311 research outputs found
Design of sequences with good correlation properties
This thesis is dedicated to exploring sequences with good correlation properties. Periodic sequences with desirable correlation properties have numerous applications in communications. Ideally, one would like to have a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. However, theoretical bounds show that the maximum magnitudes of auto-correlation and cross-correlation of a sequence set are mutually constrained, i.e., if a set of sequences possesses good auto-correlation properties, then the cross-correlation properties are not good and vice versa. The design of sequence sets that achieve those theoretical bounds is therefore of great interest. In addition, instead of pursuing the least possible correlation values within an entire period, it is also interesting to investigate families of sequences with ideal correlation in a smaller zone around the origin. Such sequences are referred to as sequences with zero correlation zone or ZCZ sequences, which have been extensively studied due to their applications in 4G LTE and 5G NR systems, as well as quasi-synchronous code-division multiple-access communication systems.
Paper I and a part of Paper II aim to construct sequence sets with low correlation within a whole period. Paper I presents a construction of sequence sets that meets the Sarwate bound. The construction builds a connection between generalised Frank sequences and combinatorial objects, circular Florentine arrays. The size of the sequence sets is determined by the existence of circular Florentine arrays of some order. Paper II further connects circular Florentine arrays to a unified construction of perfect polyphase sequences, which include generalised Frank sequences as a special case. The size of a sequence set that meets the Sarwate bound, depends on a divisor of the period of the employed sequences, as well as the existence of circular Florentine arrays.
Paper III-VI and a part of Paper II are devoted to ZCZ sequences.
Papers II and III propose infinite families of optimal ZCZ sequence sets with respect to some bound, which are used to eliminate interference within a single cell in a cellular network. Papers V, VI and a part of Paper II focus on constructions of multiple optimal ZCZ sequence sets with favorable inter-set cross-correlation, which can be used in multi-user communication environments to minimize inter-cell interference. In particular, Paper~II employs circular Florentine arrays and improves the number of the optimal ZCZ sequence sets with optimal inter-set cross-correlation property in some cases.Doktorgradsavhandlin
Feature selection and modelling methods for microarray data from acute coronary syndrome
Acute coronary syndrome (ACS) represents a leading cause of mortality and morbidity worldwide. Providing better diagnostic solutions and developing therapeutic strategies customized to the individual patient represent societal and economical urgencies. Progressive improvement in diagnosis and treatment procedures require a thorough understanding of the underlying genetic mechanisms of the disease. Recent advances in microarray technologies together with the decreasing costs of the specialized equipment enabled affordable harvesting of time-course gene expression data. The high-dimensional data generated demands for computational tools able to extract the underlying biological knowledge.
This thesis is concerned with developing new methods for analysing time-course gene expression data, focused on identifying differentially expressed genes, deconvolving heterogeneous gene expression measurements and inferring
dynamic gene regulatory interactions. The main contributions include: a novel multi-stage feature selection method, a new deconvolution approach for estimating cell-type specific signatures and quantifying the contribution of each cell type to the variance of the gene expression patters, a novel approach to identify the
cellular sources of differential gene expression, a new approach to model gene expression dynamics using sums of exponentials and a novel method to estimate stable linear dynamical systems from noisy and unequally spaced time series data.
The performance of the proposed methods was demonstrated on a time-course dataset consisting of microarray gene expression levels collected from the blood samples of patients with ACS and associated blood count measurements. The results of the feature selection study are of significant biological relevance. For the
first time is was reported high diagnostic performance of the ACS subtypes up to three months after hospital admission. The deconvolution study exposed features
of within and between groups variation in expression measurements and identified potential cell type markers and cellular sources of differential gene expression.
It was shown that the dynamics of post-admission gene expression data can be accurately modelled using sums of exponentials, suggesting that gene expression
levels undergo a transient response to the ACS events before returning to equilibrium. The linear dynamical models capturing the gene regulatory interactions
exhibit high predictive performance and can serve as platforms for system-level analysis, numerical simulations and intervention studies
Entanglement Theory and the Quantum Simulation of Many-Body Physics
In this thesis we present new results relevant to two important problems in
quantum information science: the development of a theory of entanglement and
the exploration of the use of controlled quantum systems to the simulation of
quantum many-body phenomena.
In the first part we introduce a new approach to the study of entanglement by
considering its manipulation under operations not capable of generating
entanglement and show there is a total order for multipartite quantum states in
this framework. We also present new results on hypothesis testing of correlated
sources and give further evidence on the existence of NPPT bound entanglement.
In the second part, we study the potential as well as the limitations of a
quantum computer for calculating properties of many-body systems. First we
analyse the usefulness of quantum computation to calculate additive
approximations to partition functions and spectral densities of local
Hamiltonians. We then show that the determination of ground state energies of
local Hamiltonians with an inverse polynomial spectral gap is QCMA-hard.
In the third and last part, we approach the problem of quantum simulating
many-body systems from a more pragmatic point of view. We analyze the
realization of paradigmatic condensed matter Hamiltonians in arrays of coupled
microcavities, such as the Bose-Hubbard and the anisotropic Heisenberg models,
and discuss the feasibility of an experimental realization with
state-of-the-art current technology.Comment: 230 pages. PhD thesis, Imperial College London. Chapters 6, 7 and 8
contain unpublished materia
Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays
This review is focused on tests of Einstein's theory of General Relativity
with gravitational waves that are detectable by ground-based interferometers
and pulsar timing experiments. Einstein's theory has been greatly constrained
in the quasi-linear, quasi-stationary regime, where gravity is weak and
velocities are small. Gravitational waves will allow us to probe a
complimentary, yet previously unexplored regime: the non-linear and dynamical
strong-field regime. Such a regime is, for example, applicable to compact
binaries coalescing, where characteristic velocities can reach fifty percent
the speed of light and compactnesses can reach a half. This review begins with
the theoretical basis and the predicted gravitational wave observables of
modified gravity theories. The review continues with a brief description of the
detectors, including both gravitational wave interferometers and pulsar timing
arrays, leading to a discussion of the data analysis formalism that is
applicable for such tests. The review ends with a discussion of gravitational
wave tests for compact binary systems.Comment: 123 pages, 5 figures, replaced with version accepted for publication
in the Living Reviews in Relativit
- …