A Bayesian perspective on the ring attractor for heading-direction tracking in the Drosophila central complex

Efficient navigation requires animals to track their position, velocity and heading direction (HD). Bayesian inference provides a principled framework for estimating these quantities from unreliable sensory observations, yet little is known about how and where Bayesian algorithms could be implemented in the brain's neural networks. Here, we propose a class of recurrent neural networks that track both a dynamic HD estimate and its associated uncertainty. They do so according to a circular Kalman filter, a statistically optimal algorithm for circular estimation. Our network generalizes standard ring attractor models by encoding uncertainty in the amplitude of a bump of neural activity. More generally, we show that near-Bayesian integration is inherent in ring attractor networks, as long as their connectivity strength allows them to sufficiently deviate from the attractor state. Furthermore, we identified the basic network motifs that are required to implement Bayesian inference, and show that these motifs are present in the Drosophila HD system connectome. Overall, our work demonstrates that the Drosophila HD system can in principle implement a dynamic Bayesian inference algorithm in a biologically plausible manner, consistent with recent findings that suggest ring-attractor dynamics underlie the Drosophila HD system.

Synthesis of Scalable Single Length Cycle, Single Attractor Cellular Automata in Linear Time

This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.

A Dynamic Field Theory of visual working memory

The main objective of this chapter is to introduce concepts of dynamic field theory (DFT), a continuous attractor neural network, and its implementation of visual working memory (VWM). In DFT, WM is an attractor state where representations are self-sustained through strong interactions between self-excitation and lateral inhibition. We discuss a VWM model with fields represented by stabilised attractor states. Using this model, we demonstrate how encoding, consolidation, maintenance and comparison occurs in correct and incorrect, same and different trials in a change detection task. Further, the model captures accuracy and capacity limitations when VWM load is manipulated. Critically, we review work from our research group by demonstrating how the model captures behavioural performance and makes hemodynamic predictions in early childhood, young adulthood and older adulthood. Using the model, we posit that developmental changes in VWM processing occur as a result of the modulation of strength and width of excitation and inhibition. Finally, we describe how the DFT account compares with current views on a domain-general account and distributed nature of WM processing.

Minimal intervening control of biomolecular networks leading to a desired cellular state

A cell phenotype can be represented by an attractor state of the underlying molecular regulatory network, to which other network states eventually converge. Here, the set of states converging to each attractor is called its basin of attraction. A central question is how to drive a particular cell state toward a desired attractor with minimal interventions on the network system. We develop a general control framework of complex Boolean networks to provide an answer to this question by identifying control targets on which one-time temporary perturbation can induce a state transition to the boundary of a desired attractor basin. Examples are shown to illustrate the proposed control framework which is also applicable to other types of complex Boolean networks.

The grammaticalization of object pronouns: Why differential object indexing is an attractor state

While the grammaticalization of person agreement is a widely-cited and apparently uncontroversial topos of grammaticalization theory, the striking differences in the outcome of subject pronoun, and object pronoun grammaticalization, remain unexplained, and the relevant literature continues to assume a unified grammaticalization pathway. This paper argues that the grammaticalization of object pronouns is fundamentally different to that of subject pronouns. More specifically, although object pronouns may be rapid early grammaticalizers, often losing prosodic independence and cliticizing to a verbal head, they do not advance further to reach the stage of obligatory agreement markers typical of subject agreement. Typically, object markers remain at the stage of Differential Object Indexing, where their realization is conditioned by a bundle of semantic and pragmatic factors exhibiting close parallels to those operative in Differential Object Marking. Evidence from language typology, and from the diachrony of person markers across two millennia of Iranian languages, is adduced to back up these claims. Thus the widely-assumed grammaticalization cline for the grammaticalization of agreement needs to be reconsidered; for object agreement, there is evidently an attractor state, that of Differential Object Indexing, beyond which object agreement seldom proceeds. Finally, explanations grounded in discourse data are proposed, which also account for why obligatory object agreement in the category of person is so rare, while gender and number agreement for objects is far less constrained.

Modeling the Social Dynamics of Moral Enhancement

How individuals tend to evaluate the combination of their own and other’s payoffs—social value orientations—is likely to be a potential target of future moral enhancers. However, the stability of cooperation in human societies has been buttressed by evolved mildly prosocial orientations. If they could be changed, would this destabilize the cooperative structure of society? We simulate a model of moral enhancement in which agents play games with each other and can enhance their orientations based on maximizing personal satisfaction. We find that given the assumption that very low payoffs lead agents to be removed from the population, there is a broadly stable prosocial attractor state. However, the balance between prosociality and individual payoff-maximization is affected by different factors. Agents maximizing their own satisfaction can produce emergent shifts in society that reduce everybody’s satisfaction. Moral enhancement considerations should take the issues of social emergence into account.

A Cache System Design for CMPs with Built-In Coherence Verification

This work reports an effective design of cache system for Chip Multiprocessors (CMPs). It introduces built-in logic for verification of cache coherence in CMPs realizing directory based protocol. It is developed around the cellular automata (CA) machine, invented by John von Neumann in the 1950s. A special class of CA referred to as single length cycle 2-attractor cellular automata (TACA) has been planted to detect the inconsistencies in cache line states of processors’ private caches. The TACA module captures coherence status of the CMPs’ cache system and memorizes any inconsistent recording of the cache line states during the processors’ reference to a memory block. Theory has been developed to empower a TACA to analyse the cache state updates and then to settle to an attractor state indicating quick decision on a faulty recording of cache line status. The introduction of segmentation of the CMPs’ processor pool ensures a better efficiency, in determining the inconsistencies, by reducing the number of computation steps in the verification logic. The hardware requirement for the verification logic points to the fact that the overhead of proposed coherence verification module is much lesser than that of the conventional verification units and is insignificant with respect to the cost involved in CMPs’ cache system.

An Examination of the True Reliability of Lower Limb Stiffness Measures During Overground Hopping

Evidence suggests reports describing the reliability of leg-spring (kleg) and joint stiffness (kjoint) measures are contaminated by artifacts originating from digital filtering procedures. In addition, the intraday reliability of kleg and kjoint requires investigation. This study examined the effects of experimental procedures on the inter- and intraday reliability of kleg and kjoint. Thirty-two participants completed 2 trials of single-legged hopping at 1.5, 2.2, and 3.0 Hz at the same time of day across 3 days. On the final test day a fourth experimental bout took place 6 hours before or after participants’ typical testing time. Kinematic and kinetic data were collected throughout. Stiffness was calculated using models of kleg and kjoint. Classifications of measurement agreement were established using thresholds for absolute and relative reliability statistics. Results illustrated that kleg and kankle exhibited strong agreement. In contrast, kknee and khip demonstrated weak-to-moderate consistency. Results suggest limits in kjoint reliability persist despite employment of appropriate filtering procedures. Furthermore, diurnal fluctuations in lower-limb muscle-tendon stiffness exhibit little effect on intraday reliability. The present findings support the existence of kleg as an attractor state during hopping, achieved through fluctuations in kjoint variables. Limits to kjoint reliability appear to represent biological function rather than measurement artifact.