4,405 research outputs found
Breaking boundaries:Charge density waves, quantum measurement, and black holes in theoretical physics
This thesis, titled “Breaking Boundaries” is a journey through three topics united by the theme of boundaries in physics. First, the journey begins with an investigation into charge density waves (CDWs) and their nearly commensurate phase, focusing on the materials 2H-TaSe2 and 1T-TaS2. An extensive treatment of Ginzburg-Landau theory is covered with an extension into truly two-dimensional systems. This extension is used to study spiral patches of commensurate charge density waves observed in experiment. The research leads to a novel perspective on CDW behaviour with the existence of a spiral CDW phase in a range of materials. Secondly, transitioning to the quantum realm, the thesis addresses the quantum measurement problem, emphasizing the constraints any valid theory must possess. It critiques existing models, demonstrates the non-linearity of objective collapse theories, and proposes a minimal model that bridges quantum mechanics and classical physics. Thirdly, the thesis delves into black holes and specifically the phenomena of thermal radiation due to a horizon. First, we explore analogue models that mimic the thermal spectrum near a black hole horizon, to pave the way to experimental realization. Then we focus on the region far away from a black hole horizon and challenge the notion of remnant radiation at this position. With a theoretical toy model, we study the regime and find a non-evaporating black hole. This questions the validity of standard Hawking radiation calculations.In conclusion, the thesis navigates through the boundaries of material behaviours, the quantum-classical divide, and the enigmatic nature of black holes. It highlights the blurring and breaking of boundaries in physics, offering new perspectives and promising avenues for future discoveries
Complementing Hi-C information for 3D chromatin reconstruction by ChromStruct
A multiscale method proposed elsewhere for reconstructing plausible 3D configurations of the chromatin in cell nuclei is recalled, based on the integration of contact data from Hi-C experiments and additional information coming from ChIP-seq, RNA-seq and ChIA-PET experiments. Provided that the additional data come from independent experiments, this kind of approach is supposed to leverage them to complement possibly noisy, biased or missing Hi-C records. When the different data sources are mutually concurrent, the resulting solutions are corroborated; otherwise, their validity would be weakened. Here, a problem of reliability arises, entailing an appropriate choice of the relative weights to be assigned to the different informational contributions. A series of experiments is presented that help to quantify the advantages and the limitations offered by this strategy. Whereas the advantages in accuracy are not always significant, the case of missing Hi-C data demonstrates the effectiveness of additional information in reconstructing the highly packed segments of the structure
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
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Interpretable Machine Learning Architectures for Efficient Signal Detection with Applications to Gravitational Wave Astronomy
Deep learning has seen rapid evolution in the past decade, accomplishing tasks that were previously unimaginable. At the same time, researchers strive to better understand and interpret the underlying mechanisms of the deep models, which are often justifiably regarded as "black boxes". Overcoming this deficiency will not only serve to suggest better learning architectures and training methods, but also extend deep learning to scenarios where interpretability is key to the application. One such scenario is signal detection and estimation, with gravitational wave detection as a specific example, where classic methods are often preferred for their interpretability. Nonetheless, while classic statistical detection methods such as matched filtering excel in their simplicity and intuitiveness, they can be suboptimal in terms of both accuracy and computational efficiency. Therefore, it is appealing to have methods that achieve ``the best of both worlds'', namely enjoying simultaneously excellent performance and interpretability.
In this thesis, we aim to bridge this gap between modern deep learning and classic statistical detection, by revisiting the signal detection problem from a new perspective. First, to address the perceived distinction in interpretability between classic matched filtering and deep learning, we state the intrinsic connections between the two families of methods, and identify how trainable networks can address the structural limitations of matched filtering. Based on these ideas, we propose two trainable architectures that are constructed based on matched filtering, but with learnable templates and adaptivity to unknown noise distributions, and therefore higher detection accuracy. We next turn our attention toward improving the computational efficiency of detection, where we aim to design architectures that leverage structures within the problem for efficiency gains. By leveraging the statistical structure of class imbalance, we integrate hierarchical detection into trainable networks, and use a novel loss function which explicitly encodes both detection accuracy and efficiency. Furthermore, by leveraging the geometric structure of the signal set, we consider using signal space optimization as an alternative computational primitive for detection, which is intuitively more efficient than covering with a template bank. We theoretical prove the efficiency gain by analyzing Riemannian gradient descent on the signal manifold, which reveals an exponential improvement in efficiency over matched filtering. We also propose a practical trainable architecture for template optimization, which makes use of signal embedding and kernel interpolation.
We demonstrate the performance of all proposed architectures on the task of gravitational wave detection in astrophysics, where matched filtering is the current method of choice. The architectures are also widely applicable to general signal or pattern detection tasks, which we exemplify with the handwritten digit recognition task using the template optimization architecture. Together, we hope the this work useful to scientists and engineers seeking machine learning architectures with high performance and interpretability, and contribute to our understanding of deep learning as a whole
Backpropagation Beyond the Gradient
Automatic differentiation is a key enabler of deep learning: previously, practitioners were limited to models
for which they could manually compute derivatives. Now, they can create sophisticated models with almost
no restrictions and train them using first-order, i. e. gradient, information. Popular libraries like PyTorch
and TensorFlow compute this gradient efficiently, automatically, and conveniently with a single line of
code. Under the hood, reverse-mode automatic differentiation, or gradient backpropagation, powers the
gradient computation in these libraries. Their entire design centers around gradient backpropagation.
These frameworks are specialized around one specific task—computing the average gradient in a mini-batch.
This specialization often complicates the extraction of other information like higher-order statistical moments
of the gradient, or higher-order derivatives like the Hessian. It limits practitioners and researchers to methods
that rely on the gradient. Arguably, this hampers the field from exploring the potential of higher-order
information and there is evidence that focusing solely on the gradient has not lead to significant recent
advances in deep learning optimization.
To advance algorithmic research and inspire novel ideas, information beyond the batch-averaged gradient
must be made available at the same level of computational efficiency, automation, and convenience.
This thesis presents approaches to simplify experimentation with rich information beyond the gradient
by making it more readily accessible. We present an implementation of these ideas as an extension to the
backpropagation procedure in PyTorch. Using this newly accessible information, we demonstrate possible use
cases by (i) showing how it can inform our understanding of neural network training by building a diagnostic
tool, and (ii) enabling novel methods to efficiently compute and approximate curvature information.
First, we extend gradient backpropagation for sequential feedforward models to Hessian backpropagation
which enables computing approximate per-layer curvature. This perspective unifies recently proposed block-
diagonal curvature approximations. Like gradient backpropagation, the computation of these second-order
derivatives is modular, and therefore simple to automate and extend to new operations.
Based on the insight that rich information beyond the gradient can be computed efficiently and at the
same time, we extend the backpropagation in PyTorch with the BackPACK library. It provides efficient and
convenient access to statistical moments of the gradient and approximate curvature information, often at a
small overhead compared to computing just the gradient.
Next, we showcase the utility of such information to better understand neural network training. We build
the Cockpit library that visualizes what is happening inside the model during training through various
instruments that rely on BackPACK’s statistics. We show how Cockpit provides a meaningful statistical
summary report to the deep learning engineer to identify bugs in their machine learning pipeline, guide
hyperparameter tuning, and study deep learning phenomena.
Finally, we use BackPACK’s extended automatic differentiation functionality to develop ViViT, an approach
to efficiently compute curvature information, in particular curvature noise. It uses the low-rank structure
of the generalized Gauss-Newton approximation to the Hessian and addresses shortcomings in existing
curvature approximations. Through monitoring curvature noise, we demonstrate how ViViT’s information
helps in understanding challenges to make second-order optimization methods work in practice.
This work develops new tools to experiment more easily with higher-order information in complex deep
learning models. These tools have impacted works on Bayesian applications with Laplace approximations,
out-of-distribution generalization, differential privacy, and the design of automatic differentia-
tion systems. They constitute one important step towards developing and establishing more efficient deep
learning algorithms
A Practitioner's Guide to Bayesian Inference in Pharmacometrics using Pumas
This paper provides a comprehensive tutorial for Bayesian practitioners in
pharmacometrics using Pumas workflows. We start by giving a brief motivation of
Bayesian inference for pharmacometrics highlighting limitations in existing
software that Pumas addresses. We then follow by a description of all the steps
of a standard Bayesian workflow for pharmacometrics using code snippets and
examples. This includes: model definition, prior selection, sampling from the
posterior, prior and posterior simulations and predictions, counter-factual
simulations and predictions, convergence diagnostics, visual predictive checks,
and finally model comparison with cross-validation. Finally, the background and
intuition behind many advanced concepts in Bayesian statistics are explained in
simple language. This includes many important ideas and precautions that users
need to keep in mind when performing Bayesian analysis. Many of the algorithms,
codes, and ideas presented in this paper are highly applicable to clinical
research and statistical learning at large but we chose to focus our
discussions on pharmacometrics in this paper to have a narrower scope in mind
and given the nature of Pumas as a software primarily for pharmacometricians
Curvature estimation for meshes via algebraic quadric fitting
We introduce the novel method for estimation of mean and Gaussian curvature
and several related quantities for polygonal meshes. The algebraic quadric
fitting curvature (AQFC) is based on local approximation of the mesh vertices
and associated normals by a quadratic surface. The quadric is computed as an
implicit surface, so it minimizes algebraic distances and normal deviations
from the approximated point-normal neighbourhood of the processed vertex. Its
mean and Gaussian curvature estimate is then obtained as the respective
curvature of its orthogonal projection onto the fitted quadratic surface.
Experimental results for both sampled parametric surfaces and arbitrary meshes
are provided. The proposed method AQFC approaches the true curvatures of the
reference smooth surfaces with increasing density of sampling, regardless of
its regularity. It is resilient to irregular sampling of the mesh, compared to
the contemporary curvature estimators. In the case of arbitrary meshes,
obtained from scanning, AQFC provides robust curvature estimation.Comment: 14 page
Fluidic Nozzles for Automotive Washer Systems: Computational Fluid Dynamics and Experimental Analysis
One of the main goals of this project was to cultivate an understanding of fluidic nozzle geometries and characteristic flow. Through this knowledge, three new fluidic nozzle concepts were developed to be used as components in several windscreen washer systems for an automotive part supplier, Kautex Textron CVS Ltd.Accurate and conclusive visualisation of flow through fluidic nozzles was vital in understanding how they can be best utilised for different applications. Over the past century, the specific needs of automotive cleaning systems have greatly developed with new technological discoveries, these advances allow the driver further knowledge of their surroundings. These specialised systems each require a different type of maintenance and cleaning system depending on their usage and the different size and shape of the vehicle. By completing this project, it is hoped to allow manufacturers to accurately identify what sort of fluidic nozzles are best for windscreen cleaning systems for a vehicle and how to design a nozzle to suit their specification. Fluidic nozzles have been researched experimentally and computationally to ensure an accurate comparison of results. By guaranteeing a precise comparison it will negate the need for high volume testing of nozzles in experimental situations, greatly reducing time and resources required to analyse a fluidic nozzle.The fluidic nozzles that are investigated and developed in this project were modelled and examined both experimentally and computationally, this ensured valid and accurate results were achieved by both the computational modelling and experimental testing. The development of the nozzles within this project was conducted using several experimental and computational setups to analyse the spray distribution, angle and oscillatory frequency amongst other parameters significant to the nozzle usage on a vehicle. Through this it was possible to tailor nozzle dimensions to allow for a streamlined design approach, this increased efficiency in fluidic nozzle development for any specification given by a vehicle manufacturing company customer. In addition to this the water flow emitted from the outlet was experimentally tested and modelled with both stationary and high surrounding velocities to examine how external variables affect the flow of the water from the nozzle.iiiThis project has been useful in the design manufacturing process of fluidic nozzles, by utilising computational modelling it has allowed a faster and cheaper method of analysing the effect of design alterations to fluidic nozzles. There is a greatly reduced frequency required for rapid prototyping of an array of fluidic chips with minimal dimensional differences to be used in the experimental stages of design, as once the inlet boundary conditions are established the nozzle can be redesigned completely within reason without the need for additional material wastage. This ensures a more easy and precise method of testing the manufacturing tolerances of a fluidic nozzle with a target of reaching customer specifications are always achieved.Three nozzles were aimed developed to satisfy conditions set by the customers, the vehicle manufacturers at which the new nozzle designs are aimed at are Honda, Nissan and Toyota. The nozzles to be established were designed for use on windscreen washer systems with a varying number of nozzles and with diverse windscreen sizes for different vehicles, resulting in a wide variety of specifications that must be met for each vehicle manufacturer. This meant that a single nozzle could not be utilised for all vehicles, instead a base model of fluidic chip was developed for the Nissan vehicle which was then dimensionally changed to suit the other vehicles.Throughout this project there were design specifications changes and ambiguities from the automotive company customers, leading to redesigns of the fluidic chips designed in this project. This means that although only two of the three fluidic nozzle designs are successfully in production, a much greater understanding of the mechanics of the fluid flow within the fluidic nozzle was achieved
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