A Comprehensive Workflow for General-Purpose Neural Modeling with Highly Configurable Neuromorphic Hardware Systems

In this paper we present a methodological framework that meets novel requirements emerging from upcoming types of accelerated and highly configurable neuromorphic hardware systems. We describe in detail a device with 45 million programmable and dynamic synapses that is currently under development, and we sketch the conceptual challenges that arise from taking this platform into operation. More specifically, we aim at the establishment of this neuromorphic system as a flexible and neuroscientifically valuable modeling tool that can be used by non-hardware-experts. We consider various functional aspects to be crucial for this purpose, and we introduce a consistent workflow with detailed descriptions of all involved modules that implement the suggested steps: The integration of the hardware interface into the simulator-independent model description language PyNN; a fully automated translation between the PyNN domain and appropriate hardware configurations; an executable specification of the future neuromorphic system that can be seamlessly integrated into this biology-to-hardware mapping process as a test bench for all software layers and possible hardware design modifications; an evaluation scheme that deploys models from a dedicated benchmark library, compares the results generated by virtual or prototype hardware devices with reference software simulations and analyzes the differences. The integration of these components into one hardware-software workflow provides an ecosystem for ongoing preparative studies that support the hardware design process and represents the basis for the maturity of the model-to-hardware mapping software. The functionality and flexibility of the latter is proven with a variety of experimental results

Mathematical frameworks for oscillatory network dynamics in neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience

Scalable and flexible inference framework for stochastic dynamic single-cell models

Understanding the inherited nature of how biological processes dynamically change over time and exhibit intra- and inter-individual variability, due to the different responses to environmental stimuli and when interacting with other processes, has been a major focus of systems biology. The rise of single-cell fluorescent microscopy has enabled the study of those phenomena. The analysis of single-cell data with mechanistic models offers an invaluable tool to describe dynamic cellular processes and to rationalise cell-to-cell variability within the population. However, extracting mechanistic information from single-cell data has proven difficult. This requires statistical methods to infer unknown model parameters from dynamic, multi-individual data accounting for heterogeneity caused by both intrinsic (e.g. variations in chemical reactions) and extrinsic (e.g. variability in protein concentrations) noise. Although several inference methods exist, the availability of efficient, general and accessible methods that facilitate modelling of single-cell data, remains lacking. Here we present a scalable and flexible framework for Bayesian inference in state-space mixed-effects single-cell models with stochastic dynamic. Our approach infers model parameters when intrinsic noise is modelled by either exact or approximate stochastic simulators, and when extrinsic noise is modelled by either time-varying, or time-constant parameters that vary between cells. We demonstrate the relevance of our approach by studying how cell-to-cell variation in carbon source utilisation affects heterogeneity in the budding yeast Saccharomyces cerevisiae SNF1 nutrient sensing pathway. We identify hexokinase activity as a source of extrinsic noise and deduce that sugar availability dictates cell-to-cell variability

Population Dynamics In A Model Closed Ecosystem

For almost any species in any environment, it is nearly impossible to predict its fitness from molecular knowledge. If fitness is not to be a mere tautology, reproducible measurements of the survival and reproduction of populations are needed over many generations. Laboratory microbial ecosystems afford the short time and length scales required for such measurements. Their conventional implementations, batch cultures with period refreshment of growth medium or chemostats with continuous refreshment, have a number of disadvantages, such as the introduction of additional frequencies, selection for surface growth and the distortion of chemical interactions. In closed ecosystems free energy is instead supplied as light, allowing for simpler, replicable protocols and a consistent interpretation of interactions, independent of their mode or timescale. Here, I describe a model closed ecosystem consisting of three singlecelled microbes, Escherichia coli, Chlamydomonas reinhardtii and Tetrahymena thermophila and show that these species can coexist for hundreds of days under closure. Using a custom built in situ fluorescence microscopy set up, the densities of these three species can be measured automatically and noninvasively over months with low classification error and large dynamical range. When kept under identical boundary conditions, these ecosystems reproducibly diverge in composition, with characteristic divergence times of ~20 days for T. thermophila, ~40 days for the other two species, and an approximately linear increase of an aggregate divergence measure over the first ~60 days. For two ecosystems, densities were measured continuously under constant conditions and their dynamics shown to be nonstationary for all three species \u3e100 days after closure. As a consequence, conventional time series methods assuming stationarity are inadequate and wavelet analysis is proposed as an alternative. Species-species interactions are further investigated using oscillations in illumination intensity. Densities of C. reinhardtii and, surprisingly, E. coli respond to modest perturbations of light intensity. Variation of the modulation frequency strongly implicates the circadian clock of C. reinhardtii in its response. The nonlinearity of the E. coli response suggests that it depends on C. reinhardtii density or spatial distribution rather than directly responds to the modulation of illumination. Further improvements in the detection of interactions are proposed

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Robust learning algorithms for spiking and rate-based neural networks

Inspired by the remarkable properties of the human brain, the fields of machine learning, computational neuroscience and neuromorphic engineering have achieved significant synergistic progress in the last decade. Powerful neural network models rooted in machine learning have been proposed as models for neuroscience and for applications in neuromorphic engineering. However, the aspect of robustness is often neglected in these models. Both biological and engineered substrates show diverse imperfections that deteriorate the performance of computation models or even prohibit their implementation. This thesis describes three projects aiming at implementing robust learning with local plasticity rules in neural networks. First, we demonstrate the advantages of neuromorphic computations in a pilot study on a prototype chip. Thereby, we quantify the speed and energy consumption of the system compared to a software simulation and show how on-chip learning contributes to the robustness of learning. Second, we present an implementation of spike-based Bayesian inference on accelerated neuromorphic hardware. The model copes, via learning, with the disruptive effects of the imperfect substrate and benefits from the acceleration. Finally, we present a robust model of deep reinforcement learning using local learning rules. It shows how backpropagation combined with neuromodulation could be implemented in a biologically plausible framework. The results contribute to the pursuit of robust and powerful learning networks for biological and neuromorphic substrates

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Dynamical Systems in Spiking Neuromorphic Hardware

Dynamical systems are universal computers. They can perceive stimuli, remember, learn from feedback, plan sequences of actions, and coordinate complex behavioural responses. The Neural Engineering Framework (NEF) provides a general recipe to formulate models of such systems as coupled sets of nonlinear differential equations and compile them onto recurrently connected spiking neural networks – akin to a programming language for spiking models of computation. The Nengo software ecosystem supports the NEF and compiles such models onto neuromorphic hardware. In this thesis, we analyze the theory driving the success of the NEF, and expose several core principles underpinning its correctness, scalability, completeness, robustness, and extensibility. We also derive novel theoretical extensions to the framework that enable it to far more effectively leverage a wide variety of dynamics in digital hardware, and to exploit the device-level physics in analog hardware. At the same time, we propose a novel set of spiking algorithms that recruit an optimal nonlinear encoding of time, which we call the Delay Network (DN). Backpropagation across stacked layers of DNs dramatically outperforms stacked Long Short-Term Memory (LSTM) networks—a state-of-the-art deep recurrent architecture—in accuracy and training time, on a continuous-time memory task, and a chaotic time-series prediction benchmark. The basic component of this network is shown to function on state-of-the-art spiking neuromorphic hardware including Braindrop and Loihi. This implementation approaches the energy-efficiency of the human brain in the former case, and the precision of conventional computation in the latter case