Convergence Properties of the (µ/µI, λ)-ES on the Rastrigin Function.

The highly multimodal Rastrigin test function is analyzed by deriving a new aggregated progress rate measure. It is derived as a function of the residual distance to the optimizer by assuming normally distributed positional coordinates around the global optimizer. This assumption is justified for successful ES-runs operating with sufficiently slow step-size adaptation. The measure enables the investigation of further convergence properties. For moderately large mutation strengths a characteristic distance-dependent Rastrigin noise floor is derived. For small mutation strengths local attraction is analyzed and an escape condition is established. Both mutation strength regimes combined pose a major challenge optimizing the Rastrigin function, which can be counteracted by increasing the population size. Hence, a population scaling relation to achieve high global convergence rates is derived which shows good agreement with experimental data.

Statistical Learning in Vision.

Vision and learning have long been considered to be two areas of research linked only distantly. However, recent developments in vision research have changed the conceptual definition of vision from a signal-evaluating process to a goal-oriented interpreting process, and this shift binds learning, together with the resulting internal representations, intimately to vision. In this review, we consider various types of learning (perceptual, statistical, and rule/abstract) associated with vision in the past decades and argue that they represent differently specialized versions of the fundamental learning process, which must be captured in its entirety when applied to complex visual processes. We show why the generalized version of statistical learning can provide the appropriate setup for such a unified treatment of learning in vision, what computational framework best accommodates this kind of statistical learning, and what plausible neural scheme could feasibly implement this framework. Finally, we list the challenges that the field of statistical learning faces in fulfilling the promise of being the right vehicle for advancing our understanding of vision in its entirety.

A statistical framework for quantification and visualisation of positional uncertainty in deep brain stimulation electrodes.

Deep brain stimulation (DBS) is an established therapy for treating patients with movement disorders such as Parkinson's disease. Patient-specific computational modelling and visualisation have been shown to play a key role in surgical and therapeutic decisions for DBS. The computational models use brain imaging, such as magnetic resonance (MR) and computed tomography (CT), to determine the DBS electrode positions within the patient's head. The finite resolution of brain imaging, however, introduces uncertainty in electrode positions. The DBS stimulation settings for optimal patient response are sensitive to the relative positioning of DBS electrodes to a specific neural substrate (white/grey matter). In our contribution, we study positional uncertainty in the DBS electrodes for imaging with finite resolution. In a three-step approach, we first derive a closed-form mathematical model characterising the geometry of the DBS electrodes. Second, we devise a statistical framework for quantifying the uncertainty in the positional attributes of the DBS electrodes, namely the direction of longitudinal axis and the contact-centre positions at subvoxel levels. The statistical framework leverages the analytical model derived in step one and a Bayesian probabilistic model for uncertainty quantification. Finally, the uncertainty in contact-centre positions is interactively visualised through volume rendering and isosurfacing techniques. We demonstrate the efficacy of our contribution through experiments on synthetic and real datasets. We show that the spatial variations in true electrode positions are significant for finite resolution imaging, and interactive visualisation can be instrumental in exploring probabilistic positional variations in the DBS lead.

Analog synthetic biology.

We analyse the pros and cons of analog versus digital computation in living cells. Our analysis is based on fundamental laws of noise in gene and protein expression, which set limits on the energy, time, space, molecular count and part-count resources needed to compute at a given level of precision. We conclude that analog computation is significantly more efficient in its use of resources than deterministic digital computation even at relatively high levels of precision in the cell. Based on this analysis, we conclude that synthetic biology must use analog, collective analog, probabilistic and hybrid analog-digital computational approaches; otherwise, even relatively simple synthetic computations in cells such as addition will exceed energy and molecular-count budgets. We present schematics for efficiently representing analog DNA-protein computation in cells. Analog electronic flow in subthreshold transistors and analog molecular flux in chemical reactions obey Boltzmann exponential laws of thermodynamics and are described by astoundingly similar logarithmic electrochemical potentials. Therefore, cytomorphic circuits can help to map circuit designs between electronic and biochemical domains. We review recent work that uses positive-feedback linearization circuits to architect wide-dynamic-range logarithmic analog computation in Escherichia coli using three transcription factors, nearly two orders of magnitude more efficient in parts than prior digital implementations.

Integrating probabilistic models of perception and interactive neural networks: a historical and tutorial review.

This article seeks to establish a rapprochement between explicitly Bayesian models of contextual effects in perception and neural network models of such effects, particularly the connectionist interactive activation (IA) model of perception. The article is in part an historical review and in part a tutorial, reviewing the probabilistic Bayesian approach to understanding perception and how it may be shaped by context, and also reviewing ideas about how such probabilistic computations may be carried out in neural networks, focusing on the role of context in interactive neural networks, in which both bottom-up and top-down signals affect the interpretation of sensory inputs. It is pointed out that connectionist units that use the logistic or softmax activation functions can exactly compute Bayesian posterior probabilities when the bias terms and connection weights affecting such units are set to the logarithms of appropriate probabilistic quantities. Bayesian concepts such the prior, likelihood, (joint and marginal) posterior, probability matching and maximizing, and calculating vs. sampling from the posterior are all reviewed and linked to neural network computations. Probabilistic and neural network models are explicitly linked to the concept of a probabilistic generative model that describes the relationship between the underlying target of perception (e.g., the word intended by a speaker or other source of sensory stimuli) and the sensory input that reaches the perceiver for use in inferring the underlying target. It is shown how a new version of the IA model called the multinomial interactive activation (MIA) model can sample correctly from the joint posterior of a proposed generative model for perception of letters in words, indicating that interactive processing is fully consistent with principled probabilistic computation. Ways in which these computations might be realized in real neural systems are also considered.