Importance driven environment map sampling

In this paper we present an automatic and efficient method for supporting Image Based Lighting (IBL) for bidirectional methods which improves both the sampling of the environment, and the detection and sampling of important regions of the scene, such as windows and doors. These often have a small area proportional to that of the entire scene, so paths which pass through them are generated with a low probability. The method proposed in this paper improves this by taking into account view importance, and modifies the lighting distribution to use light transport information. This also automatically constructs a sampling distribution in locations which are relevant to the camera position, thereby improving sampling. Results are presented when our method is applied to bidirectional rendering techniques, in particular we show results for Bidirectional Path Tracing, Metropolis Light Transport and Progressive Photon Mapping. Efficiency results demonstrate speed up of orders of magnitude (depending on the rendering method used), when compared to other methods

Reversible Jump Metropolis Light Transport using Inverse Mappings

We study Markov Chain Monte Carlo (MCMC) methods operating in primary sample space and their interactions with multiple sampling techniques. We observe that incorporating the sampling technique into the state of the Markov Chain, as done in Multiplexed Metropolis Light Transport (MMLT), impedes the ability of the chain to properly explore the path space, as transitions between sampling techniques lead to disruptive alterations of path samples. To address this issue, we reformulate Multiplexed MLT in the Reversible Jump MCMC framework (RJMCMC) and introduce inverse sampling techniques that turn light paths into the random numbers that would produce them. This allows us to formulate a novel perturbation that can locally transition between sampling techniques without changing the geometry of the path, and we derive the correct acceptance probability using RJMCMC. We investigate how to generalize this concept to non-invertible sampling techniques commonly found in practice, and introduce probabilistic inverses that extend our perturbation to cover most sampling methods found in light transport simulations. Our theory reconciles the inverses with RJMCMC yielding an unbiased algorithm, which we call Reversible Jump MLT (RJMLT). We verify the correctness of our implementation in canonical and practical scenarios and demonstrate improved temporal coherence, decrease in structured artifacts, and faster convergence on a wide variety of scenes

Monte Carlo Simulations and Analysis of Single-Molecule Detection and Imaging

Computer modeling and analysis methods are developed for two modes of operation of an instrument for sensitive fluorescence detection of individual dye-labeled molecules in solution. First, Monte Carlo simulations of experiments for single-molecule imaging (SMI) are extended to include effects of sample flow, sticking of molecules to surfaces, and the finite depth-of-focus of the optics. The results have a bearing on a patented method for high-speed single-molecule DNA sequencing. They indicate that the imaging of freely moving fluorescent labels within a microfluidic flowcell will be considerably more involved than that of immobilized molecules at a surface, which is the usual situation in SMI experiments. Second, the detection of single molecules as they pass through a tightly focused laser beam is discussed, with an emphasis on fluorescence correlation spectroscopy and the analysis of the autocorrelation function of the photon counts. Analysis methods are developed and applied to data from a collaborative experimental study within the topic of RNA transcription. The methods are extended to the case of flowing solution, for ongoing research with application to high-throughput pharmaceutical drug screening

Ensemble metropolis light transport

This article proposes a Markov Chain Monte Carlo (MCMC) rendering algorithm based on a family of guided transition kernels. The kernels exploit properties of ensembles of light transport paths, which are distributed according to the lighting in the scene, and utilize this information to make informed decisions for guiding local path sampling. Critically, our approach does not require caching distributions in world space, saving time and memory, yet it is able to make guided sampling decisions based on whole paths. We show how this can be implemented efficiently by organizing the paths in each ensemble and designing transition kernels for MCMC rendering based on a carefully chosen subset of paths from the ensemble. This algorithm is easy to parallelize and leads to improvements in variance when rendering a variety of scenes

Skating on spin ice: On the application of Lorentz microscopy and numerical techniques to characterise phase transitions and non-equilibrium phenomena in artificial spin ices

Artificial spin ices are arrays of nano-scale magnetic islands correlated by the interactions of their associated macrospins. They have proven an excellent playground in which to study phase transitions and non-equilibrium phenomena. Originally envisaged as a two-dimensional analogue to the frustrated rare-earth pyrochlores, they are now seen in their own right as promising candidates for a wide range of applications, including nanomagnetic computation and magnonics. At the same time, the capability of tuning their behaviour---whether by means of the constituent material, the fabrication pattern, or the application of external stimuli---enables the realisation of unusual aspects of statistical physics. This thesis comprises a combined numerical and experimental study of artificial spin ice. The aims are twofold. First, it seeks to address how magnetic order and defect textures are influenced by the choice of lattice geometry. Second, it considers one route towards making artificial spin ice configurable via a coupling to a site-specific exchange bias. In the initial segment of this thesis, the recently studied pinwheel form of artificial spin ice is described. This is created by rotating each island in the square lattice about 45 degrees through its centre. The rotation angle of the islands acts as a proxy for a mechanism to vary the interactions between spins. A transition between antiferromagnetism in the square lattice and ferromagnetism in the pinwheel lattice is predicted. The phase diagram and critical exponents of the transition are obtained numerically. The nature of this transition is confirmed experimentally using in-situ Lorentz transmission electron microscopy on thermally annealed cobalt arrays. Varying degrees of thermalisation are observed across the samples, as well as an apparent change in the nature of the defects: from one-dimensional strings in square ice to two-dimensional vortex-like structures for geometries similar to pinwheel. The numerical scaling of these quantities is consistent with that predicted by the Kibble-Zurek mechanism. Finally, a two-dimensional hybrid artificial spin ice is outlined. In this, exchange bias is inserted at specific sites to constrain the magnetisation dynamics of individual islands. By examining correlations, a model for the influence of this pinning is constructed. As the density of constrained spins is varied, different magnetic textures are observed following a simulated field demagnetisation. These simulations show good agreement with results obtained experimentally. In this manner, local control over individual islands provides a route to tuning the global response of the array, thus making the system configurable. This is an essential step towards device-based applications. Taken together, these results illustrate the interplay between topology and magnetic order in artificial spin structures, and enable the exploration of critical phenomena in frozen and glassy systems. The findings presented here demonstrate conclusively that artificial spin ice is an excellent test bed with which to probe out-of-equilibrium dynamics. They will also underpin its potential use in fields which are reliant on adressing specific microstates, such as neuromorphic computing.

Investigating the 3D chromatin architecture with fluorescence microscopy

Chromatin is an assembly of DNA and nuclear proteins, which on the one hand has the function to properly store the 2 meters of DNA of a diploid human nucleus in a small volume and on the other hand regulates the accessibility of specific DNA segments for proteins. Many cellular processes like gene expression and DNA repair are affected by the three-dimensional architecture of chromatin. Cohesin is an important and well-studied protein that affects three-dimensional chromatin organization. One of the functions of this motor protein is the active generation of specific domain structures (topologically associating domains (TADs)) by the process of loop extrusion. Studies of cohesin depleted cells showed that TAD structures were lost on a population average. Due to this finding, the question arose, to what extent the functional nuclear architecture, that can be detected by confocal and structured illumination microscopy, is impaired when cells were cohesin depleted. The work presented in this thesis could show that the structuring of the nucleus in areas with different chromatin densities including the localization of important nuclear proteins as well as replication patterns was retained. Interestingly, cohesin depleted cells proceeded through an endomitosis leading to the formation of multilobulated nuclei. Obviously, important structural features of chromatin can form even in the absence of cohesin. In the here presented work, fluorescence microscopic methods were used throughout, and an innovative technique was developed, that allows flexible labeling of proteins with different fluorophores in fixed cells. With this technique DNA as well as peptide nucleic acid (PNA) oligonucleotides can be site-specifically coupled to antibodies via the Tub-tag technology and visualized by complementary fluorescently labeled oligonucleotides. The advantages and disadvantages of PNAs as docking strands are discussed in this thesis as well as the use of PNAs in fluorescence in situ hybridization (FISH). In the next study, which is part of this work, a combination of FISH and super-resolution microscopy was used. There it could be shown that DNA segments of 5 kb can form both compact and elongated configurations in regulatory active as well as inactive chromatin. Coarse-grained modeling of these microscopic data, in agreement with published data from other groups, has suggested that elongated configurations occur more frequently in DNA segments in which the occupancy of nucleosomes is reduced. The microscopically measured distance distributions could only be simulated with models that assume different densities of nucleosomes in the population. Another result of this study was that inactive chromatin - as expected - shows a high level of compaction, which can hardly be explained with common coarse-grained models. It is possible that environmental effects that are difficult to simulate play a role here. Chromatin is a highly dynamic structure, and its architecture is constantly changing, be it through active processes such as the effect of cohesin investigated here or through thermodynamic interactions of nucleosomes as they are simulated in coarse-grained models. It will take a long time until we adequately understand these dynamic processes and their interplay