@article{LeubeGustafssonLassmannetal.2022,
  author    = {Leube, Julian and Gustafsson, Johan and Lassmann, Michael and Salas-Ramirez, Maikol and Tran-Gia, Johannes},
  title     = {Analysis of a deep learning-based method for generation of SPECT projections based on a large Monte Carlo simulated dataset},
  series = {EJNMMI Physics},
  volume    = {9},
  journal   = {EJNMMI Physics},
  issn      = {2197-7364},
  doi       = {10.1186/s40658-022-00476-w},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-300697},
  year      = {2022},
  abstract  = {Background In recent years, a lot of effort has been put in the enhancement of medical imaging using artificial intelligence. However, limited patient data in combination with the unavailability of a ground truth often pose a challenge to a systematic validation of such methodologies. The goal of this work was to investigate a recently proposed method for an artificial intelligence-based generation of synthetic SPECT projections, for acceleration of the image acquisition process based on a large dataset of realistic SPECT simulations. Methods A database of 10,000 SPECT projection datasets of heterogeneous activity distributions of randomly placed random shapes was simulated for a clinical SPECT/CT system using the SIMIND Monte Carlo program. Synthetic projections at fixed angular increments from a set of input projections at evenly distributed angles were generated by different u-shaped convolutional neural networks (u-nets). These u-nets differed in noise realization used for the training data, number of input projections, projection angle increment, and number of training/validation datasets. Synthetic projections were generated for 500 test projection datasets for each u-net, and a quantitative analysis was performed using statistical hypothesis tests based on structural similarity index measure and normalized root-mean-squared error. Additional simulations with varying detector orbits were performed on a subset of the dataset to study the effect of the detector orbit on the performance of the methodology. For verification of the results, the u-nets were applied to Jaszczak and NEMA physical phantom data obtained on a clinical SPECT/CT system. Results No statistically significant differences were observed between u-nets trained with different noise realizations. In contrast, a statistically significant deterioration was found for training with a small subset (400 datasets) of the 10,000 simulated projection datasets in comparison with using a large subset (9500 datasets) for training. A good agreement between synthetic (i.e., u-net generated) and simulated projections before adding noise demonstrates a denoising effect. Finally, the physical phantom measurements show that our findings also apply for projections measured on a clinical SPECT/CT system. Conclusion Our study shows the large potential of u-nets for accelerating SPECT/CT imaging. In addition, our analysis numerically reveals a denoising effect when generating synthetic projections with a u-net. Clinically interesting, the methodology has proven robust against camera orbit deviations in a clinically realistic range. Lastly, we found that a small number of training samples (e.g., ~ 400 datasets) may not be sufficient for reliable generalization of the u-net.},
  language  = {en}
}
@phdthesis{Volkmann2004,
  author    = {Volkmann, Thorsten},
  title     = {Lattice gas models and simulations of epitaxial growth},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-13812},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2004},
  abstract  = {In this PhD thesis, we develop models for the numerical simulation of epitaxial crystal growth, as realized, e.g., in molecular beam epitaxy (MBE). The basic idea is to use a discrete lattice gas representation of the crystal structure, and to apply kinetic Monte Carlo (KMC) simulations for the description of the growth dynamics. The main advantage of the KMC approach is the possibility to account for atomistic details and at the same time cover MBE relevant time scales in the simulation. In chapter 1, we describe the principles of MBE, pointing out relevant physical processes and the influence of experimental control parameters. We discuss various methods used in the theoretical description of epitaxial growth. Subsequently, the underlying concepts of the KMC method and the lattice gas approach are presented. Important aspects concerning the design of a lattice gas model are considered, e.g. the solid-on-solid approximation or the choice of an appropriate lattice topology. A key element of any KMC simulation is the selection of allowed events and the evaluation of Arrhenius rates for thermally activated processes. We discuss simplifying schemes that are used to approximate the corresponding energy barriers if detailed knowledge about the barriers is not available. Finally, the efficient implementation of the MC kinetics using a rejection-free algorithm is described. In chapter 2, we present a solid-on-solid lattice gas model which aims at the description of II-VI(001) semiconductor surfaces like CdTe(001). The model accounts for the zincblende structure and the relevant surface reconstructions of Cd- and Te-terminated surfaces. Particles at the surface interact via anisotropic nearest and next nearest neighbor interactions, whereas interactions in the bulk are isotropic. The anisotropic surface interactions reflect known properties of CdTe(001) like the small energy difference between the c(2x2) and (2x1) vacancy structures of Cd-terminated surfaces. A key element of the model is the presence of additional Te atoms in a weakly bound Te* state, which is motivated by experimental observations of Te coverages exceeding one monolayer at low temperatures and high Te fluxes. The true mechanism of binding excess Te to the surface is still unclear. Here, we use a mean-field approach assuming a Te* reservoir with limited occupation. In chapter 3, we perform KMC simulations of atomic layer epitaxy (ALE) of CdTe(001). We study the self-regulation of the ALE growth rate and demonstrate how the interplay of the Te* reservoir occupation with the surface kinetics results in two different regimes: at high temperatures the growth rate is limited to one half layer of CdTe per ALE cycle, whereas at low enough temperatures each cycle adds a complete layer. The temperature where the transition between the two regimes occurs depends mainly on the particle fluxes. The temperature dependence of the growth rate and the flux dependence of the transition temperature are in good qualitative agreement with experimental results. Comparing the macroscopic activation energy for Te* desorption in our model with experimental values we find semiquantitative agreement. In chapter 4, we study the formation of nanostructures with alternating stripes during submonolayer heteroepitaxy of two different adsorbate species on a given substrate. We evaluate the influence of two mechanisms: kinetic segregation due to chemically induced diffusion barriers, and strain relaxation by alternating arrangement of the adsorbate species. KMC simulations of a simple cubic lattice gas with weak inter-species binding energy show that kinetic effects are sufficient to account for stripe formation during growth. The dependence of the stripe width on control parameters is investigated. We find an Arrhenius temperature dependence, in agreement with experimental investigations of phase separation in binary or ternary material systems. Canonical MC simulations show that the observed stripes are not stable under equilibrium conditions: the adsorbate species separate into very large domains. Off-lattice simulations which account for the lattice misfit of the involved particle species show that, under equilibrium conditions, the competition between binding and strain energy results in regular stripe patterns with a well-defined width depending on both misfit and binding energies. In KMC simulations, the stripe-formation and the experimentally reported ramification of adsorbate islands are reproduced. To clarify the origin of the island ramification, we investigate an enhanced lattice gas model whose parameters are fitted to match characteristic off-lattice diffusion barriers. The simulation results show that a satisfactory explanation of experimental observations within the lattice gas framework requires a detailed incorporation of long-range elastic interactions. In the appendix we discuss supplementary topics related to the lattice gas simulations in chapter 4.},
  subject      = {Kristallwachstum},
  language  = {en}
}
@phdthesis{Luitz2012,
  author    = {Luitz, David J.},
  title     = {Numerical methods and applications in many fermion systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-75927},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {This thesis presents results covering several topics in correlated many fermion systems. A Monte Carlo technique (CT-INT) that has been implemented, used and extended by the author is discussed in great detail in chapter 3. The following chapter discusses how CT-INT can be used to calculate the two particle Green's function and explains how exact frequency summations can be obtained. A benchmark against exact diagonalization is presented. The link to the dynamical cluster approximation is made in the end of chapter 4, where these techniques are of immense importance. In chapter 5 an extensive CT-INT study of a strongly correlated Josephson junction is shown. In particular, the signature of the first order quantum phase transition between a Kondo and a local moment regime in the Josephson current is discussed. The connection to an experimental system is made with great care by developing a parameter extraction strategy. As a final result, we show that it is possible to reproduce experimental data from a numerically exact CT-INT model-calculation. The last topic is a study of graphene edge magnetism. We introduce a general effective model for the edge states, incorporating a complicated interaction Hamiltonian and perform an exact diagonalization study for different parameter regimes. This yields a strong argument for the importance of forbidden umklapp processes and of the strongly momentum dependent interaction vertex for the formation of edge magnetism. Additional fragments concerning the use of a Legendre polynomial basis for the representation of the two particle Green's function, the analytic continuation of the self energy for the Anderson Kane Mele Model, as well as the generation of test data with a given covariance matrix are documented in the appendix. A final appendix provides some very important matrix identities that are used for the discussion of technical details of CT-INT.},
  subject      = {Fermionensystem},
  language  = {en}
}
@phdthesis{Lang2010,
  author    = {Lang, Thomas C.},
  title     = {Quantum Monte Carlo methods and strongly correlated electrons on honeycomb structures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-53506},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2010},
  abstract  = {In this thesis we apply recently developed, as well as sophisticated quantum Monte Carlo methods to numerically investigate models of strongly correlated electron systems on honeycomb structures. The latter are of particular interest owing to their unique properties when simulating electrons on them, like the relativistic dispersion, strong quantum fluctuations and their resistance against instabilities. This work covers several projects including the advancement of the weak-coupling continuous time quantum Monte Carlo and its application to zero temperature and phonons, quantum phase transitions of valence bond solids in spin-1/2 Heisenberg systems using projector quantum Monte Carlo in the valence bond basis, and the magnetic field induced transition to a canted antiferromagnet of the Hubbard model on the honeycomb lattice. The emphasis lies on two projects investigating the phase diagram of the SU(2) and the SU(N)-symmetric Hubbard model on the hexagonal lattice. At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. Previously elusive in experimentally relevant microscopic two-dimensional models, we show by means of large-scale quantum Monte Carlo simulations of the SU(2) Hubbard model on the honeycomb lattice, that a quantum spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. Inspired by the rich phase diagrams of SU(N) models we study the SU(N)-symmetric Hubbard Heisenberg quantum antiferromagnet on the honeycomb lattice to investigate the reliability of 1/N corrections to large-N results by means of numerically exact QMC simulations. We study the melting of phases as correlations increase with decreasing N and determine whether the quantum spin liquid found in the SU(2) Hubbard model at intermediate coupling is a specific feature, or also exists in the unconstrained t-J model and higher symmetries.},
  subject      = {Monte-Carlo-Simulation},
  language  = {en}
}
@article{OPUS4-12785,
  title     = {Search for anomaly-mediated supersymmetry breaking with the ATLAS detector based on a disappearing-track signature in pp collisions at √s=7 TeV},
  series = {The European Physical Journal C},
  volume    = {72},
  journal   = {The European Physical Journal C},
  number    = {1993},
  organization    = {ATLAS Collaboration},
  doi       = {10.1140/epjc/s10052-012-1993-2},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-127850},
  year      = {2012},
  abstract  = {In models of anomaly-mediated supersymmetry breaking (AMSB), the lightest chargino is predicted to have a lifetime long enough to be detected in collider experiments. This letter explores AMSB scenarios in pp collisions at √s=7 TeV by attempting to identify decaying charginos which result in tracks that appear to have few associated hits in the outer region of the tracking system. The search was based on data corresponding to an integrated luminosity of 1.02 fb\(^{-1}\) collected with the ATLAS detector in 2011. The p\(_T\) spectrum of candidate tracks is found to be consistent with the expectation from Standard Model background processes and constraints on the lifetime and the production cross section were obtained. In the minimal AMSB framework with m\(_{3/2}\)<32 TeV, m\(_0\)<1.5 TeV, tanβ=5 and μ>0, a chargino having mass below 92 GeV and a lifetime between 0.5 ns and 2 ns is excluded at 95 \% confidence level.},
  language  = {en}
}
@phdthesis{Weber2008,
  author    = {Weber, Sebastian},
  title     = {Simulation of self-assembled nanopatterns in binary alloys on the fcc(111) surface},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-27914},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {In this PhD thesis, we study the heteroepitaxial crystal growth by means of Monte Carlo simulations. Of particular interest in this work is the influence of the lattice mismatch of the adsorbates relative to the substrate on surface structures. In the framework of an off-lattice model, we consider one monolayer of adsorbate and investigate the emerging nanopatterns in equilibrium and their formation during growth. In chapter 1, a brief introduction is given, which describes the role of computer simulations in the field of the physics of condensed matter. Chapter 2 is devoted to some technical basics of experimental methods of molecular beam epitaxy and the theoretical description. Before a model for the simulation can be designed, it is necessary to make some considerations of the single processes which occur during epitaxial growth. For that purpose we look at an experimental setup and extract the main microscopic processes. Afterwards a brief overview of different theoretical concepts describing that physical procedures is given. In chapter 3, the model used in the simulations is presented. The aim is to investigate the growth of an fcc crystal in the [111] direction. In order to keep the simulation times within a feasible limit a simple pair potential, the Lennard-Jones potential, with continuous particle positions is used, which are necessary to describe effects resulting from the atomic mismatch in the crystal. Furthermore the detailed algorithm is introduced which is based on the idea to calculate the barrier of each diffusion event and to use the barriers in a rejection-free method. Chapter 4 is attended to the simulation of equilibrium. The influence of different parameters on the emerging structures in the first monolayer upon the surface, which is completely covered with two adsorbate materials, is studied. Especially the competition between binding energy and strain leads to very interesting pattern formations like islands or stripes. In chapter 5 the results of growth simulations are presented. At first, we introduce a model in order to realize off-lattice Kinetic Monte Carlo simulations. Since the costs in simulation time are enormous, some simplifications in the calculation of diffusion barriers are necessary and therefore the previous model is supplemented with some elements from the so-called ball and spring model. The next point is devoted to the calculation of energy barriers followed by the presentation of the growth simulations. Binary systems with only one sort of adsorbate are investigated as well as ternary systems with two different adsorbates. Finally, a comparison to the equilibrium simulations is drawn. Chapter 6 contains some concluding remarks and gives an outlook to possible further investigations.},
  subject      = {Kristallwachstum},
  language  = {en}
}
@phdthesis{Walther2008,
  author    = {Walther, Markus},
  title     = {Simulation of strain-induced and defect-controlled self-organization of nanostructures},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-27931},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2008},
  abstract  = {In this PhD thesis, the effect of strain on heteroepitaxial growth is investigated by means of Kinetic Monte Carlo simulations. In this context the lattice misfit, arising from the different lattice constants of the adsorbate and the substrate material, is of particular interest. As a consequence, this lattice misfit leads to long-range elastic strain effects having strong influence on the entire growing crystal and its resulting surface morphology. The main focus of this work is the investigation of different strain relaxation mechanisms and their controlling parameters, revealing interesting consequences on the subsequent growth. Since epitaxial growth is carried out under conditions far away from thermodynamic equilibrium, it is strongly determined by surface kinetics. At this point the relevant kinetic microscopic processes are described, followed by theoretical considerations of heteroepitaxial growth disclosing an overview over several independent methodological streams, used to model epitaxy in different time and length scales, as well as the characterization of misfit dislocations and the classification of epitaxial growth modes based on thermodynamic considerations. The epitaxial growth is performed by means of Kinetic Monte Carlo simulations which allows for the consideration of long range effects in systems with lateral extension of few hundred atoms. By using an off-lattice simulation model the particles are able to leave their predefined lattice sites, which is an indispensable condition for simulating strain relaxation mechanisms. The main idea of our used model is calculating the activation energy of all relevant thermally activated processes by using simple pair potentials and then realizing the dynamics by performing each event according to its probability by means of a rejection-free algorithm method. In addition, the crystal relaxation procedure, the grid-based particle access method, which accelerates the simulation enormously, and the efficient implementation of the algorithm are discussed. To study the influence of long range elastic strain effects, the main part of this work was realized on the two dimensional triangular lattice, which can be treated as a cross section of the real three dimensional case. Chapter 4 deals with the formation of misfit dislocations as a strain relaxation mechanism and the resulting consequences on the subsequent heteroepitaxial growth. We can distinguish between two principally different dislocation formation mechanisms, depending strongly on the sign as well as on the magnitude of the misfit, but also the surface kinetics need to be taken into account. Additionally, the dislocations affect the lattice spacings of the crystal whose observed progression is in qualitative good agreement with experimental results. Furthermore, the dislocations influence the subsequent growth of the adsorbate film, since the potential energy of an adatom is modulated by buried dislocations. A clear correlation between the lateral positions of buried dislocations and the positions of mounds grown on the surface can be observed. In chapter 5, an alternative strain relaxation mechanism is studied: the formation of three dimensional islands enables the particles to approach their preferred lattice spacing. We demonstrate that it is possible to adjust within our simulation model each of the three epitaxial growth modes: Volmer-Weber, Frank-van der Merve or layer-by-layer, and Stranski-Krastanov growth mode. Moreover, we can show that the emerging growth mode depends in principle on two parameters: on the one hand the interaction strength of adsorbate particles with each other, compared to the interaction of adsorbate with substrate particles, and on the other hand the lattice misfit between adsorbate and substrate particles. A sensible choice of these two parameters allows the realization of each growth mode within the simulations. In conclusion, the formation of nanostructures controlled by an underlying dislocation network can be applied in the concept of self-organized pattern formation as well as by the tendency to form ordered arrays of strain-induced three dimensional grown islands. In chapter 6, we extend our model to three dimensions and investigate the effect of strain on growth on bcc(100) surfaces. We introduce an anisotropic potential yielding a stable bcc lattice structure within the off-lattice representation. We can show that the strain built up in submonolayer islands is mainly released at the island edges and the lattice misfit has strong influence on the diffusion process on the plane surface as well as on the situation at island edges with eminent consequences on the appearance of submonolayer islands.},
  subject      = {Kristallwachstum},
  language  = {en}
}