Academic literature on the topic 'Visual Number Sense'

A strong foundation in early number concepts is critical for students’ future success in mathematics. Research suggests that visual representations, like a number line, support students’ development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction to transition from concrete to visual to abstract representations of mathematics concepts supports students’ conceptual understanding. This column describes and illustrates how teachers can use number lines and features of explicit and systematic instruction to support students’ early development of number sense.

Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense . Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats : adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.

Number sense, the ability to estimate numerosity, is observed in naïve animals, but how this cognitive function emerges in the brain remains unclear. Here, using an artificial deep neural network that models the ventral visual stream of the brain, we show that number-selective neurons can arise spontaneously, even in the complete absence of learning. We also show that the responses of these neurons can induce the abstract number sense, the ability to discriminate numerosity independent of low-level visual cues. We found number tuning in a randomly initialized network originating from a combination of monotonically decreasing and increasing neuronal activities, which emerges spontaneously from the statistical properties of bottom-up projections. We confirmed that the responses of these number-selective neurons show the single- and multineuron characteristics observed in the brain and enable the network to perform number comparison tasks. These findings provide insight into the origin of innate cognitive functions.

It has been suggested that numerosity is an elementary quality of perception, similar to colour. If so (and despite considerable investigation), its mechanism remains unknown. Here, we show that observers require on average a massive difference of approximately 40% to detect a change in the number of objects that vary irrelevantly in blur, contrast and spatial separation, and that some naive observers require even more than this. We suggest that relative numerosity is a type of texture discrimination and that a simple model computing the contrast energy at fine spatial scales in the image can perform at least as well as human observers. Like some human observers, this mechanism finds it harder to discriminate relative numerosity in two patterns with different degrees of blur, but it still outpaces the human. We propose energy discrimination as a benchmark model against which more complex models and new data can be tested.

L'ambiente naturale in cui gli animali sono costretti a sopravvivere modella il loro cervello e il modo in cui si comportano per adattarsi e superare le pressioni naturali. Queste pressioni selettive potrebbero aver determinato l'emergere di un antico sistema neurale adatto a estrarre rapidamente informazioni astratte da set di oggetti, come la loro numerosità, per prendere decisioni informate fondamentali per la sopravvivenza e l'adattamento. La teoria del "Senso numerico" rappresenta il modello neurale più influente che tiene conto delle prove neuropsicologiche e psicofisiche negli esseri umani e negli animali. Tuttavia, questo modello è ancora ampiamente dibattuto a causa delle difficoltà metodologiche nell'isolare i segnali neurali relativi all'elaborazione della numerosità astratta "discreta" (cioè il numero reale di oggetti in un set) da quelli relativi ad altre caratteristiche correlate o confuse con la numerosità nell’input sensoriale grezzo (p. es., area, densità, frequenza spaziale, ecc.). La presente tesi si proponeva di indagare quali meccanismi potrebbero essere alla base delle rappresentazioni della numerosità visiva, superando le difficoltà nell'isolare le caratteristiche discrete da quelle continue. Dopo aver esaminato i principali modelli teorici e i risultati della letteratura (Capitolo 1 e 2), nel Capitolo 3 abbiamo presentato un paradigma psicofisico in cui le linee dei contorni illusori (IC) simili alla famosa illusione di Kanizsa, sono state utilizzate per manipolare la connessione (ad es., grouping) degli elementi nel set, controllando tutte le caratteristiche continue attraverso i livelli di connessione. Abbiamo mostrato che la numerosità era sottostimata quando le connessioni aumentavano, suggerendo che la numerosità si basa su oggetti percettivi segmentati piuttosto che su caratteristiche grezze di basso livello. Nel Capitolo 4, abbiamo controllato la luminosità illusoria che accompagna gli ICs. Sfruttando le proprietà percettive dell'illusione di Kanizsa generata con induttori con contrasto inverso, abbiamo scoperto che la sottostima era insensibile alla direzione del contrasto dell'induttore, suggerendo che l'effetto era specificamente indotto da un raggruppamento di bordi indipendente dalla polarità del contrasto e non dovuto alla luminosità percepita. Nel Capitolo 5, abbiamo manipolato contemporaneamente il raggruppamento con le linee IC e la dimensione percepita dei set numerici usando illusioni di dimensioni classiche (Ponzo Illusion). Utilizzando una combinazione di illusioni visive, abbiamo dimostrato che la percezione della numerosità non si basa su segnali continui percepiti, nonostante il segnale continuo possa influenzare la percezione numerica. Nel capitolo 6 abbiamo affrontato la questione con un approccio fisico diretto: utilizzando l'analisi di Fourier per equalizzare la frequenza spaziale (SF) negli stimoli, abbiamo mostrato che l'energia dello stimolo non è coinvolta nella rappresentazione della numerosità. Piuttosto la segmentazione degli elementi e l'organizzazione percettiva hanno spiegato i nostri risultati principali. Nel capitolo 7 abbiamo anche mostrato che l'effetto del rapporto, un importante segno distintivo della codifica Weber-like della percezione numerica, non è principalmente spiegato dall'energia dello stimolo o SF. Infine, nel Capitolo 8, abbiamo anche fornito la prima evidenza empirica che la numerosità non simbolica è rappresentata spazialmente indipendentemente dal contenuto fisico (SF) degli stimoli. Nel complesso, questa tesi supporta l'idea che l'elaborazione della numerosità non si basa semplicemente su caratteristiche di basso livello, ma suggerisce piuttosto direttamente che le informazioni discrete sono al centro del senso del numero.
The natural environment in which animals are forced to survive shapes their brain and the way in which they behave to adapt and overcome natural pressures. These selective pressures may have determined the emergence of an evolutionary ancient neural system suited to rapidly extract abstract information from collections, such as their numerosity, to take informed decisions pivotal for survivance and adaptation. The “Number Sense” theory represents the most influential neural model accounting for neuropsychological and psychophysical evidence in humans and animals. However, this model is still largely debated because of the methodological difficulties in isolating neural signals related to “discrete” (i.e., the real number of objects in a collection) abstract numerosity processing from those related to other features correlated or confounded with numerosity in the raw sensory input (e.g., visual area, density, spatial frequency, etc). The present thesis aimed to investigate which mechanisms might be at the basis of visual numerosity representations, overcoming the difficulties in isolating discrete from continuous features. After reviewing the main theoretical models and findings from the literature (Chapter 1 and 2), in the Chapter 3 we presented a psychophysical paradigm in which Kanizsa-like illusory contours (ICs) lines were used to manipulate the connectedness (e.g., grouping strength) of the items in the set, controlling all the continuous features across connectedness levels. We showed that numerosity was underestimated when connections increased, suggesting that numerosity relies on segmented perceptual objects rather than on raw low-level features. In Chapter 4, we controlled for illusory brightness confounds accompanying ICs. Exploiting perceptual properties of the reverse-contrast Kanizsa illusion, we found that underestimation was insensitive to inducer contrast direction, suggesting that the effect was specifically induced by a sign invariant boundary grouping and not due to perceived brightness confounds. In Chapter 5, we concurrently manipulated grouping with ICs lines and the perceived size of the collections using classic size illusions (Ponzo Illusion). By using a combination of visual illusions, we showed that numerosity perception is not based on perceived continuous cues, despite continuous cue might affect numerical perception. In Chapter 6 we tackled the issue with a direct physical approach: using Fourier analysis to equalize spatial frequency (SF) in the stimuli, we showed that stimulus energy is not involved in numerosity representation. Rather segmentation of the items and perceptual organization explained our main findings. In Chapter 7 we also showed that the ratio effect, an important hallmark of Weber-like encoding of numerical perception, is not primarily explained by stimulus energy or SF. Finally, in Chapter 8, we also provided the first empirical evidence that non-symbolic numerosity are represented spatially regardless of the physical SF content of the stimuli. Overall, this thesis strongly supports the view that numerosity processing is not merely based on low-level features, and rather strongly suggests that discrete information is at the core of the Number Sense.

Davis and Pérusse (1988) argued that, although animals can be trained to make numerical discriminations, they do so only as a last-resort strategy, when extensive training is provided and all other cues are eliminated. In spite of this criticism, in the last decade various types of numerical competences have been demonstrated in nonverbal creatures - namely pre-verbal infants and non-human species - that demonstrated the presence of number competence in the absence of language (reviews in Gallistel and Gelman, 1992; Dehaene, 1997; Hauser and Spelke, 2004). In the present study three separate sets of experiments were carried out to investigate respectively: Spontaneous numerical discrimination following imprinting, number discrimination using a conditioning procedure and ordinal numerical competence. In the first set of experiments, by employing a spontaneous choice paradigm, the ability to discriminate small sets of objects was confirmed in 3-day-old-chicks even when the continuous variables were controlled for. These data showed, for the first time, that spontaneous number discrimination can be based on numerical cues only. In the second set of experiment, chicks' ability to discriminate between small sets of object (up to 3) was confirmed by employing operant conditioning procedures. What is interesting is that although training was done with only one specific set of stimuli, in which number co-varied with several continuous physical variables, the chicks seemed to encode number rather than physical variables. These data also provided the first evidence of numerical discrimination of partly occluded objects. Furthermore, discrimination of small numerosities in young chicks seems to be carried out using an Object File System, with a set-size limit of around 4 elements. In the third set of experiments investigating ordinal abilities show that 5-day-old-chicks can successfully learn to identify a target on the exclusive basis of its serial position in a series of 10. A peculiar finding, in Experiment 4.3, was that whenever position had to be identified on a left/right oriented series, in the generalization test, chicks would more often find the correct position by starting from the left end of the series rather than from the right end. In the absence of environmental asymmetries a possible explanation would be that there is a right hemispheric dominance (left visual hemifield) for this sort of task. It would be interesting for future experiments to establish the limit of such ordinal ability, using a different apparatus with more positions as well as trying to understand the hemispheric asymmetry raised in this experiment. All these data demonstrated the presence of rudimentary numerical competence even in a species so distant and so different from humans. These results support the hypothesis that numerical competences are not only a prerogative of adult humans but that such abilities should have an evolutionary precursor in animals.

Visualisation is increasingly being recognised as having a significant role in the learning of mathematics especially when students are solving mathematical problems (Thornton, 2001). It is argued that visualisation is a powerful tool for learners to construct mental and physical representations that correctly mirror mathematical relationships and concepts. To gain a thorough understanding of the scope of visualisation, three Visual Technology for Autonomous Learning of Mathematics (VITALmaths) (www.vitalmaths.com) video clips were uploaded on mobile phones of each of the eleven participating student teachers who used them in their teaching practice. This is in cognisance of the educational potential offered by mobile phones and their current pervasiveness in the daily lives of both teachers and learners in Zambia (Zambia. Ministry of Education [M.O.E], 2013]). This study sought to investigate how VITALmaths video clips on mobile phones could be used by student teachers as a visualisation tool in the teaching of Number Sense. The videos of the lessons formed the core of my analysis. The study was conducted at four primary schools by eleven student teachers of a public university in Zambia. The study is framed as a case study and is grounded within the interpretive paradigm. The findings revealed that the student teachers’ use of the video clips in the classrooms for teaching was generally approached from two perspectives: at the beginning of the lesson or at the end. The videos were used at the beginning of the lesson as a means to introduce a topic or an idea, and at the end of the lesson to consolidate what was taught. The videos were also used to enhance the conceptual understanding of Number Sense. The findings also revealed that students encountered both enabling and constraining factors in their use of mobile phones to teach number sense. The overall findings revealed that, if well utilised, mobile phones as visualisation tools had the potential to enhance the teaching of Mathematics in general and Number Sense in particular, and therefore teachers should be encouraged to use them in their teaching.

La capacité à estimer rapidement le nombre d'éléments dans une scène sans compter explicitement a fait l'objet de nombreuses recherches.Les études expérimentales et les modèles computationnels ont cherché à révéler les mécanismes permettant au cerveau humain de percevoir la numérosité d'un seul coup d'œil. Les récentes avancées en imagerie, incluant l'IRM fonctionnelle, l'analyse multivariée et la modélisation du champ récepteur des neurones, ont permis d'en apprendre davantage sur la manière dont l'information numérique est encodée dans le cerveau. En particulier, ces travaux ont mis en lumière le rôle de régions telles que les cortex frontal et pariétal dans la perception numérique. Malgré ces avancées, la recherche sur la perception de la numérosité a souvent reposé sur des stimuli visuels simplifiés. Bien que pratiques, ces stimuli ne reflètent pas la complexité des environnements visuels réels et négligent souvent l'impact de leurs statistiques non numériques, qui covarient pourtant avec la numérosité. Cette dépendance soulève des questions sur la validité écologique des résultats actuels et questionne si la numérosité est une propriété perçue directement ou inférée à partir d'autres caractéristiques visuelles. Les mécanismes sous-jacents à la perception visuelle de la numérosité restent donc une question ouverte. Dans cette thèse, nous avons développé un ensemble de stimuli synthétiques photoréalistes afin de pallier ces limites. Ces stimuli présentent une grande variabilité visuelles tout en permettant un contrôle expérimental précis. Ce jeu de données permet d'étudier la perception de la numérosité dans des contextes plus proches des images naturelles. À l'aide de ces stimuli photoréalistes, constitués d'objets 3D intégrés dans des scènes variées, nos analyses ont montré que les réseaux de neurones convolutifs profonds (CNN) optimisés pour la reconnaissance d'objets peuvent encoder des informations numériques dans divers contextes. À l'inverse, les réseaux non entraînés ne parviennent pas à discriminer le contenu numérique, se limitant à encoder des statistiques visuelles de bas niveau. Ces résultats indiquent que les modèles non entraînés sont inadaptés pour comprendre notre capacité à extraire le contenu numérique d'une scène et soulignent l'importance d'utiliser des stimuli complexes pour étudier la représentation de la numérosité. Étant donné le rôle des CNN en tant que modèles de la voie visuelle ventrale, nous avons ensuite exploré la représentation numérique au-delà des régions dorsales traditionnelles. Ainsi, nous avons enregistré l'activité cérébrale de participants portant leur attention sur le contenu numérique de nos stimuli visuels photoréalistes. Ce paradigme expérimental a permis de dissocier l'information numérique des statistiques visuelles corrélées, et ainsi d'examiner leurs contributions distinctes. Nos résultats ont révélé que les zones occipito-latérales, souvent associées à la reconnaissance d'objets, peuvent traiter simultanément des informations numériques et liées aux objets. De plus, les régions pariétales ont démontré un rôle spécialisé dans l'encodage de l'information numérique. En revanche, les statistiques visuelles de bas niveau influencent principalement les régions visuelles primaires et ventrales temporales, avec un impact minimal sur les régions dorsales supérieures. Ces résultats soulignent l'existence d'une organisation hiérarchique dans le traitement visuel, avec une progression de l'encodage de caractéristiques élémentaires à la représentation abstraite d'objets et de la numérosité dans les régions avancées du cerveau. Nos travaux mettent en lumière la nature abstraite de la représentation de la numérosité et approfondissent ainsi notre compréhension de la cognition numérique dans des environnements visuels réalistes. Ils soulignent également l'importance d'utiliser des stimuli complexes pour découvrir les mécanismes sous-jacents à l'extraction de la numérosité dans le cerveau
The ability to rapidly estimate the number of items in a scene without explicit counting, known as visual number sense, has been the focus of extensive research. Experimental studies and computational models have sought to uncover the mechanisms that enable the human brain to extract numerosity at a glance. Recent advances in imaging techniques, including ultra-high-field functional MRI (fMRI), multivariate pattern analysis, and population receptive field (pRF) modeling, have provided deeper insights into how numerical information is encoded in the brain.These studies have highlighted the involvement of higher-order regions, such as the frontal and parietal cortices, but also lower-level areas, in numerical perception. Most research on numerosity perception has relied on simplified visual stimuli, such as binary dot arrays. While useful, these stimuli fail to capture the complexity of real-world visual environments and present a special case where numerosity is tightly correlated with some low-level statistics of the visual input. This raises questions about ecological validity, and about the extent to which previous findings reflected the discrete number of items per se as opposed to correlated low-level factors. In this thesis, we developed a synthetic photorealistic stimulus dataset to address these limitations, introducing high variability in the characteristics of both objects and scenes while maintaining precise experimental control. This dataset allows for the study of numerosity perception in contexts closer to natural images. Using this new dataset of photorealistic renderings of 3D objects embedded in diverse background scenes, our analyses demonstrated that deep convolutional neural networks (CNNs) optimized for object recognition could encode numerical information with robustness to diverse objects and scenes in distributed activity patterns of their higher convolutional layers. Conversely, untrained networks failed to discriminate numerical content across changes in those other high-level visual properties and mainly encoded low-level summary statistics.These findings suggest that untrained models may not truly encode discrete numerosity and emphasize the importance of using complex stimuli to probe the neural mechanisms of visual number sense. Given the role of CNNs' as models of the ventral visual stream, this research motivates further investigation of how numerical information is represented in the brain beyond commonly studied dorsal-parietal areas. Therefore, in an independent 7T fMRI study, we recorded brain activity of both ventral and dorsal visual pathways while participants viewed and attended to the numerical content of similar synthetic photorealistic stimuli.This experimental paradigm enabled us to disentangle numerical information from correlated visual statistics, allowing for the examination of their distinct contributions to brain activity. Our findings revealed that lateral occipital areas, commonly linked to object recognition, could simultaneously represent numerical and object-related information. Additionally, dorsal parietal regions demonstrated a specialized role in encoding numerical information beyond basic visual features. In contrast, low-level visual statistics primarily influenced early visual and higher-level ventral temporal areas, with minimal impact on higher-order dorsal regions. These findings illustrate a hierarchical organization in visual processing, transitioning from encoding of low-level features to more invariant representations of objects and numerosity in higher-level brain areas. Our work underscores the abstract nature of numerosity representations, advancing our understanding of numerical cognition under more realistic visual conditions

Consumers are constantly evaluating quantitative information, such as the prices of different products, the time spent on an activity, or the distance covered during one day. Substantial research in psychology has demonstrated that judgments of quantity in one dimension (e.g., numbers) influence subsequent judgments on another dimension (e.g., time). The present research contributes to a growing body of work by exploring how the shared representation of time, space, and numbers affects consumer perceptions and behaviors. My first dissertation essay explores how the organization of time on a spatial plane affects temporal judgments, product evaluations, and intertemporal discounting (i.e., time-space interaction). It has been well documented that Western consumers typically arrange temporal sequences following a past-left, future-right spatial pattern. Merging insights gained from numerical cognition and time psychology, the author develops a framework to explain how displaying temporal sequences congruently with this spatial organization of time increases subjective estimations of time and biases consumers toward present rewards. My second dissertation essay seeks to understand how and why expressing quantitative information in symbolic code (i.e., “6”) compared to verbal code (i.e., “six”) affects magnitude judgments and product evaluations (i.e., time-number interaction). Two rival accounts to explain the symbol-verbal effect are described and tested: (1) a systematic processing account based on Arabic symbols’ perceptual and cognitive features and (2) a fluency account based on the frequency of use and facilitation of processing Arabic symbols. This research has important managerial implications related to the effective communication of quantitative information.

The cognitive predictors of mathematical abilities and disabilities/disorders (MD) were investigated. An overview is given of the prediction by early numeracy skills such as Piagetian logical thinking, counting, and number comparison skills. In addition, studies of relationships between language and numeracy in kindergarten and grade 1 are discussed. Moreover, the chapter sought out to extend our knowledge regarding the relationship between motor, visual and visuomotor skills and mathematical abilities and disabilities. Furthermore, the chapter discusses studies of working memory, inhibition, naming speed and inference control as cognitive predictors for mathematical abilities and MD. Finally findings about the sensitivity of number sense for MD are provided.

AbstractNew communication patterns define market preferences, while the constant use of e-devices in daily life impacted the common sense through the interpretation of visual codes. It is necessary to determine the quintessential steps to define a strategic approach to the European audio-visual aarket and find new opportunities for research, application and creation of new iconic audiovisuals to design and deliver cognitive-emotional experiences for an inclusive and accessible cultural heritage. The digital revolution has altered the production of various industrial sectors, the audio-visual market including and the use of outdated languages and technologies results in the loss of the audience in the sector. Transferring domain specific expertise and know how into new technologies, is not only adding to the quality of contents and the tradition of the sector, but it is becoming a factor for further developments and progress. Supported by the EU funded project BSB/831/ HERiPRENEURSHIP “Establishing long-lasting partnerships to upgrade heritage-based offers and create new investment opportunities in tourism and the cultural and creative industries”, a novel cultural experience pattern is introduced for the 6 Unesco-listed properties in Greece, Romania, Bulgaria, Moldova, Georgia, and Türkiye in the form of a multimedia eBook collection. The design is articulated in two central moments: (a) the presentation of a methodology acquired from many years of research in new media languages and applied in a number of European case studies on the use of tangible or intangible cultural heritage as instruments of social cohesion; (b) from a practical point of view, this methodology is applied to stories, myths, traditions and history reconfigured for the construction of new stories for an unlimited global audience. This paper discusses the process to lead a multicultural and multigenerational audience towards quality experiences at places of cultural significance through an integrated word-image relationship in the digital environment.

Abstract This chapter assesses a simple but immensely powerful concept-the number of times a loop winds around a point. As the name suggests, the winding number v(L, 0) of a closed loop L about the origin 0 is simply the net number of revolutions of the direction of z as it traces out L once in its given sense. A loop is called simple if it does not intersect itself; in the case of a loop that is not simple, it is no longer obvious which points are to be considered inside the loop, and which are outside. The winding number concept allows one to make the desired distinction clearly. The chapter then looks at Hopf’s Degree Theorem; polynomials and the Argument Principle; Rouché’s Theorem; the Maximum-Modulus Theorem; and the Schwarz-Pick Lemma.

This project concerns the application of haptic feedback to a virtual reality laparoscopic surgery simulator. It investigates the hardware required to display haptic forces, and the software required to generate realistic and stable haptic properties. A number of surgery-based studies are undertaken using the developed haptic device. The human sense of touch, or haptic sensory system, is investigated in the context of laparoscopic surgery, where the long laparoscopic instruments reduce haptic sensation. Nonetheless, the sense of touch plays a vital role in navigation, palpation, cutting, tissue manipulation, and pathology detection in surgery. The overall haptic effect has been decomposed into a finite number of haptic attributes. The haptic attributes of mass, friction, stiction, elasticity, and viscosity are individually modeled, validated, and applied to virtual anatomical objects in visual simulations. There are times in surgery when the view from the camera cannot be depended upon. When visual feedback is impeded, haptic feedback must be relied upon more by the surgeon. A realistic simulator should include some sort of visual impedance. Results from a simple tissue holding task suggested the inclusion of haptic feedback in a simulator aids the user when visual feedback is impeded.

They were known as the Harlem Hellfighters, though the origin of the term is a matter of debate. Some say that their German enemies gave them the name, but there is no conclusive proof to back this up. The unit was originally called the 15th New York National Guard. It was put together in 1913 and reconstituted as the 369th Infantry Regiment after the United States’ entry into World War I on April 6, 1917. This photo of some of the medal of honor recipients from the 369th was among a great number of images put out by various branches of government to highlight positive aspects of America’s involvement in the conflict on the side of the Allies. The intent was to sustain morale and support on the home front and to foster a sense of pride as the soldiers returned home.

In this study using Bayesian network method to learn the structure of effective connectivity among brain regions involved in a functional MRI. The approach is exploratory in the sense that it does not require a priori model as in the earlier approaches, such as the Structural Equation Modeling or Dynamic Causal Modeling, which can only affirm or refute the connectivity of a previously known anatomical model or a hypothesized model. The conditional probabilities that render the interactions among brain regions in Bayesian networks represent the connectivity in the complete statistical sense. This method is applicable even when the number of regions involved in the cognitive network is large or unknown. In this study, we demonstrated the present approach using synthetic data and fMRI data collected in attention to motion in the visual system task.

New designs of Aspherics, in the most general sense of the word (including PAL’s), demand higher degrees of freedom in the mathematical formalism that supports the surface definition. The last 20 years have seen the arising of powerful surface design methods that have been succesfully exploited in different areas such as: aeronautics (wings and bodies of planes), naval craft (ship hulls, sails), car body design and so on. These methods, generally known as Sculptured Surface methods have a high number of degrees of freedom, which make them ideal for the design of PAL’s and Aspherics in general.

The number of students diagnosed with Specific Learning Disabilities with Math (SLDwM) has been estimated to be 6%. These students face daily challenges related to their disability and as a result have a reduced quality of life. The triple code theory developed by Dehaene (1992) explores the issue of number representation, which is split into three codes: verbal, visual and semantic. The semantic code belongs to the preverbal system in which the Approximate Number System (ANS) plays an important role. In a previous study we have shown that ANS and math disability are causally related. These findings, demonstrated with a short ANS test applied to 50 students (7-11 years old) from three schools in Bucharest, Romania, support the hypothesis of a correlation between low ANS performances and low math ability. However, according to Park & Brannon (2013,) training on approximate addition and subtraction of arrays of dots improves the appropriate symbolic skills. This study describes a computer game with 62 arrays (ratios from 1:2 to 9:10) which can improve appropriate math abilities. Each array of the computer game (i.e., ANS - 62), consists of 4 to 30 images of identical familiar objects (e.g., apples, ice-creams, balloons) of varying sizes. Shrek and Puss in Boots (i.e., two characters well known to children in Romania) divide the objects in ratios from 1:2 to 9:10. Each of the numerosities comparison is presented for 2000 ms and the students indicate the character that has more objects by pressing the key associated with respective character. We hypothesize that the daily use of this game by children at risk for SLDwM, together with other types of interventions directed at memory or visual-spatial orientation, will help improve their ANS. Through this improvement, students can develop their Number Sense and the ability to manipulate symbolic and non-symbolic quantities.

This paper presents a number of issues related to the development of dynamic assessment and learning strategies for visual recovery of children with visual dysfunction . In the first part of the paper are analyzed techniques and general methodologies for assessing visual performance . In the same sense are developed and applied in actions we correlative concepts to identify and optimize visual recovery techniques variants . The second part of the paper presents design and development of these visual recovery techniques through various methods and considering the diversity of the target group. In this respect have been built and applied to a target group of students assessment strategies and recovery of visual function that allows obtaining quick answers and finding effective solutions customized to each casuistry in part . Every time was looked adaptation of language but also methodologies to streamline assessment and recovery both in terms of duration as well as the final results .Tests construction is simple, safe and easy to handle both the subject of the target group as well as examiner. In the final part of the research are analyzed and the results obtained from the responses that target group , assessment and learning strategies for visual recovery . Such results as well as our observations developed during the investigations have revealed a number of issues related to the teaching of subjects in the target group have led to efficiency improvements and optimization . These mechanisms lead to the creation of the characteristics of adaptability and flexibility of methods for recovery of visual dysfunction resulting from various causes .

Sensory Substitution Devices (SSDs) are a relatively novel concept, based on the idea of the multisensory brain. Research on synaesthesia and sensory pairings has revealed that sensory modalities of the brain are interconnected. Nature has demonstrated examples of people who have lost one sense, which has then been substituted by increased ability in another, for example the case of Daniel Kish who navigates like a bat (Burgess, 2021) by clicking of the tongue (echolocation principle). To find a methodology for translating information from one sense to another, or substitute one sense with another is the principle for all SSDs. A number of approaches to assistive technologies for different impairments have been developed, for example for blind people, such as the vOICe “seeing with sound” and EyeMusic Apps, which convert visual images and colours into sound. While most SSDs are focused on functionality to offer life assistance, such as for navigation, little or no work has been done to include the blind into the emotional world of Visual Arts, despite the fact that there are 45 million blind people in the world (Amir Amedi). In this paper, we present an audio GPS based walking app that presents a translation of the visual expression of artworks by sound/music to deliver the emotional content of the paintings to blind people. The music is composed for six artworks of Irish artist symbolist Jack B. Yeats (1871-1957), specifically reflecting on shapes, colours and emotional content of painting by composer experienced in audio-visual synchronisation via synaesthesia (Rudenko and Córdoba Serrano, 2017). The project is centred around the development of a new methodology for multisensory design (MSD) through the design, implementation, and evaluation of a locative art experience with Augmented Reality (AR), hosted by Haunted Planet Studios (director Mads Haahr).

The human perception arises from an inner sense intrinsically dependent on the sensitive channels. Vision is considered the dominating sense in humans, while hearing, touch, taste, smell, kinesthetic sense and balance are complementary in most cases, with numerous exceptions. Until now, most studies suggest that the greater the number of sensory modalities stimulated at the same time, the richer the experience will be. As a result, the increase in the number of sensory modalities presented in a virtual environment can help people feel immersed and also help to improve the memory of existing objects in the virtual environment (Schifferstein and Spenser, 2008). This study aimed to evaluate the influence of multisensory integration in the user experience with different categories of products. Participants were 60 volunteer subjects of both genders and all users of these products; they evaluated 25 different products in three levels of multisensory integration: vision, vision+touch and multisensory. Results indicated that intrinsic characteristics of each product were responsible for the emergence of differences between multisensory phases, and the relationship between usability and visual aesthetics were less evident in the process. More specific studies are necessary to recognize more accurately the relationship between product characteristics and user perception.

The study is theoretical in the sense that it examines the visual attention in reference to tourism images and builds on this research by integrating the eye movement data from the tourism ads. It offers direction in selecting better images for promotional purposes in tourism by underscoring the needs for considering specific features of images necessary for diverse and unique markets. In this study, eye tracking measurements with survey data research design will be employed in comprehending how foreign people are attracted to visuals used in tourism marketing in Oman. Ultimately enabling further investigation into the impact of image features on the traveler's attraction towards the tourism images in Oman and how the influence varies between the travel teams. Strictly speaking, the following image features were investigated: (1) underexposure vs overexposure, (2) monochromatic vs chromatic and (3) image with human presence and without. We are using Tobii eye tracking glasses pro-2, a wearable tool to collect real and accurate visual attention. The study was performed at Turku University of Applied Sciences in Finland. The experiment managed to recruit eighty-six participants (students and staff) from different age ranges. After the participants read the instruction paper, they were instructed to wear the Tobii eye tracking glasses, while sitting in a room Infront of 42-inch Tv screen. Participants were instructed to browse images on screen and selecting the most attractive image to move to another screen and so on. Dwell times (DTs) for AOIs (area of interests), first fixation, fixation duration and number of fixations were collected. Statistical analysis show significant impact of the image features on people visual attraction and attention.

The ventilation network related to a mining unit for the exploitation of the useful mineral substance aims to ensure optimal microclimate conditions in underground. An ventilation network is made up of nodes and branches in order to establish its structure. In this sense, the mine ventilation must be seen as a source of life, in which the ramifications represent at the same time the arteries that transport the air to the working fronts and the evacuation of the poluted air to the surface. In order to establish the optimal air flows at the level of ventilation networks, specialized programs are used with the help of which it is possible to model, solve and optimize them. The solution or calculation of the ventilation system consists in establishing the quantitative distribution of air flow, in terms of network elements and the characteristics of depression sources. The Ventsim Visual Advanced program was developed to respond to the requirements regarding the simulation and design of underground environmental conditions, to ensure adequate conditions for miners and equipment. Primarily, it was designed as a ventilation tool, which can work independently of other mine planning software, but ensures a high level of compatibility. The analysis carried out on the ventilation network of the Lonea mine leads to the conclusion that the ventilation network of the mine is particularly complex, complexity amplified by the large number of ventilation constructions. In the framework of this work, the update of the ventilation network of the Lonea mine will be treated with the help of the Ventsim Visual Advanced program.

Spatial ability is the ability to generate, store, retrieve, and transform visual information to mentally represent a space and make sense of it. This ability is a critical facet of human cognition that affects knowledge acquisition, productivity, and workplace safety. Although having improved spatial ability is essential for safely navigating and perceiving a space on earth, it is more critical in altered environments of other planets and deep space, which may pose extreme and unfamiliar visuospatial conditions. Such conditions may range from microgravity settings with the misalignment of body and visual axes to a lack of landmark objects that offer spatial cues to perceive size, distance, and speed. These altered visuospatial conditions may pose challenges to human spatial cognitive processing, which assists humans in locating objects in space, perceiving them visually, and comprehending spatial relationships between the objects and surroundings. The main goal of this paper is to examine if eye-tracking data of gaze pattern can indicate whether such altered conditions may demand more mental efforts and attention. The key dimensions of spatial ability (i.e., spatial visualization, spatial relations, and spatial orientation) are examined under the three simulated conditions: (1) aligned body and visual axes (control group); (2) statically misaligned body and visual axes (experiment group I); and dynamically misaligned body and visual axes (experiment group II). The three conditions were simulated in Virtual Reality (VR) using Unity 3D game engine. Participants were recruited from Texas A&M University student population who wore HTC VIVE Head-Mounted Displays (HMDs) equipped with eye-tracking technology to work on three spatial tests to measure spatial visualization, orientation, and relations. The Purdue Spatial Visualization Test: Rotations (PSVT: R), the Mental Cutting Test (MCT), and the Perspective Taking Ability (PTA) test were used to evaluate the spatial visualization, spatial relations, and spatial orientation of 78 participants, respectively. For each test, gaze data was collected through Tobii eye-tracker integrated in the HTC Vive HMDs. Quick eye movements, known as saccades, were identified by analyzing raw eye-tracking data using the rate of change of gaze position over time as a measure of mental effort. The results showed that the mean number of saccades in MCT and PSVT: R tests was statistically larger in experiment group II than in the control group or experiment group I. However, PTA test data did not meet the required assumptions to compare the mean number of saccades in the three groups. The results suggest that spatial relations and visualization may require more mental effort under dynamically misaligned idiotropic and visual axes than aligned or statically misaligned idiotropic and visual axes. However, the data could not reveal whether spatial orientation requires more/less mental effort under aligned, statically misaligned, and dynamically misaligned idiotropic and visual axes. The results of this study are important to understand how altered visuospatial conditions impact spatial cognition and how simulation- or game-based training tools can be developed to train people in adapting to extreme or altered work environments and working more productively and safely.

There is a growing number of technical communication devices, not least wearables, which take use of the haptic sense(s). Then tactors (vibrotactile elements, heating elements, cooling elements, pressure generators, active indentators, electro-stimulating electrodes etc.), are employed. Haptic technologies are often limited to binary, point-wise actuation (one vibrator). However, as we discuss, in a semiotic sense, this can only generate a representamen that is symbolic, thus only also concerning symbolic communication. For a richer communication coming closer to what exists for visual and audial displays also haptic communication that is semiologically iconical and indexical are of interest. We here present a classification of tactile displays. For this, we make a distinction between the stimulus (the tactor characteristics and relationship to human reception) and the spatial arrangement i.e. the geometrical placement of tactors. For wearables, in the latter case, the human body shape and anatomy is taken into concern.From this, we build two (partially ordered) hierarchies, the stimulus richness hierarchy and the spatial ordering hierarchy, respectively.Combining these hierarchies gives a (partially ordered) hierarchy of tactile displays for the human body. We show that the informatical richness is fast growing with placement complexity. However, such displays need space. Hands and fingers are sensitive for haptic stimuli but are better reserved for active touch. Instead, other body parts might be used. For this, textiles are employed. We demonstrate a chairable i.e. a portable textile based haptic display for communication to (deafblind) humans, arena spectators etc., that can be applied to furniture, thus enriching the Umwelt of the users.

Abstract: The article presents the results of a psychophysiological examination of drivers of passenger and export traffic, working in the day and night shifts, respectively. The dynamics of performing psychophysiological tests (changes in the reaction rate, the number of errors, perception of time intervals, etc.) after day and night shifts was revealed, and differences in the subjective perception of the specifics of work in the daytime and at night were also noted. Working the night shift requires the driver to mobilize psychophysiological resources aimed at maintaining active wakefulness and fighting monotony. Day trips are perceived to be more stressful due to more input and traffic. Target: The study of the functional state dynamics of train drivers working without an assistant during day and night trips with an increase in the duration of working hours up to 8 hours in passenger traffic and up to 12 - in export traffic. Methods: 1. Express test of the functional state; 2. «Sense of time» test; 3. Stress resistance test; 4. Survey «Well-being. Activity, mood (SAN)»; 5. Survey «Diagnostics of states of reduced performance (DORS)». Results: The dynamics of the speed and stability of the visual-motor reaction, the accuracy of the perception of time intervals, as well as the subjective perception of the features of day and night shifts by train drivers themselves, makes it possible to distinguish differences in the specifics of shift work: in the daytime it is distinguished by greater intensity, tension, which is reflected in the number of erroneous actions during testing after a day's ride on the simulator, and in the subjective experience of stress noted by the drivers. The need to work at night requires considerable efforts from train drivers to mobilize, which is manifested during a psychophysiological examination before the night shift, however, forced wakefulness during night work leads to a state of monotony among train drivers.

Executive Summary This report describes a series of experiments carried out by PRICE Lab, a research programme at the Economic and Social Research Institute (ESRI) jointly funded by the Central Bank of Ireland, the Commission for Energy Regulation, the Competition and Consumer Protection Commission and the Commission for Communications Regulation. The experiments were conducted with samples of Irish consumers aged 18-70 years and were designed to answer the following general research question: At what point do products become too complex for consumers to choose accurately between the good ones and the bad ones? BACKGROUND AND METHODS PRICE Lab represents a departure from traditional methods employed for economic research in Ireland. It belongs to the rapidly expanding area of ‘behavioural economics’, which is the application of psychological insights to economic analysis. In recent years, behavioural economics has developed novel methods and generated many new findings, especially in relation to the choices made by consumers. These scientific advances have implications both for economics and for policy. They suggest that consumers often do not make decisions in the way that economists have traditionally assumed. The findings show that consumers have limited capacity for attending to and processing information and that they are prone to systematic biases, all of which may lead to disadvantageous choices. In short, consumers may make costly mistakes. Research has indeed documented that in several key consumer markets, including financial services, utilities and telecommunications, many consumers struggle to choose the best products for themselves. It is often argued that these markets involve ‘complex’ products. The obvious question that arises is whether consumer policy can be used to help them to make better choices when faced with complex products. Policies are more likely to be successful where they are informed by an accurate understanding of how real consumers make decisions between products. To provide evidence for consumer policy, PRICE Lab has developed a method for measuring the accuracy with which consumers make choices, using techniques adapted from the scientific study of human perception. The method allows researchers to measure how reliably consumers can distinguish a good deal from a bad one. A good deal is defined here as one where the product is more valuable than the price paid. In other words, it offers good value for money or, in the jargon of economics, offers the consumer a ‘surplus’. Conversely, a bad deal offers poor value for money, providing no (or a negative) surplus. PRICE Lab’s main experimental method, which we call the ‘Surplus Identification’ (S-ID) task, allows researchers to measure how accurately consumers can spot a surplus and whether they are prone to systematic biases. Most importantly, the S-ID task can be used to study how the accuracy of consumers’ decisions changes as the type of product changes. For the experiments we report here, samples of consumers arrived at the ESRI one at a time and spent approximately one hour doing the S-ID task with different kinds of products, which were displayed on a computer screen. They had to learn to judge the value of one or more products against prices and were then tested for accuracy. As well as people’s intrinsic motivation to do well when their performance on a task like this is tested, we provided an incentive: one in every ten consumers who attended PRICE Lab won a prize, based on their performance. Across a series of these experiments, we were able to test how the accuracy of consumers’ decisions was affected by the number and nature of the product’s characteristics, or ‘attributes’, which they had to take into account in order to distinguish good deals from bad ones. In other words, we were able to study what exactly makes for a ‘complex’ product, in the sense that consumers find it difficult to choose good deals. FINDINGS Overall, across all ten experiments described in this report, we found that consumers’ judgements of the value of products against prices were surprisingly inaccurate. Even when the product was simple, meaning that it consisted of just one clearly perceptible attribute (e.g. the product was worth more when it was larger), consumers required a surplus of around 16-26 per cent of the total price range in order to be able to judge accurately that a deal was a good one rather than a bad one. Put another way, when most people have to map a characteristic of a product onto a range of prices, they are able to distinguish at best between five and seven levels of value (e.g. five levels might be thought of as equivalent to ‘very bad’, ‘bad’, ‘average’, ‘good’, ‘very good’). Furthermore, we found that judgements of products against prices were not only imprecise, but systematically biased. Consumers generally overestimated what products at the top end of the range were worth and underestimated what products at the bottom end of the range were worth, typically by as much as 10-15 per cent and sometimes more. We then systematically increased the complexity of the products, first by adding more attributes, so that the consumers had to take into account, two, three, then four different characteristics of the product simultaneously. One product might be good on attribute A, not so good on attribute B and available at just above the xii | PRICE Lab: An Investigation of Consumers’ Capabilities with Complex Products average price; another might be very good on A, middling on B, but relatively expensive. Each time the consumer’s task was to judge whether the deal was good or bad. We would then add complexity by introducing attribute C, then attribute D, and so on. Thus, consumers had to negotiate multiple trade-offs. Performance deteriorated quite rapidly once multiple attributes were in play. Even the best performers could not integrate all of the product information efficiently – they became substantially more likely to make mistakes. Once people had to consider four product characteristics simultaneously, all of which contributed equally to the monetary value of the product, a surplus of more than half the price range was required for them to identify a good deal reliably. This was a fundamental finding of the present experiments: once consumers had to take into account more than two or three different factors simultaneously their ability to distinguish good and bad deals became strikingly imprecise. This finding therefore offered a clear answer to our primary research question: a product might be considered ‘complex’ once consumers must take into account more than two or three factors simultaneously in order to judge whether a deal is good or bad. Most of the experiments conducted after we obtained these strong initial findings were designed to test whether consumers could improve on this level of performance, perhaps for certain types of products or with sufficient practice, or whether the performance limits uncovered were likely to apply across many different types of product. An examination of individual differences revealed that some people were significantly better than others at judging good deals from bad ones. However the differences were not large in comparison to the overall effects recorded; everyone tested struggled once there were more than two or three product attributes to contend with. People with high levels of numeracy and educational attainment performed slightly better than those without, but the improvement was small. We also found that both the high level of imprecision and systematic bias were not reduced substantially by giving people substantial practice and opportunities to learn – any improvements were slow and incremental. A series of experiments was also designed to test whether consumers’ capability was different depending on the type of product attribute. In our initial experiments the characteristics of the products were all visual (e.g., size, fineness of texture, etc.). We then performed similar experiments where the relevant product information was supplied as numbers (e.g., percentages, amounts) or in categories (e.g., Type A, Rating D, Brand X), to see whether performance might improve. This question is important, as most financial and contractual information is supplied to consumers in a numeric or categorical form. The results showed clearly that the type of product information did not matter for the level of imprecision and bias in consumers’ decisions – the results were essentially the same whether the product attributes were visual, numeric or categorical. What continued to drive performance was how many characteristics the consumer had to judge simultaneously. Thus, our findings were not the result of people failing to perceive or take in information accurately. Rather, the limiting factor in consumers’ capability was how many different factors they had to weigh against each other at the same time. In most of our experiments the characteristics of the product and its monetary value were related by a one-to-one mapping; each extra unit of an attribute added the same amount of monetary value. In other words, the relationships were all linear. Because other findings in behavioural economics suggest that consumers might struggle more with non-linear relationships, we designed experiments to test them. For example, the monetary value of a product might increase more when the amount of one attribute moves from very low to low, than when it moves from high to very high. We found that this made no difference to either the imprecision or bias in consumers’ decisions provided that the relationship was monotonic (i.e. the direction of the relationship was consistent, so that more or less of the attribute always meant more or less monetary value respectively). When the relationship involved a turning point (i.e. more of the attribute meant higher monetary value but only up to a certain point, after which more of the attribute meant less value) consumers’ judgements were more imprecise still. Finally, we tested whether familiarity with the type of product improved performance. In most of the experiments we intentionally used products that were new to the experimental participants. This was done to ensure experimental control and so that we could monitor learning. In the final experiment reported here, we used two familiar products (Dublin houses and residential broadband packages) and tested whether consumers could distinguish good deals from bad deals any better among these familiar products than they could among products that they had never seen before, but which had the same number and type of attributes and price range. We found that consumers’ performance was the same for these familiar products as for unfamiliar ones. Again, what primarily determined the amount of imprecision and bias in consumers’ judgments was the number of attributes that they had to balance against each other, regardless of whether these were familiar or novel. POLICY IMPLICATIONS There is a menu of consumer polices designed to assist consumers in negotiating complex products. A review, including international examples, is given in the main body of the report. The primary aim is often to simplify the consumer’s task. Potential policies, versions of which already exist in various forms and which cover a spectrum of interventionist strength, might include: the provision and endorsement of independent, transparent price comparison websites and other choice engines (e.g. mobile applications, decision software); the provision of high quality independent consumer advice; ‘mandated simplification’, whereby regulations stipulate that providers must present product information in a simplified and standardised format specifically determined by regulation; and more strident interventions such as devising and enforcing prescriptive rules and regulations in relation to permissible product descriptions, product features or price structures. The present findings have implications for such policies. However, while the experimental findings have implications for policy, it needs to be borne in mind that the evidence supplied here is only one factor in determining whether any given intervention in markets is likely to be beneficial. The findings imply that consumers are likely to struggle to choose well in markets with products consisting of multiple important attributes that must all be factored in when making a choice. Interventions that reduce this kind of complexity for consumers may therefore be beneficial, but nothing in the present research addresses the potential costs of such interventions, or how providers are likely to respond to them. The findings are also general in nature and are intended to give insights into consumer choices across markets. There are likely to be additional factors specific to certain markets that need to be considered in any analysis of the costs and benefits of a potential policy change. Most importantly, the policy implications discussed here are not specific to Ireland or to any particular product market. Furthermore, they should not be read as criticisms of existing regulatory regimes, which already go to some lengths in assisting consumers to deal with complex products. Ireland currently has extensive regulations designed to protect consumers, both in general and in specific markets, descriptions of which can be found in Section 9.1 of the main report. Nevertheless, the experiments described here do offer relevant guidance for future policy designs. For instance, they imply that while policies that make it easier for consumers to switch providers may be necessary to encourage active consumers, they may not be sufficient, especially in markets where products are complex. In order for consumers to benefit, policies that help them to identify better deals reliably may also be required, given the scale of inaccuracy in consumers’ decisions that we record in this report when products have multiple important attributes. Where policies are designed to assist consumer decisions, the present findings imply quite severe limits in relation to the volume of information consumers can simultaneously take into account. Good impartial Executive Summary | xv consumer advice may limit the volume of information and focus on ensuring that the most important product attributes are recognised by consumers. The findings also have implications for the role of competition. While consumers may obtain substantial potential benefits from competition, their capabilities when faced with more complex products are likely to reduce such benefits. Pressure from competition requires sufficient numbers of consumers to spot and exploit better value offerings. Given our results, providers with larger market shares may face incentives to increase the complexity of products in an effort to dampen competitive pressure and generate more market power. Where marketing or pricing practices result in prices or attributes with multiple components, our findings imply that consumer choices are likely to become less accurate. Policymakers must of course be careful in determining whether such practices amount to legitimate innovations with potential consumer benefit. Yet there is a genuine danger that spurious complexity can be generated that confuses consumers and protects market power. The results described here provide backing for the promotion and/or provision by policymakers of high-quality independent choice engines, including but not limited to price comparison sites, especially in circumstances where the number of relevant product attributes is high. A longer discussion of the potential benefits and caveats associated with such policies is contained in the main body of the report. Mandated simplification policies are gaining in popularity internationally. Examples include limiting the number of tariffs a single energy company can offer or standardising health insurance products, both of which are designed to simplify the comparisons between prices and/or product attributes. The present research has some implications for what might make a good mandate. Consumer decisions are likely to be improved where a mandate brings to the consumer’s attention the most important product attributes at the point of decision. The present results offer guidance with respect to how many key attributes consumers are able simultaneously to trade off, with implications for the design of standardised disclosures. While bearing in mind the potential for imposing costs, the results also suggest benefits to compulsory ‘meta-attributes’ (such as APRs, energy ratings, total costs, etc.), which may help consumers to integrate otherwise separate sources of information. FUTURE RESEARCH The experiments described here were designed to produce findings that generalise across multiple product markets. However, in addition to the results outlined in this report, the work has resulted in new experimental methods that can be applied to more specific consumer policy issues. This is possible because the methods generate experimental measures of the accuracy of consumers’ decision-making. As such, they can be adapted to assess the quality of consumers’ decisions in relation to specific products, pricing and marketing practices. Work is underway in PRICE Lab that applies these methods to issues in specific markets, including those for personal loans, energy and mobile phones.