| 1. |
- Bogsjö, Klas
(författare)
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Road profile statistics relevant for vehicle fatigue
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Road profiles are studied from a vehicle fatigue point of view. A wide range of roads have been measured: from smooth motorways to very rough gravel roads. It is observed that the road profiles consist of irregular sections, which makes the stationary Gaussian model unsuitable (Paper A). In Paper B, a method for automatic identification of such irregularities is presented. It is verified that the irregular sections cause the major part of the fatigue damage induced in vehicles. Based on this result, a new single track model is proposed, which includes randomly shaped and located irregularities. In Paper C, an evaluation method of single track models is proposed. This evaluation method is extended to models of parallel tracks in Paper D. A new "parallel tracks" model is proposed and evaluated accordingly. In Paper E, the coherence between the parallel road tracks is studied. A simple one-parametric model is proposed for the coherence. In Paper F a new theoretical method to compute the expected vehicle fatigue damage caused by road irregularities is presented.
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| 2. |
- Ebelin, Pontus
(författare)
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Evaluating and Improving Rendered Visual Experiences : Metrics, Compression, Higher Frame Rates & Recoloring
- 2024
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Rendered imagery is presented to us daily. Special effects in movies, video games, scientific visualizations, and marketing catalogs all often rely on images generated through computer graphics. However, with all the possibilities that rendering offers come also a plethora of challenges. This thesis proposes novel ways of evaluating the visual errors caused when some of those challenges are not completely overcome. The thesis also suggests ways to improve on the visual experience observers have when viewing rendered content.In the introduction of this thesis, I provide an overview of a subset of the many and fantastic aspects of the human visual system. I also describe how images are rendered using computer graphics, some of the related challenges, and how the final result is displayed to users. Finally, I discuss some of the basics of image and video quality assessment. The scientific publications contained in this thesis focus on image quality metrics, compression, and rendering at high frame rates. In addition, one paper considers the recoloring of images with the goal of giving people with color vision deficiencies an improved visual experience in a process known as daltonization.Papers I–III suggest ways to evaluate and communicate the errors that users may see in rendered images. In those papers, an image’s error is determined by how much it visually differs from a perfect-quality version of the same view. The focus is on the error map, an image that indicates the magnitude and locations of errors. In Paper IV, tools proposed in the first three papers are used to convey how a novel material texture compression algorithm results in lower visual error compared to competing techniques at similar, low bit rates. To achieve good quality at high compression rates, the proposed algorithm exploits similarities in the textures used for materials.Starting with Paper V, the thesis puts increased emphasis on temporal effects. That paper estimates the temporal edge detection filters in human vision, while previous research had mainly examined spatial edge detection filters. Paper VI demonstrates how perceived quality in rendering can be improved by leveraging the human visual system. The paper suggests a method for rendering ~4× more frames per second, which, paired with content-dependent sampling patterns and reconstruction, improves the overall visual experience of rendered image sequences despite reducing the quality of individual frames. This thesis’ final paper, Paper VII, presents a real-time daltonization algorithm that recolors images in a temporally consistent manner, so as to avoid flickering hue changes in image sequences, which are often an issue for competing algorithms that target single images. The proposed recoloring preserves luminance and, thus, the important visual ques it provides.
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| 3. |
- Goriachkin, Vasilii
(författare)
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Critical Scaling in Particle Systems and Random Graphs
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of this thesis is to study the behavior of macro-systems through their micro-parameters. In particular, we are interested in finding critical scaling in various models.Paper I investigates the influence of discrete-time collisions on particle dynamics. By analyzing two models — one involving external forces and friction, and another incorporating collisions with lighter particles — a nuanced understanding of particle trajectories emerges. Conditions for the equivalence of these models are established, encompassing both deterministic and stochastic collision scenarios.Paper II focuses on scaling properties within critical geometric random graphs on a 2-dimensional torus. This is an example of an inhomogeneous random graph that is not of rank 1. Drawing parallels with classic Erdős-Rényi graphs, the study unveils scaling patterns of the size of the largest connected component and its diffusion approximation.In Paper III and Paper IV, we examine axon tree growth models in dimensions 2 and 3. We uncover the relationship between the probability of neuron connections and micro-level growth parameters. Notably, we demonstrate that connection probabilities do not strictly decrease exponentially or polynomially with the distance between neurons. While finding the critical scaling for the connection probability over time (determined by distance) remains challenging, the insights from Papers III and IV will aid in addressing this issue.
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| 4. |
- Nilsson, David
(författare)
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Data-Efficient Learning of Semantic Segmentation
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Semantic segmentation is a fundamental problem in visual perception with a wide range of applications ranging from robotics to autonomous vehicles, and recent approaches based on deep learning have achieved excellent performance. However, to train such systems there is in general a need for very large datasets of annotated images. In this thesis we investigate and propose methods and setups for which it is possible to use unlabelled data to increase the performance or to use limited application specific data to reduce the need for large datasets when learning semantic segmentation.In the first paper we study semantic video segmentation. We present a deep end-to-end trainable model that uses propagated labelling information in unlabelled frames in addition to sparsely labelled frames to predict semantic segmentation. Extensive experiments on the CityScapes and CamVid datasets show that the model can improve accuracy and temporal consistency by using extra unlabelled video frames in training and testing.In the second, third and fourth paper we study active learning for semantic segmentation in an embodied context where navigation is part of the problem. A navigable agent should explore a building and query for the labelling of informative views that increase the visual perception of the agent. In the second paper we introduce the embodied visual active learning problem, and propose and evaluate a range of methods from heuristic baselines to a fully trainable agent using reinforcement learning (RL) on the Matterport3D dataset. We show that the learned agent outperforms several comparable pre-specified baselines. In the third paper we study the embodied visual active learning problem in a lifelong setup, where the visual learning spans the exploration of multiple buildings, and the learning in one scene should influence the active learning in the next e.g. by not annotating already accurately segmented object classes. We introduce new methodology to encourage global exploration of scenes, via an RL-formulation that combines local navigation with global exploration by frontier exploration. We show that the RL-agent can learn adaptable behaviour such as annotating less frequently when it already has explored a number of buildings. Finally we study the embodied visual active learning problem with region-based active learning in the fourth paper. Instead of querying for annotations for a whole image, an agent can query for annotations of just parts of images, and we show that it is significantly more labelling efficient to just annotate regions in the image instead of the full images.
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| 5. |
- Nilsson, Mårten
(författare)
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Boundary singularities of plurisubharmonic functions
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study the Perron–Bremermann envelope P(μ, φ):=sup{u(z) ; u ∈ PSH(Ω), (ddcu)n≥ μ, u^* ≤ φ} on a B-regular domain Ω. Such envelopes occupy a central position within pluripotential theory as they, for suitable μ and φ harmonic and continuous on the closure of Ω, constitute unique solutions to the Dirichlet problem for the complex Monge–Ampère operator. Much is also known about the measures that guarantee that the solution is continuous, but the corresponding problems for unbounded or discontinuous φ have received very little attention. This is the main theme of this thesis. In paper I and II, by adapting and expanding Leutwiler and Arsove's theory of quasibounded harmonic functions, we introduce a set of positive plurisubharmonic functions which may be approximated from below by functions in L∞(Ω) ∩ PSH(Ω) outside a pluripolar set. This approximation property is exploited to show that P(μ, φ) is continuous outside a pluripolar set for a large class of measures, given that φ is bounded from below, is continuous in the extended reals, and have a non-trivial strong majorant, i.e. a plurisuperharmonic majorant whose singularities in a precise sense surpass those of φ. We also show that P(μ, φ) then corresponds to a unique solution to a Dirichlet problem with unbounded boundary data.In paper III, we show that the Dirichlet problem is uniquely solvable for bounded boundary data with a b-pluripolar discontinuity set, by modifying an extended version of the comparison principle due to Rashkovskii. We also show that the discontinuity set being b-pluripolar is not necessary for the uniqueness. In particular, we construct a class of boundary data for which the Dirichlet problem is uniquely solvable, but where the Lebesgue measure of the set of discontinuities is positive.In paper IV, we discuss two variations of Edwards' theorem. We prove one version of the theorem for cones not necessarily containing all constant functions, and in particular, we allow the functions in the cone to have a non-empty common zero set. In the other variation, we replace suprema of point evaluations and infima over Jensen measures by suprema of other continuous functionals and infima over a set measures defined through a natural order relation induced by the cone. As applications, we give some results on propagation of discontinuities for Perron–Bremermann envelopes on hyperconvex domains, as well as a characterization of minimal elements in the order relation mentioned above.
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| 6. |
- Trimmel, Martin
(författare)
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Network Parameterisation and Activation Functions in Deep Learning
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Deep learning, the study of multi-layered artificial neural networks, has received tremendous attention over the course of the last few years. Neural networks are now able to outperform humans in a growing variety of tasks and increasingly have an impact on our day-to-day lives. There is a wide range of potential directions to advance deep learning, two of which we investigate in this thesis:(1) One of the key components of a network are its activation functions. The activations have a big impact on the overall mathematical form of the network. The \textit{first paper} studies generalisation of neural networks with rectified linear activations units (“ReLUs”). Such networks partition the input space into so-called linear regions, which are the maximally connected subsets on which the network is affine. In contrast to previous work, which focused on obtaining estimates of the number of linear regions, we proposed a tropical algebra-based algorithm called TropEx to extract coefficients of the linear regions. Applied to fully-connected and convolutional neural networks, TropEx shows significant differences between the linear regions of these network types. The \textit{second paper} proposes a parametric rational activation function called ERA, which is learnable during network training. Although ERA only adds about ten parameters per layer, the activation significantly increases network expressivity and makes small architectures have a performance close to large ones. ERA outperforms previous activations when used in small architectures. This is relevant because neural networks keep growing larger and larger and the computational resources they require result in greater costs and electricity usage (which in turn increases the CO2 footprint).(2) For a given network architecture, each parameter configuration gives rise to a mathematical function. This functional realisation is far from unique and many different parameterisations can give rise to the same function. Changes to the parameterisation that do not change the function are called symmetries. The \textit{third paper} theoretically studies and classifies all the symmetries of 2-layer networks using the ReLU activation. Finally, the \textit{fourth paper} studies the effect of network parameterisation on network training. We provide a theoretical analysis of the effect that scaling layers have on the gradient updates. This provides a motivation for us to propose a Cooling method, which automatically scales the network parameters during training. Cooling reduces the reliance of the network on specific tricks, in particular the use of a learning rate schedule.
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| 7. |
- Truong, Tien
(författare)
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Steady waves in local and nonlocal models for water waves
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study the steady Euler equations for inviscid, incompressible, and irrotational water waves of constant density. The thesis consists of three papers. The first paper approaches the Euler equations through a famous nonlocal model equation for gravity waves, namely the Whitham equation. We prove the existence of a highest gravity solitary wave which reaches the largest amplitude and forms a $C^{1/2}$ cusp at its crest. This confirms a 50-year-old conjecture by Whitham in the case of solitary waves, that the full linear dispersion in the Whitham equation would allow for high-frequency phenomena such as highest waves. In the second paper, we use a recently developed center manifold theorem for nonlocal and nonlinear equations to study small-amplitude gravity--capillary generalized and modulated solitary waves in a Whitham equation with small surface tension. The last paper treats the steady Euler equations directly. Here, the gravity and capillary coefficients are fixed but arbitrary, and for simplicity we place a non-resonance condition on the problem. We address the transverse dynamics of two-dimensional gravity--capillary periodic waves using a spatial dynamics technique, followed by a perturbation argument.
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| 8. |
- Sandberg, Johan
(författare)
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Discrete Stochastic Time-Frequency Analysis and Cepstrum Estimation
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The theory of stochastic time-frequency analysis of non-stationary random processes has mostly been developed for processes in continuous time. In practice however, random processes are observed, processed, and interpreted at a finite set of time points. For processes in continuous time, the ambiguity domain has interesting properties which makes it particularly useful. One such property is that there exists a certain relationship between scaling in the ambiguity domain and convolution in the time-lag domain. For processes in discrete time, several different definitions of the ambiguity domain have been proposed. Paper A and B of this thesis contributes to the discretization of time-frequency theory, where we in Paper A compare three of the most common definitions: the Claasen-Mecklenbräuker, the Nuttall, and the Jeong-Williams ambiguity domain. We prove that amongst these three, only the Jeong-Williams ambiguity domain has the property that there exists a bijection between scaling in this domain and convolution in the time-lag domain. For processes in continuous time, there is also a certain mapping between the mean square error (MSE) optimal smoothing covariance function estimator and the MSE optimal ambiguity function estimator. This mapping allows us to compute the MSE optimal smoothing estimator in a convenient way. In Paper B, we prove that a similar relationship is not valid between the scaling estimators in the Jeong-Williams ambiguity domain and the smoothing covariance function estimators for processes in discrete time. However, we show that the MSE optimal smoothing covariance function estimator for a non-stationary random process in discrete time can be found as the solution to a linear system of equations. It allows us to find the lower MSE bound of this family of estimators. In Paper C, we show that it is possible to compute a covariance function estimator which is MSE optimal to a set of processes in order to increase the robustness. The cepstrum of a stationary random process has a lot of interesting applications. It is usually estimated as the Fourier transform of the log-periodogram. In Paper D, we propose a multitaper based estimator and we derive approximations of its bias and variance. We demonstrate the performance of the multitaper based estimator in a speaker verification task. In Paper E we discuss four different families of cepstrum estimators based on smoothing. We find the MSE optimal smoother in each family and the lower MSE bound of each family of estimators. The robustness of the optimal estimators within each family is also considered.
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| 9. |
- Abkar, Ali
(författare)
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Invariant Subspaces in Spaces of Analytic Functions
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Let D be a finitely connected bounded domain with smooth boundary in the complex plane. We first study Banach spaces of analytic functions on D . The main result is a theorem which converts the study of hyperinvariant subspaces on multiply connected domains into the study of hyperinvariant subspaces on domains with fewer holes. The Banach spaces are defined by a natural set of axioms fulfilled by the familiar Hardy, Dirichlet, and Bergman spaces. Let D_1 be a bounded domain obtained from D by adding some of the connectivity components of the complement of D ; hence D_1 has fewer holes. Let B and B_1 be the Banach spaces of analytic functions on the domains D and D_1 , respectively. Assume that I is a hyperinvariant subspace of B_1 , and consider the smallest hyperinvariant subspace of B containing I ; this is Lambda (I) , the closure in B of the span of I cdot M(B) , where M(B) denotes the space of multipliers of B . Under reasonable assumptions, we prove that I mapsto Lambda (I) gives a one-to-one correspondence between a class of hyperinvariant subspaces of B_1 , and a class of hyperinvariant subspaces of B . The inverse mapping is given by J mapsto J cap B_1 . We then generalize the above result to the setting of the quasi-Banach spaces of analytic functions on D . In Chapter IV, we shall establish a Riesz-type representation formula for super-biharmonic functions satisfying certain growth conditions on the unit disk. This representation formula can be regarded as an analogue of the Poisson-Jensen representation formula for subharmonic functions. In Chapter V, this representation formula will be used to prove an approximation theorem in certain weighted Bergman spaces. More precisely, we consider those weighted Bergman spaces whose (non-radial) weights are super-biharmonic and fulfill a certain growth condition. We shall prove that the polynomials are dense in such weighted Bergman spaces.
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| 10. |
- Alpkvist, Erik
(författare)
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Mathematical Modeling of Biofilms: Theory, Numerics and Applications
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- A biofilm is a complex and diverse aggregation of microorganisms at surface comprised of among different things a protective adhesive matrix of extracellular polymeric substance. Biofilm research represents a broad range of sciences joining efforts within an interdisciplinary field of research. This thesis deals with the modeling of biofilms using the most fundamental laws of physics; the conservation laws of mass and momentum for fluids. Common to all parts of this work is an aim to develop robust and general mathematical models readily applicable for computational use. Two new biofilm models for growth are derived in this thesis; one describing and combining an individual description of microbial particles with a continuum representation of the biofilm matrix, and one a model based solely on a continuum framework of partial differential equations. The latter is applied in a bottom-up approach as a mass balance model for a Moving Bed biofilm process. Finally, an attempt of capturing the conservation of momentum for both water and biomass is presented. This will allow for viscoelastic and other constitutive properties to influence biomass structure (through growth or fluid shear stresses) as well as erosion and sloughing detachment; under basic laws of physics. All models are applied and demonstrated in silico; for examples such as growth, deformation and detachment under fluid shear stress.
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