Representations of visual proportions in the primate posterior parietal and prefrontal cortices

Sequential neuronal processing of number values, abstract decision, and action in the primate prefrontal cortex

Decision-making requires processing of sensory information, comparing the gathered evidence to make a judgment, and performing the action to communicate it. How neuronal representations transform during this cascade of representations remains a matter of debate. Here, we studied the succession of neuronal representations in the primate prefrontal cortex (PFC). We trained monkeys to judge whether a pair of sequentially presented displays had the same number of items. We used a combination of single neuron and population-level analyses and discovered a sequential transformation of represented information with trial progression. While numerical values were initially represented with high precision and in conjunction with detailed information such as order, the decision was encoded in a low-dimensional subspace of neural activity. This decision encoding was invariant to both retrospective numerical values and prospective motor plans, representing only the binary judgment of "same number" versus "different number," thus facilitating the generalization of decisions to novel number pairs. We conclude that this transformation of neuronal codes within the prefrontal cortex supports cognitive flexibility and generalizability of decisions to new conditions.

Comparison of visual quantities in untrained neural networks

The ability to compare quantities of visual objects with two distinct measures, proportion and difference, is observed even in newborn animals. However, how this function originates in the brain, even before visual experience, remains unknown. Here, we propose a model in which neuronal tuning for quantity comparisons can arise spontaneously in completely untrained neural circuits. Using a biologically inspired model neural network, we find that single units selective to proportions and differences between visual quantities emerge in randomly initialized feedforward wirings and that they enable the network to perform quantity comparison tasks. Notably, we find that two distinct tunings to proportion and difference originate from a random summation of monotonic, nonlinear neural activities and that a slight difference in the nonlinear response function determines the type of measure. Our results suggest that visual quantity comparisons are primitive types of functions that can emerge spontaneously before learning in young brains.

Near-optimal integration of the magnitude information of time and numerosity

Magnitude information is often correlated in the external world, providing complementary information about the environment. As if to reflect this relationship, the perceptions of different magnitudes (e.g. time and numerosity) are known to influence one another. Recent studies suggest that such magnitude interaction is similar to cue integration, such as multisensory integration. Here, we tested whether human observers could integrate the magnitudes of two quantities with distinct physical units (i.e. time and numerosity) as abstract magnitude information. The participants compared the magnitudes of two visual stimuli based on time, numerosity, or both. Consistent with the predictions of the maximum-likelihood estimation model, the participants integrated time and numerosity in a near-optimal manner; the weight of each dimension was proportional to their relative reliability, and the integrated estimate was more reliable than either the time or numerosity estimate. Furthermore, the integration approached a statistical optimum as the temporal discrepancy of the acquisition of each piece of information became smaller. These results suggest that magnitude interaction arises through a similar computational mechanism to cue integration. They are also consistent with the idea that different magnitudes are processed by a generalized magnitude system.

Shared Neural Activity But Distinct Neural Dynamics for Cognitive Control in Monkey Prefrontal and Parietal Cortex

To better understand how prefrontal networks mediate forms of cognitive control disrupted in schizophrenia, we translated a variant of the AX continuous performance task that measures specific deficits in the human disease to 2 male monkeys and recorded neurons in PFC and parietal cortex during task performance. In the task, contextual information instructed by cue stimuli determines the response required to a subsequent probe stimulus. We found parietal neurons encoding the behavioral context instructed by cues that exhibited nearly identical activity to their prefrontal counterparts (Blackman et al., 2016). This neural population switched their preference for stimuli over the course of the trial depending on whether the stimuli signaled the need to engage cognitive control to override a prepotent response. Cues evoked visual responses that appeared in parietal neurons first, whereas population activity encoding contextual information instructed by cues was stronger and more persistent in PFC. Increasing cognitive control demand biased the representation of contextual information toward the PFC and augmented the temporal correlation of task-defined information encoded by neurons in the two areas. Oscillatory dynamics in local field potentials differed between cortical areas and carried as much information about task conditions as spike rates. We found that, at the single-neuron level, patterns of activity evoked by the task were nearly identical between the two cortical areas. Nonetheless, distinct population dynamics in PFC and parietal cortex were evident. suggesting differential contributions to cognitive control.SIGNIFICANCE STATEMENT We recorded neural activity in PFC and parietal cortex of monkeys performing a task that measures cognitive control deficits in schizophrenia. This allowed us to characterize computations performed by neurons in the two areas to support forms of cognitive control disrupted in the disease. Subpopulations of neurons in the two areas exhibited parallel modulations in firing rate; and as a result, all patterns of task-evoked activity were distributed between PFC and parietal cortex. This included the presence in both cortical areas of neurons reflecting proactive and reactive cognitive control dissociated from stimuli or responses in the task. However, differences in the timing, strength, synchrony, and correlation of information encoded by neural activity were evident, indicating differential contributions to cognitive control.

The developmental relationship between nonsymbolic and symbolic fraction abilities

A fundamental research question in quantitative cognition concerns the developmental relationship between nonsymbolic and symbolic quantitative abilities. This study examined this developmental relationship in abilities to process nonsymbolic and symbolic fractions. There were 99 6th graders (M_age = 11.86 years), 101 10th graders (M_age = 15.71 years), and 102 undergraduate and graduate students (M_age = 21.97 years) participating in this study, and their nonsymbolic and symbolic fraction abilities were measured with nonsymbolic and symbolic fraction comparison tasks, respectively. Nonsymbolic and symbolic fraction abilities were significantly correlated in all age groups even after controlling for the ability to process nonsymbolic absolute quantity and general cognitive abilities, including working memory and inhibitory control. Moreover, the strength of nonsymbolic-symbolic correlations was higher in 6th graders than in 10th graders and adults. These findings suggest a weakened association between nonsymbolic and symbolic fraction abilities during development, and this developmental pattern may be related with participants' increasing proficiency in symbolic fractions.

Symbolic fractions elicit an analog magnitude representation in school-age children

A fundamental question about fractions is whether they are grounded in an abstract nonsymbolic magnitude code similar to that postulated for whole numbers. Mounting evidence suggests that symbolic fractions could be grounded in mechanisms for perceiving nonsymbolic ratio magnitudes. However, systematic examination of such mechanisms in children has been lacking. We asked second- and fifth-grade children (prior to and after formal instructions with fractions, respectively) to compare pairs of symbolic fractions, nonsymbolic ratios, and mixed symbolic-nonsymbolic pairs. This paradigm allowed us to test three key questions: (a) whether children show an analog magnitude code for rational numbers, (b) whether that code is compatible with mental representations of symbolic fractions, and (c) how formal education with fractions affects the symbolic-nonsymbolic relation. We examined distance effects as a marker of analog ratio magnitude processing and notation effects as a marker of converting across numerical codes. Second and fifth graders' reaction times and error rates showed classic distance and notation effects. Nonsymbolic ratios were processed most efficiently, with mixed and symbolic notations being relatively slower. Children with more formal instruction in symbolic fractions had a significant advantage in comparing symbolic fractions but had a smaller advantage for nonsymbolic ratio stimuli. Supplemental analyses showed that second graders relied on numerator distance more than holistic distance and that fifth graders relied on holistic fraction magnitude distance more than numerator distance. These results suggest that children have a nonsymbolic ratio magnitude code and that symbolic fractions can be translated into that magnitude code.

Natural Alternatives to Natural Number: The Case of Ratio

The overwhelming majority of efforts to cultivate early mathematical thinking rely primarily on counting and associated natural number concepts. Unfortunately, natural numbers and discretized thinking do not align well with a large swath of the mathematical concepts we wish for children to learn. This misalignment presents an important impediment to teaching and learning. We suggest that one way to circumvent these pitfalls is to leverage students' non-numerical experiences that can provide intuitive access to foundational mathematical concepts. Specifically, we advocate for explicitly leveraging a) students' perceptually based intuitions about quantity and b) students' reasoning about change and variation, and we address the affordances offered by this approach. We argue that it can support ways of thinking that may at times align better with to-be-learned mathematical ideas, and thus may serve as a productive alternative for particular mathematical concepts when compared to number. We illustrate this argument using the domain of ratio, and we do so from the distinct disciplinary lenses we employ respectively as a cognitive psychologist and as a mathematics education researcher. Finally, we discuss the potential for productive synthesis given the substantial differences in our preferred methods and general epistemologies.

Spatially Tuned Neurons in Corvid Nidopallium Caudolaterale Signal Target Position During Visual Search

The avian pallial endbrain area nidopallium caudolaterale (NCL) shows important similarities to mammalian prefrontal cortex in connectivity, dopamine neurochemistry, and function. Neuronal processing in NCL has been studied with respect to sensory, cognitive, and reward information, but little is known about its role in more direct control of motor behavior. We investigated NCL activity during the choice period of a delayed match-to-sample task, as 2 trained crows searched and selected a previously remembered visual target among an array of 4 pictures. The crows exhibited behavioral response patterns consistent with serial visual search. Many single NCL neurons were spatially tuned to specific target positions during visual search and directed motor behavior. Moreover, single NCL neurons dynamically changed their tuning properties to represent different behaviorally relevant task variables across the trial. In consecutive task periods, single neurons responded to visual stimuli, stored stimulus information in working memory, guided goal-directed behavior depending on the remembered target picture, and encoded trial outcomes. This flexible encoding of all task-relevant aspects in the executive control of goal-directed behavior represents a striking convergence to neuronal encoding in primate prefrontal cortex. These data highlight key properties of associative endbrain areas underlying flexible cognitive behavior in corvids and primates.

Numerical Proportion Representation: A Neurocomputational Account

Proportion representation is an emerging subdomain in numerical cognition. However, its nature and its correlation with simple number representation remain elusive, especially at the theoretical level. To fill this gap, we propose a gain-field model of proportion representation to shed light on the neural and computational basis of proportion representation. The model is based on two well-supported neuroscientific findings. The first, gain modulation, is a general mechanism for information integration in the brain; the second relevant finding is how simple quantity is neurally represented. Based on these principles, the model accounts for recent relevant proportion representation data at both behavioral and neural levels. The model further addresses two key computational problems for the cognitive processing of proportions: invariance and generalization. Finally, the model provides pointers for future empirical testing.

Spontaneous, modality-general abstraction of a ratio scale

The existence of a generalized magnitude system in the human mind and brain has been studied extensively but remains elusive because it has not been clearly defined. Here we show that one possibility is the representation of relative magnitudes via ratio calculations: ratios are a naturally dimensionless or abstract quantity that could qualify as a common currency for magnitudes measured on vastly different psychophysical scales and in different sensory modalities like size, number, duration, and loudness. In a series of demonstrations based on comparisons of item sequences, we demonstrate that subjects spontaneously use knowledge of inter-item ratios within and across sensory modalities and across magnitude domains to rate sequences as more or less similar on a sliding scale. Moreover, they rate ratio-preserved sequences as more similar to each other than sequences in which only ordinal relations are preserved, indicating that subjects are aware of differences in levels of relative-magnitude information preservation. The ubiquity of this ability across many different magnitude pairs, even those sharing no sensory information, suggests a highly general code that could qualify as a candidate for a generalized magnitude representation.

From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition

In this review, we are pitting two theories against each other: the more accepted theory, the number sense theory, suggesting that a sense of number is innate and non-symbolic numerosity is being processed independently of continuous magnitudes (e.g., size, area, and density); and the newly emerging theory suggesting that (1) both numerosities and continuous magnitudes are processed holistically when comparing numerosities and (2) a sense of number might not be innate. In the first part of this review, we discuss the number sense theory. Against this background, we demonstrate how the natural correlation between numerosities and continuous magnitudes makes it nearly impossible to study non-symbolic numerosity processing in isolation from continuous magnitudes, and therefore, the results of behavioral and imaging studies with infants, adults, and animals can be explained, at least in part, by relying on continuous magnitudes. In the second part, we explain the sense of magnitude theory and review studies that directly demonstrate that continuous magnitudes are more automatic and basic than numerosities. Finally, we present outstanding questions. Our conclusion is that there is not enough convincing evidence to support the number sense theory anymore. Therefore, we encourage researchers not to assume that number sense is simply innate, but to put this hypothesis to the test and consider whether such an assumption is even testable in the light of the correlation of numerosity and continuous magnitudes.

Ratio abstraction over discrete magnitudes by newly hatched domestic chicks (Gallus gallus)

A large body of literature shows that non-human animals master a variety of numerical tasks, but studies involving proportional discrimination are sparse and primarily done with mature animals. Here we trained 4-day-old domestic chicks (Gallus gallus) to respond to stimuli depicting multiple examples of the proportion 4:1 when compared with the proportion 2:1. Stimuli were composed of green and red dot arrays; for the rewarded 4:1 proportion, 4 green dots for every red dot (e.g. ratios: 32:8, 12:3, and 44:11). The birds continued to discriminate when presented with new ratios at test (such as 20:5), characterized by new numbers of dots and new spatial configurations (Experiment 1). This indicates that chicks can extract the common proportional value shared by different ratios and apply it to new ones. In Experiment 2, chicks identified a specific proportion (2:1) from either a smaller (4:1) or a larger one (1:1), demonstrating an ability to represent the specific, and not relative, value of a particular proportion. Again, at test, chicks selectively responded to the previously reinforced proportion from new ratios. These findings provide strong evidence for very young animals’ ability to extract, identify, and productively use proportion information across a range of different amounts.

Pain and Laboratory Animals: Publication Practices for Better Data Reproducibility and Better Animal Welfare

Scientists who perform major survival surgery on laboratory animals face a dual welfare and methodological challenge: how to choose surgical anesthetics and post-operative analgesics that will best control animal suffering, knowing that both pain and the drugs that manage pain can all affect research outcomes. Scientists who publish full descriptions of animal procedures allow critical and systematic reviews of data, demonstrate their adherence to animal welfare norms, and guide other scientists on how to conduct their own studies in the field. We investigated what information on animal pain management a reasonably diligent scientist might find in planning for a successful experiment. To explore how scientists in a range of fields describe their management of this ethical and methodological concern, we scored 400 scientific articles that included major animal survival surgeries as part of their experimental methods, for the completeness of information on anesthesia and analgesia. The 400 articles (250 accepted for publication pre-2011, and 150 in 2014–15, along with 174 articles they reference) included thoracotomies, craniotomies, gonadectomies, organ transplants, peripheral nerve injuries, spinal laminectomies and orthopedic procedures in dogs, primates, swine, mice, rats and other rodents. We scored articles for Publication Completeness (PC), which was any mention of use of anesthetics or analgesics; Analgesia Use (AU) which was any use of post-surgical analgesics, and Analgesia Completeness (a composite score comprising intra-operative analgesia, extended post-surgical analgesia, and use of multimodal analgesia). 338 of 400 articles were PC. 98 of these 338 were AU, with some mention of analgesia, while 240 of 338 mentioned anesthesia only but not post-surgical analgesia. Journals’ caliber, as measured by their 2013 Impact Factor, had no effect on PC or AU. We found no effect of whether a journal instructs authors to consult the ARRIVE publishing guidelines published in 2010 on PC or AC for the 150 mouse and rat articles in our 2014–15 dataset. None of the 302 articles that were silent about analgesic use included an explicit statement that analgesics were withheld, or a discussion of how pain management or untreated pain might affect results. We conclude that current scientific literature cannot be trusted to present full detail on use of animal anesthetics and analgesics. We report that publication guidelines focus more on other potential sources of bias in experimental results, under-appreciate the potential for pain and pain drugs to skew data, and thus mostly treat pain management as solely an animal welfare concern, in the jurisdiction of animal care and use committees. At the same time, animal welfare regulations do not include guidance on publishing animal data, even though publication is an integral part of the cycle of research and can affect the welfare of animals in studies building on published work, leaving it to journals and authors to voluntarily decide what details of animal use to publish. We suggest that journals, scientists and animal welfare regulators should revise current guidelines and regulations, on treatment of pain and on transparent reporting of treatment of pain, to improve this dual welfare and data-quality deficiency.

The neuronal code for number

Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions.

Eye movements reflect and shape strategies in fraction comparison

The comparison of fractions is a difficult task that can often be facilitated by separately comparing components (numerators and denominators) of the fractions—that is, by applying so-called component-based strategies. The usefulness of such strategies depends on the type of fraction pair to be compared. We investigated the temporal organization and the flexibility of strategy deployment in fraction comparison by evaluating sequences of eye movements in 20 young adults. We found that component-based strategies could account for the response times and the overall number of fixations observed for the different fraction pairs. The analysis of eye movement sequences showed that the initial eye movements in a trial were characterized by stereotypical scanning patterns indicative of an exploratory phase that served to establish the kind of fraction pair presented. Eye movements that followed this phase adapted to the particular type of fraction pair and indicated the deployment of specific comparison strategies. These results demonstrate that participants employ eye movements systematically to support strategy use in fraction comparison. Participants showed a remarkable flexibility to adapt to the most efficient strategy on a trial-by-trial basis. Our results confirm the value of eye movement measurements in the exploration of strategic adaptation in complex tasks.

The use of proportion by young domestic chicks (Gallus gallus)

We investigated whether 4-day-old domestic chicks can discriminate proportions. Chicks were trained to respond, via food reinforcement, to one of the two stimuli, each characterized by different proportions of red and green areas (¼ vs. ¾). In Experiment 1, chicks approached the proportion associated with food, even if at test the spatial dispositions of the two areas were novel. In Experiment 2, chicks responded on the basis of proportion even when the testing stimuli were of enlarged dimensions, creating a conflict between the absolute positive area experienced during training and the relative proportion of the two areas. However, chicks could have responded on the basis of the overall colour (red or green) of the figures rather than proportion per se. To control for this objection, in Experiment 3, we used new pairs of testing stimuli, each depicting a different number of small squares on a white background (i.e. 1 green and 3 red vs. 3 green and 1 red or 5 green and 15 red vs. 5 red and 15 green). Chicks were again able to respond to the correct proportion, showing they discriminated on the basis of proportion of continuous quantities and not on the basis of the prevalent colour or on the absolute amount of it. Data indicate that chicks can track continuous quantities through various manipulations, suggesting that proportions are information that can be processed by very young animals.

Neuronal correlates of visual working memory in the corvid endbrain

The concept of working memory is key to cognitive functioning. Working memory encompasses the capacity to retain immediately past information, to process this information, and to use it to guide goal-directed behavior. Corvid songbirds are renowned for their high-level cognitive capabilities, but where and how visual information is temporarily retained by neurons in the avian brain in a behaviorally relevant way remains poorly understood. We trained four carrion crows (Corvus corone) on versions of a delayed match-to-sample task that required the crows to remember a visual stimulus for later comparison. While the crows performed the task, we recorded the activity of single neurons in the nidopallium caudolaterale (NCL), a pallial association area of the avian endbrain. We show that many NCL neurons encode information about visual stimuli and temporarily maintain this information after the stimulus disappeared by sustained delay activity. Selective delay activity allows the birds to hold relevant information in memory and correlates with discrimination behavior. This suggests that sustained activity of NCL neurons is a neuronal correlate of visual working memory in the corvid brain and serves to bridge temporal gaps, thereby offering a workspace for processing immediately past visual information.

Prefrontal neurons transmit signals to parietal neurons that reflect executive control of cognition

Prefrontal cortex influences behavior largely through its connections with other association cortices; however the nature of the information conveyed by prefrontal output signals and what effect these signals have on computations performed by target structures is largely unknown. To address these questions, we simultaneously recorded the activity of neurons in prefrontal and posterior parietal cortex of monkeys performing a rule-based spatial categorization task. Parietal cortex receives direct prefrontal input, and parietal neurons, like their prefrontal counterparts, exhibit signals that reflect rule-based cognitive processing in this task. By analyzing rapid fluctuations in the cognitive information encoded by activity in the two areas, we obtained evidence that signals reflecting rule-dependent categories were selectively transmitted in a top-down direction from prefrontal to parietal neurons, suggesting prefrontal output is important for the executive control of distributed cognitive processing.

Non-symbolic halving in an Amazonian indigene group

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS.

Coding of abstract quantity by 'number neurons' of the primate brain

Humans share with nonhuman animals a quantification system for representing the number of items as nonverbal mental magnitudes. Over the past decade, the anatomical substrates and neuronal mechanisms of this quantification system have been unraveled down to the level of single neurons. Work with behaviorally trained nonhuman primates identified a parieto-frontal cortical network with individual neurons selectively tuned to the number of items. Such 'number neurons' can track items across space, time, and modality to encode numerosity in a most abstract, supramodal way. The physiological properties of these neurons can explain fundamental psychophysical phenomena during numerosity judgments. Functionally overlapping groups of parietal neurons represent not only numerable-discrete quantity (numerosity), but also innumerable-continuous quantity (extent) and relations between quantities (proportions), supporting the idea of a generalized magnitude system in the brain. These studies establish putative homologies between the monkey and human brain and demonstrate the suitability of nonhuman primates as model system to explore the neurobiological roots of the brain's nonverbal quantification system, which may constitute the evolutionary foundation of all further, more elaborate numerical skills in humans.

Numerical rule coding in the prefrontal, premotor, and posterior parietal cortices of macaques

Switching flexibly between behavioral goals is a hallmark of executive control and requires integration of external and internal information. We recorded single-neuron correlates of different numerical representations (sensory-, working memory-, and rule-related activity) in the dorsal premotor area (PMd), the cingulate motor areas (CMA), and the ventral intraparietal sulcus (VIP) and compared them to previous recordings in the lateral prefrontal cortex (PFC). Two monkeys were trained to encode and memorize numerosities and flexibly switch between two abstract quantitative rules based on rule cues. Almost 20% of randomly selected PFC and PMd neurons significantly represented the numerical rule in a behaviorally relevant manner, approximately twice as many as in the CMA and VIP. Rule selectivity was significantly better for PMd neurons than for PFC cells. Seemingly at the expense of rule selectivity, however, sensory- and memory-related numerosity activity was greatly diminished compared with previous delayed match-to-numerosity studies. These findings suggest the involvement of the frontal premotor areas in strategic planning such as rule following. Moreover, the results emphasize that the coding capacities of neurons in association cortical areas are far more dynamic depending on task demands than previously thought.

Relating magnitudes: the brain's code for proportions

Whereas much is known about how we categorize and reason based on absolute quantity, data exploring ratios of quantities, as in proportions and fractions, are comparatively sparse. Until recently, it remained elusive whether these two representations of number are connected, how proportions are implemented by neurons and how language shapes this code. New data derived with complementary methods and from different model systems now shed light on the mechanisms of magnitude ratio representations. A coding scheme for proportions has emerged that is remarkably reminiscent of the representation of absolute number. These novel findings suggest a sense for ratios that grants the brain automatic access to proportions independently of language and the format of presentation.

No inherent left and right side in human 'mental number line': evidence from right brain damage

Spatial reasoning has a relevant role in mathematics and helps daily computational activities. It is widely assumed that in cultures with left-to-right reading, numbers are organized along the mental equivalent of a ruler, the mental number line, with small magnitudes located to the left of larger ones. Patients with right brain damage can disregard smaller numbers while mentally setting the midpoint of number intervals. This has been interpreted as a sign of spatial neglect for numbers on the left side of the mental number line and taken as a strong argument for the intrinsic left-to-right organization of the mental number line. Here, we put forward the understanding of this cognitive disability by discovering that patients with right brain damage disregard smaller numbers both when these are mapped on the left side of the mental number line and on the right side of an imagined clock face. This shows that the right hemisphere supports the representation of small numerical magnitudes independently from their mapping on the left or the right side of a spatial-mental layout. In addition, the study of the anatomical correlates through voxel-based lesion-symptom mapping and the mapping of lesion peaks on the diffusion tensor imaging-based reconstruction of white matter pathways showed that the rightward bias in the imagined clock-face was correlated with lesions of high-level middle temporal visual areas that code stimuli in object-centred spatial coordinates, i.e. stimuli that, like a clock face, have an inherent left and right side. In contrast, bias towards higher numbers on the mental number line was linked to white matter damage in the frontal component of the parietal-frontal number network. These anatomical findings show that the human brain does not represent the mental number line as an object with an inherent left and right side. We conclude that the bias towards higher numbers in the mental bisection of number intervals does not depend on left side spatial, imagery or object-centred neglect and that it rather depends on disruption of an abstract non-spatial representation of small numerical magnitudes.

Generalized associative representations in parietal cortex

Making associations between sensory stimuli is a critical aspect of behavior. Our laboratory previously showed that neurons in the lateral intraparietal (LIP) area of Macaca mulatta reflect learned associations between directions of moving visual stimuli. Individual LIP neurons might encode associations only for specific stimuli, such as motion directions; alternatively, they may encode more general associations whenever animals must decide between discrete alternatives. To test this, we asked whether LIP neurons encode learned associations between pairs of arbitrarily chosen static shapes and, in a separate task, whether the same neurons also encode associations between motion directions. The experimental design dissociated the visual associations from the movements used to report those associations. We found robust encoding of the learned pair associations between shapes, and shape-pair selective neurons tended to also be selective for direction associations. These findings suggest that representing generic categorical outcomes may be a fundamental role of parietal neurons.