Numerical Distance Research Articles

The distance effect on discrimination ability and response bias during magnitude comparison in a go/no-go task

The distance effect is the change in the performance during numerical magnitude comparison, depending on the numerical distance between the compared numbers (Moyer & Landauer, Nature, 215[5109], 1519-1520, 1967). This effect is generally accepted as evidence for the mental number line (MNL) hypothesis, which proposes that the mental representation of the numbers align in an increasing linear (or monotone) order. The majority of studies investigating the distance effect are focused on the reaction time (RT) findings, which show slower responses for closer numbers. In the present study, we examined the distance effect by applying signal detection theory (SDT) to a magnitude comparison task. We aimed to reveal whether discrimination ability and the response bias measures were affected by the location of numbers on the MNL. To accomplish this, we developed a magnitude comparison task using a go/no-go procedure in which participants performed a magnitude comparison based on a reference number (i.e., 5). Results revealed a substantial distance effect in both sensitivity and response bias measures-a better discrimination performance for far numbers, and a larger response bias for close numbers. In addition, an RT distribution analysis revealed that the distance effect seems to originate mainly from slower responses. Based on the current data, we suggest that sensitivity and response bias measures could offer comprehensive information in the understanding of number-based decisions.

The olfactory capability of dogs to discriminate between different quantities of food.

A previous study failed to find evidence that dogs could use olfactory cues to discriminate between 1 and 5 hot dog slices presented on a single trial (Horowitz et al., Learning and Motivation, 44, 207-217, 2013). In the experiments reported here, multiple trials were used to test dogs' ability to use olfaction to choose one of two opaque containers under which a larger number of food items was placed. In Experiment 1, dogs chose between 1 and 5 hot dog slices. In Experiments 2 and 3, we examined dogs' ability to discriminate between numbers of hot dog slices that varied in the numerical distance and the ratio between the smaller and larger quantities. Experiment 4 explored olfactory discrimination between quantities of a different food, dog kibble. Experiments 1-3 all showed that dogs used olfactory stimuli to choose the larger number of hot dog slices, but Experiments 2 and 3 revealed no effects of distance or ratio between numerical quantities. In Experiment 4, dogs failed to discriminate between 1 and 5 pieces of dog kibble. Factors that allow dogs to use olfactory cues to discriminate between quantities are discussed.

Inhaled Medication Use in Smokers With Normal Spirometry.

The objective of our study was to identify variables associated with inhaled medication use in smokers with normal spirometry (GOLD-0) and to examine the association of inhaled medication use with development of exacerbations and obstructive spirometry in the future. We performed a retrospective multivariable analysis of GOLD-0 subjects identified in data from the COPDGene study to examine factors associated with medication use. Five categories were identified: (1) no medications, (2) short-acting bronchodilator, (3) long-acting bronchodilator; long-acting muscarinic antagonists and/or long-acting β agonist, (4) inhaled corticosteroids (ICS) with or without long-acting bronchodilator, and (5) dual bronchodilator with ICS. Sensitivity analysis was performed excluding subjects with history of asthma. We also evaluated whether long-acting inhaled medication use was associated with exacerbations and obstructive spirometry at the follow-up visit 5 y after enrollment. Of 4,303 GOLD-0 subjects within the analysis, 541 of them (12.6%) received inhaled medications. Of these, 259 (6%) were using long-acting inhaled medications and 282 (6.6%) were taking short-acting bronchodilator. Female sex (odds ratio [OR] 1.47, P = .003), numerous medical comorbidities, radiographic emphysema (OR 2.22, P = .02), chronic bronchitis (OR 1.77, P < .001), dyspnea (OR 2.24, P < .001), asthma history (OR 15.56, P < .001), prior exacerbation (OR 8.45, P < .001), and 6-min walk distance (OR 0.9, P < .001) were associated with medication use. Minimal changes were noted in a sensitivity analysis. Additionally, inhaled medications were associated with increased total (incidence rate ratio 2.83, P < .001) and severe respiratory exacerbations (incidence rate ratio 3.64, P < .001) and presence of obstructive spirometry (OR 2.83, P = .002) at follow-up. Respiratory symptoms, history of asthma, and radiographic emphysema were associated with inhaled medication use in smokers with normal spirometry. These individuals were more likely to develop obstructive spirometry, which suggests that health care providers may be able to identify obstructive lung disease prior to meeting the current criteria for COPD.

Ordinal Approximation for Social Choice, Matching, and Facility Location Problems Given Candidate Positions

In this work, we consider general facility location and social choice problems, in which sets of agents A and facilities F are located in a metric space, and our goal is to assign agents to facilities (as well as choose which facilities to open) to optimize the social cost. We form new algorithms to do this in the presence of only ordinal information , i.e., when the true costs or distances of the agents from the facilities are unknown , and only the ordinal preferences of the agents for the facilities are available. The main difference between our work and previous work in this area is that, while we assume that only ordinal information about agent preferences is known, we also know the exact locations of the possible facilities F. Due to this extra information about the facilities, we are able to form powerful algorithms that have small distortion , i.e., perform almost as well as omniscient algorithms (which know the true numerical distances between agents and facilities) but use only ordinal information about agent preferences. For example, we present natural social choice mechanisms for choosing a single facility to open with distortion of at most 3 for minimizing both the total and the median social cost; this factor is provably the best possible. We analyze many general problems including matching, k -center, and k -median, and we present black-box reductions from omniscient approximation algorithms with approximation factor β to ordinal algorithms with approximation factor 1+2β doing this gives new ordinal algorithms for many important problems and establishes a toolkit for analyzing such problems in the future.

Choosing a servicing company’s strategy while interacting with freight owners at the road transport market

Purpose. To develop the methodology for choosing the strategies of freight forwarding companies in the situation of interaction with freight owners as customers of forwarding services. Methodology. The game-theoretical approach is used to formalize the conflict situation between a freight forwarding company and a cargo owner. A set of services proposed by forwarders is used as the base in order to represent possible strategies of a forwarder as the vector of probabilities that the respective services are provided for a client. The strategies of the cargo owner are represented as a binary variable that shows whether the client uses the provided services or not. The payoff function for a forwarder is defined as the companys profit and the clients payoff function as fee paid for forwarding services. To determine the influence of the demand parameters on the forwarders optimal strategies, the demand for transport services is represented as a flow of requests characterized by two numeric parameters delivery distance and consignment weight. Findings. The conducted experimental studies have shown that as a result of the use of the proposed methodology, the optimal strategy of a forwarding company can always be determined from the payoff matrix. The performed simulation experiment allowed us to state that in most cases the forwarders optimal strategy is mixed (the technological and commercial services should be provided with the given probability while servicing the flow of requests from freight owners). Originality. The studies on the influence of the request flow parameters on the probabilities of choosing the elementary strategies are carried in the paper for the first time. Practical value. The proposed methodology can be used as the basic tool for supporting decisions of freight forwarders while servicing the cargo owners at the market of road freight transportation.

The research and application of intuitionistic fuzzy decision making

This paper studies intuitionistic fuzzy (IF) decision making problems using an integrated approach. Firstly, an IF induced generalized ordered weighted averaging distance (IFIGOWAD) operator is introduced, that covers numerous IF aggregations distance operators. Then, two more generalized operators named IF quasi induced OWAD (Quasi-IFIOWAD) and IF induced generalized hybrid average distance (IFIGHAD) operator are presented. Furthermore, a new method using above operators is introduced to IF decision making problem and online trade systems. Finally, two real cases are present to show the effect of the method.

Empirische Arbeit: Motivationsprofile bei Verwendung eines Lernspiels zur Messung des Bruchverständnisses in der Schule – Eine latente Profilanalyse

Lernspiele gewinnen auch in der Schule zunehmend an Bedeutung als motivationsforderliche Lehr- und Lernmethode. In einer Feldstudie mit 256 Schulerinnen und Schulern der siebten Schulstufe wurde daher untersucht i) inwiefern sich grundlegende Effekte der Forschung zu numerischer Kognition mit einem digitalen Lernspiel zur Messung des Verstandnisses von Bruchen replizieren lassen und ii) ob sich spezifische Motivationsprofile bei der Benutzung des Lernspiels identifizieren lassen. Die beobachtete spezifische Assoziation der Leistung im Lernspiel mit Mathematiknoten als auch der aus der Grundlagenforschung bekannte Distanzeffekt belegen die Validitat des Lernspiels. Mittels latenter Profilanalyse wurden drei Gruppen von Schulerinnen und Schulern identifiziert, die sich hinsichtlich selbst- und fremdbestimmter Motivation sowie dem wahrgenommenen positiven Affekt wahrend des Spielens unterschieden. Erwartungsgemas verbrachten selbstregulierte Schulerinnen und Schuler die meiste Zeit mit dem Spiel und hatten das positivste Spielerleben. Diese Ergebnisse spezifizieren die motivationalen Moglichkeiten (digitaler) Lernspiele im Schulunterricht.

Impact of the COVID-19 pandemic on travel behavior in Istanbul: A panel data analysis

The COVID-19 pandemic, which was reported in early January 2020 in China and spread rapidly around the globe, will certainly remain as one of the most impactful disruptive events of the 21st century. To contain the spread of the virus while awaiting a vaccine, countries applied different approaches from simply giving advice on personal hygiene and applying progressive measures to total lockdown. This paper aims to investigate the impacts of the pandemic on travel behavior in Istanbul, Turkey, through a longitudinal panel study conducted in three phases during the early stages of the epidemic and pandemic. The paper reflects the travel behavior evolution during the development of the outbreak resulting from residents’ self- regulation and governmental measures, distinguishing travel for commute, Social/Recreational/Leisure (SRL), and shopping activities, as well as use of different travel modes based on various socio-economic characteristics. Due to the application of the social distancing of at least 1.5 m, closure of numerous non-essential venues, encouraging teleworking and distance education, job losses and cancellation of all social gatherings in Istanbul between the second and third phase of our data collection, the transition in travel activity pattern and transport mobility appears to be quite extreme, particularly for commuting and SRL trips.

Tactile to visual number priming in the left intraparietal cortex of sighted Braille readers

Numbers can be presented in different notations and sensory modalities. It is currently debated to what extent these formats overlap onto a single representation. We asked whether such an overlap exists between symbolic numbers represented in two sensory modalities: Arabic digits and Braille numbers. A unique group of sighted Braille readers underwent extensive Braille reading training and was tested in an fMRI repetition-suppression paradigm with tactile Braille digit primes and visual Arabic digit targets. Our results reveal cross-modal priming: compared to repetition of two different quantities (e.g., Braille “5” and Arabic “2”), repetition of the same quantity presented in two modalities (e.g., Braille “5” and Arabic “5”) led to a reduction of activation in several sub-regions of the Intraparietal Sulcus (IPS), a key cortical region for magnitude processing. Thus, in sighted Braille readers, the representations of numbers read by sight and by touch overlap to a degree sufficient to cause repetition suppression. This effect was modulated by the numerical prime-probe distance. Altogether this indicates that the left parietal cortex hosts neural assemblies that are sensitive to numerical information from different notations (number words or Arabic digits) and modalities (tactile and visual).

Cognitive control in number processing: new evidence from task switching

Recently, it was demonstrated that even basic numerical cognition such as the processing of number magnitude is under cognitive control. However, evidence so far primarily came from adaptation effects to stimulus characteristics (e.g., relative frequency of specific stimulus categories). Expanding this approach, we evaluated a possible influence of more active exertion of cognitive control on basic number processing in task switching. Participants had to perform a magnitude comparison task while we manipulated the order of compatible and incompatible input–output modalities (i.e., auditory/vocal input–visual/manual output vs. auditory/visual input–manual/vocal output, respectively) on the trial level, differentiating repeat vs. switch trials. Results indicated that the numerical distance effect but not the problem size effect was increased after a switch in input–output modality compatibility. In sum, these findings substantiate that basic number processing is under cognitive control by providing first evidence that it is influenced by the active exertion of cognitive control as required in task switching.

An algorithm based on bidirectional searching and geometric constrained sampling for automatic manipulation planning in aircraft cable assembly

Robotic manipulation of deformable linear objects has potential application in aircraft cable assembly. However, it is difficult to be implemented in real tasks due to requiring prediction of the object’s deformation and obstacle-free manipulation planning with high efficiency. Aiming at exploring automatic assembly planning for aircraft cables assembly in narrow cabins with obstacles, this paper proposes a novel planning algorithm named RRT-BwC (Bi-direction with Constrain). Firstly, formulation of the question and the manipulation objects are presented with geometric definitions. Then a bi-RRT-tree searching method is developed to design the planner for overcoming obstacles in the high dimensional planning space. The numerical distance between configurations in the cable shape space are defined to measure the demands for their transition in consideration of the manipulation logics. And the sampling zone constrains to the shape configuration nodes are also discussed. Finally, the algorithm presents a valid manipulation sequence for robotic manipulation. The functionality and performance of the improved RRT approach are demonstrated with a simulated real-world problem of aircraft cable assembly, exhibiting computation efficiency promotion.

Neurofunctional plasticity in fraction learning: An fMRI training study.

Fractions are known to be difficult forchildren and adults. Behavioral studies suggest that magnitude processing of fractions can be improved via number line estimation (NLE) trainings, but little is known about the neural correlates of fraction learning. To examine the neuro-cognitive foundations of fraction learning, behavioral performance and neural correlates were measured before and after a five-day NLE training. In all evaluation tasks behavioral performance increased after training. We observed a fronto-parietal network associated with number magnitude processing to be recruited in all tasks as indicated by a numerical distance effect. For symbolic fractions, the distance effect onintraparietal activation was only observed after training. The absence of a distance effect of symbolic fractions before the training could indicate an initially less automatic access to their overall magnitude. NLE training facilitates processing of overall fraction magnitude as indicated by the distance effect in neural activation.

Using fake text vectors to improve the sensitivity of minority class for macro malware detection

To detect new malware, machine learning approaches require many training samples. These training samples contribute to build an accurate model. To maintain the accuracy, collecting comprehensive samples continuously is very important. However, new malicious samples appear one after another, and thereby making it difficult. Hence, actual small training samples do not likely to represent the entire population adequately. Despite this gap between ideal and reality, few studies have addressed this practical problem in macro malware. To enhance small training samples, data augmentation is efficient in the field of image recognition. Data augmentation with Generative Adversarial Networks (GANs) is a reasonable approach for oversampling the minority class. A major difficulty of GANs is to generate fake samples that represent the context. This paper attempts to generate fake text vectors with Paragraph Vector to enhance small training samples. Paragraph Vector is a model to convert text into vectors, which represents the context and numerical distance. These features allow to directly vary each element of the vectors. Our method adds random noise to the vectors to generate fake text vectors which represent the context. This paper applies this technique to detect new malicious VBA (Visual Basic for Applications) macros to address the practical problem. This generic technique could be used for not only malware detection, but also any imbalanced and contextual data. To simulate small training samples, we reduce the malicious samples, and generate fake samples from the reduced ones. The experimental result shows that the fake samples enhance our model, and improve the detection rate.

Record Linkage of Crashes with Injuries and Medical Cost in Puerto Rico

Cost considerations are critical in the analysis and prevention of traffic crashes. Integration of cost data into crash datasets facilitates the crash-cost analyses with all their related attributes. It is, however, a challenging task because of the lack of availability of unique identifiers across the databases and because of privacy and confidentiality regulations. This study performed a record linkage comparison between the deterministic and probabilistic approaches using attributes matching techniques with numerical distance and weight patterns under the Fellegi–Sunter approach. As a result, the deterministic algorithm developed using the exact match of the 14-digit police accident record number had an overall matching performance of 52.38% of real matched records, while the probabilistic algorithm had an overall matching performance of 70.41% with a quality measurement of the sensitivity of 99.99%. The deterministic approach was thus outperformed by the probabilistic approach by approximately 20% of records matched. The probabilistic matching with numerical variables seems to be a good matching strategy supported by quality variables. On record matching, a multivariable regression model was developed to model medical costs and identify factors that increase the costs of treating injured claimants in Puerto Rico.

Professional mathematicians do not differ from others in the symbolic numerical distance and size effects

The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes.

Further insights into the operation of the Chinese number system: Competing effects of Arabic and Mandarin number formats

Here we report the results of a speeded relative quantity task with Chinese participants. On each trial a single numeral (the probe) was presented and the instructions were to respond as to whether it signified a quantity less than or greater than five (the standard). In separate blocks of trials, the numerals were presented either in Mandarin or in Arabic number formats. In addition to the standard influence of numerical distance, a significant predictor of performance was the degree of physical similarity between the probe and the standard as depicted in Mandarin. Additionally, competing effects of physical similarity, defined in terms of the Arabic number format, were also found. Critically the size of these different effects of physical similarity varied systematically across individuals such that larger effects of one compensated for smaller effects of the other. It is argued that the data favor accounts of processing that assume that different number formats access different format-specific representations of quantities. Moreover, for Chinese participants the default is to translate numerals into a Mandarin format prior to accessing quantity information. The efficacy of this translation process is itself influenced by a competing tendency to carry out a translation into Arabic format.

Food Quantity Discrimination in Angelfish (Pterophyllum scalare): The Role of Number, Density, Size and Area Occupied by the Food Items.

Quantity discrimination, the ability to identify, process, and respond to differences in number, has been shown in a variety of animal species and may have fitness value. In fish, the ability to distinguish between numerically different shoals has been well studied. However, little work has been devoted to the investigation of such ability in a foraging context. Nevertheless, angelfish (Pterophyllum scalare) have been previously shown to be able to discriminate numerically different sets of food items, with variables such as size and density of the food items playing important roles in making the choice. Here, we examine the possible role of other numerical and non-numerical variables. Using a spontaneous binary choice task, we contrasted sets of food items differing in specifically controlled ways: (1) different numerical size but equal inter-item distance; (2) different numerical size and different inter-item distance; and (3) identical total contour length and area occupied but different individual food size and inter-food distance between the contrasted food sets. In Experiment 1, angelfish were found to prefer the sets with a large number of food items. In Experiment 2, they preferred the numerically smaller sets with clustered items to the numerically larger sets with scattered items, but only when the sets were in the large number range (10 vs. 5 food items). Finally, in Experiment 3 fish preferred numerically smaller sets with large-sized and scattered food items in the large number range sets. We conclude that food item number, density, and size may not be considered individually by angelfish, but instead, the fish respond to all these factors attempting to maximize energy gained from eating the food while minimizing energy expenditure collecting and/or protecting the food.

A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students

School mathematics comprises a diversity of concepts whose cognitive complexity is still poorly understood, a chief example being fractions. These are typically taught in middle school, but many students fail to master them, and misconceptions frequently persist into adulthood. In this study, we investigate fraction comparison, a task that taps into both conceptual and procedural knowledge of fractions, by looking at performance of highly mathematically skilled young adults. Fifty-seven Chilean engineering undergraduate students answered a computerized fraction comparison task, while their answers and response times were recorded. Task items were selected according to a number of mathematically and/or cognitively relevant characteristics: (a) whether the fractions to be compared shared a common component, (b) the numerical distance between fractions, and (c) the applicability of two strategies to answer successfully: a congruency strategy (a fraction is larger if it has larger natural number components than another) and gap thinking (a fraction is larger if it is missing fewer pieces than another to complete the whole). In line with previous research, our data indicated that the congruency strategy is inadequate to describe participants’ performance, as congruent items turned out to be more difficult than incongruent ones when fractions had no common component. Although we hypothesized that this lower performance for congruent items would be explained by the use of gap thinking, this turned out not to be the case: evidence was insufficient to show that the applicability of the gap thinking strategy modulated either participants’ accuracy rates or response times (although individual-level data suggest that there is an effect for response times). When fractions shared a common component, instead, our data display a more complex pattern that expected: an advantage for congruent items is present in the first experimental block but fades as the experiment progresses. Numerical distance had an effect in fraction comparison that was statistically significant for items without common components only. Altogether, our results from experts’ reasoning reveal nuances in the fraction comparison task with respect to previous studies and contribute to future models of reasoning in this task.

An improved numerical distance relay based on CCVT transient characteristic matching

The transients of the coupling capacitor voltage transformer (CCVT) have an impact on the performance of distance relays and result in the overreach problem. Based on the equal transfer process of transmission lines (ETPTL) theory, the virtual digital CCVT can be applied to reduce the impact of the CCVT transients and improve the operation speed of distance relays. The virtual digital CCVT is required to have the same transient characteristics as the actual CCVT. This paper proposes a simple and universal design method of virtual digital CCVT. Based on the CCVT transient characteristic matching and the ETPTL theory, this paper proposes an improved numerical distance relay algorithm to prevent the overreach problem of distance relays without sacrificing the operation speed of distance relay under the internal fault conditions. An extensive performance evaluation using PSCAD/EMTDC simulation corroborates the effectiveness of the proposed distance relay under different fault conditions. Finally, a prototype device based on the proposed distance relay is developed in laboratory and evaluated through a hardware in loop test using real-time digital simulator (RTDS).

Judging the order of numbers relies on familiarity rather than activating the mental number line

A series of effects characterises the processing of symbolic numbers (i.e., distance effect, size effect, SNARC effect, size congruency effect). The combination of these effects supports the view that numbers are represented on a compressed and spatially oriented mental number line (MNL) as well as the presence of an interaction between numerical and other magnitude representations. However, when individuals process the order of digits, response times are faster when the distance between digits is small (e.g., 1-2-3) compared to large (e.g., 1-3-5; i.e., reversed distance effect), suggesting that the processing of magnitude and order may be distinct. Here, we investigated whether the effects related to the MNL also emerge in the processing of symbolic number ordering. In Experiment 1, participants judged whether three digits were presented in order while spatial distance, numerical distance, numerical size, and the side of presentation were manipulated. Participants were faster in determining the ascending order of small triplets compared to large ones (i.e., size effect) and faster when the numerical distance between digits was small (i.e., reversed distance effect). In Experiment 2, we explored the size effect across all possible consecutive triplets between 1 and 9 and the effect that physical size has on order processing. Participants showed faster reactions times only for the triplet 1-2-3 compared to the other triplets, and the effect of physical magnitude was negligible. Symbolic order processing lacks the signatures of the MNL and suggests the presence of a familiarity effect related to well-known consecutive triplets in the long-term memory.