## 80.00.00 INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

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#### Document Type

- ZIB-Report (8)
- Doctoral Thesis (1)
- Master's Thesis (1)

#### Keywords

- GPGPU (2)
- model-based inversion (2)
- 2-photon microscopy (1)
- Concurrent Kernel Execution (1)
- Connected Component Labeling (1)
- Gaussian mixture model (1)
- Hyper-Q (1)
- Ising Model (1)
- Monte Carlo (1)
- Monte Carlo methods for light transport (1)

Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses.

Quantitative photoacoustic tomography aims to recover maps of the local concentrations of tissue chromophores from multispectral images. While model-based inversion schemes are promising approaches, major challenges to their practical implementation include the unknown fluence distribution and the scale of the inverse problem. This paper describes an inversion scheme based on a radiance Monte Carlo model and an adjoint-assisted gradient optimization that incorporates fluence-dependent step sizes and adaptive moment estimation. The inversion is shown to recover absolute chromophore concentrations, blood oxygen saturation and the Grüneisen parameter from in silico 3D phantom images for different radiance approximations. The scattering coefficient was assumed to be homogeneous and known a priori.

The goal of quantitative photoacoustic tomography (qPAT) is to recover maps of the chromophore distributions from multiwavelength images of the initial pressure. Model-based inversions that incorporate the physical processes underlying the photoacoustic (PA) signal generation represent a promising approach. Monte-Carlo models of the light transport are computationally expensive, but provide accurate fluence distributions predictions, especially in the ballistic and quasi-ballistic regimes. Here, we focus on the inverse problem of 3D qPAT of blood oxygenation and investigate the application of the Monte-Carlo method in a model-based inversion scheme. A forward model of the light transport based on the MCX simulator and acoustic propagation modeled by the k-Wave toolbox was used to generate a PA image data set acquired in a tissue phantom over a planar detection geometry. The combination of the optical and acoustic models is shown to account for limited-view artifacts. In addition, the errors in the fluence due to, for example, partial volume artifacts and absorbers immediately adjacent to the region of interest are investigated. To accomplish large-scale inversions in 3D, the number of degrees of freedom is reduced by applying image segmentation to the initial pressure distribution to extract a limited number of regions with homogeneous optical parameters. The absorber concentration in the tissue phantom was estimated using a coordinate descent parameter search based on the comparison between measured and modeled PA spectra. The estimated relative concentrations using this approach lie within 5 % compared to the known concentrations. Finally, we discuss the feasibility of this approach to recover the blood oxygenation from experimental data.

Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.

Neural circuit mapping is generating datasets of 10,000s of labeled neurons. New computational tools are needed to search and organize these data. We present NBLAST, a sensitive and rapid algorithm, for measuring pairwise neuronal similarity. NBLAST considers both position and local geometry, decomposing neurons into short segments; matched segments are scored using a probabilistic scoring matrix defined by statistics of matches and non-matches.
We validated NBLAST on a published dataset of 16,129 single Drosophila neurons. NBLAST can distinguish neuronal types down to the finest level (single identified neurons) without a priori information. Cluster analysis of extensively studied neuronal classes identified new types and unreported topographical features. Fully automated clustering organized the validation dataset into 1052 clusters, many of which map onto previously described neuronal types. NBLAST supports additional query types including searching neurons against transgene expression patterns. Finally we show that NBLAST is effective with data from other invertebrates and zebrafish.

Small-scale computations usually cannot fully utilize the compute capabilities of modern GPGPUs. With the Fermi GPU architecture Nvidia introduced the concurrent kernel execution feature allowing up to 16 GPU kernels to execute simultaneously on a shared GPU device for a better utilization of the respective resources. Insufficient scheduling capabilities in this respect, however, can significantly reduce the theoretical concurrency level. With the Kepler GPU architecture Nvidia addresses this issue by introducing the Hyper-Q feature with 32 hardware managed work queues for concurrent kernel execution.
We investigate the Hyper-Q feature within heterogeneous workloads with multiple concurrent host threads or processes offloading computations to the GPU each.
By means of a synthetic benchmark kernel and a hybrid parallel CPU-GPU real-world application, we evaluate the performance obtained with Hyper-Q on GPU and compare it against a kernel reordering mechanism introduced by the authors for the Fermi architecture.

This thesis firstly presents a nonlinear extended deterministic model for the transmission dynamics of tuberculosis, based on realistic assumptions and data collected from the WHO. This model enables a comprehensive qualitative analysis of various aspects in the outbreak and control of tuberculosis in Sub-Saharan Africa countries and successfully reproduces the epidemiology of tuberculosis in Cameroon for the past (from 1994-2010). Some particular properties of the model and its solution have been presented using the comparison theorem applied to the theory of differential equations. The existence and the stability of a disease free equilibrium has been discussed using the Perron-Frobenius theorem and Metzler stable matrices.
Furthermore, we computed the basic reproduction number, i.e. the number of cases that one case generates on average over the course of its infectious period. Rigorous qualitative analysis of the model reveals that, in contrast to the model without reinfections, the full model with reinfection exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the basic reproduction ratio (R0), is less than unity. The global stability of the disease-free equilibrium has been discussed using the concepts of Lyapunov stability and bifurcation theory.
With the help of a sensitivity analysis using data of Cameroon, we identified the relevant parameters which play a key role for the transmission and the control of the disease. This was possible applying sophisticated numerical methods (POEM) developed at ZIB. Using advanced approaches for optimal control considering the costs for chemoprophylaxis, treatment and educational campaigns should provide a framework for designing realistic cost effective strategies with different intervention methods. The forward-backward sweep method has been used to solve the numerical optimal control problem. The numerical result of the optimal control problem reveals that combined effort in education and chemoprophylaxis may lead to a reduction of 80\% in the number of infected people in 10 years.
The mathematical and numerical approaches developed in this thesis could be similarly applied in many other Sub-Saharan countries where TB is a public health problem.

Simulations of the critical Ising model by means of local update algorithms suffer from critical slowing down. One way to partially compensate for the influence of this phenomenon on the runtime of simulations is using increasingly faster and parallel computer hardware. Another approach is using algorithms that do not suffer
from critical slowing down, such as cluster algorithms. This paper reports on the Swendsen-Wang multi-cluster algorithm on Intel Xeon Phi coprocessor 5110P, Nvidia Tesla M2090 GPU, and x86
multi-core CPU. We present shared memory versions of the said algorithm for the simulation of the two- and three-dimensional Ising model. We use a combination of local cluster search and global label reduction by means of atomic hardware primitives. Further, we
describe an MPI version of the algorithm on Xeon Phi and CPU, respectively. Significant performance improvements over known im
plementations of the Swendsen-Wang algorithm are demonstrated.

This thesis reports on simulating spin models on Nvidia graphics cards using the CUDA programming model; a particular approach for making GPGPU (General Purpose Computation on Graphics Processing Units) available for a wide range of software developers not necessarily acquainted with (massively) parallel programming. By comparing program execution times for simulations of the Ising model and the Ising spin glass by means of the Metropolis algorithm on Nvidia Tesla C1060 graphics cards and an Intel Core i7-920 quad-core x86 CPU (we used OpenMP to make our simulations run on all 4 execution units of the CPU), we noticed that the Tesla C1060 performed about a factor 5-10 faster than the Core i7-920, depending on the particular model and the accuracy of the calculations (32-bit or 64-bit). We also investigated the reliability of GPGPU computations, especially with respect to the occurrence of soft-errors as suggested in [23]. We noticed faulty program outputs during long-time simulations of the Ising model on ''large'' lattices. We were able to link these problems to overheating of the corresponding graphics cards. Doing Monte Carlo simulations on parallel computer architectures, as was the case in this thesis, suggests to also generate random numbers in a parallel manner. We present implementations of the random number generators Ranlux and Mersenne Twister. In addition, we give an alternative and very efficient approach for producing parallel random numbers on Nvidia graphics cards. We successfully tested all random number generators used in this thesis for their quality by comparing Monte Carlo estimates against exact calculations.

We present a level of detail method for trees based on ellipsoids and lines. We leverage the Expectation Maximization algorithm with a Gaussian Mixture Model to create a hierarchy of high-quality leaf clusterings, while the branches are simplified using agglomerative bottom-up clustering to preserve the connectivity. The simplification runs in a preprocessing step and requires no human interaction. For a fly by over and through a scene of 10k trees, our method renders on average at 40 ms/frame, up to 6 times faster than billboard clouds with comparable artifacts.