548 research outputs found
Wireless transmission protocols using relays for broadcast and information exchange channels
Relays have been used to overcome existing network performance bottlenecks in meeting the growing
demand for large bandwidth and high quality of service (QoS) in wireless networks. This thesis
proposes several wireless transmission protocols using relays in practical multi-user broadcast and
information exchange channels. The main theme is to demonstrate that efficient use of relays provides
an additional dimension to improve reliability, throughput, power efficiency and secrecy. First,
a spectrally efficient cooperative transmission protocol is proposed for the multiple-input and singleoutput
(MISO) broadcast channel to improve the reliability of wireless transmission. The proposed
protocol mitigates co-channel interference and provides another dimension to improve the diversity
gain. Analytical and simulation results show that outage probability and the diversity and multiplexing
tradeoff of the proposed cooperative protocol outperforms the non-cooperative scheme. Second,
a two-way relaying protocol is proposed for the multi-pair, two-way relaying channel to improve the
throughput and reliability. The proposed protocol enables both the users and the relay to participate
in interference cancellation. Several beamforming schemes are proposed for the multi-antenna
relay. Analytical and simulation results reveal that the proposed protocol delivers significant improvements
in ergodic capacity, outage probability and the diversity and multiplexing tradeoff if compared
to existing schemes. Third, a joint beamforming and power management scheme is proposed for
multiple-input and multiple-output (MIMO) two-way relaying channel to improve the sum-rate. Network
power allocation and power control optimisation problems are formulated and solved using
convex optimisation techniques. Simulation results verify that the proposed scheme delivers better
sum-rate or consumes lower power when compared to existing schemes. Fourth, two-way secrecy
schemes which combine one-time pad and wiretap coding are proposed for the scalar broadcast channel
to improve secrecy rate. The proposed schemes utilise the channel reciprocity and employ relays
to forward secret messages. Analytical and simulation results reveal that the proposed schemes are
able to achieve positive secrecy rates even when the number of users is large. All of these new wireless
transmission protocols help to realise better throughput, reliability, power efficiency and secrecy
for wireless broadcast and information exchange channels through the efficient use of relays
Spectral properties of the trap model on sparse networks
One of the simplest models for the slow relaxation and aging of glasses is
the trap model by Bouchaud and others, which represents a system as a point in
configuration-space hopping between local energy minima. The time evolution
depends on the transition rates and the network of allowed jumps between the
minima. We consider the case of sparse configuration-space connectivity given
by a random graph, and study the spectral properties of the resulting master
operator. We develop a general approach using the cavity method that gives
access to the density of states in large systems, as well as localisation
properties of the eigenvectors, which are important for the dynamics. We
illustrate how, for a system with sparse connectivity and finite temperature,
the density of states and the average inverse participation ratio have
attributes that arise from a non-trivial combination of the corresponding mean
field (fully connected) and random walk (infinite temperature) limits. In
particular, we find a range of eigenvalues for which the density of states is
of mean-field form but localisation properties are not, and speculate that the
corresponding eigenvectors may be concentrated on extensively many clusters of
network sites.Comment: 41 pages, 15 figure
Spectral Theory of Sparse Non-Hermitian Random Matrices
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matrices provide crucial information on system
stability and susceptibility, however, their study is greatly complicated by
the twin challenges of a lack of symmetry and a sparse interaction structure.
In this review we provide a concise and systematic introduction to the main
tools and results in this field. We show how the spectra of sparse
non-Hermitian matrices can be computed via an analogy with infinite dimensional
operators obeying certain recursion relations. With reference to three
illustrative examples --- adjacency matrices of regular oriented graphs,
adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency
matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the
use of these methods to obtain both analytic and numerical results for the
spectrum, the spectral distribution, the location of outlier eigenvalues, and
the statistical properties of eigenvectors.Comment: 60 pages, 10 figure
From Quantum Entanglement to Interactions of Elementary Excitations in Coupled Spin Chains : An Introduction to Numerical Many-Body Physics with Matrix Product States and Tensor Networks
Matrix product states provide an efficient parametrisation of low-entanglement many-body quantum states.
In this thesis, the underlying theory is developed from scratch, requiring only
basic notions of quantum mechanics and quantum information theory. A full introduction to
matrix product state algebra and matrix product operators is given, culminating in the
derivation of the density matrix renormalisation group algorithm. The latter provides a simple
variational scheme to determine the ground state of arbitrary one-dimensional many-body
quantum systems with supreme precision.
As an application of matrix-product state technology, the kernel polynomial method is
introduced in detail as a state-of-the art numerical tool to find the spectral function or the
dynamical correlator of a given quantum system. This in turn gives access to the elementary
excitations of the system, such that the locations of the low-energy eigenstates can be studied
directly in real space.
To illustrate those theoretical tools concretely, the ground state energy, the entanglement
entropy and the elementary excitations of a simple interface model of a Heisenberg ferromagnet
and a Heisenberg antiferromagnet are studied. By changing the location of the model in
parameter space, the dependence of the above-mentioned quantities on the transverse field and
the coupling strength is investigated. Most notably, we find that the entanglement entropy
characteristic to the antiferromagnetic ground state stretches across the interface into the
ferromagnetic half-chain. The dependence of the physics on the value of the coupling strength
is, overall, small, with exception of the appearance of a boundary mode whose eigenenergy
grows with the coupling. A comparison with a localised edge field shows however that the
boundary mode is a true interaction effect of the two half-chains.
Various algorithmic and physics extensions of the present project are discussed, such that the
code written as part of this thesis could be turned into a state-of-the-art MPS library with
managable effort. In particular, an application of the kernel polynomial method to calculate
finite-temperature correlators is derived in detail
Dynamic rewiring in small world networks
We investigate equilibrium properties of small world networks, in which both
connectivity and spin variables are dynamic, using replicated transfer matrices
within the replica symmetric approximation. Population dynamics techniques
allow us to examine order parameters of our system at total equilibrium,
probing both spin- and graph-statistics. Of these, interestingly, the degree
distribution is found to acquire a Poisson-like form (both within and outside
the ordered phase). Comparison with Glauber simulations confirms our results
satisfactorily.Comment: 21 pages, 5 figure
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Dynamic asset (and liability) management under market and credit risk
We introduce a modelling paradigm which integrates credit risk and market
risk in describing the random dynamical behaviour of the underlying fixed income assets.
We then consider an asset and liability management (ALM) problem and develop a mul-
tistage stochastic programming model which focuses on optimum risk decisions. These
models exploit the dynamical multiperiod structure of credit risk and provide insight
into the corrective recourse decisions whereby issues such as the timing risk of default is
appropriately taken into consideration. We also present a index tracking model in which
risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the
index. Both in- and out-of-sample (backtesting) experiments are undertaken to validate
our approach. In this way we are able to demonstrate the feasibility and flexibility of
the chosen framework
Latent variable regression and applications to planetary seismic instrumentation
The work presented in this thesis is framed by the concept of latent variables, a modern data analytics approach. A latent variable represents an extracted component from a dataset which is not directly measured.
The concept is first applied to combat the problem of ill-posed regression through the promising method of partial least squares (PLS). In this context the latent variables within a data matrix are extracted through an iterative algorithm based on cross-covariance as an optimisation criterion. This work first extends the PLS algorithm, using adaptive and recursive techniques, for online, non-stationary data applications. The standard PLS algorithm is further generalised for complex-, quaternion- and tensor-valued data. In doing so it is shown that the multidimensional algebras facilitate physically meaningful representations, demonstrated through smart-grid frequency estimation and image-classification tasks.
The second part of the thesis uses this knowledge to inform a performance analysis of the MEMS microseismometer implemented for the InSight mission to Mars. This is given in terms of the sensor's intrinsic self-noise, the estimation of which is achieved from experimental data with a colocated instrument. The standard coherence and proposed delta noise estimators are analysed with respect to practical issues. The implementation of algorithms for the alignment, calibration and post-processing of the data then enabled a definitive self-noise estimate, validated from data acquired in ultra-quiet, deep-space environment.
A method for the decorrelation of the microseismometer's output from its thermal response is proposed. To do so a novel sensor fusion approach based on the Kalman filter is developed for a full-band transfer-function correction, in contrast to the traditional ill-posed frequency division method. This algorithm was applied to experimental data which determined the thermal model coefficients while validating the sensor's performance at tidal frequencies 1E-5Hz and in extreme environments at -65C.
This thesis, therefore, provides a definitive view of the latent variables perspective. This is achieved through the general algorithms developed for regression with multidimensional data and the bespoke application to seismic instrumentation.Open Acces
Finding The Lazy Programmer's Bugs
Traditionally developers and testers created huge numbers of explicit tests, enumerating interesting cases, perhaps
biased by what they believe to be the current boundary conditions of the function being tested. Or at
least, they were supposed to.
A major step forward was the development of property testing. Property testing requires the user to write a few
functional properties that are used to generate tests, and requires an external library or tool to create test data
for the tests. As such many thousands of tests can be created for a single property. For the purely functional
programming language Haskell there are several such libraries; for example QuickCheck [CH00], SmallCheck
and Lazy SmallCheck [RNL08].
Unfortunately, property testing still requires the user to write explicit tests. Fortunately, we note there are
already many implicit tests present in programs. Developers may throw assertion errors, or the compiler may
silently insert runtime exceptions for incomplete pattern matches.
We attempt to automate the testing process using these implicit tests. Our contributions are in four main
areas: (1) We have developed algorithms to automatically infer appropriate constructors and functions needed
to generate test data without requiring additional programmer work or annotations. (2) To combine the
constructors and functions into test expressions we take advantage of Haskell's lazy evaluation semantics by
applying the techniques of needed narrowing and lazy instantiation to guide generation. (3) We keep the type
of test data at its most general, in order to prevent committing too early to monomorphic types that cause
needless wasted tests. (4) We have developed novel ways of creating Haskell case expressions to inspect elements
inside returned data structures, in order to discover exceptions that may be hidden by laziness, and to make
our test data generation algorithm more expressive.
In order to validate our claims, we have implemented these techniques in Irulan, a fully automatic tool for
generating systematic black-box unit tests for Haskell library code. We have designed Irulan to generate high
coverage test suites and detect common programming errors in the process
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