Questions About Quantifiers: Symbolic and Nonsymbolic Quantity Processing by the Brain.

One approach to understanding how the human cognitive system stores and operates with quantifiers such as "some," "many," and "all" is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between processing exact number symbols (such as "3" or "three") and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing.

On truth and polarity in negation processing: language-specific effects in non-linguistic contexts.

Introduction: This study examines how negation is processed in a nonverbal context (e.g., when assessing ▲ ≠ ▲) by speakers of a truth-based system like Mandarin and a polarity-based system like English. In a truth-based system, negation may take longer to process because it is typically attached to the negation as a whole (it is not true that triangle does not equal triangle), whereas in polarity-based systems, negation is processed relatively faster because it is attached to just the equation symbol (triangle does not equal triangle), which is processed relatively faster. Our hypothesis was that negation processing routines previously observed for verbal contexts, namely that speakers of Mandarin get slowed down more when processing negative stimuli than positive stimuli compared to speakers of English, also extend to contexts when language use is not obligatory. Methods: To test this, we asked participants to agree/disagree with equations comprising simple shapes and positive '=' or negative '≠' equation symbols. English speakers showed a response-time advantage over Mandarin speakers in negation conditions. In a separate experiment, we also tested the contribution of equation symbols '≠'/'=' to the cognitive demands by asking participants to judge shape sameness in symbol-free trials, such as ▲ ■. This comparison allowed us to test whether crosslinguistic differences arise not because of shape congruence judgement but arguably due to negation attachment. Results and discussion: The effect of the '≠' symbol on shape congruence was language-specific, speeding up English speakers but slowing down Mandarin speakers when the two shapes differed. These findings suggest language-specific processing of negation in negative equations, interpreted as novel support for linguistic relativity.

What are large language models supposed to model?

Do large language models (LLMs) constitute a computational account of how humans process language? And if so, what is the role of (psycho)linguistic theory in understanding the relationship between artificial and biological minds? The answer depends on choosing among several, fundamentally distinct ways of interpreting these models as hypotheses about humans.

The neural ingredients for a language of thought are available.

The classical notion of a 'language of thought' (LoT), advanced prominently by the philosopher Jerry Fodor, is an influential position in cognitive science whereby the mental representations underpinning thought are considered to be compositional and productive, enabling the construction of new complex thoughts from more primitive symbolic concepts. LoT theory has been challenged because a neural implementation has been deemed implausible. We disagree. Examples of critical computational ingredients needed for a neural implementation of a LoT have in fact been demonstrated, in particular in the hippocampal spatial navigation system of rodents. Here, we show that cell types found in spatial navigation (border cells, object cells, head-direction cells, etc.) provide key types of representation and computation required for the LoT, underscoring its neurobiological viability.

Dialectics of Sign and Symbol and the Utterance of Archetype Theory.

Debates surrounding Jung's archetype theory could be characterized as tacit attempts to contend with the concept's dual function as referring to something known to psychologists (sign) and standing for something that is fundamentally unknowable (symbol). This essay considers implications of the term "archetype," outlines and critiques some of the conundrums of categorization and scientific credibility posed by Jung's formulation of the theory, and prompts locating the archetypal "human quality" of being human in imaginaries of typical patterning of the experiential realm.

Les débats entourant la théorie des archétypes de Jung peuvent être caractérisés comme des tentatives tacites de lutter contre la double fonction du concept, qui fait référence à quelque chose de connu des psychologues (le signe) et qui représente quelque chose de fondamentalement mystérieux (le symbole). Cet essai examine les implications du terme « archétype ¼. Il expose et fait la critique de quelques problématiques de la catégorisation et de la crédibilité scientifique posées par la formulation de la théorie par Jung. L'article incite à localiser la «qualité humaine¼ archétypale de l'être humain dans des imaginaires de modèles typiques du domaine expérientiel.

Los debates en torno a la teoría de los arquetipos de Jung podrían caracterizarse como intentos tácitos de lidiar con la doble función del concepto: referirse a algo conocido por los psicólogos (signo) y representar algo que es fundamentalmente incognoscible (símbolo). Este ensayo examina las implicaciones del término "arquetipo", describe y critica algunos de los enigmas de categorización y credibilidad científica que plantea la formulación de la teoría de Jung, e incita a situar la "cualidad humana" arquetípica del ser humano en los imaginarios de patrones típicos del ámbito experiencial.

SymCog: An open-source toolkit for assessing human symbolic cognition.

Symbol systems have a profound influence on human behavior, spanning countless modalities such as natural language, clothing styles, monetary systems, and gestural conventions (e.g., handshaking). Selective impairments in understanding and manipulating symbols are collectively known as asymbolia. Here we address open questions about the nature of asymbolia in the context of both historical and contemporary approaches to human symbolic cognition. We describe a tripartite perspective on symbolic cognition premised upon (1) mental representation of a concept, (2) a stored pool of symbols segregated from their respective referents, and (3) fast and accurate mapping between concepts and symbols. We present an open-source toolkit for assessing symbolic knowledge premised upon matching animated video depictions of abstract concepts to their corresponding verbal and nonverbal symbols. Animations include simple geometric shapes (e.g., filled circles, squares) moving in semantically meaningful ways. For example, a rectangle bending under the implied weight of a large square denotes "heaviness." We report normative data for matching words and images to these target animations. In a second norming study, participants rated target animations across a range of semantic dimensions (e.g., valence, dominance). In a third study, we normed a set of concepts familiar to American English speakers but lacking verbal labels (e.g., the feeling of a Sunday evening). We describe how these tools may be used to assess human symbolic processing and identify asymbolic deficits across the span of human development.

Ethical Investigation of the Living Will and the Comparison and Enlightenment of Chinese and Japanese Practical Experience / 中国医学伦理学

The revised revision of the Shenzhen Special Economic Zone Medical Regulations passed in 2022 is an important institutional innovation in China, while many problems still need to be solved in the specific practice and application. This paper compared the practical development characteristics of the living will system between China and Japan, and analyzed the relationship between doctor-patients relationship under the intervention of the living will system and the symbolic representation mechanism of living will by using the semiotics theory. According to the links of "addresser-symbolic text" and "symbolic text-addressee", the six types of problems faced by current living will system in China were discussed, and the relevant experience and enlightenment were summarized to provided reference for the development of the living will system in China.

A topological solution to object segmentation and tracking.

The world is composed of objects, the ground, and the sky. Visual perception of objects requires solving two fundamental challenges: 1) segmenting visual input into discrete units and 2) tracking identities of these units despite appearance changes due to object deformation, changing perspective, and dynamic occlusion. Current computer vision approaches to segmentation and tracking that approach human performance all require learning, raising the question, Can objects be segmented and tracked without learning? Here, we show that the mathematical structure of light rays reflected from environment surfaces yields a natural representation of persistent surfaces, and this surface representation provides a solution to both the segmentation and tracking problems. We describe how to generate this surface representation from continuous visual input and demonstrate that our approach can segment and invariantly track objects in cluttered synthetic video despite severe appearance changes, without requiring learning.

Symbolic distancing in sharing situations restrains children's economic behavior and potentially also their inequity aversion.

We examined whether representing a resource non-symbolically (i.e., as stickers) or symbolically (i.e., as tokens that could be exchanged for stickers) affected kindergartner's decisions in an Ultimatum/Inequity Game (N = 93). The game involved distribution offers, made by a fictitious child, that were either fair (i.e., same quantity for each child, i.e., 3:3) or disadvantageously unfair (i.e., less for the target child than for the fictitious child, i.e., 2:4 or 1:5). Children had to decide whether to accept or reject the offers. In the latter case, none of the children would get anything of the resource. Children rejected unfair offers more frequently than fair offers, and they rejected the offers involving the symbolic resource more frequently than offers involving the non-symbolic resource, which applied to a similar degree to fair and unfair offers. However, exploratory follow-up analyses of children's reactions to unfair offers revealed that children rejected the more unfair offer (i.e., 1:5) more frequently than the less unfair offer (i.e., 2:4) when the resource was represented non-symbolically instead of symbolically. The results suggest that the symbolic representation of a resource evokes economically less rational behavior in children and diminished their potential gain. Moreover, symbolic representations might level out children's differentiation of differently unfair offers. These findings are discussed in light of the subjective value approach and the Construal Level Theory.

Using environmental nudges to reduce academic cheating in young children.

Previous research on nudges conducted with adults suggests that the accessibility of behavioral options can influence people's decisions. The present study examined whether accessibility can be used to reduce academic cheating among young children. We gave children a challenging math test in the presence of an answer key they were instructed not to peek at, and manipulated the accessibility of the answer key by placing various familiar objects on top of it. In Study 1, we used an opaque sheet of paper as a two-dimensional occluder, and found that it significantly reduced cheating compared to a transparent plastic sheet. In Study 2, we used a three-dimensional occluder in the form of a tissue box to make the answer key appear even less accessible, and found it was significantly more effective in reducing cheating than the opaque paper. In Study 3, we used two symbolic representations of the tissue box: a realistic color photo and a line drawing. Both representations were effective in reducing cheating, but the realistic photo was more effective than the drawing. These findings demonstrate that manipulating accessibility can be an effective strategy to nudge children away from cheating in an academic context. They further suggest that different types of everyday objects and their symbolic representations can differentially impact children's moral behavior.

A Smartphone Lightweight Method for Human Activity Recognition Based on Information Theory.

Smartphones have emerged as a revolutionary technology for monitoring everyday life, and they have played an important role in Human Activity Recognition (HAR) due to its ubiquity. The sensors embedded in these devices allows recognizing human behaviors using machine learning techniques. However, not all solutions are feasible for implementation in smartphones, mainly because of its high computational cost. In this context, the proposed method, called HAR-SR, introduces information theory quantifiers as new features extracted from sensors data to create simple activity classification models, increasing in this way the efficiency in terms of computational cost. Three public databases (SHOAIB, UCI, WISDM) are used in the evaluation process. The results have shown that HAR-SR can classify activities with 93% accuracy when using a leave-one-subject-out cross-validation procedure (LOSO).

TrSAX-An improved time series symbolic representation for classification.

As a major symbolic representation method that has been widely used in time series data mining, Symbolic Aggregate approXimation (SAX) uses the mean value of a segment as the symbol. However, the SAX representation ignores the trend of the value change in the segment, which may cause incorrect classification in some cases, because it cannot distinguish different time series with different trends but the same average value symbol. In this paper, we propose an improved symbolic representation by integrating SAX with the least squares method to describe the time series' mean value and trend information. By comparing the classifiers using the original SAX, two improved SAX representations and another two classifiers that are highly representative and competitive for short time series classification, the results show that the error rate of the classifier that uses our representation is lower than that of those five classifiers on their own in most datasets.

The Relationship Between Non-symbolic and Symbolic Numerosity Representations in Elementary School: The Role of Intelligence.

This study aimed to estimate the extent to which the development of symbolic numerosity representations relies on pre-existing non-symbolic numerosity representations that refer to the Approximate Number System. To achieve this aim, we estimated the longitudinal relationships between accuracy in the Number Line (NL) test and "blue-yellow dots" test across elementary school children. Data from a four-wave longitudinal study involving schoolchildren in grades 1-4 in Russia and Kyrgyzstan (N = 490, mean age 7.65 years in grade 1) were analyzed. We applied structural equation modeling and tested several competing models. The results revealed that at the start of schooling, the accuracy in the NL test predicted subsequent accuracy in the "blue-yellow dots" test, whereas subsequently, non-symbolic representation in grades 2 and 3 predicted subsequent symbolic representation. These results indicate that the effect of non-symbolic representation on symbolic representation emerges after a child masters the basics of symbolic number knowledge, such as counting in the range of twenty and simple arithmetic. We also examined the extent to which the relationships between non-symbolic and symbolic representations might be explained by fluid intelligence, which was measured by Raven's Standard Progressive Matrices test. The results revealed that the effect of symbolic representation on non-symbolic representation was explained by fluid intelligence, whereas at the end of elementary school, non-symbolic representation predicted subsequent symbolic representation independently of fluid intelligence.

Three-dimensional segmentation and symbolic representation of cerebral vessels on 3DRA images of arteriovenous malformations.

BACKGROUND: Endovascular embolization is a minimally invasive interventional method for the treatment of neurovascular pathologies such as aneurysms, arterial stenosis or arteriovenous malformations (AVMs). In this context, neuroradiologists need efficient tools for interventional planning and microcatheter embolization procedures optimization. Thus, the development of helpful methods is necessary to solve this challenging issue. METHODS: A complete pipeline aiming to assist neuroradiologists in the visualization, interpretation and exploitation of three-dimensional rotational angiographic (3DRA) images for interventions planning in case of AVM is proposed. The developed method consists of two steps. First, an automated 3D region-based segmentation of the cerebral vessels which feed and drain the AVM is performed. From this, a graph-like tree representation of these connected vessels is then built. This symbolic representation provides a vascular network modelization with hierarchical and geometrical features that helps in the understanding of the complex angioarchitecture of the AVM. RESULTS: The developed workflow achieves the segmentation of the vessels and of the malformation. It improves the 3D visualization of this complex network and highlights its three main components that are the arteries, the veins and the nidus. The symbolic representation then brings a better comprehension of the vessels angioarchitecture. It provides decomposition into topologically related vessels, offering the possibility to reduce the complexity due to the malformed vessels and also determine the optimal paths for AVM embolization during interventions planning. CONCLUSIONS: A relevant vascular network modelization has been developed that constitutes a breakthrough in the assistance of neuroradiologists for AVM endovascular embolization planning.

A Two-Stage Method for Online Signature Verification Using Shape Contexts and Function Features.

As a behavioral biometric trait, an online signature is extensively used to verify a person's identity in many applications. In this paper, we present a method using shape contexts and function features as well as a two-stage strategy for accurate online signature verification. Specifically, in the first stage, features of shape contexts are extracted from the input and classification is made based on distance metric. Only the inputs passing by the first stage are represented by a set of function features and verified. To improve the matching accuracy and efficiency, we propose shape context-dynamic time warping (SC-DTW) to compare the test signature with the enrolled reference ones based on the extracted function features. Then, classification based on interval-valued symbolic representation is employed to decide if the test signature is a genuine one. The proposed method is evaluated on SVC2004 Task 2 achieving an Equal Error Rate of 2.39% which is competitive to the state-of-the-art approaches. The experiment results demonstrate the effectiveness of the proposed method.

Symbolic-Based Recognition of Contact States for Learning Assembly Skills.

Imitation learning is gaining more attention because it enables robots to learn skills from human demonstrations. One of the major industrial activities that can benefit from imitation learning is the learning of new assembly processes. An essential characteristic of an assembly skill is its different contact states (CS). They determine how to adjust movements in order to perform the assembly task successfully. Humans can recognize CSs through haptic feedback. They execute complex assembly tasks accordingly. Hence, CSs are generally recognized using force and torque information. This process is not straightforward due to the variations in assembly tasks, signal noise and ambiguity in interpreting force/torque (F/T) information. In this research, an investigation has been conducted to recognize the CSs during an assembly process with a geometrical variation on the mating parts. The F/T data collected from several human trials were pre-processed, segmented and represented as symbols. Those symbols were used to train a probabilistic model. Then, the trained model was validated using unseen datasets. The primary goal of the proposed approach aims to improve recognition accuracy and reduce the computational effort by employing symbolic and probabilistic approaches. The model successfully recognized CS based only on force information. This shows that such models can assist in imitation learning.

MBOSS: A Symbolic Representation of Human Activity Recognition Using Mobile Sensors.

Human activity recognition (HAR) through sensors embedded in smartphones has allowed for the development of systems that are capable of detecting and monitoring human behavior. However, such systems have been affected by the high consumption of computational resources (e.g., memory and processing) needed to effectively recognize activities. In addition, existing HAR systems are mostly based on supervised classification techniques, in which the feature extraction process is done manually, and depends on the knowledge of a specialist. To overcome these limitations, this paper proposes a new method for recognizing human activities based on symbolic representation algorithms. The method, called "Multivariate Bag-Of-SFA-Symbols" (MBOSS), aims to increase the efficiency of HAR systems and maintain accuracy levels similar to those of conventional systems based on time and frequency domain features. The experiments conducted on three public datasets showed that MBOSS performed the best in terms of accuracy, processing time, and memory consumption.

Characterizing the neural coding of symbolic quantities.

How the brain encodes abstract numerical symbols is a fundamental question in philosophy and cognitive neuroscience alike. Here we probe the nature of symbolic number representation in the brain by characterizing the neural similarity space for symbolic quantities in regions sensitive to their semantic content. In parietal and occipital regions, the similarity space of number symbols was positively predicted by the lexical frequency of numerals in parietal and occipital areas, and was unrelated to numerical ratio. These results are more consistent with a categorical, frequency-based account of symbolic quantity encoding. In contrast, the similarity space of analog quantities was positively predicted by ratio in prefrontal, parietal and occipital regions. We thus provide an explanation for why previous work has indicated that symbolic and analog quantities are distinct: number symbols operate primarily like discrete categories sensitive to input frequency, while analog quantities operate more like approximate perceptual magnitudes. In addition, we find substantial evidence for related patterns of activity across formats in prefrontal, parietal and occipital regions. Crucially however, between-format relations were not specific to individual quantities, indicating common processing as opposed to common representation. Moreover, evidence for between-format processing was strongest for quantities that could be represented as exact, discrete values in both systems (quantities in the 'subitizing' range: 1-4). In sum, converging evidence presented here indicates that symbolic quantities are coded in the brain as discrete categories sensitive to input frequency and largely independent of approximate, analog quantities.

Parallel Distributed Processing Theory in the Age of Deep Networks.

Parallel distributed processing (PDP) models in psychology are the precursors of deep networks used in computer science. However, only PDP models are associated with two core psychological claims, namely that all knowledge is coded in a distributed format and cognition is mediated by non-symbolic computations. These claims have long been debated in cognitive science, and recent work with deep networks speaks to this debate. Specifically, single-unit recordings show that deep networks learn units that respond selectively to meaningful categories, and researchers are finding that deep networks need to be supplemented with symbolic systems to perform some tasks. Given the close links between PDP and deep networks, it is surprising that research with deep networks is challenging PDP theory.

EXPLICIT LEAST-DEGREE BOUNDARY FILTERS FOR DISCONTINUOUS GALERKIN.

Convolving the output of Discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for non-periodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-preserving (PSIAC) filters were shown to be a superset of the well-known one-sided RLKV and SRV filters. Since PSIAC filters can be formulated symbolically, PSIAC filtering amounts to forming linear products with local DG output and so offers a more stable and efficient implementation. The paper introduces a new class of PSIAC filters NP0 that have small support and are piecewise constant. Extensive numerical experiments for the canonical hyperbolic test equation show NP0 filters outperform the more complex known boundary filters. NP0 filters typically reduce the L∞ error in the boundary region below that of the interior where optimally superconvergent symmetric filters of the same support are applied. NP0 filtering can be implemented as forming linear combinations of the data with short rational weights. Exact derivatives of the convolved output are easy to compute.