Neural mechanisms of information processing and transmission

This (cumulative) dissertation is concerned with mechanisms and models of information processing and transmission by individual neurons and small neural assemblies. In this document, I first provide historical context for these ideas and highlight similarities and differences to related concepts from machine learning and neuromorphic engineering. With this background, I then discuss the four main themes of my work, namely dendritic filtering and delays, homeostatic plasticity and adaptation, rate-coding with spiking neurons, and spike-timing based alternatives to rate-coding. The content of this discussion is in large part derived from several of my own publications included in Appendix C, but it has been extended and revised to provide a more accessible and broad explanation of the main ideas, as well as to show their inherent connections. I conclude that fundamental differences remain between our understanding of information processing and transmission in machine learning on the one hand and theoretical neuroscience on the other, which should provide a strong incentive for further interdisciplinary work on the domain boundaries between neuroscience, machine learning and neuromorphic engineering

Dendritic plateau potentials can process spike sequences across multiple time-scales

The brain constantly processes information encoded in temporal sequences of spiking activity. This sequential activity emerges from sensory inputs as well as from the brain's own recurrent connectivity and spans multiple dynamically changing timescales. Decoding the temporal order of spiking activity across these varying timescales is a critical function of the brain, but we do not yet understand its neural implementation. The problem is, that the passive dynamics of neural membrane potentials occur on a short millisecond timescale, whereas many cognitive tasks require the integration of information across much slower behavioral timescales. However, actively generated dendritic plateau potentials do occur on such longer timescales, and their essential role for many aspects of cognition has been firmly established by recent experiments. Here, we build on these discoveries and propose a new model of neural computation that emerges from the interaction of localized plateau potentials across a functionally compartmentalized dendritic tree. We show how this interaction offers a robust solution to the timing invariant detection and processing of sequential spike patterns in single neurons. Stochastic synaptic transmission complements the deterministic all-or-none plateau process and improves information transmission by allowing ensembles of neurons to produce graded responses to continuous combinations of features. We found that networks of such neurons can solve highly complex sequence detection tasks by breaking down long inputs into sequences of shorter, random features that can be classified reliably. These results suggest that active dendritic processes are fundamental to neural computation

A Bayesian Monte Carlo approach for predicting the spread of infectious diseases.

In this paper, a simple yet interpretable, probabilistic model is proposed for the prediction of reported case counts of infectious diseases. A spatio-temporal kernel is derived from training data to capture the typical interaction effects of reported infections across time and space, which provides insight into the dynamics of the spread of infectious diseases. Testing the model on a one-week-ahead prediction task for campylobacteriosis and rotavirus infections across Germany, as well as Lyme borreliosis across the federal state of Bavaria, shows that the proposed model performs on-par with the state-of-the-art hhh4 model. However, it provides a full posterior distribution over parameters in addition to model predictions, which aides in the assessment of the model. The employed Bayesian Monte Carlo regression framework is easily extensible and allows for incorporating prior domain knowledge, which makes it suitable for use on limited, yet complex datasets as often encountered in epidemiology

Bayesian Hierarchical Models can Infer Interpretable Predictions of Leaf Area Index From Heterogeneous Datasets

Environmental scientists often face the challenge of predicting a complex phenomenon from a heterogeneous collection of datasets that exhibit systematic differences. Accounting for these differences usually requires including additional parameters in the predictive models, which increases the probability of overfitting, particularly on small datasets. We investigate how Bayesian hierarchical models can help mitigate this problem by allowing the practitioner to incorporate information about the structure of the dataset explicitly. To this end, we look at a typical application in remote sensing: the estimation of leaf area index of white winter wheat, an important indicator for agronomical modeling, using measurements of reflectance spectra collected at different locations and growth stages. Since the insights gained from such a model could be used to inform policy or business decisions, the interpretability of the model is a primary concern. We, therefore, focus on models that capture the association between leaf area index and the spectral reflectance at various wavelengths by spline-based kernel functions, which can be visually inspected and analyzed. We compare models with three different levels of hierarchy: a non-hierarchical baseline model, a model with hierarchical bias parameter, and a model in which bias and kernel parameters are hierarchically structured. We analyze them using Markov Chain Monte Carlo sampling diagnostics and an intervention-based measure of feature importance. The improved robustness and interpretability of this approach show that Bayesian hierarchical models are a versatile tool for the prediction of leaf area index, particularly in scenarios where the available data sources are heterogeneous

Bayesian Hierarchical Models can Infer Interpretable Predictions of Leaf Area Index From Heterogeneous Datasets

Environmental scientists often face the challenge of predicting a complex phenomenon from a heterogeneous collection of datasets that exhibit systematic differences. Accounting for these differences usually requires including additional parameters in the predictive models, which increases the probability of overfitting, particularly on small datasets. We investigate how Bayesian hierarchical models can help mitigate this problem by allowing the practitioner to incorporate information about the structure of the dataset explicitly. To this end, we look at a typical application in remote sensing: the estimation of leaf area index of white winter wheat, an important indicator for agronomical modeling, using measurements of reflectance spectra collected at different locations and growth stages. Since the insights gained from such a model could be used to inform policy or business decisions, the interpretability of the model is a primary concern. We, therefore, focus on models that capture the association between leaf area index and the spectral reflectance at various wavelengths by spline-based kernel functions, which can be visually inspected and analyzed. We compare models with three different levels of hierarchy: a non-hierarchical baseline model, a model with hierarchical bias parameter, and a model in which bias and kernel parameters are hierarchically structured. We analyze them using Markov Chain Monte Carlo sampling diagnostics and an intervention-based measure of feature importance. The improved robustness and interpretability of this approach show that Bayesian hierarchical models are a versatile tool for the prediction of leaf area index, particularly in scenarios where the available data sources are heterogeneous

Simulation and structural optimization of 3d Timoshenko beam networks based on fully analytic network solutions

This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, from which the solutions along the beams can be reconstructed. Consequently analytic solutions for the network can be computed by a numerical scheme without applying a spacial discretization. While the assembly of the local stiffness matrices is slightly more expensive compared to an FE model using, e.g., linear ansatz-functions, the complexity of the solution of the FE-system is not. This is particularly interesting for topology and material optimization problems formulated on the network. In order to demonstrate the efficiency of the approach a numerical comparison to the case of linear ansatz-functions is provided followed by a series of studies with topology and multi-material optimization problems on networks