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Ensuring Access to Safe and Nutritious Food for All Through the Transformation of Food Systems
An iterative warping and clustering algorithm to estimate multiple wave-shape functions from a nonstationary oscillatory signal
Nonsinusoidal oscillatory signals are everywhere. In practice, the
nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function
(WSF), might vary from cycle to cycle. When there are finite different WSFs,
, so that the WSF jumps from one to another suddenly, the
different WSFs and jumps encode useful information. We present an iterative
warping and clustering algorithm to estimate from a
nonstationary oscillatory signal with time-varying amplitude and frequency, and
hence the change points of the WSFs. The algorithm is a novel combination of
time-frequency analysis, singular value decomposition entropy and vector
spectral clustering. We demonstrate the efficiency of the proposed algorithm
with simulated and real signals, including the voice signal, arterial blood
pressure, electrocardiogram and accelerometer signal. Moreover, we provide a
mathematical justification of the algorithm under the assumption that the
amplitude and frequency of the signal are slowly time-varying and there are
finite change points that model sudden changes from one wave-shape function to
another one.Comment: 39 pages, 11 figure
Soliton Gas: Theory, Numerics and Experiments
The concept of soliton gas was introduced in 1971 by V. Zakharov as an
infinite collection of weakly interacting solitons in the framework of
Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted
soliton gas, solitons with random parameters are almost non-overlapping. More
recently, the concept has been extended to dense gases in which solitons
strongly and continuously interact. The notion of soliton gas is inherently
associated with integrable wave systems described by nonlinear partial
differential equations like the KdV equation or the one-dimensional nonlinear
Schr\"odinger equation that can be solved using the inverse scattering
transform. Over the last few years, the field of soliton gases has received a
rapidly growing interest from both the theoretical and experimental points of
view. In particular, it has been realized that the soliton gas dynamics
underlies some fundamental nonlinear wave phenomena such as spontaneous
modulation instability and the formation of rogue waves. The recently
discovered deep connections of soliton gas theory with generalized
hydrodynamics have broadened the field and opened new fundamental questions
related to the soliton gas statistics and thermodynamics. We review the main
recent theoretical and experimental results in the field of soliton gas. The
key conceptual tools of the field, such as the inverse scattering transform,
the thermodynamic limit of finite-gap potentials and the Generalized Gibbs
Ensembles are introduced and various open questions and future challenges are
discussed.Comment: 35 pages, 8 figure
Cluster Index Modulation for Reconfigurable Intelligent Surface-Assisted mmWave Massive MIMO
In this paper, we propose a transmission mechanism for a reconfigurable
intelligent surface (RIS)-assisted millimeter wave (mmWave) system based on
cluster index modulation (CIM), named best-gain optimized cluster selection CIM
(BGCS-CIM). The proposed BGCS-CIM scheme considers effective cluster power gain
and spatial diversity gain obtained by the additional paths within the indexed
cluster to construct an efficient codebook. We also integrate the proposed
scheme into a practical system model to create a virtual path between
transmitter and receiver where the direct link has been blocked. Thanks to the
designed whitening filter, a closed-form expression for the upper bound on the
average bit error rate (ABER) is derived and used to validate the simulation
results. It has been shown that the proposed BGCS-CIM scheme outperforms the
existing benchmarks thanks to its higher effective cluster gain, spatial
diversity of indexed clusters, and lower inter-cluster interference.Comment: Submitted in IEE
Statistical-dynamical analyses and modelling of multi-scale ocean variability
This thesis aims to provide a comprehensive analysis of multi-scale oceanic variabilities using various statistical and dynamical tools and explore the data-driven methods for correct statistical emulation of the oceans. We considered the classical, wind-driven, double-gyre ocean circulation model in quasi-geostrophic approximation and obtained its eddy-resolving solutions in terms of potential vorticity anomaly and geostrophic streamfunctions. The reference solutions possess two asymmetric gyres of opposite circulations and a strong meandering eastward jet separating them with rich eddy activities around it, such as the Gulf Stream in the North Atlantic and Kuroshio in the North Pacific.
This thesis is divided into two parts. The first part discusses a novel scale-separation method based on the local spatial correlations, called correlation-based decomposition (CBD), and provides a comprehensive analysis of mesoscale eddy forcing. In particular, we analyse the instantaneous and time-lagged interactions between the diagnosed eddy forcing and the evolving large-scale PVA using the novel `product integral' characteristics. The product integral time series uncover robust causality between two drastically different yet interacting flow quantities, termed `eddy backscatter'. We also show data-driven augmentation of non-eddy-resolving ocean models by feeding them the eddy fields to restore the missing eddy-driven features, such as the merging western boundary currents, their eastward extension and low-frequency variabilities of gyres.
In the second part, we present a systematic inter-comparison of Linear Regression (LR), stochastic and deep-learning methods to build low-cost reduced-order statistical emulators of the oceans. We obtain the forecasts on seasonal and centennial timescales and assess them for their skill, cost and complexity. We found that the multi-level linear stochastic model performs the best, followed by the ``hybrid stochastically-augmented deep learning models''. The superiority of these methods underscores the importance of incorporating core dynamics, memory effects and model errors for robust emulation of multi-scale dynamical systems, such as the oceans.Open Acces
Non-Thermal Optical Engineering of Strongly-Correlated Quantum Materials
This thesis develops multiple optical engineering mechanisms to modulate the electronic, magnetic, and optical properties of strongly-correlated quantum materials, including polar metals, transition metal trichalcogenides, and copper oxides. We established the mechanisms of Floquet engineering and magnon bath engineering, and used optical probes, especially optical nonlinearity, to study the dynamics of these quantum systems.
Strongly-correlated quantum materials host complex interactions between different degrees of freedom, offering a rich phase diagram to explore both in and out of equilibrium. While static tuning methods of the phases have witnessed great success, the emerging optical engineering methods have provided a more versatile platform. For optical engineering, the key to success lies in achieving the desired tuning while suppressing other unwanted effects, such as laser heating.
We used sub-gap optical driving in order to avoid electronic excitation. Therefore, we managed to directly couple to low-energy excitation, or to induce coherent light-matter interactions. In order to elucidate the exact microscopic mechanisms of the optical engineering effects, we performed photon energy-dependent measurements and thorough theoretical analysis. To experimentally access the engineered quantum states, we leveraged various probe techniques, including the symmetry-sensitive optical second harmonic generation (SHG), and performed pump-probe type experiments to study the dynamics of quantum materials.
I will first introduce the background and the motivation of this thesis, with an emphasis on the principles of optical engineering within the big picture of achieving quantum material properties on demand (Chapter I). I will then continue to introduce the main probe technique used in this thesis: SHG. I will also introduce the experimental setups which we developed and where we conducted the works contained in this thesis (Chapter II). In Chapter III, I will introduce an often overlooked aspect of SHG studies -- using SHG to study short-range structural correlations. Chapter IV will contain the theoretical analysis and experimental realizations of using sub-gap and resonant optical driving to tune electronic and optical properties of MnPS₃. The main tuning mechanism used in this chapter is Floquet engineering, where light modulates material properties without being absorbed. In Chapter V, I will turn to another useful material property: magnetism. First I will describe the extension of the Floquet mechanism to the renormalization of spin exchange interaction. Then I will switch gears and describe the demagnetization in Sr₂Cu₃O₄Cl₂ by resonant coupling between photons and magnons. I will end the thesis with a brief closing remark (Chapter VI).</p
Applications of higher-form symmetries at strong and weak coupling
In this thesis we consider two distinct applications of higher-form symmetries in quantum field theory. First we explore the spontaneous breaking of higher-form symmetry in a holographic quantum field theory containing matter fields in the fundamental representation of the gauge group U(N). At strong coupling, we numerically solve the bulk equations of motion to compute the current-current Green’s function and demonstrate the existence of a goldstone mode. We then compare to direct analytic perturbative results obtained at weak coupling. In the second half of the thesis we work with a hydrodynamic effective field theory which possesses a higher-form symmetry. In particular, we consider a natural higher-derivative correction to force-free electrodynamics and compute a hydrodynamic transport coefficient from microscopics. Concretely, this is a perturbative QED calculation in a background magnetic field. Finally we compare our findings to astrophysical observations
Exploring the Structure of Scattering Amplitudes in Quantum Field Theory: Scattering Equations, On-Shell Diagrams and Ambitwistor String Models in Gauge Theory and Gravity
In this thesis I analyse the structure of scattering amplitudes in super-symmetric gauge and gravitational theories in four dimensional spacetime, starting with a detailed review of background material accessible to a non-expert. I then analyse the 4D scattering equations, developing the theory of how they can be used to express scattering amplitudes at tree level. I go on to explain how the equations can be solved numerically using a Monte Carlo algorithm, and introduce my Mathematica package treeamps4dJAF which performs these calculations. Next I analyse the relation between the 4D scattering equations and on-shell diagrams in N = 4 super Yang-Mills, which provides a new perspective on the tree level amplitudes of the theory. I apply a similar analysis to N = 8 supergravity, developing the theory of on-shell diagrams to derive new Grassmannian integral formulae for the amplitudes of the theory. In both theories I derive a new worldsheet expression for the 4 point one loop amplitude supported on 4D scattering equations. Finally I use 4D ambitwistor string theory to analyse scattering amplitudes in N = 4 conformal supergravity, deriving new worldsheet formulae for both plane wave and non-plane wave amplitudes supported on 4D scattering equations. I introduce a new prescription to calculate the derivatives of on-shell variables with respect to momenta, and I use this to show that certain non-plane wave amplitudes can be calculated as momentum derivatives of amplitudes with plane wave states
An explicit stabilised finite element method for Navier-Stokes-Brinkman equations
We present an explicit stabilised finite element method for solving Navier-Stokes-Brinkman equations. The proposed algorithm has several advantages. First, the lower equal-order finite element space for velocity and pressure is ideal for presenting the pixel images. Stabilised finite element allows the continuity of both tangential and normal velocities at the interface between regions of different micro-permeability or at the interface free/porous domain. Second, the algorithm is fully explicit and versatile for describing complex boundary conditions. Third, the fully explicit matrix–free finite element implementation is ideal for parallelism on high-performance computers. In the last, the implicit treatment of Darcy term allowed larger time stepping and a stable computation, even if the velocity varies for several orders of magnitude in the micro-porous regions (Darcy regime).
The stabilisation parameter, that may affect the velocity field, has been discussed and an optimal parameter was chosen based on the numerical examples. Velocity stability at interface between different micro-permeability has been also studied with mesh refinement. We analysed the influence of the micro-permeability field on the regime of the flow (Stokes flow, Darcy flow or a transitional regime). These benchmark tests provide guidelines for choosing the resolution of the grayscale image and its segmentation. We applied the method on real Berea Sandstone micro-CT images, and proceeded the three-phases segmentation. We studied the influence of the micro-porosity field, using the well-known Kozeny-Carman relation to derive the micro-permeability field from the micro-porosity field, on the effective permeability computed. Our analysis shows that a small fraction of micro-porosity in the rock has a significant influence on the effective permeability computed
A suite of quantum algorithms for the shortestvector problem
Crytography has come to be an essential part of the cybersecurity infrastructure that provides a safe environment for communications in an increasingly connected world. The advent of quantum computing poses a threat to the foundations of the current widely-used cryptographic model, due to the breaking of most of the cryptographic algorithms used to provide confidentiality, authenticity, and more. Consequently a new set of cryptographic protocols have been designed to be secure against quantum computers, and are collectively known as post-quantum cryptography (PQC). A forerunner among PQC is lattice-based cryptography, whose security relies upon the hardness of a number of closely related mathematical problems, one of which is known as the shortest vector problem (SVP).
In this thesis I describe a suite of quantum algorithms that utilize the energy minimization principle to attack the shortest vector problem. The algorithms outlined span the gate-model and continuous time quantum computing, and explore methods of parameter optimization via variational methods, which are thought to be effective on near-term quantum computers. The performance of the algorithms are analyzed numerically, analytically, and on quantum hardware where possible. I explain how the results obtained in the pursuit of solving SVP apply more broadly to quantum algorithms seeking to solve general real-world problems; minimize the effect of noise on imperfect hardware; and improve efficiency of parameter optimization.Open Acces
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