Wolfgang Grodd

A B S T R A C T In the present work, we used resting state-fMRI to investigate the functional anatomy of the thalamus at rest by applying an Independent Component Analysis to delineate thalamic substructures into stable and reproducible parcels for the left and right thalamus. We determined 15 functionally distinct thalamic parcels, which differed in laterality and size but exhibited a correspondence with 18 cytoarchitectonally defined nuclei. We characterized their structural connectivity in determining DWI based cortical fiber pathways and found selected projections to different cortical areas. In contrast, the functional connections of these parcels were not confined to certain cortical areas or lobes. We, finally evaluated cortical projections and found particular subcortical and cortical pattern for each parcel, which partly exhibited a correspondence with the thalamo-cortical connectivity maps of the mouse.

The integration of auditory and visual spatial information is an important prerequisite for accurate orientation in the environment. However, while visual spatial information is based on retinal coordinates, the auditory system receives information on sound location in relation to the head. Thus, any deviation of the eyes from a central position results in a divergence between the retinal visual and

Fast and accurate segmentation of deep gray matter structures is important for clinical applications such as for example surgery planning for the placement of deep brain stimulation implants. We implemented a segmentation method that is solely based on local diffusion information and did evaluate it on a group of 53 healthy volunteers to investigate the reproducibility and thereby the usability of this method. We were able to show that the segmentation produces subdivisions which are reproducible for a large population. We could also show that not only the three previously reported large clusters were reproducible but also four smaller clusters could be found in the same position in more than 60% of the subjects.

Activation maps in the primary motor cortex (M1) were investigated in three patients with complete spinal cord injury (SCI) at the level of TH3, TH7 and TH9 and in one patient with an incomplete spinal cord injury at the level of L1 during right elbow (4 patients), right thumb (4 patients), bilateral lip (2 pa- tients) and right foot (3

Early left-hemispheric brain lesions may lead to a reorganization of language into the right hemisphere. Language functions are consecutively spared, but visuospatial functions show slight deficits. Cortical 'crowding' of the right hemisphere has been suggested as an explanation for this effect, but no direct evidence has as yet been put forward. We examined six patients with early left-hemispheric brain lesions and subsequent right-hemispheric language organization with functional magnetic resonance imaging and compared their activation patterns in a verbal and two nonverbal tasks with the patterns of six controls. In the patient group, nonverbal functions were reorganized neither interhemispherically nor intrahemispherically. Instead, verbal and nonverbal functions were mediated by a common right-hemispheric network. This argues in favour of the 'crowding hypothesis'.

Hemispheric dominance for language is an important issue in functional neuroimaging, particularly driven by efforts to overcome the need for the invasive Wada test, which is all the more pressing in children. Here, we aimed at developing new paradigms for functional magnetic resonance imaging (fMRI) for assessment of language dominance that can be used in younger children and allow for performance monitoring. Two new tasks (letter and animal task) were developed and compared to two reference tasks (synonyms and verb generation task) from the literature. Overall, 23 healthy children participated (13 boys, 10 girls, 10.2 +/- 2.5 years, range 6.1-15.3 years). Analysis was done using statistical nonparametrical mapping (SnPM2) on SPM2. Both reference tasks show activation in a number of left-frontal brain regions. The letter task induced a very localized activation in the left hemisphere's Broca's region, while not activating other frontal brain regions. Lateralization (as asses...

Noninvasive language mapping is a frequently used application of functional magnetic resonance imaging. The examination of children, however, poses both practical and technical challenges. To this effect, we have developed two new paradigms mainly requiring passive listening to stories from which several key words were removed. Results were compared with a standard active verb-generation task, particularly with regard to hemispheric dominance in frontal brain areas. Fifteen healthy children (seven boys, eight girls, 6-14 years) were scanned. Distinct frontal activation was seen in our new tasks, which was stronger when the tasks were analyzed specifically with regard to the missing words. This confirms the hypothesis that the removal of these words is the key in inducing frontal activation. Frontal lateralization was consistent and strong in all three paradigms. Additionally, receptive language areas are also mapped by our new tasks. We conclude that our two new, child-friendly func...

Recordings of neuronal activity were made in cortical and subcortical structures of monkeys performing visual recognition memory tasks in which the novelty/familiarity of the stimuli was varied. A population of neurons with memory-like activity was recorded in a periventricular region at the border of the anterior thalamus and dorsal hypothalamus. These neurons responded with decreases in firing rate to novel stimuli and increases in firing rate to the same stimuli when they were familiar. The calculated memory spans of these neurons ranged from 7 to hundreds of intervening trials. The afferent connections of this region were traced by an injection of HRP into the periventricular region. Retrogradely labeled cells were observed in the ventromedial prefrontal cortex, the ventromedial temporal cortex, amygdala, medial thalamus and supramammillary region. Recordings were then made in the hippocampus and ventromedial temporal cortex. A population of neurons in the ventromedial temporal ...

How the brain enables humans to reach an outstanding level of performance typical of expertise is of great interest to cognitive neuroscience, as demonstrated by the number and diversity of the articles in this Research Topic (RT). The RT presents a collection of 23 articles written by 80 authors on traditional expertise topics such as sport, board games, and music, but also on the expertise aspects of everyday skills, such as language and the perception of faces and objects. Just as the topics in the RT are diverse, so are the neuroimaging techniques employed and the article formats. Here we will briefly summarize the articles published in the RT.
Board Games

The traditional expertise domain of board games has been covered in the RT by two articles, both employing the expertise approach of pitting experts against novices (Bilalić et al., 2010, 2012, 2014) but employing differing neuroimaging techniques. Bartlett et al. (2013) employed fMRI to demonstrate that chess experts engage the fronto-parietal network when they try to find a logical pattern in a “constellation” of randomly placed chess pieces. Jung et al. (2013) found structural differences as well as differences in brain networks between Baduk (Korean name for the board game Go) experts and novices, which point out the importance of visuospatial processing in problem solving and decision making of board-game experts.
Sport

Wright et al. (2013) extended the research on anticipation of action in sport by showing that the neural basis for deception involves, besides the well-known action observation network, the structures responsible for social cognition and affection. Turella et al. (2013) review other recent studies on the anticipation of action in sport and connect them with the mirror neurons in animal research. The review by Chang (2014) deals with motor domains such as sports and music and the structural and functional changes associated with expertise. Debarnot et al. (2014) go a step further in their review and contrast the neural changes during skill acquisition with those in mental training techniques such motor imagery and mediation.
Music

Music has been one of the most often investigated domains in expertise because its complexity and richness enable researchers to tackle diverse topics. The variety of themes in the domain of music is also evident in this RT. Tervaniemi et al. (2014), for example, pitted expert musicians against novices in a novel paradigm to investigate memory and attentional processes with EEG. On the other hand, Bergman Nutley et al. (2014) used the music domain to investigate longitudinal effects on cognitive processes such as working memory, speed of processing, and reasoning, while Fauvel et al. (2013) apply the promising findings of transfer and neural plasticity associated with musical practice to cognitive aging in their review.
Language

Unlike the previous articles, which deal with specialized expertise domains, a number of contributions highlight the fact that even the everyday skills we often take for granted represent impressive feats of human expertise. One group of articles deals with language, which is one such everyday skill. Reichle and Reingold (2013) review the electrophysiological evidence of the link between eye movements and the mind during reading. The learning of a second language based on its similarity to one's native language was investigated by Grimaldi et al. (2014), while Dietrich et al. (2013) demonstrated the neural changes associated with the process of learning to comprehend speech that was several times faster than normal speech. Finally, Lotze et al. (2014) demonstrate by means of resting-state fMRI that people who write highly creatively have increased functional connectivity between the task-related brain regions in the right hemisphere but reduced interhemispheric connectivity.
Perception

Similarly, a couple of articles deal with perception of own-race and other-race faces (Wiese, 2013) as well as with perception of familiar faces and objects and the functional connectivity within the medial temporal lobe (McLelland et al., 2014). The role of the fusiform face area (FFA) in expertise has been a bone of contention between Harel et al. (2013, 2014), on the one hand, and Wong and Wong (2014), on the other.
Theoretical and Simulation Work

Finally, a number of articles provide either new theoretical ideas or revisions of already established theories. Campitelli and Speelman (2013) highlight the advantages of using the expertise paradigm in investigating memory, while Brogliato et al. (2014) expand the Sparse Distributed Memory (SDM) model to incorporate the effects of practice on memory retrieval. Guida et al. (2013) extend their two-stage framework of skill acquisition (Guida et al., 2012) by arguing for the functional cerebral reorganization (FCR) as being the neural signature of expertise. The way one structures training studies is considered by Coffey and Herholz (2013), who suggest a new approach for characterizing and deconstructing the task requirements in training studies. Finally, Harré (2013) demonstrates the parallels between two seemingly unrelated fields, perceptual expertise and social cognition.
Conclusion

It is clear that we cannot do justice to all submissions in this brief editorial. We hope, however, that our brief summary demonstrates the diversity in topics and methods employed in research on human expertise and also, indirectly, the growing interest in the field of expertise. It should become evident that research on expertise is not only relevant for understanding exceptional human performance but also for understanding how mind and brain work more generally. We are grateful to all authors for their contribution and hope that the RT, with its broad and deep coverage, will provide a useful reference for the reader interested in expertise and, particularly, current approaches to its neural implementation.
Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Despite the importance of mathematics in our educational systems, little is known about how abstract mathematical thinking emerges. Most research on mathematical cognition has been dedicated to understanding its more simple forms such as seriation and counting. Although these forms constitute the foundational plinth upon which all other maths skills develop, the gap between basic skills and the processing of complex mathematical concepts is poorly understood. What has come to be sufficiently well understood, however, is how numeracy is acquired. The 90s marked a change in our approach to human cognition in general and to mathematical cognition in particular. Neuroimaging technologies have enabled localization of neural activity, revealing that mathematical cognition, like other forms of cognition and skills, depends upon a network of activation. The key finding from neuroimaging and single cell recording is that numerical information is held in the intraparietal sulcus. Now that the core of mathematical cognition has been identified it is time to understand how basic skills are used to support the acquisition and use of abstract mathematical concepts. Chassy and Grodd (2012) opened the door for abstract mathematical cognition by examining for the first time the neural correlates of negative numbers, an abstract mathematical concept that emerges early on in mathematical curricula. The present issue reports crucial advances in our understanding of the neural underpinnings of abstract mathematical cognition.

For a general introduction to the topic the reader is referred to the article signed by Moeller et al. The article offers an excellent overview of the networks that are involved to some degree in processing quantities, the very basis of mathematical cognition. The authors' conclusion strengthens the view that a frontal parietal network constitutes the essence of our abilities in mathematics. The fronto-parietal network has been highlighted by a number of studies and is thought to underpin the learning of mathematical concepts. By increasing the complexity of the concepts stored in our memory, we improve the quality of our understanding of the physical world in the first stages of mathematical cognition. Abstract concepts are then able to emerge from concrete, physical quantities.

On the path of mathematical development, the first step toward an abstract representation of concepts is the shift from concrete, object-based cognition to the use of symbols. The symbols, though arbitrary, represent concrete quantities that help children quantify and thus understand the world around them. Roesch and Moeller support this view by suggesting that an internal representation of fingers contributes to the actual ability to represent quantities. In a similar vein, a cross cultural study authored by Bender and Beller compares the Western counting system to a Polynesian language of the Tonga island, offering a unique view of how concrete counting of different objects leads to an abstract representation of numbers; thus demonstrating that the roots of abstract mathematical cognition emerge from basic, sensory abilities (a long standing view that finds a new echo here). By highlighting the concrete roots of mathematical cognition, the authors of these studies open the debate on the inheritance of mathematical skill by pointing toward very concrete sensory performance.

The symbols in a later stage of mathematical development are used to represent concepts of an abstract nature. That is, once the notion of natural number is acquired, the next step toward expertise is to formalize operations as abstract entities. For example, the operation 5 + 4 = 9 is concrete and can be taught by using objects. Dowker demonstrates that pupils tend to use the same problem-solving strategies to solve problems in subtraction and addition problems. Since the properties of the two operations differ the application of the same strategy leads the pupil to commit errors. Pupils have to learn a new set of properties to be able to solve subtraction. Similarly, Huber et al. argue that mental representations of fractions do not differ from natural numbers; what do differ are the strategies used to encode information. Dowker's and Hubet et al.'s views are in line with the study of Mihulowicz et al. who, by comparing left and right lesioned patients, showed that arithmetic operations are underpinned by different networks. The view of some educators, that subtraction and addition are mirror operations, is mistaken. It is interesting to note that teaching might be adapted so that different approaches could be used to teach different operations. The studies highlight the fact that learning arithmetic includes knowledge that is not purely numerical. This is our first hint indicating that educational strategies might have a huge influence on the ability of students to learn abstract concepts. The next stage in mathematical learning is the step consisting in moving from concrete (arithmetic) to abstract (algebraic) relationships. A study by Susac et al. looked at this move and showed that it requires about 4 years of training to master this new step toward abstract thinking in mathematics. It is crucial to note that these 4 years are in addition to the many years required for correctly mastering the basics. Mathematical learning is a long road. It calls for pedagogical approaches that are specific to each level.

Two main variables might modulate the acquisition of mathematical expertise: Educational system and inherited factors. The idea that teaching practices impact heavily on the ability of students to develop their skills in abstract mathematical cognition is demonstrated by Prado et al. The authors ran a cross cultural study comparing Chinese and American students on problem-size effects, and show that educational practices, which differ in the 2 countries, impact on the wiring of the network in charge of symbolic arithmetic. In line with this result, McLean and Rusconi attempt to bridge the gap between the findings of academic science and the practical problems faced by teaching institutions when dealing with students with mathematical difficulties. After revealing the cognitive factors underpinning the acquisition of mathematical knowledge, McLean and Rusconi discuss the types of interventions that may help students with mathematical difficulties. With respect to inherited factors, Zhang et al. have shown that gifted adolescents display a highly integrated fronto-parietal network, hence displaying a more efficient link between the representation of numbers in the parietal cortex and working memory in the prefrontal cortex.

The many findings of the articles in this special topic call for further research to see how specific neural networks serve various abstract mathematical concepts.