Showing papers in "Biological Cybernetics in 2014"

Distribution of axon diameters in cortical white matter: an electron-microscopic study on three human brains and a macaque

Abstract: The aim of this study was to obtain information on the axonal diameters of cortico-cortical fibres in the human brain, connecting distant regions of the same hemisphere via the white matter. Samples for electron microscopy were taken from the region of the superior longitudinal fascicle and from the transitional white matter between temporal and frontal lobe where the uncinate and inferior occipitofrontal fascicle merge. We measured the inner diameter of cross sections of myelinated axons. For comparison with data from the literature on the human corpus callosum, we also took samples from that region. For comparison with well-fixed material, we also included samples from corresponding regions of a monkey brain (Macaca mulatta). Fibre diameters in human brains ranged from 0.16 to 9 $$\upmu \hbox {m}$$μm. Distributions of diameters were similar in the three systems of cortico-cortical fibres investigated, both in humans and the monkey, with most of the average values below 1 $$\upmu $$μm diameter and a small population of much thicker fibres. Within individual human brains, the averages were larger in the superior longitudinal fascicle than in the transitional zone between temporal and frontal lobe. An asymmetry between left and right could be found in one of the human brains, as well as in the monkey brain. A correlation was also found between the thickness of the myelin sheath and the inner axon diameter for axons whose calibre was greater than about 0.6 $$\upmu \hbox {m}$$μm. The results are compared to white matter data in other mammals and are discussed with respect to conduction velocity, brain size, cognition, as well as diffusion weighted imaging studies.

Cell assemblies in the cerebral cortex

Abstract: Donald Hebb's concept of cell assemblies is a physiology-based idea for a distributed neural representation of behaviorally relevant objects, concepts, or constellations. In the late 70s Valentino Braitenberg started the endeavor to spell out the hypothesis that the cerebral cortex is the structure where cell assemblies are formed, maintained and used, in terms of neuroanatomy (which was his main concern) and also neurophysiology. This endeavor has been carried on over the last 30 years corroborating most of his findings and interpretations. This paper summarizes the present state of cell assembly theory, realized in a network of associative memories, and of the anatomical evidence for its location in the cerebral cortex.

Stimulus-specific adaptation and deviance detection in the auditory system: experiments and models

Abstract: Stimulus-specific adaptation (SSA) is the reduction in the response to a common stimulus that does not generalize, or only partially generalizes, to other, rare stimuli. SSA has been proposed to be a correlate of `deviance detection', an important computational task of sensory systems. SSA is ubiquitous in the auditory system: It is found both in cortex and in subcortical stations, and it has been demonstrated in many mammalian species as well as in birds. A number of models have been suggested in the literature to account for SSA in the auditory domain. In this review, the experimental literature is critically examined in relationship to these models. While current models can all account for auditory SSA to some degree, none is fully compatible with the available findings.

Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots

Abstract: In this paper, we present an extended mathematical model of the central pattern generator (CPG) in the spinal cord. The proposed CPG model is used as the underlying low-level controller of a humanoid robot to generate various walking patterns. Such biological mechanisms have been demonstrated to be robust in locomotion of animal. Our model is supported by two neurophysiological studies. The first study identified a neural circuitry consisting of a two-layered CPG, in which pattern formation and rhythm generation are produced at different levels. The second study focused on a specific neural model that can generate different patterns, including oscillation. This neural model was employed in the pattern generation layer of our CPG, which enables it to produce different motion patterns--rhythmic as well as non-rhythmic motions. Due to the pattern-formation layer, the CPG is able to produce behaviors related to the dominating rhythm (extension/flexion) and rhythm deletion without rhythm resetting. The proposed multi-layered multi-pattern CPG model (MLMP-CPG) has been deployed in a 3D humanoid robot (NAO) while it performs locomotion tasks. The effectiveness of our model is demonstrated in simulations and through experimental results.

Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis

Abstract: Stochastic dynamics and critical slowing down were studied experimentally and numerically near the onset of dynamical bistability in visual perception under the influence of noise. Exploring the Necker cube as the essential example of an ambiguous figure, and using its wire contrast as a control parameter, we measured dynamical hysteresis in two coexisting percepts as a function of both the velocity of the parameter change and the background luminance. The bifurcation analysis allowed us to estimate the level of cognitive noise inherent to brain neural cells activity, which induced intermittent switches between different perception states. The results of numerical simulations with a simple energy model are in good qualitative agreement with psychological experiments.

Thinking in circuits: toward neurobiological explanation in cognitive neuroscience

Abstract: Cognitive theory has decomposed human mental abilities into cognitive (sub) systems, and cognitive neuroscience succeeded in disclosing a host of relationships between cognitive systems and specific structures of the human brain. However, an explanation of why specific functions are located in specific brain loci had still been missing, along with a neurobiological model that makes concrete the neuronal circuits that carry thoughts and meaning. Brain theory, in particular the Hebb-inspired neurocybernetic proposals by Braitenberg, now offers an avenue toward explaining brain---mind relationships and to spell out cognition in terms of neuron circuits in a neuromechanistic sense. Central to this endeavor is the theoretical construct of an elementary functional neuronal unit above the level of individual neurons and below that of whole brain areas and systems: the distributed neuronal assembly (DNA) or thought circuit (TC). It is shown that DNA/TC theory of cognition offers an integrated explanatory perspective on brain mechanisms of perception, action, language, attention, memory, decision and conceptual thought. We argue that DNAs carry all of these functions and that their inner structure (e.g., core and halo subcomponents), and their functional activation dynamics (e.g., ignition and reverberation processes) answer crucial localist questions, such as why memory and decisions draw on prefrontal areas although memory formation is normally driven by information in the senses and in the motor system. We suggest that the ability of building DNAs/TCs spread out over different cortical areas is the key mechanism for a range of specifically human sensorimotor, linguistic and conceptual capacities and that the cell assembly mechanism of overlap reduction is crucial for differentiating a vocabulary of actions, symbols and concepts.

Estimating parameters and predicting membrane voltages with conductance-based neuron models

Abstract: Recent results demonstrate techniques for fully quantitative, statistical inference of the dynamics of individual neurons under the Hodgkin---Huxley framework of voltage-gated conductances. Using a variational approximation, this approach has been successfully applied to simulated data from model neurons. Here, we use this method to analyze a population of real neurons recorded in a slice preparation of the zebra finch forebrain nucleus HVC. Our results demonstrate that using only 1,500 ms of voltage recorded while injecting a complex current waveform, we can estimate the values of 12 state variables and 72 parameters in a dynamical model, such that the model accurately predicts the responses of the neuron to novel injected currents. A less complex model produced consistently worse predictions, indicating that the additional currents contribute significantly to the dynamics of these neurons. Preliminary results indicate some differences in the channel complement of the models for different classes of HVC neurons, which accords with expectations from the biology. Whereas the model for each cell is incomplete (representing only the somatic compartment, and likely to be missing classes of channels that the real neurons possess), our approach opens the possibility to investigate in modeling the plausibility of additional classes of channels the cell might possess, thus improving the models over time. These results provide an important foundational basis for building biologically realistic network models, such as the one in HVC that contributes to the process of song production and developmental vocal learning in songbirds.

Intermittent control models of human standing: similarities and differences

Abstract: Two architectures of intermittent control are compared and contrasted in the context of the single inverted pendulum model often used for describing standing in humans. The architectures are similar insofar as they use periods of open-loop control punctuated by switching events when crossing a switching surface to keep the system state trajectories close to trajectories leading to equilibrium. The architectures differ in two significant ways. Firstly, in one case, the open-loop control trajectory is generated by a system-matched hold, and in the other case, the open-loop control signal is zero. Secondly, prediction is used in one case but not the other. The former difference is examined in this paper. The zero control alternative leads to periodic oscillations associated with limit cycles; whereas the system-matched control alternative gives trajectories (including homoclinic orbits) which contain the equilibrium point and do not have oscillatory behaviour. Despite this difference in behaviour, it is further shown that behaviour can appear similar when either the system is perturbed by additive noise or the system-matched trajectory generation is perturbed. The purpose of the research is to come to a common approach for understanding the theoretical properties of the two alternatives with the twin aims of choosing which provides the best explanation of current experimental data (which may not, by itself, distinguish beween the two alternatives) and suggesting future experiments to distinguish beween the two alternatives.

Sensory uncertainty and stick balancing at the fingertip

Abstract: The effects of sensory input uncertainty, $$\varepsilon $$ ? , on the stability of time-delayed human motor control are investigated by calculating the minimum stick length, $$\ell _\mathrm{crit}$$ l crit , that can be stabilized in the inverted position for a given time delay, $$\tau $$ ? . Five control strategies often discussed in the context of human motor control are examined: three time-invariant controllers [proportional---derivative, proportional---derivative---acceleration (PDA), model predictive (MP) controllers] and two time-varying controllers [act-and-wait (AAW) and intermittent predictive controllers]. The uncertainties of the sensory input are modeled as a multiplicative term in the system output. Estimates based on the variability of neural spike trains and neural population responses suggest that $$\varepsilon \approx 7$$ ? ? 7 ---13 %. It is found that for this range of uncertainty, a tapped delay-line type of MP controller is the most robust controller. In particular, this controller can stabilize inverted sticks of the length balanced by expert stick balancers (0.25---0.5 m when $$\tau \approx 0.08$$ ? ? 0.08 s). However, a PDA controller becomes more effective when $$\varepsilon > 15\,\%$$ ? > 15 % . A comparison between $$\ell _\mathrm{crit}$$ l crit for human stick balancing at the fingertip and balancing on the rubberized surface of a table tennis racket suggest that friction likely plays a role in balance control. Measurements of $$\ell _\mathrm{crit},\,\tau $$ l crit , ? , and a variability of the fluctuations in the vertical displacement angle, an estimate of $$\varepsilon $$ ? , may make it possible to study the changes in control strategy as motor skill develops.

A neuromechanical simulation of insect walking and transition to turning of the cockroach Blaberus discoidalis

Abstract: A neuromechanical simulation of the cockroach Blaberus discoidalis was developed to explore changes in locomotion when the animal transitions from walking straight to turning. The simulation was based upon the biological data taken from three sources. Neural circuitry was adapted from the extensive literature primarily obtained from the studies of neural connections within thoracic ganglia of stick insect and adapted to cockroach. The 3D joint kinematic data on straight, forward walking for cockroach were taken from a paper that describes these movements in all joints simultaneously as the cockroach walked on an oiled-plate tether (Bender et al. in PloS one 5(10):1---15, 2010b). Joint kinematics for turning were only available for some leg joints (Mu and Ritzmann in J Comp Physiol A Neuroethol Sens Neural Behav Physiol 191(11):1037---54, 2005) and thus had to be obtained using the methods that were applied for straight walking by Bender et al. (PloS one 5(10):1---15, 2010b). Once walking, inside turning, and outside turning were characterized, phase and amplitude changes for each joint of each leg were quantified. Apparent reflex reversals and joint activity changes were used to modify sensory coupling pathways between the CPG at each joint of the simulation. Oiled-plate experiments in simulation produced tarsus trajectories in stance similar to those seen in the animal. Simulations including forces that would be experienced if the insect was walking freely (i.e., weight support and friction) again produced similar results. These data were not considered during the design of the simulation, suggesting that the simulation captures some key underlying the principles of walking, turning, and transitioning in the cockroach. In addition, since the nervous system was modeled with realistic neuron models, biologically plausible reflex reversals are simulated, motivating future neurobiological research.

Learning strategies in table tennis using inverse reinforcement learning

Abstract: Learning a complex task such as table tennis is a challenging problem for both robots and humans. Even after acquiring the necessary motor skills, a strategy is needed to choose where and how to return the ball to the opponent's court in order to win the game. The data-driven identification of basic strategies in interactive tasks, such as table tennis, is a largely unexplored problem. In this paper, we suggest a computational model for representing and inferring strategies, based on a Markov decision problem, where the reward function models the goal of the task as well as the strategic information. We show how this reward function can be discovered from demonstrations of table tennis matches using model-free inverse reinforcement learning. The resulting framework allows to identify basic elements on which the selection of striking movements is based. We tested our approach on data collected from players with different playing styles and under different playing conditions. The estimated reward function was able to capture expert-specific strategic information that sufficed to distinguish the expert among players with different skill levels as well as different playing styles.

Bifurcation analysis of a Morris---Lecar neuron model

Abstract: In this paper, we investigate the dynamical behaviors of a Morris---Lecar neuron model. By using bifurcation methods and numerical simulations, we examine the global structure of bifurcations of the model. Results are summarized in various two-parameter bifurcation diagrams with the stimulating current as the abscissa and the other parameter as the ordinate. We also give the one-parameter bifurcation diagrams and pay much attention to the emergence of periodic solutions and bistability. Different membrane excitability is obtained by bifurcation analysis and frequency-current curves. The alteration of the membrane properties of the Morris---Lecar neurons is discussed.

Active inference, eye movements and oculomotor delays

Abstract: This paper considers the problem of sensorimotor delays in the optimal control of (smooth) eye movements under uncertainty. Specifically, we consider delays in the visuo-oculomotor loop and their implications for active inference. Active inference uses a generalisation of Kalman filtering to provide Bayes optimal estimates of hidden states and action in generalised coordinates of motion. Representing hidden states in generalised coordinates provides a simple way of compensating for both sensory and oculomotor delays. The efficacy of this scheme is illustrated using neuronal simulations of pursuit initiation responses, with and without compensation. We then consider an extension of the generative model to simulate smooth pursuit eye movements--in which the visuo-oculomotor system believes both the target and its centre of gaze are attracted to a (hidden) point moving in the visual field. Finally, the generative model is equipped with a hierarchical structure, so that it can recognise and remember unseen (occluded) trajectories and emit anticipatory responses. These simulations speak to a straightforward and neurobiologically plausible solution to the generic problem of integrating information from different sources with different temporal delays and the particular difficulties encountered when a system--like the oculomotor system--tries to control its environment with delayed signals.

Integrate-and-fire neurons driven by asymmetric dichotomous noise

Abstract: We consider a general integrate-and-fire (IF) neuron driven by asymmetric dichotomous noise. In contrast to the Gaussian white noise usually used in the so-called diffusion approximation, this noise is colored, i.e., it exhibits temporal correlations. We give an analytical expression for the stationary voltage distribution of a neuron receiving such noise and derive recursive relations for the moments of the first passage time density, which allow us to calculate the firing rate and the coefficient of variation of interspike intervals. We study how correlations in the input affect the rate and regularity of firing under variation of the model's parameters for leaky and quadratic IF neurons. Further, we consider the limit of small correlation times and find lowest order corrections to the first passage time moments to be proportional to the square root of the correlation time. We show analytically that to this lowest order, correlations always lead to a decrease in firing rate for a leaky IF neuron. All theoretical expressions are compared to simulations of leaky and quadratic IF neurons.

Adaptive dynamic programming as a theory of sensorimotor control

Abstract: Many characteristics of sensorimotor control can be explained by models based on optimization and optimal control theories. However, most of the previous models assume that the central nervous system has access to the precise knowledge of the sensorimotor system and its interacting environment. This viewpoint is difficult to be justified theoretically and has not been convincingly validated by experiments. To address this problem, this paper presents a new computational mechanism for sensorimotor control from a perspective of adaptive dynamic programming (ADP), which shares some features of reinforcement learning. The ADP-based model for sensorimotor control suggests that a command signal for the human movement is derived directly from the real-time sensory data, without the need to identify the system dynamics. An iterative learning scheme based on the proposed ADP theory is developed, along with rigorous convergence analysis. Interestingly, the computational model as advocated here is able to reproduce the motor learning behavior observed in experiments where a divergent force field or velocity-dependent force field was present. In addition, this modeling strategy provides a clear way to perform stability analysis of the overall system. Hence, we conjecture that human sensorimotor systems use an ADP-type mechanism to control movements and to achieve successful adaptation to uncertainties present in the environment.

A feedforward model for the formation of a grid field where spatial information is provided solely from place cells

Abstract: Grid cells (GCs) in the medial entorhinal cortex (mEC) have the property of having their firing activity spatially tuned to a regular triangular lattice. Several theoretical models for grid field formation have been proposed, but most assume that place cells (PCs) are a product of the grid cell system. There is, however, an alternative possibility that is supported by various strands of experimental data. Here we present a novel model for the emergence of gridlike firing patterns that stands on two key hypotheses: (1) spatial information in GCs is provided from PC activity and (2) grid fields result from a combined synaptic plasticity mechanism involving inhibitory and excitatory neurons mediating the connections between PCs and GCs. Depending on the spatial location, each PC can contribute with excitatory or inhibitory inputs to GC activity. The nature and magnitude of the PC input is a function of the distance to the place field center, which is inferred from rate decoding. A biologically plausible learning rule drives the evolution of the connection strengths from PCs to a GC. In this model, PCs compete for GC activation, and the plasticity rule favors efficient packing of the space representation. This leads to gridlike firing patterns. In a new environment, GCs continuously recruit new PCs to cover the entire space. The model described here makes important predictions and can represent the feedforward connections from hippocampus CA1 to deeper mEC layers.

An ideal-observer model of human sound localization

Abstract: In recent years, a great deal of research within the field of sound localization has been aimed at finding the acoustic cues that human listeners use to localize sounds and understanding the mechanisms by which they process these cues. In this paper, we propose a complementary approach by constructing an ideal-observer model, by which we mean a model that performs optimal information processing within a Bayesian context. The model considers all available spatial information contained within the acoustic signals encoded by each ear. Parameters for the optimal Bayesian model are determined based on psychoacoustic discrimination experiments on interaural time difference and sound intensity. Without regard as to how the human auditory system actually processes information, we examine the best possible localization performance that could be achieved based only on analysis of the input information, given the constraints of the normal auditory system. We show that the model performance is generally in good agreement with the actual human localization performance, as assessed in a meta-analysis of many localization experiments (Best et al. in Principles and applications of spatial hearing, pp 14---23. World Scientific Publishing, Singapore, 2011). We believe this approach can shed new light on the optimality (or otherwise) of human sound localization, especially with regard to the level of uncertainty in the input information. Moreover, the proposed model allows one to study the relative importance of various (combinations of) acoustic cues for spatial localization and enables a prediction of which cues are most informative and therefore likely to be used by humans in various circumstances.

Frequency modulation of large oscillatory neural networks

Abstract: Dynamical systems which generate periodic signals are of interest as models of biological central pattern generators and in a number of robotic applications. A basic functionality that is required in both biological modelling and robotics is frequency modulation. This leads to the question of whether there are generic mechanisms to control the frequency of neural oscillators. Here we describe why this objective is of a different nature, and more difficult to achieve, than modulating other oscillation characteristics (like amplitude, offset, signal shape). We propose a generic way to solve this task which makes use of a simple linear controller. It rests on the insight that there is a bidirectional dependency between the frequency of an oscillation and geometric properties of the neural oscillator's phase portrait. By controlling the geometry of the neural state orbits, it is possible to control the frequency on the condition that the state space can be shaped such that it can be pushed easily to any frequency.

Learning robotic eye---arm---hand coordination from human demonstration: a coupled dynamical systems approach

Abstract: We investigate the role of obstacle avoidance in visually guided reaching and grasping movements. We report on a human study in which subjects performed prehensile motion with obstacle avoidance where the position of the obstacle was systematically varied across trials. These experiments suggest that reaching with obstacle avoidance is organized in a sequential manner, where the obstacle acts as an intermediary target. Furthermore, we demonstrate that the notion of workspace travelled by the hand is embedded explicitly in a forward planning scheme, which is actively involved in detecting obstacles on the way when performing reaching. We find that the gaze proactively coordinates the pattern of eye---arm motion during obstacle avoidance. This study provides also a quantitative assessment of the coupling between the eye---arm---hand motion. We show that the coupling follows regular phase dependencies and is unaltered during obstacle avoidance. These observations provide a basis for the design of a computational model. Our controller extends the coupled dynamical systems framework and provides fast and synchronous control of the eyes, the arm and the hand within a single and compact framework, mimicking similar control system found in humans. We validate our model for visuomotor control of a humanoid robot.

Classification using sparse representations: a biologically plausible approach

Abstract: Representing signals as linear combinations of basis vectors sparsely selected from an overcomplete dictionary has proven to be advantageous for many applications in pattern recognition, machine learning, signal processing, and computer vision. While this approach was originally inspired by insights into cortical information processing, biologically plausible approaches have been limited to exploring the functionality of early sensory processing in the brain, while more practical applications have employed non-biologically plausible sparse coding algorithms. Here, a biologically plausible algorithm is proposed that can be applied to practical problems. This algorithm is evaluated using standard benchmark tasks in the domain of pattern classification, and its performance is compared to a wide range of alternative algorithms that are widely used in signal and image processing. The results show that for the classification tasks performed here, the proposed method is competitive with the best of the alternative algorithms that have been evaluated. This demonstrates that classification using sparse representations can be performed in a neurally plausible manner, and hence, that this mechanism of classification might be exploited by the brain.

Emotions in robot psychology

Abstract: In his famous thought experiments on synthetic vehicles, Valentino Braitenberg stipulated that simple stimulus-response reactions in an organism could evoke the appearance of complex behavior, which, to the unsuspecting human observer, may even appear to be driven by emotions such as fear, aggression, and even love (Braitenberg, Vehikel. Experimente mit kunstlichen Wesen, Lit Verlag, 2004). In fact, humans appear to have a strong propensity to anthropomorphize, driven by our inherent desire for predictability that will quickly lead us to discern patterns, cause-and-effect relationships, and yes, emotions, in animated entities, be they natural or artificial. But might there be reasons, that we should intentionally "implement" emotions into artificial entities, such as robots? How would we proceed in creating robot emotions? And what, if any, are the ethical implications of creating "emotional" robots? The following article aims to shed some light on these questions with a multi-disciplinary review of recent empirical investigations into the various facets of emotions in robot psychology.

Torque---stiffness-controlled dynamic walking with central pattern generators

Abstract: Walking behavior is modulated by controlling joint torques in most existing passivity-based bipeds. Controlled Passive Walking with adaptable stiffness exhibits controllable natural motions and energy efficient gaits. In this paper, we propose torque---stiffness-controlled dynamic bipedal walking, which extends the concept of Controlled Passive Walking by introducing structured control parameters and a bio-inspired control method with central pattern generators. The proposed walking paradigm is beneficial in clarifying the respective effects of the external actuation and the internal natural dynamics. We present a seven-link biped model to validate the presented walking. Effects of joint torque and joint stiffness on gait selection, walking performance and walking pattern transitions are studied in simulations. The work in this paper develops a new solution of motion control of bipedal robots with adaptable stiffness and provides insights of efficient and sophisticated walking gaits of humans.

Bio-inspired modeling and implementation of the ocelli visual system of flying insects

Abstract: Two visual sensing modalities in insects, the ocelli and compound eyes, provide signals used for flight stabilization and navigation. In this article, a generalized model of the ocellar visual system is developed for a 3-D visual simulation environment based on behavioral, anatomical, and electrophysiological data from several species. A linear measurement model is estimated from Monte Carlo simulation in a cluttered urban environment relating state changes of the vehicle to the outputs of the ocellar model. A fully analog-printed circuit board sensor based on this model is designed and fabricated. Open-loop characterization of the sensor to visual stimuli induced by self motion is performed. Closed-loop stabilizing feedback of the sensor in combination with optic flow sensors is implemented onboard a quadrotor micro-air vehicle and its impulse response is characterized.

Bifurcation and oscillation in a time-delay neural mass model

Abstract: The neural mass model developed by Lopes da Silva et al. simulates complex dynamics between cortical areas and is able to describe a limit cycle behavior for alpha rhythms in electroencephalography (EEG). In this work, we propose a modified neural mass model that incorporates a time delay. This time-delay model can be used to simulate several different types of EEG activity including alpha wave, interictal EEG, and ictal EEG. We present a detailed description of the model's behavior with bifurcation diagrams. Through simulation and an analysis of the influence of the time delay on the model's oscillatory behavior, we demonstrate that a time delay in neuronal signal transmission could cause seizure-like activity in the brain. Further study of the bifurcations in this new neural mass model could provide a theoretical reference for the understanding of the neurodynamics in epileptic seizures.

Analysis of chaotic oscillations induced in two coupled Wilson---Cowan models

Abstract: Although it is known that two coupled Wilson---Cowan models with reciprocal connections induce aperiodic oscillations, little attention has been paid to the dynamical mechanism for such oscillations so far. In this study, we aim to elucidate the fundamental mechanism to induce the aperiodic oscillations in the coupled model. First, aperiodic oscillations observed are investigated for the case when the connections are unidirectional and when the input signal is a periodic oscillation. By the phase portrait analysis, we determine that the aperiodic oscillations are caused by periodically forced state transitions between a stable equilibrium and a stable limit cycle attractors around the saddle-node and saddle separatrix loop bifurcation points. It is revealed that the dynamical mechanism where the state crosses over the saddle-node and saddle separatrix loop bifurcations significantly contributes to the occurrence of chaotic oscillations forced by a periodic input. In addition, this mechanism can also give rise to chaotic oscillations in reciprocally connected Wilson---Cowan models. These results suggest that the dynamic attractor transition underlies chaotic behaviors in two coupled Wilson---Cowan oscillators.

Conditioning and time representation in long short-term memory networks

Abstract: Dopaminergic models based on the temporal-difference learning algorithm usually do not differentiate trace from delay conditioning. Instead, they use a fixed temporal representation of elapsed time since conditioned stimulus onset. Recently, a new model was proposed in which timing is learned within a long short-term memory (LSTM) artificial neural network representing the cerebral cortex (Rivest et al. in J Comput Neurosci 28(1):107---130, 2010). In this paper, that model's ability to reproduce and explain relevant data, as well as its ability to make interesting new predictions, are evaluated. The model reveals a strikingly different temporal representation between trace and delay conditioning since trace conditioning requires working memory to remember the past conditioned stimulus while delay conditioning does not. On the other hand, the model predicts no important difference in DA responses between those two conditions when trained on one conditioning paradigm and tested on the other. The model predicts that in trace conditioning, animal timing starts with the conditioned stimulus offset as opposed to its onset. In classical conditioning, it predicts that if the conditioned stimulus does not disappear after the reward, the animal may expect a second reward. Finally, the last simulation reveals that the buildup of activity of some units in the networks can adapt to new delays by adjusting their rate of integration. Most importantly, the paper shows that it is possible, with the proposed architecture, to acquire discharge patterns similar to those observed in dopaminergic neurons and in the cerebral cortex on those tasks simply by minimizing a predictive cost function.

A parsimonious oscillatory model of handwriting

Abstract: We propose an oscillatory model that is theoretically parsimonious, empirically efficient and biologically plausible. Building on Hollerbach's (Biol Cybern 39:139---156, 1981) model, our Parsimonious Oscillatory Model of Handwriting (POMH) overcomes the latter's main shortcomings by making it possible to extract its parameters from the trace itself and by reinstating symmetry between the $$x$$ x and $$y$$ y coordinates. The benefit is a capacity to autonomously generate a smooth continuous trace that reproduces the dynamics of the handwriting movements through an extremely sparse model, whose efficiency matches that of other, more computationally expensive optimizing methods. Moreover, the model applies to 2D trajectories, irrespective of their shape, size, orientation and length. It is also independent of the endeffectors mobilized and of the writing direction.

Neuroscience from a mathematical perspective: key concepts, scales and scaling hypothesis, universality

Abstract: This article analyzes the question of whether neuroscience allows for mathematical descriptions and whether an interaction between experimental and theoretical neuroscience can be expected to benefit both of them. It is argued that a mathematization of natural phenomena never happens by itself. First, appropriate key concepts must be found that are intimately connected with the phenomena one wishes to describe and explain mathematically. Second, the scale on, and not beyond, which a specific description can hold must be specified. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis. Third, can a mathematical description be universally valid and, if so, how? Here we put forth the argument that universals also exist in theoretical neuroscience, that evolution proves the rule, and that theoretical neuroscience is a domain with still lots of space for new developments initiated by an intensive interaction with experiment. Finally, major insight is provided by a careful analysis of the way in which particular brain structures respond to perceptual input and in so doing induce action in an animal's surroundings.

Structural aspects of biological cybernetics: Valentino Braitenberg, neuroanatomy, and brain function

Abstract: A. Aertsen Faculty of Biology and Bernstein Center Freiburg, University of Freiburg, 79104 Freiburg, Germany e-mail: aertsen@biologie.unifreiburg.de “When a new science emerges every couple of centuries, those who are privileged enough to witness it from its very beginnings to its full development during the span of their own lifetime can indeed count themselves lucky. My colleagues and I, who became fully fledged after World War II, had precisely this privilege. The science to which I refer still has no proper name, but its existence can be testified to by the matter-of-course way in which physicists, biologists, and logicians discuss issues that do not fall into any of the categories of physics, biology or logic. Their consensus is not so much interdisciplinary (which does not bring us much more than admiration from people who don’t know much about it) as decidedly neodisciplinary, i.e., based on a new language and terminology that convinces all sides and that is already so well established that it hardly needs to be discussed any further. Some call this new discipline informatics, others information science; it may sometimes be narrowed down to neuroinformatics or ’technical informatics.’ The term cybernetics, which does not meet with universal approval, has, nonetheless, a good chance of asserting itself in the long run. This is not least due to the fact that the term was coined by its most brilliant founder, the mathematician Norbert Wiener. His solid philosophical and philological background is reflected in the fitting name that he gave to this science. The designation cognitive science, which is currently popular, might well one day apply to everything that we still refer to as informatics and cybernetics. But then again, the plain (and rather sloppy) term computer science might come up trumps at the end of the day, as a tribute, if you like, to the fact that the whole thing did not get off the ground until large electronic data processors were invented. Yet one thing is for sure; this new area that has arisen between the humanities and natural sciences, while not professing to belong to either discipline, actually succeeds in

Statistics and geometry of orientation selectivity in primary visual cortex

Abstract: Orientation maps are a prominent feature of the primary visual cortex of higher mammals. In macaques and cats, for example, preferred orientations of neurons are organized in a specific pattern, where cells with similar selectivity are clustered in iso-orientation domains. However, the map is not always continuous, and there are pinwheel-like singularities around which all orientations are arranged in an orderly fashion. Although subject of intense investigation for half a century now, it is still not entirely clear how these maps emerge and what function they might serve. Here, we suggest a new model of orientation selectivity that combines the geometry and statistics of clustered thalamocortical afferents to explain the emergence of orientation maps. We show that the model can generate spatial patterns of orientation selectivity closely resembling the maps found in cats or monkeys. Without any additional assumptions, we further show that the pattern of ocular dominance columns is inherently connected to the spatial pattern of orientation.