Dynamical Field Theory Research Articles

Dynamic Neural Fields as Building Blocks of a Cortex-Inspired Architecture for Robotic Scene Representation

Based on the concepts of dynamic field theory (DFT), we present an architecture that autonomously generates scene representations by controlling gaze and attention, creating visual objects in the foreground, tracking objects, reading them into working memory, and taking into account their visibility. At the core of this architecture are three-dimensional dynamic neural fields (DNFs) that link feature to spatial information. These three-dimensional fields couple into lower dimensional fields, which provide the links to the sensory surface and to the motor systems. We discuss how DNFs can be used as building blocks for cognitive architectures, characterize the critical bifurcations in DNFs, as well as the possible coupling structures among DNFs. In a series of robotic experiments, we demonstrate how the DNF architecture provides the core functionalities of a scene representation.

Schrödinger-like Dilaton Gravity

We investigate possibilities for a Schr\"odinger-like gravity with the dynamical critical exponent $z=2$, where the action only contains the first-order time derivative. The Horava gravity always admits such a relevant deformation because the full $(d+1)$ dimensional diffeomorphism of the Einstein gravity is replaced by the foliation preserving diffeomorphism. The dynamics is locally trivial or topological in the pure gravity case, but we can construct a dynamical field theory with a $z=2$ dispersion relation by introducing a dilaton degree of freedom. Our model provides a classical starting point for the possible quantum dilaton gravity which may be applied to a membrane quantization.

Universality beyond power laws and the average avalanche shape

We report the measurement of multivariable scaling functions for the temporal average shape of Barkhausen noise avalanches, and show that they are consistent with the predictions of simple mean-field theories. We bypass the confounding factors of time-retarded interactions (eddy currents) by measuring thin permal- loy films, and bypass thresholding effects and amplifier distortions by applying Wiener deconvolution. We find experimental shapes that are approximately symmetric, and track the evolution of the scaling function. We solve a mean- field theory for the magnetization dynamics and calculate the form of the scaling function in the presence of a demagnetizing field and a finite field ramp-rate, yielding quantitative agreement with the experiment.

Critical dynamics of nonconservedN-vector models with anisotropic nonequilibrium perturbations

We study dynamic field theories for nonconserving N-vector models that are subject to spatial-anisotropic bias perturbations. We first investigate the conditions under which these field theories can have a single length scale. When N=2 or N≥4, it turns out that there are no such field theories and, hence, the corresponding models are pushed by the bias into the Ising class. We further construct nontrivial field theories for the N=3 case with certain bias perturbations and analyze the renormalization-group flow equations. We find that the three-component systems can exhibit rich critical behavior belonging to two different universality classes.

No clock to rule them all

This article introduces general concepts and definitions related to the notion of asynchronous computation in the framework of artificial neural networks. Using the dynamic field theory as an illustrative example, we explain why one may want to perform such asynchronous computation and how one can implement it since this computational scheme draws several consequences on both the trajectories and the stability of the whole system. After giving an unequivocal definition of asynchronous computation, we present a few practically usable methods and quantitative bounds that can guarantee most of the mesoscopic properties of the system.

A robotics-based approach to modelling choice reaching tasks

Event Abstract Back to Event A robotics-based approach to modelling choice reaching tasks Sören Strauss1* and Dietmar Heinke1 1 University of Birmingham, School of Psychology, United Kingdom The work presented here aims to develop a robotics-based model for choice reaching experiments (see [1]; for a review). In these experiments participants are asked to make rapid reach movements towards a target. Here we focus on modelling choice reaching experiments which gave some insight as to how visual attention operates by using an odd-colour search task, i.e. reaching for a green square among red squares and vice versa (e.g.[1]). In these studies Song and Nakayama showed that the attentional selection of the movement target operates in parallel with the execution of movements and that it is possible for the selection process to correct movements during their execution. Their conclusion is based on the finding that in a high number of trials movements were initially directed towards a distractor and only later were adjusted towards the target. These “curved” trajectories occurred particularly frequently when the target in the directly preceding trial had a different colour (priming effect). To mimic these visually-guided movements we embedded our current modelling approach to visual attention (e.g. [2]) in a closed-loop control of a robot arm (see [3] for examples of similar robotics-based research). The robot arm was built with LEGO Mindstorms NXT. The model input is provided by a camera filming the arm from a birds-eye view. Our modelling framework of visual attention assumes that target selection is implemented through parallel interactions between competitive and cooperative processes in the brain. In order to link this model with the control of the robot arm it was extended with the aid of the dynamic neural field theory (DNFT) by [4]. Like our attentional model DNFT also postulates that dynamic processes are crucial for understanding human behaviour. Furthermore DNFT assumes that movement parameters are topologically represented in the brain. In the resulting model the attentional stage determines the location of the odd-colour target and, parallel to this, the dynamic neural fields calculate the movement parameters. The resulting model is able to mimic the results of the odd-colour search task including the priming effect. Interestingly the model also generates human-like trajectories with a bell-shaped velocity profile as a direct consequence of the way the dynamic neural fields generate movement parameters. In the future we plan to extend our model to be able to simulate a broader range of choice reaching experiments, e.g. the Simon effect [5].

External potential dynamics simulation of the compatibility of T-shaped graft copolymer compatibilizing two immiscible homopolymers

AbstractThe compatibilizing effect of T-shaped graft copolymers between two incompatible homopolymers A and B was studied by using the external potential dynamics (EPD) method based on dynamic self-consistent field theory. We specifically focus on the role of the concentration and the junction position of the graft copolymer on the compatibility. The blend containing compatibilizers exhibits slow dynamics during the phase separation. We observed that the compatiblizers are particularly efficient when the graft point is close to the free end of the backbone chain.

Filling the Gap on Developmental Change: Tests of a Dynamic Field Theory of Spatial Cognition

In early childhood, there is a developmental transition in spatial memory biases. Before the transition, children's memory responses are biased toward the midline of a space, while after the transition responses are biased away from midline. The Dynamic Field Theory (DFT) posits that changes in neural interaction and changes in how children perceive frames of reference underlie the transition. Here, we tested a prediction of the DFT that children younger than the transitional age would show the more advanced developmental pattern when tested with a perceptually salient midline axis. Four age groups (3 years, 6 months; 3 years, 8 months; 4 years; and 5 years) were tested at targets near midline. As predicted, children's responses were biased away from midline.

An embodied account of serial order: How instabilities drive sequence generation

Learning and generating serially ordered sequences of actions is a core component of cognition both in organisms and in artificial cognitive systems. When these systems are embodied and situated in partially unknown environments, specific constraints arise for any neural mechanism of sequence generation. In particular, sequential action must resist fluctuating sensory information and be capable of generating sequences in which the individual actions may vary unpredictably in duration. We provide a solution to this problem within the framework of Dynamic Field Theory by proposing an architecture in which dynamic neural networks create stable states at each stage of a sequence. These neural attractors are destabilized in a cascade of bifurcations triggered by a neural representation of a condition of satisfaction for each action. We implement the architecture on a robotic vehicle in a color search task, demonstrating both sequence learning and sequence generation on the basis of low-level sensory information.

Drag forces on inclusions in classical fields with dissipative dynamics

We study the drag force on uniformly moving inclusions which interact linearly with dynamical free field theories commonly used to study soft condensed matter systems. Drag forces are shown to be nonlinear functions of the inclusion velocity and depend strongly on the field dynamics. The general results obtained can be used to explain drag forces in Ising systems and also predict the existence of drag forces on proteins in membranes due to couplings to various physical parameters of the membrane such as composition, phase and height fluctuations.

Biased feedback in spatial recall yields a violation of delta rule learning

This study investigates whether inductive processes influencing spatial memory performance generalize to supervised learning scenarios with differential feedback. After providing a location memory response in a spatial recall task, participants received visual feedback showing the target location. In critical blocks, feedback was systematically biased either 4 degrees toward the vertical axis (toward condition) or 4 degrees farther away from the vertical axis (away condition). Results showed that the weaker teaching signal (i.e., a smaller difference between the remembered location and the feedback location) produced a stronger experience-dependent change over blocks in the away condition than in the toward condition. This violates delta rule learning. Subsequent simulations of the dynamic field theory of spatial cognition provide a theoretically unified account of these results.

Fixed points and limit cycles in the population dynamics of lysogenic viruses and their hosts

Starting with stochastic rate equations for the fundamental interactions between microbes and their viruses, we derive a mean-field theory for the population dynamics of microbe-virus systems, including the effects of lysogeny. In the absence of lysogeny, our model is a generalization of that proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny, we analyze the possible states of the system, identifying a limit cycle, which we interpret physically. To test the robustness of our mean-field calculations to demographic fluctuations, we have compared our results with stochastic simulations using the Gillespie algorithm. Finally, we estimate the range of parameters that delineate the various steady states of our model.

The relationship between the perception of axes of symmetry and spatial memory during early childhood

Early in development, there is a transition in spatial working memory (SWM). When remembering a location in a homogeneous space (e.g., in a sandbox), young children are biased toward the midline symmetry axis of the space. Over development, a transition occurs that leads to older children being biased away from midline. The dynamic field theory (DFT) explains this transition in biases as being caused by a change in the precision of neural interaction in SWM and improvements in the perception of midline. According to the DFT, young children perceive midline, but there is a quantitative improvement in the perception of midline over development. In the experiment reported here, children and adults needed to determine on which half of a large monitor a target was located. In support of the DFT, even the youngest children performed above chance at most locations, but performance also improved gradually with age.

Concordances among electromagnetic, fluid dynamical, and gravitational field theories

We demonstrate mathematical concordances among the theories of electrodynamics, fluid dynamics, and gravitation when the latter two are extended by including a differential geometric structure that we call a vortex field. Experimental data and theoretical arguments for considering such vortex fields in these theories are discussed.

The role of experience in location estimation: Target distributions shift location memory biases

Research based on the Category Adjustment model concluded that the spatial distribution of target locations does not influence location estimation responses [Huttenlocher, J., Hedges, L., Corrigan, B., & Crawford, L. E. (2004). Spatial categories and the estimation of location. Cognition, 93, 75-97]. This conflicts with earlier results showing that location estimation is biased relative to the spatial distribution of targets [Spencer, J. P., & Hund, A. M. (2002). Prototypes and particulars: Geometric and experience-dependent spatial categories. Journal of Experimental Psychology: General, 131, 16-37]. Here, we resolve this controversy by using a task based on Huttenlocher et al. (Experiment 4) with minor modifications to enhance our ability to detect experience-dependent effects. Results after the first block of trials replicate the pattern reported in Huttenlocher et al. After additional experience, however, participants showed biases that significantly shifted according to the target distributions. These results are consistent with the Dynamic Field Theory, an alternative theory of spatial cognition that integrates long-term memory traces across trials relative to the perceived structure of the task space.

Scene Representation Based on Dynamic Field Theory: From Human to Machine

Event Abstract Back to Event Scene Representation Based on Dynamic Field Theory: From Human to Machine Stephan K. Zibner1*, Christian Faubel1, Ioannis Iossifidis1 and Gregor Schöner1 1 Ruhr-Universität Bochum, Institut für Neuroinformatik, Germany A typical human-robot cooperation task puts an autonomous robot in the role of an assistant for the human user. Fulfilling requests of the human user like “hand me the red screwdriver” demands an internal representation of the spatial layout of the scene as well as an understanding of labels and identifiers like “red”, associated with the spatial information. In addition, the representation of the scene must be updated according to ongoing changes in the outside world.Studies trying to comprehend the nature and extent of the internal representation of humans [1] hint that we keep a limited, non-pictorial representation of our perception in memory. Experimental studies on human visual working memory using a change detection paradigm [2] define space as being the key to bind multiple features of an object. Dynamic Field Theory, which is a theory of embodied cognition[4], provides the process models to explain such results. The models are based on Dynamic Neural Fields, which are a model of neural activity in the human cortex related to metric spaces.Applying the theory in the paradigm of autonomous robots provides a guideline for designing a neurally plausible robotic scene representation.We approach the problems of building up, maintaining, and updating a robotic scene representation with an architecture built from a set of Dynamic Neural Fields [5]. Core of this architecture are three-dimensional Dynamic Neural Fields, which, inspired by [2], dynamically associate two-dimensional object locations in an allocentric reference frame with extracted low-dimensional object features like color. The unit of information representing an association in these fields is localized supra-threshold activity, called a peak, that both gives a detection decision on input and an estimate of continuous parameters like space or color hue represented by the field’s dimensions. Through the architectural connections, the three-dimensional fields are sequentially filled up with associative peaks as soon as the robot perceives a scene. Using the stability characteristics of fields and a steady coupling to current camera input, changes in object positions are tracked even for multiple moving objects, objects are memorized when they get out of view, and associations are removed automatically once an object is removed from the scene.The resulting application is tested on the robotic platform CoRA (Cooperative Robotic Assistant).The resulting peaks of an autonomous scanning sequence can be successfully held in the three-dimensional associative Dynamic Neural Field, even when objects get out of view. Here, the application shows a capacity limit of four to five objects that can be kept concurrently in the scene representation. If multiple objects are moved within the robot’s field of view, a smaller amount of objects can be tracked simultaneously. The capacity limit is reduced to three objects for multiobject tracking, bearing in mind that not only the spatial position of the objects is updated correctly, but the stored feature associations are carried along as well. The decrease of capacity between static and moving objects is also observable in the human counterpart [3].

Neural dynamics of sequence generation: concepts and robotic demonstrations. A Dynamic Field Theory approach.

Event Abstract Back to Event Neural dynamics of sequence generation: concepts and robotic demonstrations. A Dynamic Field Theory approach. Yulia Sandamirskaya1* and Gregor Schoner1 1 Ruhr-Universität Bochum, Institut für Neuroninformatik, Germany Serial order is central to behavior of both human and artificial agents. The neural mechanisms for storing, processing and producing sequences of neural states are widely discussed in the literature [1,2]. Although multiple models fit the behavioral data on serial order (error patterns, reaction times, storage capacity), issues of embodiment have not been seriously examined. When a sequence of neural events is coupled to the actuators of a real-world agent, whose behavior is controlled by unreliable sensor information and is executed in a partially unknown and time variable environment, additional constraints on sequence generation arise, which are not addressed by most contemporary models for serial order: (1) Flexible timing: The duration of each action may vary in unpredictable ways on the time scale of behavior, which is much longer than that of the underlying neuronal processes. (2) Stability: Actions must be generated autonomously based on graded, time-varying sensory information. Recently we introduced a Dynamic Fields Theory (DFT) model for sequence learning and production, which addresses these issues [3]. Here, actions are represented as stable states of the dynamics of a collection of neural fields. This enables stability and gradedness of action representations and thus makes it possible to use graded low-level sensory information to guide cognitive behavior. The sequential transitions between the stable states are controlled by a neural representation of a condition of satisfaction that signals successful accomplishment of an action. This first model required all actions to be embedded in a uniform dimension represented by the neuronal fields. Here, we revise and extend this model, to accommodate increased flexibility and, in particular, to enable sequences that contain different categories of actions and perceptual representations. The dynamical representation of serial order is projected onto a distributed multimodal neural representation of actions and perceptual states. The agent acquires a sequence of actions perceived with low-level sensors, and then acts out that sequence in new, unknown environments. The concept of a condition of satisfaction, represented in a dynamic neural field that reflects the convergence of expected and real sensory information, is central to controlling the switch of attractor states that occurs at every step of a sequence. The model is implemented on an autonomous robot and its functionality - flexible timing and coupling to real behavior - is demonstrated in a simple robotic scenario. Although the model does not address statistics of experimental data on sequential behavior, it demonstrates neuronal principles of sequential action and their functional implications. In particular, the model shows how the problems of stability and flexible timing of sequence generation can be solved.

Discretization of nonlinear evolution equations over associative function algebras

A general approach is proposed for discretizing nonlinear dynamical systems and field theories on suitable functional spaces, defined over a regular lattice of points, in such a way that both their symmetry and integrability properties are preserved. A class of discrete KdV equations is introduced. Also, new hierarchies of discrete evolution equations of Gelfand–Dickey type are defined.

Renormalized field theory of collapsing directed randomly branched polymers

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with epsilon expansion that this transition belongs to the same universality class as directed percolation.

CPviolation in low-energy photon-photon interactions

CP-violation in the loop-mediated photon-photon interactions would modify the birefringence of the quantum vacuum. We discuss the implications of this effect on the PVLAS-Phase II experiment, in which a time-dependent magnetic field is modulated. We show that the violation of CP would imply the existence of characteristic Fourier components, in the intensity spectrum of the outgoing wave. In order to estimate the magnitude of this effect within the Standard Model, we use chiral perturbation theory to compute the theta-term contribution to the coefficient of the leading CP-odd vertex, in the low-energy effective field theory for photon dynamics.