A Probabilistic Approach to the Primary Visual Cortex

What can the statistical structure of natural images teach us about the human brain? Even though the visual cortex is one of the most studied parts of the brain, surprisingly little is known about how exactly images are processed to leave us with a coherent percept of the world around us, so we can recognize a friend or drive on a crowded street without any effort. By constructing probabilistic models of natural images, the goal of this thesis is to understand the structure of the stimulus that is the raison d etre for the visual system. Following the hypothesis that the optimal processing has to be matched to the structure of that stimulus, we attempt to derive computational principles, features that the visual system should compute, and properties that cells in the visual system should have. Starting from machine learning techniques such as principal component analysis and independent component analysis we construct a variety of sta- tistical models to discover structure in natural images that can be linked to receptive field properties of neurons in primary visual cortex such as simple and complex cells. We show that by representing images with phase invariant, complex cell-like units, a better statistical description of the vi- sual environment is obtained than with linear simple cell units, and that complex cell pooling can be learned by estimating both layers of a two-layer model of natural images. We investigate how a simplified model of the processing in the retina, where adaptation and contrast normalization take place, is connected to the nat- ural stimulus statistics. Analyzing the effect that retinal gain control has on later cortical processing, we propose a novel method to perform gain control in a data-driven way. Finally we show how models like those pre- sented here can be extended to capture whole visual scenes rather than just small image patches. By using a Markov random field approach we can model images of arbitrary size, while still being able to estimate the model parameters from the data.

The Path to a Porous Semiconductor Multilayer

Thin films are the basis of much of recent technological advance, ranging from coatings with mechanical or optical benefits to platforms for nanoscale electronics. In the latter, semiconductors have been the norm ever since silicon became the main construction material for a multitude of electronical components. The array of characteristics of silicon-based systems can be widened by manipulating the structure of the thin films at the nanoscale - for instance, by making them porous. The different characteristics of different films can then to some extent be combined by simple superposition. Thin films can be manufactured using many different methods. One emerging field is cluster beam deposition, where aggregates of hundreds or thousands of atoms are deposited one by one to form a layer, the characteristics of which depend on the parameters of deposition. One critical parameter is deposition energy, which dictates how porous, if at all, the layer becomes. Other parameters, such as sputtering rate and aggregation conditions, have an effect on the size and consistency of the individual clusters. Understanding nanoscale processes, which cannot be observed experimentally, is fundamental to optimizing experimental techniques and inventing new possibilities for advances at this scale. Atomistic computer simulations offer a window to the world of nanometers and nanoseconds in a way unparalleled by the most accurate of microscopes. Transmission electron microscope image simulations can then bridge this gap by providing a tangible link between the simulated and the experimental. In this thesis, the entire process of cluster beam deposition is explored using molecular dynamics and image simulations. The process begins with the formation of the clusters, which is investigated for Si/Ge in an Ar atmosphere. The structure of the clusters is optimized to bring it as close to the experimental ideal as possible. Then, clusters are deposited, one by one, onto a substrate, until a sufficiently thick layer has been produced. Finally, the concept is expanded by further deposition with different parameters, resulting in multiple superimposed layers of different porosities. This work demonstrates how the aggregation of clusters is not entirely understood within the scope of the approximations used in the simulations; yet, it is also shown how the continued deposition of clusters with a varying deposition energy can lead to a novel kind of nanostructured thin film: a multielemental porous multilayer. According to theory, these new structures have characteristics that can be tailored for a variety of applications, with precision heretofore unseen in conventional multilayer manufacture.

The Influence of World Factors on Finnish Stock Market Volatility

This paper investigates to what extent the volatility of Finnish stock portfolios is transmitted through the "world volatility". We operationalize the volatility processes of Finnish leverage, industry, and size portfolio returns by asymmetric GARCH specifications according to Glosten et al. (1993). We use daily return data for January, 2, 1987 to December 30, 1998. We find that the world shock significantly enters the domestic models, and that the impact has increased over time. This applies also for the variance ratios, and the correlations to the world. The larger the firm, the larger is the world impact. The conditional variance is higher during recessions. The asymmetry parameter is surprisingly non-significant, and the leverage hypothesis cannot be verified. The return generating process of the domestic portfolio returns does usually not include the world information set, thus indicating that the returns are generated by a segmented conditional asset pricing model.