Conventional and frugal methods of estimating COVID-19-related excess deaths and undercount factors.

Across the world, the officially reported number of COVID-19 deaths is likely an undercount. Establishing true mortality is key to improving data transparency and strengthening public health systems to tackle future disease outbreaks. In this study, we estimated excess deaths during the COVID-19 pandemic in the Pune region of India. Excess deaths are defined as the number of additional deaths relative to those expected from pre-COVID-19-pandemic trends. We integrated data from: (a) epidemiological modeling using pre-pandemic all-cause mortality data, (b) discrepancies between media-reported death compensation claims and official reported mortality, and (c) the "wisdom of crowds" public surveying. Our results point to an estimated 14,770 excess deaths [95% CI 9820-22,790] in Pune from March 2020 to December 2021, of which 9093 were officially counted as COVID-19 deaths. We further calculated the undercount factor-the ratio of excess deaths to officially reported COVID-19 deaths. Our results point to an estimated undercount factor of 1.6 [95% CI 1.1-2.5]. Besides providing similar conclusions about excess deaths estimates across different methods, our study demonstrates the utility of frugal methods such as the analysis of death compensation claims and the wisdom of crowds in estimating excess mortality.

Entropy, complexity, and maturity in children's neural responses to naturalistic video lessons.

Temporal characteristics of neural signals are often overlooked in traditional fMRI developmental studies but are critical to studying brain functions in ecologically valid settings. In the present study, we explore the temporal properties of children's neural responses during naturalistic mathematics and grammar tasks. To do so, we introduce a novel measure in developmental fMRI: neural entropy, which indicates temporal complexity of BOLD signals. We show that temporal patterns of neural activity have lower complexity and greater variability in children than in adults in the association cortex but not in the sensory-motor cortex. We also show that neural entropy is associated with both child-adult similarity in functional connectivity and neural synchrony, and that neural entropy increases with the size of functionally connected networks in the association cortex. In addition, neural entropy increases with functional maturity (i.e., child-adult neural synchrony) in content-specific regions. These exploratory findings suggest the hypothesis that neural entropy indexes the increasing breadth and diversity of neural processes available to children for analyzing mathematical information over development.

Cognitive Mechanisms Underlying Recursive Pattern Processing in Human Adults.

The capacity to generate recursive sequences is a marker of rich, algorithmic cognition, and perhaps unique to humans. Yet, the precise processes driving recursive sequence generation remain mysterious. We investigated three potential cognitive mechanisms underlying recursive pattern processing: hierarchical reasoning, ordinal reasoning, and associative chaining. We developed a Bayesian mixture model to quantify the extent to which these three cognitive mechanisms contribute to adult humans' performance in a sequence generation task. We further tested whether recursive rule discovery depends upon relational information, either perceptual or semantic. We found that the presence of relational information facilitates hierarchical reasoning and drives the generation of recursive sequences across novel depths of center embedding. In the absence of relational information, the use of ordinal reasoning predominates. Our results suggest that hierarchical reasoning is an important cognitive mechanism underlying recursive pattern processing and can be deployed across embedding depths and relational domains.

Origins of Hierarchical Logical Reasoning.

Hierarchical cognitive mechanisms underlie sophisticated behaviors, including language, music, mathematics, tool-use, and theory of mind. The origins of hierarchical logical reasoning have long been, and continue to be, an important puzzle for cognitive science. Prior approaches to hierarchical logical reasoning have often failed to distinguish between observable hierarchical behavior and unobservable hierarchical cognitive mechanisms. Furthermore, past research has been largely methodologically restricted to passive recognition tasks as compared to active generation tasks that are stronger tests of hierarchical rules. We argue that it is necessary to implement learning studies in humans, non-human species, and machines that are analyzed with formal models comparing the contribution of different cognitive mechanisms implicated in the generation of hierarchical behavior. These studies are critical to advance theories in the domains of recursion, rule-learning, symbolic reasoning, and the potentially uniquely human cognitive origins of hierarchical logical reasoning.

Common Neural Functions during Children's Learning from Naturalistic and Controlled Mathematics Paradigms.

Two major goals of human neuroscience are to understand how the brain functions in the real world and to measure neural processes under conditions that are ecologically valid. A critical step toward these goals is understanding how brain activity during naturalistic tasks that mimic the real world relates to brain activity in more traditional laboratory tasks. In this study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in a naturalistic setting.

The evolution of quantitative sensitivity.

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability. This article is part of the theme issue 'Systems neuroscience through the lens of evolutionary theory'.

Spatial concepts of number, size, and time in an indigenous culture.

In industrialized groups, adults implicitly map numbers, time, and size onto space according to cultural practices like reading and counting (e.g., from left to right). Here, we tested the mental mappings of the Tsimane', an indigenous population with few such cultural practices. Tsimane' adults spatially arranged number, size, and time stimuli according to their relative magnitudes but showed no directional bias for any domain on any spatial axis; different mappings went in different directions, even in the same participant. These findings challenge claims that people have an innate left-to-right mapping of numbers and that these mappings arise from a domain-general magnitude system. Rather, the direction-specific mappings found in industrialized cultures may originate from direction-agnostic mappings that reflect the correlational structure of the natural world.

Reasoning Through the Disjunctive Syllogism in Monkeys.

The capacity for logical inference is a critical aspect of human learning, reasoning, and decision-making. One important logical inference is the disjunctive syllogism: given A or B, if not A, then B. Although the explicit formation of this logic requires symbolic thought, previous work has shown that nonhuman animals are capable of reasoning by exclusion, one aspect of the disjunctive syllogism (e.g., not A = avoid empty). However, it is unknown whether nonhuman animals are capable of the deductive aspects of a disjunctive syllogism (the dependent relation between A and B and the inference that "if not A, then B" must be true). Here, we used a food-choice task to test whether monkeys can reason through an entire disjunctive syllogism. Our results show that monkeys do have this capacity. Therefore, the capacity is not unique to humans and does not require language.

Recursive sequence generation in monkeys, children, U.S. adults, and native Amazonians.

The question of what computational capacities, if any, differ between humans and nonhuman animals has been at the core of foundational debates in cognitive psychology, anthropology, linguistics, and animal behavior. The capacity to form nested hierarchical representations is hypothesized to be essential to uniquely human thought, but its origins in evolution, development, and culture are controversial. We used a nonlinguistic sequence generation task to test whether subjects generalize sequential groupings of items to a center-embedded, recursive structure. Children (3 to 5 years old), U.S. adults, and adults from a Bolivian indigenous group spontaneously induced recursive structures from ambiguous training data. In contrast, monkeys did so only with additional exposure. We quantify these patterns using a Bayesian mixture model over logically possible strategies. Our results show that recursive hierarchical strategies are robust in human thought, both early in development and across cultures, but the capacity itself is not unique to humans.

The balance of rigor and reality in developmental neuroscience.

The balance realism and rigor in psychological research is essential to the development of rich and accurate theories about the developing brain. In the field of neuroimaging researchers have used predominantly controlled laboratory methods to decompose neural signals into meaningful functions but there is currently a push to integrate naturalistic conditions into neural measurement. Sometimes naturalistic methods are used to validate existing functional theories ecologically, and other times they are used in data-driven studies for exploration. This article assesses the value and risk of these approaches for understanding the developing brain.

One-to-one correspondence without language.

A logical rule important in counting and representing exact number is one-to-one correspondence, the understanding that two sets are equal if each item in one set corresponds to exactly one item in the second set. The role of this rule in children's development of counting remains unclear, possibly due to individual differences in the development of language. We report that non-human primates, which do not have language, have at least a partial understanding of this principle. Baboons were given a quantity discrimination task where two caches were baited with different quantities of food. When the quantities were baited in a manner that highlighted the one-to-one relation between those quantities, baboons performed significantly better than when one-to-one correspondence cues were not provided. The implication is that one-to-one correspondence, which requires intuitions about equality and is a possible building block of counting, has a pre-linguistic origin.

Gender similarities in the brain during mathematics development.

Some scientists and public figures have hypothesized that women and men differ in their pursuit of careers in science, technology, engineering, and mathematics (STEM) owing to biological differences in mathematics aptitude. However, little evidence supports such claims. Some studies of children and adults show gender differences in mathematics performance but in those studies it is impossible to disentangle intrinsic, biological differences from sociocultural influences. To investigate the early biology of mathematics and gender, we tested for gender differences in the neural processes of mathematics in young children. We measured 3-10-year-old children's neural development with functional magnetic resonance imaging (fMRI) during naturalistic viewing of mathematics education videos. We implemented both frequentist and Bayesian analyses that quantify gender similarities and differences in neural processes. Across all analyses girls and boys showed significant gender similarities in neural functioning, indicating that boys and girls engage the same neural system during mathematics development.

Developing, mature, and unique functions of the child's brain in reading and mathematics.

Cognitive development research shows that children use basic "child-unique" strategies for reading and mathematics. This suggests that children's neural processes will differ qualitatively from those of adults during this developmental period. The goals of the current study were to 1) establish whether a within-subjects neural dissociation between reading and mathematics exists in early childhood as it does in adulthood, and 2) use a novel, developmental intersubject correlation method to test for "child-unique", developing, and adult-like patterns of neural activation within those networks. Across multiple tasks, children's reading and mathematics activity converged in prefrontal cortex, but dissociated in temporal and parietal cortices, showing similarities to the adult pattern of dissociation. "Child-unique" patterns of neural activity were observed in multiple regions, including the anterior temporal lobe and inferior frontal gyri, and showed "child-unique" profiles of functional connectivity to prefrontal cortex. This provides a new demonstration that "children are not just little adults" - the developing brain is not only quantitatively different from adults, it is also qualitatively different.

Intrinsic whole number bias in humans.

Humans have great difficulty comparing quotients including fractions, proportions, and probabilities and often erroneously isolate the whole numbers of the numerators and denominators to compare them. Some have argued that the whole number bias is a compensatory strategy to deal with difficult comparisons. We examined adult humans' preferences for gambles that differed only in numerosity, and not in factors that influence their expected value (probabilities and stakes). Subjects consistently preferred gambles with more winning balls to ones with fewer, even though the probabilities were mathematically identical, replicating prior results. In a second experiment, we found that subjects accurately represented the relative probabilities of the choice options during rapid nonverbal probability judgments but nonetheless showed biases based on whole numbers. We mathematically formalized and quantitatively evaluated cognitive rules based on existing hypotheses that attempt to explain subjects' whole number biases during quotient comparisons. The results show that the whole number bias is intrinsic to the way humans solve quotient comparisons rather than a compensatory strategy. (PsycINFO Database Record

A threshold-free model of numerosity comparisons.

A dominant mechanism in the Judgment and Decision Making literature states that information is accumulated about each choice option until a decision threshold is met. Only after that threshold does a subject start to execute a motor response to indicate their choice. However, recent research has revealed spatial gradients in motor responses as a function of comparison difficulty as well as changes-of-mind in the middle of an action, both suggesting continued accumulation and processing of decision-related signals after the decision boundary. Here we present a formal model and supporting data from a number comparison task that a continuous motor planner, combined with a simple statistical inference scheme, can model detailed behavioral effects without assuming a threshold. This threshold-free model reproduces subjects' sensitivity to numerical distance in reaching, accuracy, reaction time, and changes of mind. We argue that the motor system positions the effectors using an optimal biomechanical feedback controller, and continuous statistical inference on outputs from cognitive processes.

Confidence judgments during ratio comparisons reveal a Bayesian bias.

Rational numbers are essential in mathematics and decision-making but humans often and erroneously rely on the magnitude of the numerator or denominator to determine the relative size of a quotient. The source of this flawed whole number strategy is poorly understood. Here we test the Bayesian hypothesis that the human bias toward large values in the numerator or denominator of a ratio estimate is the result of higher confidence in large samples. Larger values are considered a better (more certain) instance of that ratio than the same ratio composed of smaller values. We collected confidence measures explicitly (Experiment 1) and implicitly (Experiment 2) during subjects' comparisons of non-symbolic proportions (images with arrays of orange and blue dots). We manipulated the discernibility of the fractions to control difficulty and varied the cardinality and congruency of the numerators, denominators, and ratio values (e.g. 8/20 vs. 5/10 and 16/40 vs. 10/20). The results revealed that subjects' confidence during ratio comparisons was modulated by the numerical magnitude of the fraction's components, consistent with a Bayesian perception of relative ratios. The results suggest that the large number bias could arise from greater confidence in large samples.

No intrinsic gender differences in children's earliest numerical abilities.

Recent public discussions have suggested that the under-representation of women in science and mathematics careers can be traced back to intrinsic differences in aptitude. However, true gender differences are difficult to assess because sociocultural influences enter at an early point in childhood. If these claims of intrinsic differences are true, then gender differences in quantitative and mathematical abilities should emerge early in human development. We examined cross-sectional gender differences in mathematical cognition from over 500 children aged 6 months to 8 years by compiling data from five published studies with unpublished data from longitudinal records. We targeted three key milestones of numerical development: numerosity perception, culturally trained counting, and formal and informal elementary mathematics concepts. In addition to testing for statistical differences between boys' and girls' mean performance and variability, we also tested for statistical equivalence between boys' and girls' performance. Across all stages of numerical development, analyses consistently revealed that boys and girls do not differ in early quantitative and mathematical ability. These findings indicate that boys and girls are equally equipped to reason about mathematics during early childhood.

How Evolution Constrains Human Numerical Concepts.

The types of cognitive and neural mechanisms available to children for making concepts depend on the problems their brains evolved to solve over the past millions of years. Comparative research on numerical cognition with humans and nonhuman primates has revealed a system for quantity representation that lays the foundation for quantitative development. Nonhuman primates in particular share many human abilities to compute quantities, and are likely to exhibit evolutionary continuity with humans. While humans conceive of quantity in ways that are similar to other primates, they are unique in their capacity for symbolic counting and logic. These uniquely human constructs interact with primitive systems of numerical reasoning. In this article, I discuss how evolution shapes human numerical concepts through evolutionary constraints on human object-based perception and cognition, neural homologies among primates, and interactions between uniquely human concepts and primitive logic.

A metacognitive illusion in monkeys.

Like humans, monkeys can make accurate judgements about their own memory by reporting their confidence during cognitive tasks. Some have suggested that animals use associative learning to make accurate confidence judgements, while others have suggested animals directly access and estimate the strength of their memories. Here we test a third, non-exclusive possibility: perhaps monkeys, like humans, base metacognitive inferences on heuristic cues. Humans are known to use cues like perceptual fluency (e.g. how easy something is to see) when making metacognitive judgements. We tested monkeys using a match-to-sample task in which the perceptual fluency of the stimuli was manipulated. The monkeys made confidence wagers on their accuracy before or after each trial. We found that monkeys' wagers were affected by perceptual fluency even when their accuracy was not. This is novel evidence that animals are susceptible to metacognitive illusions similar to those experienced by humans.

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.