that with only a slightly higher spectrum utilization, the system can admit as much as twice LTE-A users than LTE users when the user traffic is bursty. Second, we study the RRM in the single-tier LTE-A system and propose a cross-layer dynamic CC selection and power control strategy for uplink CA. Specifically, the uplink power offset effects caused by multi-CC transmission are considered. An estimation method for user bandwidth allocation is developed and a combinatorial optimization problem is formulated to improve the user throughput via maximizing the user power utilization. Third, we explore the interference management problem in multi-tier HetNets considering the CC-resolution frequency reuse. An analytical model is devised to capture the randomness behaviors of the femtocells exploiting the stochastic geometry theory. The interaction between the base stations of different tiers are formulated into a two-level Stackelberg game, and a backward induction method is exploited to obtain the Nash equilibrium. Last, we focus on the mechanism design for licensed and unlicensed spectrum aggregation. An LTE MAC protocol on unlicensed spectrum is developed considering the coexistence with the Wi-Fi systems. The protocol captures the asynchronous nature of Wi-Fi transmissions in time-slotted LTE frame structure and strike a tunable tradeoff between LTE and Wi-Fi performance. Analytical analysis is also presented to reveal the essential relation among different parameters of the two systems. In summary, the dissertation aims at fully evaluating the benefits of CA in different scenarios and making full use of the benefits to develop efficient and effective RRM strategies for better LTE-Advanced system performance

Training issues and learning algorithms for feedforward and recurrent neural networks

Ph.DDOCTOR OF PHILOSOPH