Numerical Judgments Research Articles

Increased intra-individual variability among individuals with ADHD: first evidence from numerosity judgment and verbal and quantitative reasoning.

This article presents the results of two studies investigating increased intra-individual variability (IIV) in the performance of individuals with attention deficit hyperactivity disorder (ADHD), in two cognitive domains: numerosity judgments and quantitative and verbal reasoning. Study 1, a pre-registered experiment, involved approximately 200 participants (42.66% female; mean age: 36.86; standard deviation of age: 10.70) making numerical judgments at two time-points. ADHD-symptom severity was assessed on a continuous scale. In Study 2, we collected the data of approximately 3000 examinees who had taken a high-stakes admissions test for higher education (assessing quantitative and verbal reasoning). The sample comprised only people formally diagnosed with ADHD. The control group consisted of approximately 200 000 examinees, none of whom presented with ADHD. The results of Study 1 revealed a positive correlation between IIV (distance between judgments at the two time-points) and ADHD symptom severity. The results of Study 2 demonstrated that IIV (distance between the scores on two test chapters assessing the same type of reasoning) was greater among examinees diagnosed with ADHD. In both studies, the findings persisted even after controlling for performance level. The results indicate that individuals with ADHD, v. those without, exhibit less consistent numerosity judgments and greater fluctuation in performance on verbal and quantitative reasoning. The measurement of the same psychological constructs appears to be less precise among individuals with ADHD compared to those without. We discuss the theoretical contributions and practical implications of our results for two fields: judgment and decision-making, and assessment.

The Mechanisms and Neural Signature of Time-averaged Numerosity Perception.

The animal brain is endowed with an innate sense of number allowing to intuitively perceive the approximate quantity of items in a scene, or "numerosity." This ability is not limited to items distributed in space, but also to events unfolding in time and to the average numerosity of dynamic scenes. How the brain computes and represents the average numerosity over time, however, remains unclear. Here, we investigate the mechanisms and EEG signature of the perception of average numerosity over time. To do so, we used stimuli composed of a variable number (3-12) of briefly presented dot arrays (50 msec each) and asked participants to judge the average numerosity of the sequence. We first show that the weight of different portions of the stimuli in determining the judgment depends on how many arrays are included in the sequence itself: the longer the sequence, the lower the weight of the latest arrays. Second, we show systematic adaptation effects across stimuli in consecutive trials. Importantly, the EEG results highlight two processing stages whereby the amplitude of occipital ERPs reflects the adaptation effect (∼300 msec after stimulus onset) and the accuracy and precision of average numerosity judgments (∼450-700 msec). These two stages are consistent with processes involved with the representation of perceived average numerosity and with perceptual decision-making, respectively. Overall, our findings provide new evidence showing how the visual system computes the average numerosity of dynamic visual stimuli, and support the existence of a dedicated, relatively low-level perceptual mechanism mediating this process.

Temporal error monitoring: Does agency matter?

Error monitoring is the ability to report one's errors without relying on feedback. Although error monitoring is investigated mostly with choice tasks, recent studies have discovered that participants parametrically also keep track of the magnitude and direction of their temporal, spatial, and numerical judgment errors. We investigated whether temporal error monitoring relies on internal generative processes that lead to the to-be-judged first-order timing performance. We hypothesized that if the endogenous processes underlie temporal error monitoring, one can monitor timing errors in emitted but not observed timing behaviors. We conducted six experiments to test this hypothesis. The first two experiments showed that confidence ratings were negatively related to error magnitude only in emitted behaviors, but error directionality judgments of observed behaviors were more precise. Experiment 3 replicated these effects even after controlling for the motor aspects of first-order timing performance. The last three experiments demonstrated that belief of agency (i.e., believing that the error belongs to the self or someone else) was critical in accounting for the confidence rating effects observed in the first two experiments. The precision of error directionality judgments was higherin thenon-agency condition. These results show that confidence is sensitive to belief, and short-long judgment is sensitive to the actual agency of timing behavior (i.e., whether the behavior was emitted by the self or someone else).

Geological characteristics and volume fracturing adaptability of tight oil reservoirs in the Ordos Basin of China

Abstract In recent years, China’s dependence on foreign crude oil has gradually increased. The Ordos Basin has abundant oil, gas, and coal resource. Tight oil and shale reservoirs have become very important replacement resources. This article studies the geological characteristics and volume fracturing adaptability of the Yanchang Formation tight oil reservoir in the central region of the Ordos Basin, and uses X-ray diffraction experiments to analyze the mineral composition of the reservoir; Utilizing high-pressure mercury intrusion technology to achieve precise quantitative characterization of multi-scale pore structures in reservoirs; Using the Analytic Hierarchy Process, establish a numerical judgment matrix and factor weights to study the adaptability of volume fracturing in the region. The results indicate that the volume fracturing adaptability of tight oil reservoirs in the Ordos Basin is good.

Investigating an effort avoidance account of attentional strategy choice.

People often choose suboptimal attentional control strategies during visual search. This has been at least partially attributed to the avoidance of the cognitive effort associated with the optimal strategy, but aspects of the task triggering such avoidance remain unclear. Here, we attempted to measure effort avoidance of an isolated task component to assess whether this component might drive suboptimal behavior. We adopted a modified version of the Adaptive Choice Visual Search (ACVS), a task designed to measure people's visual search strategies. To perform optimally, participants must make a numerosity judgment-estimating and comparing two color sets-before they can advantageously search through the less numerous of the two. If participants skip the numerosity judgment step, they can still perform accurately, albeit substantially more slowly. To study whether effort associated with performing the optional numerosity judgment could be an obstacle to optimal performance, we created a variant of the demand selection task to quantify the avoidance of numerosity judgment effort. Results revealed a robust avoidance of the numerosity judgment, offering a potential explanation for why individuals choose suboptimal strategies in the ACVS task. Nevertheless, we did not find a significant relationship between individual numerosity judgment avoidance and ACVS optimality, and we discussed potential reasons for this lack of an observed relationship. Altogether, our results showed that the effort avoidance for specific subcomponents of a visual search task can be probed and linked to overall strategy choices.

Weaker number sense accounts for impaired numerosity perception in dyscalculia: Behavioral and computational evidence.

Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical visual information, in line with alternative accounts that highlight impairments in executive functions and visuospatial abilities in the etiology of dyscalculia. To resolve this debate, we used a psychophysical method designed to disentangle the contribution of numerical and non-numerical features to explicit numerosity judgments in a dot comparison task and we assessed the relative saliency of numerosity in a spontaneous categorization task. Children with dyscalculia were compared to control children with average mathematical skills matched for age, IQ, and visuospatial memory. In the comparison task, the lower accuracy of dyscalculics compared to controls was linked to weaker encoding of numerosity, but not to the strength of non-numerical biases. Similarly, in the spontaneous categorization task, children with dyscalculia showed a weaker number-based categorization compared to the control group, with no evidence of a stronger influence of non-numerical information on category choice. Simulations with a neurocomputational model of numerosity perception showed that the reduction of representational resources affected the progressive refinement of number acuity, with little effect on non-numerical bias in numerosity judgments. Together, these results suggest that impaired numerosity perception in dyscalculia cannot be explained by increased interference from non-numerical visual cues, thereby supporting the hypothesis of a core number sense deficit. RESEARCH HIGHLIGHTS: A strongly debated issue is whether impaired numerosity perception in dyscalculia stems from a deficit in number sense or from poor executive and visuospatial functions. Dyscalculic children show reduced precision in visual numerosity judgments and weaker number-based spontaneous categorization, but no increasing reliance on continuous visual properties. Simulations with deep neural networks demonstrate that reduced neural/computational resources affect the developmental trajectory of number acuity and account for impaired numerosity judgments. Our findings show that weaker number acuity in developmental dyscalculia is not necessarily related to increased interference from non-numerical visual cues.

Measuring temporal bias in sequential numerosity comparison

While several methods have been proposed to assess the influence of continuous visual cues in parallel numerosity estimation, the impact of temporal magnitudes on sequential numerosity judgments has been largely ignored. To overcome this issue, we extend a recently proposed framework that makes it possible to separate the contribution of numerical and non-numerical information in numerosity comparison by introducing a novel stimulus space designed for sequential tasks. Our method systematically varies the temporal magnitudes embedded into event sequences through the orthogonal manipulation of numerosity and two latent factors, which we designate as “duration” and “temporal spacing”. This allows us to measure the contribution of finer-grained temporal features on numerosity judgments in several sensory modalities. We validate the proposed method on two different experiments in both visual and auditory modalities: results show that adult participants discriminated sequences primarily by relying on numerosity, with similar acuity in the visual and auditory modality. However, participants were similarly influenced by non-numerical cues, such as the total duration of the stimuli, suggesting that temporal cues can significantly bias numerical processing. Our findings highlight the need to carefully consider the continuous properties of numerical stimuli in a sequential mode of presentation as well, with particular relevance in multimodal and cross-modal investigations. We provide the complete code for creating sequential stimuli and analyzing participants’ responses.

Artiruno: A free‐software tool for multi‐criteria decision‐making with verbal decision analysis

AbstractVerbal decision analysis (VDA) is a family of methods for multi‐criteria decision analysis that require no numerical judgements from the agent. Although many such methods have been developed, they share the potential issue of asking the agent many more questions than necessary, particularly under multilevel approaches. Furthermore, whether VDA improves decisions, compared to no intervention, has yet to be investigated empirically. I introduce a new VDA method, Artiruno, with a freely licensed implementation in Python. Artiruno makes inferences mid‐interview so as to require minimal input from the agent, while using a multilevel scheme that allows it to ask complex questions when necessary. Inferences are facilitated by an axiom allowing comparisons to be partitioned across groups of criteria. Artiruno's performance in a variety of simple and complex scenarios can be verified with automated software tests. For an empirical test, I conducted an experiment in which 107 people from an Internet subject pool considered an important decision they faced in their own lives, and were randomly assigned to use Artiruno or to receive no intervention. These subjects proved mostly able to use Artiruno, and they found it helpful, but Artiruno seemed to have little influence on their decisions or outcomes.

Understanding the Concept of Phonetic and Visual Similarity Vis-A-Vis To Letter Trademarks Through Judicial Precedents

The assessment of the distinctiveness of trademarks, despite the criteria outlined in the Trademark’s Act of 1999, specifically under sections 9 and 11, presents a formidable challenge, often necessitating the discerning perspective of the judiciary. As a fundamental guiding principle, both examiner and courts are obliged to evaluate a trademark as a unified entity. In recent years, there has been a discernible rise in the scrutiny of phonetic similarities between marks. The legal framework for dealing with the infringement of a registered mark due to phonetic resemblance is encapsulated within section 29(9) of trademarks act 1999. This section expressly stipulates that a mark may be infringed by the oral as well as the visual representation of words. The Supreme Court has consistently affirmed the imperative need to consider both auditory and visual aspects when comparing trademark. This paper delves into an analysis of numerous judgements handed down by the Supreme Court and various High Courts, primarily focusing on the assessment of both phonetic and visual aspects of trademarks. Special emphasis has been placed upon letter trademarks and their susceptibility to both visual and phonetic infringement. While trademarks typically encompass various elements such as devices, color combinations, letters and images, letter trademarks, often consisting of a single letter with descriptive trade connotations, are generally considered weaker trade makers. To establish trademark rights in such instances compelling evidence of usage is requisite. Conversely, trademarks comprised of more than one letter, devoid of descriptive elements pertaining to goods and trade, are regarded as stronger trademarks. In cases where a letter trademark incorporates a unique device, it offers robust protection for the trademark. This paper references multiple case laws where esteemed courts have recognised unequivocally rights with respect to letter trademarks.

Numerical Representation for Action in Crows Obeys the Weber-Fechner Law

The psychophysical laws governing the judgment of perceived numbers of objects or events, called the number sense, have been studied in detail. However, the behavioral principles of equally important numerical representations for action are largely unexplored in both humans and animals. We trained two male carrion crows (Corvus corone) to judge numerical values of instruction stimuli from one to five and to flexibly perform a matching number of pecks. Our quantitative analysis of the crows’ number production performance shows the same behavioral regularities that have previously been demonstrated for the judgment of sensory numerosity, such as the numerical distance effect, the numerical magnitude effect, and the logarithmical compression of the number line. The presence of these psychophysical phenomena in crows producing number of pecks suggests a unified sensorimotor number representation system underlying the judgment of the number of external stimuli and internally generated actions.

Visual event boundaries restrict anchoring effects in decision-making.

Research on higher-level thought has revealed many principles of reasoning and decision-making but has rarely made contact with how we perceive the world in the first place. Here we show how a lower-level property of perception-the spontaneous and task-irrelevant segmentation of continuous visual stimulation into discrete events-can restrict one of the most notorious biases in decision-making: numerical anchoring. Subjects walked down a long room in an immersive three dimensional (3D) animation and then made a numerical judgment (e.g., of how much a suitcase is worth, or of how many hours of community service a minor crime deserved). Critically, some subjects passed through a doorway (a visual event boundary) during their virtual walk, while others did not-equating time, distance traveled, and visual complexity. The anchoring manipulation was especially innocuous, not appearing to be part of the experiment at all. Before the online trial began, subjects reported the two-digit numerical value from a visually distorted "CAPTCHA" ("to verify that you are human")-where this task-irrelevant anchor was either low (e.g., 29) or high (e.g., 92). With no doorway, we observed reliable anchoring effects: Higher CAPTCHA values produced higher estimates. With the doorway, however, such effects were attenuated or even eliminated. This generalized across tasks involving item valuations, factual questions, and legal judgments and in tests of both incidental and explicit anchoring. This demonstrates how spontaneous visual event segmentation can have profound consequences for higher-level thought.

Autistic individuals show less grouping-induced bias in numerosity judgments

IntroductionWhen items are connected together, they tend to be perceived as an integrated whole rather than as individual dots, causing a strong underestimation of the numerosity of the ensemble. Previous evidence on grouping-induced biases of numerosity has shown a dependency on autistic-like personality traits in neurotypical adults, with a weaker tendency for grouping into meaningful segmented objects in individuals with strong autistic traits. Here we asked whether this result would generalize to the autistic population.MethodsTwenty-two adults with a diagnosis of Autism Spectrum Disorder (ASD) and 22 matched neurotypical controls judged the numerosity of clouds of dot-pairs connected by thin lines.ResultsResults showed no significant group difference in discrimination precision, suggesting that both groups were equally capable performing the task. However, while connecting pairs of dots at moderate numerosities caused large changes in apparent numerosity in the neurotypical controls, particularly those with low autistic-like traits, it had little effect in the group of autistic participants, suggesting significant differences in numerosity estimation between autistic and neurotypical perception. Consistent with earlier studies, the magnitude of the effect covaried strongly with AQ-defined autistic traits in the neurotypical range, reinforcing the idea that autistic traits predict the strength of grouping.DiscussionThese results provide strong support for the theories of autistic perception that highlight dissimilarities in global vs. local processing, and open the door to study grouping mechanisms indirectly, by asking participants to report on the apparent numerosity rather than on the grouping organization per se.

Relationship between the Obligations from the European Convention on Human Rights and the Accession to the European Union

Bosnia and Herzegovina (B&H) has difficulty integrating and moving closer to the goal of becoming a member of the European Union (EU). From the legal perspective, the main issue is the need to fulfil the accession criteria. The article aims to examine the relationship between the obligations under the European Convention on Human Rights and Basic Freedoms (ECHR) and the obligations related to the European Union (EU) accession process, with emphasis on Bosnia and Herzegovina (B&H) as an EU membership candidate country. At first sight, those two obligations are separate. However, upon close examination, a strong link between those two obligations can be established using normative research with a historical approach, statute and case-based approach. On the other hand, the constitutional system of B&H has been described as discriminatory by numerous judgments of the European Court of Human Rights (ECtHR) and, most prominently, by the Sejdic-Finci case. B&H has difficulties implementing those judgments. Implementing those judgments is also set as one of the requirements of EU accession. Even if the two obligations seem separate at first sight, the ECHR has a special position within the law of the EU and is especially important in the accession of new Member States, including B&H. The research results show a special position of the ECHR in EU law and a link between the obligations under the ECHR and EU accession.

Cross-modal anchoring: magnitude priming based on length leads to contrast effect in numerosity judgment

Cross-modal anchoring: magnitude priming based on length leads to contrast effect in numerosity judgment

The neural correlates of individual differences in numerosity perception: A voxel-based morphometry study

Numerosity perception is a fundamental cognitive function in humans and animals. Using an individual difference approach with a comprehensive dataset (N= 249), we performed a voxel-based morphometry analysis to unravel the neuroanatomical substrates associated with individual differences in numerosity perception sensitivity, measured by a classical non-symbolic numerical judgment task. Results showed that greater gray matter volume (GMV) in the left cerebellum, right temporal pole, and right parahippocampal was positively correlated to higher perceptual sensitivity to numerosity. In contrast, the GMV in the left intraparietal sulcus, and bilateral precentral/postcentral gyrus was negatively correlated to the sensitivity of numerosity perception. These findings indicate that a wide range of brain structures, rather than a specific anatomical structure or circuit, forms the neuroanatomical basis of numerosity perception, lending support to the emerging network view of the neural representation of numerosity. This work contributes to a more comprehensive understanding of how the brain processes numerical information.

Numerosity depends on normalized contrast energy: Review and square-root law model

The perceived numerosity of many randomly-located items of fixed contrast depends on the integrated contrast energy (CE) of the display. We show here that a model based on √(CE), normalized by contrast amplitude, can fit numerosity judgment data in various tasks and over a wide range of numerosities. The model shows that judged numerosity increases linearly with √(N), where N is the number of displayed items above the subitization range, and can explain: 1) the general underestimation in absolute judgement of numerosity; 2) the contrast independence (constancy) of numerosity judgment in segregated displays, i.e., judged numerosities are not affected by item contrast; 2) a contrast-dependent illusion where the numerosity of higher-contrast items is further underestimated when intermingled with lower-contrast items; and 3) both the threshold and sensitivity of numerosity discrimination between displays of N and M items. The nearly perfect fit of numerosity judgment data by a square-root law over a wide range of numerosities, including the range typically described by Weber’s law, but excluding subitization, suggests that normalized contrast energy might be the prevailing sensory code underlying numerosity perception.

Learning artificial number symbols with ordinal and magnitude information

The question of how numerical symbols gain semantic meaning is a key focus of mathematical cognition research. Some have suggested that symbols gain meaning from magnitude information, by being mapped onto the approximate number system, whereas others have suggested symbols gain meaning from their ordinal relations to other symbols. Here we used an artificial symbol learning paradigm to investigate the effects of magnitude and ordinal information on number symbol learning. Across two experiments, we found that after either magnitude or ordinal training, adults successfully learned novel symbols and were able to infer their ordinal and magnitude meanings. Furthermore, adults were able to make relatively accurate judgements about, and map between, the novel symbols and non-symbolic quantities (dot arrays). Although both ordinal and magnitude training was sufficient to attach meaning to the symbols, we found beneficial effects on the ability to learn and make numerical judgements about novel symbols when combining small amounts of magnitude information for a symbol subset with ordinal information about the whole set. These results suggest that a combination of magnitude and ordinal information is a plausible account of the symbol learning process.

Age similarities in the anchoring effect in emotion intensity judgment

BackgroundThe anchoring effect refers to the tendency that an individual’s numerical judgment would assimilate to an anchor (a numerical value) that appears before that judgment. This study investigated whether the anchoring effect exists in the emotion judgment of younger and older adults and observed the age-related characteristics. This could not only broaden the explanation of the anchoring effect but also link this classic judgment bias with daily emotion judgment to refresh our understanding of older adults’ ability in emotional perspective taking.MethodParticipants (older adults: n = 64, age range: 60–74, 27 males; younger adults: n = 68, age range: 18–34, 34 males) read a brief emotional story and compared the protagonist’s emotion intensity to a given numerical anchor (lower or higher than the anchor) and then estimated the protagonist’s possible emotion intensity in that story. The task was divided into two cases according to anchor relevance (anchors are relevant or irrelevant relative to the judgment target).ResultsThe results showed that the estimates were higher under high-anchor than low-anchor conditions, suggesting the robust anchoring effect. Further, the anchoring effect was greater for anchor-relevant than anchor-irrelevant tasks and for negative rather than positive emotions. No age differences were found.Discussion and conclusionsThe results indicated that the anchoring effect is robust and stable for younger and older adults, even though the anchor information seemed irrelevant. Finally, perceiving others’ negative emotions is a crucial but rather difficult aspect of empathy, which could be a challenge and requires more caution for accurate interpretation.

Integrated multiple criteria decision-making framework for ranking Pareto optimal solutions of the multiobjective optimization problem of tuned mass dampers

Tuned mass dampers (TMD) have demonstrated effectiveness and robustness in controlling vibrations in marine structures. Solutions to the TMD's Multi-objectives optimization problem (MOOP) always yield a set of Pareto compromise solutions for different conflicting objectives. However, because all the Pareto solutions are non-dominated, the solution of the MOOP still needs to be completed since a single Pareto solution must be selected from a large set of Pareto solutions. Researchers in the literature concentrated on obtaining the Pareto front by solving the MOOP of the TMD for different objective functions. Nonetheless, no effort has been put into selecting the best solution from the Pareto set. Therefore, this paper presents the novel application of the multiple-criteria decision-making (MCDM) techniques in the solution of the MOOP of the TMD applied to a marine structure. The presented framework ensures that the decision-makers (DMs) obtain the most optimal solution from the Pareto set of solutions of the TMD. In this paper, the problem of the TMD applied to a jacket platform is formulated as a MOOP, which comprises conflicting objectives related to TMD cost and performance. NSGA-II is utilized to find a large set of non-dominated TMD tuning parameters from which the DMs must select only one solution. Then, the DMs' preferences are prioritized using the Analytical Hierarchy Process (AHP). Meanwhile, the reasonableness of the DMs' preferences is assessed. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is utilized for ranking the non-dominated set of solutions by assessing the relative closeness of each solution to the ideal solution and farness away from the negative ideal solution. A Finite Element (FE) model of a fixed offshore platform under the dynamic disturbance of irregular waves is numerically solved using COMSOL multiphysics to assess the goals mentioned earlier. A TMD is applied to the marine structure to mitigate wave-induced vibrations. The hydrodynamic forces affecting the structure are computed using Morison's equation, and the irregular waves are characterized using the Joint North Sea Wave Project (JONSWAP) wave spectrum. The presented framework will be used for ranking the Pareto solutions of the TMD applied to the deck of the FE model. The TMD tuning parameters considered in this regard are the TMD mass ratio μ, damping ratio ξopt, and frequency ratio fopt. The findings indicate that the framework presented provides an efficient decision-making methodology for selecting the best solution in various design scenarios. These scenarios can be presented in 2D, 3D, or high-dimensional objective space. Meanwhile, the DMs will be able to select the best compromise among the objectives without the need for numerical judgments. As a result, an efficient TMD that provides valuable response mitigation in a low-cost and effective space was presented.

Absolute or relative size: What do we perceive when we look at a glass that is half full?

Given that both children and adults struggle with fractions in mathematics education, we investigated the processing of nonsymbolic fractions in a continuous form of part-of-the-whole. Continuous features of nonsymbolic numbers (e.g., the size of dots in an array) were found to influence numerosity judgment, but it should be noted that the (continuous) size of a part can be processed relative to a whole or as an absolute size. This study tested which of these size types (i.e., absolute and relative) influences comparison of parts. In two Stroop-like comparison tasks, we measured the interference of each size type on the processing of the other. In Experiment 1, stimuli were three-dimensional-like partially filled glasses of water. In both tasks, congruent trials (in which the larger absolute size was also the larger part-of-the-whole) were processed more efficiently than incongruent trials (in which the larger absolute size was the smaller part-of-the-whole). In Experiment 2, where stimuli were two-dimensional rectangles, this result was replicated under improved experimental control. We conclude that both absolute size and relative size of a part are automatically processed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).