Finding numbers in the brain

How auditory neurons count temporal intervals and decode information

The numerical sense of animals includes identifying the numerosity of a sequence of events that occur with specific intervals, e.g., notes in a call or bar of music. Across nervous systems, the temporal patterning of spikes can code these events, but how this information is decoded (counted) remains elusive. In the anuran auditory system, temporal information of this type is decoded in the midbrain, where "interval-counting" neurons spike only after at least a threshold number of sound pulses have occurred with specific timing. We show that this decoding process, i.e., interval counting, arises from integrating phasic, onset-type and offset inhibition with excitation that augments across successive intervals, possibly due to a progressive decrease in "shunting" effects of inhibition. Because these physiological properties are ubiquitous within and across central nervous systems, interval counting may be a general mechanism for decoding diverse information coded/encoded in temporal patterns of spikes, including "bursts," and estimating elapsed time.

Formalising the role of behaviour in neuroscience

We develop a mathematical approach to formally proving that certain neural computations and representations exist based on patterns observed in an organism's behaviour. To illustrate, we provide a simple set of conditions under which an ant's ability to determine how far it is from its nest would logically imply neural structures isomorphic to the natural numbersℕ $$ \mathrm{\mathbb{N}} $$ . We generalise these results to arbitrary behaviours and representations and show what mathematical characterisation of neural computation and representation is simplest while being maximally predictive of behaviour. We develop this framework in detail using a path integration example, where an organism's ability to search for its nest in the correct location implies representational structures isomorphic to two-dimensional coordinates under addition. We also study a system for processinga n b n $$ {a}^n{b}^n $$ strings common in comparative work. Our approach provides an objective way to determine what theory of a physical system is best, addressing a fundamental challenge in neuroscientific inference. These results motivate considering which neurobiological structures have the requisite formal structure and are otherwise physically plausible given relevant physical considerations such as generalisability, information density, thermodynamic stability and energetic cost.

Bringing Bayes and Shannon to the Study of Behavioural and Neurobiological Timing and Associative Learning

Bayesian parameter estimation and Shannon’s theory of information provide tools for analysing and understanding data from behavioural and neurobiological experiments on interval timing—and from experiments on Pavlovian and operant conditioning, because timing plays a fundamental role in associative learning. In this tutorial, we explain basic concepts behind these tools and show how to apply them to estimating, on a trial-by-trial, reinforcement-by-reinforcement and response-by-response basis, important parameters of timing behaviour and of the neurobiological manifestations of timing in the brain. These tools enable quantification of relevant variables in the trade-off between acting as an ideal observer should act and acting as an ideal agent should act, which is also known as the trade-off between exploration (information gathering) and exploitation (information utilization) in reinforcement learning. They enable comparing the strength of the evidence for a measurable association to the strength of the behavioural evidence that the association has been perceived. A GitHub site and an OSF site give public access to well-documented Matlab and Python code and to raw data to which these tools have been applied.

Cognitive Function Trajectories and Factors among Chinese Older Adults with Subjective Memory Decline: CHARLS Longitudinal Study Results (2011-2018)

Older adults with subjective cognitive decline are at increased risk of future pathological cognitive decline and dementia. Subjective memory decline is an early sign of cognitive decline; preventing or slowing cognitive decline in at-risk populations remains an elusive issue. This study aimed to examine the cognitive trajectories and factors in older adults with subjective memory decline. Latent growth curve models (LGCMs) were fitted to examine the cognitive function trajectories and factors among 1465 older adults (aged 60+ years) with subjective memory decline. Data were obtained from four waves from the China Health and Retirement Longitudinal Study (CHARLS, 2011-2018), which is a large nationally representative sample of the Chinese population. The results showed that older adults with better initial cognition had a slower decline rate, which may be accelerated by advanced age, low-level education, a rapid decrease in instrumental activities of daily living (IADL) ability, and rapid increase in depression levels. This study was the first to examine the trajectories of cognitive function and its factors in a high-risk population with subjective memory decline. These findings may guide prevention approaches to tackle the issues of cognitive function decline and dementia.

An RNA-Based Theory of Natural Universal Computation

Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of universal computation, i.e., Turing-equivalent in scope. Generic finite-dimensional dynamical systems (which encompass most models of neural networks, intracellular signaling cascades, and gene regulatory networks) fall short of universal computation, but are assumed to be capable of explaining cognition and development. I present a class of models that bridge two concepts from distant fields: combinatory logic (or, equivalently, lambda calculus) and RNA molecular biology. A set of basic RNA editing rules can make it possible to compute any computable function with identical algorithmic complexity to that of Turing machines. The models do not assume extraordinarily complex molecular machinery or any processes that radically differ from what we already know to occur in cells. Distinct independent enzymes can mediate each of the rules and RNA molecules solve the problem of parenthesis matching through their secondary structure. In the most plausible of these models all of the editing rules can be implemented with merely cleavage and ligation operations at fixed positions relative to predefined motifs. This demonstrates that universal computation is well within the reach of molecular biology. It is therefore reasonable to assume that life has evolved - or possibly began with - a universal computer that yet remains to be discovered. The variety of seemingly unrelated computational problems across many scales can potentially be solved using the same RNA-based computation system. Experimental validation of this theory may immensely impact our understanding of memory, cognition, development, disease, evolution, and the early stages of life.

The learning of prospective and retrospective cognitive maps within neural circuits

Brain circuits are thought to form a "cognitive map" to process and store statistical relationships in the environment. A cognitive map is commonly defined as a mental representation that describes environmental states (i.e., variables or events) and the relationship between these states. This process is commonly conceptualized as a prospective process, as it is based on the relationships between states in chronological order (e.g., does reward follow a given state?). In this perspective, we expand this concept on the basis of recent findings to postulate that in addition to a prospective map, the brain forms and uses a retrospective cognitive map (e.g., does a given state precede reward?). In doing so, we demonstrate that many neural signals and behaviors (e.g., habits) that seem inflexible and non-cognitive can result from retrospective cognitive maps. Together, we present a significant conceptual reframing of the neurobiological study of associative learning, memory, and decision making.

Rats delay gratification during a time-based diminishing returns task

The rat is a common animal model used to uncover the neural underpinnings of decision making and their disruption in psychiatric illness. Here, we ask if rats can perform a decision-making task that assesses self-control by delayed gratification in the context of diminishing returns. In this task, rats could choose to press one of two levers. One lever was associated with a fixed delay (FD) schedule that delivered reward after a fixed time delay (10 s). The other lever was associated with a progressive delay (PD) schedule; the delay increased by a fixed amount of time (1 s) after each PD lever press. Rats were tested under two conditions: a reset condition where rats could reset the PD schedule back to its initial 0-s delay by pressing the FD lever and a no-reset condition in which resetting the PD schedule was unavailable. We found that rats adapted behavior within reset sessions by delaying gratification to obtain more reward in the long run. That is, they selected the FD lever with the longer delay to reset the PD delay back to zero prior to the equality point, thus achieving more reward over the course of the session. These results are consistent with other species, demonstrating that rats can also maximize the net rate of reward by selecting an option that is not immediately beneficial. Moreover, use of this task in rodents might provide insights into how the brain governs normal and abnormal behavior, as well as treatments that can improve self-control. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

A unified account of numerosity perception

People can identify the number of objects in sets of four or fewer items with near-perfect accuracy but exhibit linearly increasing error for larger sets. Some researchers have taken this discontinuity as evidence of two distinct representational systems. Here, we present a mathematical derivation showing that this behaviour is an optimal representation of cardinalities under a limited informational capacity, indicating that this behaviour can emerge from a single system. Our derivation predicts how the amount of information accessible to viewers should influence the perception of quantity for both large and small sets. In a series of four preregistered experiments (N = 100 each), we varied the amount of information accessible to participants in number estimation. We find tight alignment between the model and human performance for both small and large quantities, implicating efficient representation as the common origin behind key phenomena of human and animal numerical cognition.

Locating the engram: Should we look for plastic synapses or information-storing molecules?

Karl Lashley began the search for the engram nearly seventy years ago. In the time since, much has been learned but divisions remain. In the contemporary neurobiology of learning and memory, two profoundly different conceptions contend: the associative/connectionist (A/C) conception and the computational/representational (C/R) conception. Both theories ground themselves in the belief that the mind is emergent from the properties and processes of a material brain. Where these theories differ is in their description of what the neurobiological substrate of memory is and where it resides in the brain. The A/C theory of memory emphasizes the need to distinguish memory cognition from the memory engram and postulates that memory cognition is an emergent property of patterned neural activity routed through engram circuits. In this model, learning re-organizes synapse association strengths to guide future neural activity. Importantly, the version of the A/C theory advocated for here contends that synaptic change is not symbolic and, despite normally being necessary, is not sufficient for memory cognition. Instead, synaptic change provides the capacity and a blueprint for reinstating symbolic patterns of neural activity. Unlike the A/C theory, which posits that memory emerges at the circuit level, the C/R conception suggests that memory manifests at the level of intracellular molecular structures. In C/R theory, these intracellular structures are information-conveying and have properties compatible with the view that brain computation utilizes a read/write memory, functionally similar to that in a computer. New research has energized both sides and highlighted the need for new discussion. Both theories, the key questions each theory has yet to resolve and several potential paths forward are presented here.

Our understanding of neural codes rests on Shannon's foundations

Shannon's theory lays the foundation for understanding the flow of information from world into brain: There must be a set of possible messages. Brain structure determines what they are. Many messages convey quantitative facts (distances, directions, durations, etc.). It is impossible to consider how neural tissue processes these numbers without first considering how it encodes them.

The problem with percentages

A great many students at a major research university make basic conceptual mistakes in responding to simple questions about two successive percentage changes. The mistakes they make follow a pattern already familiar from research on the difficulties that elementary school students have in coming to terms with fractions and decimals. The intuitive core knowledge of arithmetic with the natural numbers makes learning to count and do simple arithmetic relatively easy. Those same principles become obstacles to understanding how to operate with rational numbers.This article is part of a discussion meeting issue 'The origins of numerical abilities'.