**Human Attention Modelization and Data Reduction**

Matei Mancas, Dominique De Beul, Nicolas Riche and Xavier Siebert *IT Department, Faculty of Engineering (FPMs), University of Mons (UMONS), Mons Belgium*

#### **1.  In reality as William James, the father of psychology said: "Everybody knows what attention is". It is precisely because everybody "knows" what attention is that few people tried to analyze it before the 19th century. Even though the study of attention was initially developed in the field of psychology, it quickly spread into new domains such as neuroscience to understand its biological mechanisms and, most recently, computer science to model attention mechanisms. There is no common definition of attention, and one can find variations depending on the domain (psychology, neuroscience, engineering, . . . ) or the approach which is taken into account. But, to remain general, human attention can be defined as the natural capacity to selectively focus on part of the incoming stimuli, discarding less "interesting" signals. The main purpose of the attentional process is to make best use of the parallel processing resources of our brains to identify as quickly as possible those parts of our environment that are key to our survival.

This natural tendency in data selection shows that raw data is not even used by our multi-billion cells brain which prefers to focus on restricted regions of interest instead of processing the whole data. Human attention is thus the first natural compression algorithm. Several attempts towards the definition of attention state that it is very closely related to data compression and focus resources on the less redundant, thus less compressible data. Tsotosos suggested in Itti et al. (2005) that the one core issue which justifies attention regardless the discipline, methodology or intuition is "information reduction". Schmidhuber (2009) stated that . . . "we pointed out that a surprisingly simple algorithmic principle based on the notions of data compression and data compression progress informally explains fundamental aspects of attention, novelty, surprise, interestingness . . . ". Attention modeling in engineering and computer science domain has very wide applications such as machine vision, audio processing, HCI (Human Computer Interfaces), advertising assessment, robotics and, of course, data reduction and compression.

In section 2, an introduction to the notions of saliency and attention will be given and the main computational models working on images, video and audio signals will be presented. In section 3 the ideas which either aims at replacing or complementing classical compression algorithms are reviewed. Saliency-based techniques to reduce the spatial and/or temporal resolution of non-interesting events are listed in section 4. Finally, in section 5, a discussion on the use of attention-based methods for data compression will conclude the chapter.

more or less naturally. Another difficult point is to judge the biological plausibility which can be obvious for some methods but much less for the others. Another criterion is the computational time or the algorithmic complexity, but it is very difficult to make this comparison as all the existing models do not provide cues about their complexity. Finally a classification of methods based on center-surround contrast compared to information theory based methods do not take into account different approaches as the spectral residual one for example. Therefore, we introduce here a new taxonomy of the saliency methods which is based on the context that those methods take into account to exhibit signal novelty. In this framework, there are three classes of methods. The first one is pixel's surroundings: here a pixel or patch is compared with its surroundings at one or several scales. A second class of methods will use as a context the entire image and compare pixels or patches of pixels with other pixels or patches from other locations in the image but not necessarily in the surroundings of the initial patch. Finally, the third class will take into account a context which is based on a model of what the normality should be. This model can be described as a priori probabilities, Fourier spectrum models . . . In the following sections, the main methods from

Human Attention Modelization and Data Reduction 105

This approach is based on a biological motivation and dates back to the work of Koch & Ullman (1985) on attention modeling. The main principle is to initially compute visual features at several scales in parallel, then to apply center-surround inhibition, combination into conspicuity maps (one per feature) and finally to fuse them into a single saliency map. There are a lot of models derived from this approach which mainly use local center-surround contrast as a local measure of novelty. A good example of this family of approaches is the Itti's model (Figure 1) Itti et al. (1998) which is the first implementation of the Koch and Ullman model. It is composed of three main steps. First, three types of static visual features are selected (colors, intensity and orientations) at several scales. The second step is the center-surround inhibition which will provide high response in case of high contrast, and low response in case of low contrast. This step results in a set of feature maps for each scale. The third step consists in an across-scale combination, followed by normalization to form "conspicuity" maps which are single multiscale contrast maps for each feature. Finally, a linear combination is made to achieve inter-features fusion. Itti proposed several combination strategies: a simple and efficient one is to provide higher weights to conspicuity maps which have global peaks much bigger than their mean. This is an interesting step which integrates

This implementation proved to be the first successful approach of attention computation by providing better predictions of the human gaze than chance or simple descriptors like entropy. Following this success, most computational models of bottom-up attention use the comparison of a central patch to its surroundings as a novelty indicator. An update is obtained by adding other features to the same architecture such as symmetry Privitera & Stark (2000) or curvedness Valenti et al. (2009). Le Meur et al. (2006) refined the model by using more biological cues like contrast sensitivity functions, perceptual decomposition, visual masking, and center-surround interactions. Another popular and efficient model is the Graph Based Visual Saliency model (GVBS, Harel et al. (2007)), which is very close to Itti et al. (1998) regarding feature extraction and center-surround, but differs from it in the fusion step where GBVS computes an activation map before normalization and combination. Other models like Gao et al. (2008) also used center-surround approaches even if the rest of the computation is

global information in addition to the local multi-scale contrast information.

made in a different mathematical framework based on a Bayesian approach.

those three classes are described for still images.

<IP_ADDRESS> Context: pixel's surroundings


*Review* **Application of Fundamental Techniques for Physicochemical Characterizations to Understand Post-Formulation Performance of Pharmaceutical Nanocrystalline Materials**

**Bwalya A. Witika 1,2,\*, Marique Aucamp 3 , Larry L. Mweetwa 2 and Pedzisai A. Makoni 4,\***

**Abstract:** Nanocrystalline materials (NCM, i.e., crystalline nanoparticles) have become an important class of materials with great potential for applications ranging from drug delivery and electronics to optics. Drug nanocrystals (NC) and nano co-crystals (NCC) are examples of NCM with fascinating physicochemical properties and have attracted significant attention in drug delivery. NCM are categorized by advantageous properties, such as high drug-loading efficiency, good long-term physical stability, steady and predictable drug release, and long systemic circulation time. These properties make them excellent formulations for the efficient delivery of a variety of active pharmaceutical ingredients (API). In this review, we summarize the recent advances in drug NCM-based therapy options. Currently, there are three main methods to synthesize drug NCM, including top-down, bottom-up, and combination methods. The fundamental characterization methods of drug NCM are elaborated. Furthermore, the applications of these characterizations and their implications on the post-formulation performance of NCM are introduced.

**Keywords:** nanocrystalline materials; physicochemical characterization; vibrational spectroscopy; X-ray analysis; thermal analysis; critical quality attributes


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Collectively, these findings suggest a non-linear effect of age on total reported content; the age-related increase in the amount of detail reported in typical autobiographical recollection emerges most noticeably in subjects in their mid-to-late 40s and persists into old age (i.e., late 70s; **Figure 2A**). Given this pattern, to simply describe the magnitude of these effects, AMs were divided into two groups: those collected from subjects 45 years old or younger (Mean Age = 27, SD = 8, range: 18–45 years old; 72% female, 80% native English speakers) and those from subjects 46 years old or older (Mean Age = 57, SD = 8, range: 46–78 years old; 65% female, 89% native English speakers; **Figure 2B**). This grouping revealed a ∼16% increase in the number of reported details for a given AM in older compared with younger subjects (∼25 vs. ∼21; *p <* 0.001, *d* = 0.23; **Figure 2B**; **Table 2**). While reported content was quite variable from memory to memory, the coefficient of variation was similar across all ages (∼0.6–0.7; **Table 2**). The distributions of total content underscore the moderate effect of age on reported details (**Figure 2C**). Half of all scored memories in younger subjects were comprised of ∼16 or fewer elements; half of all scored AMs in older subjects contained more than ∼20 elements.

## Total Content Decays with the Age of the Memory Across Younger and Older Subjects Alike

Older subjects reported significantly more content than younger subjects for memories of all life periods, both when comparing equivalent decades of life (**Figure 3**), and when comparing relative life periods (e.g., Recent: the most recent 10 years, and Remote: *>* 10 years from the present; see Materials and Methods; **Figure 3** Inset; **Table 2**). The numerical results of content analysis of Recent and Remote AMs only marginally fluctuated depending on how these temporal intervals were defined (e.g., restricting Recent AMs to the most recent 5 years; restricting Remote AMs to the first decade of life). In addition, all reported conclusions remained unchanged and did not depend on the particular grouping applied (data not shown).

Older subjects reported ∼24 elements from AMs dated to the first two decades of life compared with ∼20 elements in younger subjects (*p <* 0.001; *d* = 0.27). Likewise, Recent AMs from older subjects were comprised of ∼27 elements compared with ∼21 elements in those from younger individuals (**Figure 3** Inset; *p <* 0.001; *d* = 0.38). Total content declined with the age of the episode among all age groups. For example, Remote AMs were

comprised of significantly fewer details compared with Recent AMs (*p <* 0.01; **Table 2**; **Figure 3**). These results confirm those previously reported in college-aged subjects (Gardner et al., 2012) and extend these findings to older adults.

## Features Selectively Contribute to the Age-Related Increase in Total Content

A relatively high proportion of AM content (∼46%; ∼10.1 elements) was associated with *Places, Things*, and *People*. In contrast, *Times*, *Contexts*, and *Episodes* were less represented, together comprising just ∼29% (∼6.4 elements). *Details* and *Feelings* were close to the average at ∼13% and ∼12%, respectively (**Figure 4A**). Largely in line with these distributions, the proportion of AMs containing at least one element of a particular feature was highest for *Places* (98%) followed by *People* and *Feelings* (92% each), *Things* (89%), *Details* (84%), *Times* (83%), *Contexts* (78%), *and Episodes* (63%). Feature variation was higher than that observed for total content, but equivalent across age groups (*Mean Feature CV* = 1.0). All these findings uphold those previously reported in younger subjects (Gardner et al., 2012).

Adding to this research, we found that older adults reported a greater number of elements among all features. *Episodes* and *Things* showed the most prominent age-related content increase (∼30% and 27%, respectively; *p <* 0.001), while content associated with *People* and *Times* remained close to that observed in young subjects (*p >* 0.10; **Figures 4A,B**). These data collectively indicate that the age-related increase in total content is not uniformly distributed across features (in terms of either absolute or relative value). In particular, *Things* (24%), *Episodes* (16%), and *Details* (15%) contributed more substantially to the age-related increase observed in total content (**Figure 4C**), whereas contributions from *People* (4%) and *Times* (3%) were definitively smaller. The proportion of AMs containing at least one element from a given feature was significantly higher in older compared with younger subjects for *Feelings, Things, Details, Contexts,* and *Episodes* (∼5% higher on average; *p <* 0.001) but not for *People, Places*, and *Times* (*p >* 0.10). These feature distributions were consistent between Remote and Recent AMs in both younger and older subjects (Supplementary Figure S1); notably, the feature *Times* appeared to be least resilient to temporal decay of content among all subjects.

## People is a Relatively Independent Feature of Recall Among All Ages

Content correlation analysis showed positive relationships among all features (*mean Pearson r* = 0.37). Moreover, these relationships were similar across age groups (younger: *r* = 0.36; older: *r* = 0.40) as well as between Remote and Recent intervals (Remote: *r* = 0.39; Recent: *r* = 0.37). To further evaluate feature dependence, the correlation between each feature and all other content was computed. The average of these values across all features was equivalent between age groups (younger: *r* = 0.53; older: *r* = 0.57; Supplementary Figure S2A) and across life periods (not shown). However, the feature *People* exhibited a comparatively mild relationship (*r* = 0.37; 32% less than the average: Supplementary Figure S2B) across all conditions, suggesting that it is a relatively independent component of recall. The inter-feature relationships found here confirm those previously reported among younger subjects (Gardner et al., 2012) and extend these findings to individuals distributed across the life span.

## Estimates of Retrieved Content across Age Groups and Life Periods

This work provides numerical description of AM retrieval probabilities and reported content associated with distinct life periods. Combining these two measurements, we can estimate the relative distribution of retrieved content across temporal intervals and age groups (**Figure 5**). Specifically, given the number of elements typically reported for a single retrieved AM, for each of the various age groups (as outlined in **Figure 2A** and plotted in **Figure 5** by mean age), we computed a probabilistic content distribution among life periods. For example, when experiencing AM, a typical 70 year old, on average, reports a similar content amount from his or her middle teenage years compared with that from the last few years of his or her life. In contrast, content from events dated to the most recent 2 years of the life of a 21 year old is ∼5 times more represented in memory than that associated with events from his or her middle teenage years. Assuming that the frequency of AM recollection is stable across age groups (e.g., see Gardner and Ascoli, 2015), we can further estimate the relative probability that a particular recalled element is associated with a certain age group and life period. For example, the likelihood for a 30 year old to retrieve content from his or her early 20s (∼1.3%) is equivalent to that for a 60 year old to retrieve content from his or her early thirties.

## The Bump is Unrelated to Changes in Total Content and Feature Content

Autobiographical memories found within the reminiscence bump may have distinct recall characteristics. For example, AMs that compose the bump may be comparatively rich with recalled detail. Such a finding would explain, at least in part, why this life period plays a particularly prominent role in subjective experience. We evaluated reported content from AMs within and beyond life periods associated with the bump in older subjects (46–78 years old) for whom this phenomenon was most pronounced. In this age range, we observed a relatively high AM retrieval probability (excluding temporal bins associated with the retention interval) from ages 11–20 and a relatively low probability from ages 31–40 (see **Figure 1**). However, measures of total content from these life periods did not significantly differ (*M* = 24.90 and *M* = 25.28, respectively; *p >* 0.10, *d* = 0.02; **Figure 3**). The composition of memories dated to these life periods was also quite stable (*p >* 0.10), with any given feature showing a deviation of ∼2% or less (*Mean deviation*: ∼1%).

All the main findings of this work are robust to gender, native language, and changes in experimental procedures (see Supplementary Tables S1 and S2). For example, total reported content moderately increased with age both for females and males, as well as for native and non-native English speakers (see Supplementary Material). However, several minor quantitative distinctions in AM recall were observed between males and females, between native and non-native English speakers, and among testing conditions. A full review of these results is included as Supplementary Material.

## Age Effects are Corroborated Using Subject As the Level of Analysis

As prior reports suggest that different individuals have distinct recollection experiences (Rubin et al., 2004), the main conclusions of this work were evaluated using a subjectlevel analysis. Given the relatively large amount of variability in content scores from memory to memory (see **Table 2**), the analysis was restricted to those subjects who scored five or more memories (18–45 years old: *n* = 496; 46–78 years old: *n* = 118). This restriction permitted measures that more closely represent typical recollection from a given individual. In addition, for inclusion in comparisons across Recent and Remote intervals, subjects were required to have an AM scored in each temporal period (18–45 years old: *n* = 420; 46–78 years old: *n* = 69). Content measures reported independent of temporal periods were weighted according to the temporal distribution of AM retrieval computed separately for each subject on the basis of his or her dated AMs.

Age effects on the temporal distribution of AMs and AM content are confirmed by subject-level analysis. In particular, the proportion of AMs from Recent life intervals was relatively high in young subjects (18–25 years old: ∼77%) and decreased with increasing age (26–45 years old: ∼40%; 46–78 years old: ∼17%). Moreover, older adults (46–78 years old) reported ∼15% more elements than younger (18–45 years old) subjects (Mean ± SD: 25 ± 13 compared with 21 ± 10 details; *p <* 0.01), replicating age differences found using memory as the observational unit. Remote memories contained fewer elements (18 ± 11) than Recent memories (23 ± 13; *p <* 0.001) across all subjects, and older compared with younger subjects reported more elements from Recent (Older subjects: 29 ± 18; Younger subjects: 22 ± 11; *p <* 0.001) and Remote events (Older subjects: 23 ± 13; Younger subjects: 18 ± 10; *p <* 0.001). In addition, an age-related increase in total reported content was most drastic for Episodes (∼31%) and Things (∼30%), whereas considerably less dramatic for Times ( *<* 1%) and People (∼4%), closely resembling findings using memory as the unit of analysis. Likewise, total content scores from older subjects did not discriminate between bump and non-bump memories (e.g., comparing content from AMs dated to when subjects were 11–20 years old with those dated to when subjects were 31–40 years old; *p >* 0.10; data not shown).

the number of elements per life period was computed for each of the six age

## Discussion

This work provides quantitative measures of reported AM content from individuals that represent a substantial segment of the adult population (18–78 years old). This was accomplished using CRAM, an instrument designed to collect counts of details that fall within specified features from naturalistically elicited AMs dated to particular life periods. Relying on participant counts of memory content (rather than experimenter-scored participant narratives) facilitates data collection and thus enables fine-scale analysis of AMs (e.g., as shown in **Figure 5**).

particular age and life period (shown as content retrieval probabilities).

We previously demonstrated that CRAM replicates several noted observations of AM recall (e.g., on the retention of recent AMs and their associated content; Rubin and Schulkind, 1997; Levine et al., 2002; Piolino et al., 2002; Janssen et al., 2011). The present study upholds our previous findings from college-aged subjects. In particular, the current estimate of AM total content (∼21 elements) among younger subjects is almost identical to that reported (∼20 elements) by Gardner et al. (2012). In addition, the current work supports previous findings on the temporal decay of content (Remote AMs contain fewer elements), AM content variability (from memory to memory, total content remains relatively stable compared to feature content), AM composition (*Places, Things, and People* are prominent features of recall), and inter-feature correlations (*People* is a relatively independent recall characteristic).

Extending CRAM to older adults, we replicated prior reports of age-modulation of the temporal distribution of AMs. Specifically, Recent AMs were considerably less likely to be recalled in older subjects (Rubin and Schulkind, 1997; Janssen et al., 2011), and the reminiscence bump emerged in subjects in their mid-to-late 20s. While some studies have found that the bump is not apparent until ∼40 years of age, using relatively small temporal bins, Janssen et al.(2011) reported a similar onset to that found here. In addition, the temporal interval associated with the bump using CRAM (i.e., 8–20 years old) is consistent with these studies.

Total content moderately but significantly increased with subject age. Older adults reported ∼25 details for a given AM, ∼4 elements more than the number reported from younger subjects. Moreover, this age-related increase in content was observed for Recent and Remote memories, and was most drastic for the features *Episodes* (sequences of event) and *Things* (objects) while negligible for *People* (unique individuals) and *Times* (temporal detail). Altogether, these data quantitatively describe an ageassociated shift in the reported details of subjectively remembered events.

As older adults reported more content than younger adults from memories that originated in the same decade of life (i.e., those AMs that have similar ages of encoding), these findings appear to highlight the re-constructive nature of AM (Bartlett, 1932; Conway and Pleydell-Pearce, 2000; Hupbach et al., 2007). This interpretation assumes that the initial number of encoded event details and encoding depth are similar between age groups. However, as with all cross-sectional aging research, any intergroup differences may reflect generational differences rather than (or in addition to) changes that occur among individuals across their life span.

It also remains possible that older and younger adults used divergent strategies to establish feature counts. However, the finding that the age effects on content were feature-specific (see **Figure 4**) argues against a general change in interpretation of CRAM's instruction, and/or adjustment in content evaluation (e.g., a pervasive tendency for older individuals to report higher scores). Similarly, older subjects may be more motivated to recall and report event details. Nevertheless, the selection of online test types (which differed in their time commitment) was equivalent across age groups, suggesting that motivation may not underlie our findings. A similar conclusion can be drawn from the finding that content data collected in-person were equivalent to those collected online (see Supplementary Material), assuming that, on average, testing conditions correlate with task motivation. Further work, including the use of longitudinal designs, is required to clarify the mechanisms underlying the current findings.

Older individuals are proposed to have altered narrative attention and to tell more interesting life stories (James et al., 1998). Although more detail is not always better, inclusion of information about sequences of happenings (the feature that was most strongly augmented from younger to older subjects) within a life narrative enables placement of an episodic snapshot into a broader context of surrounding events (and may enhance storytelling). It would be interesting to establish how our findings on feature-specific age-related modulation of reported AM content compare with the types and amount of detail shared through social communication of event memories and during the narration of life stories.

Despite the moderate change in total reported content, several properties of recollection were stable across age groups. In particular, AMs from younger and older subjects, and those from Remote and Recent life periods, showed similar feature distributions. In addition, among all ages, fewer details were reported from Remote than from Recent AMs. Thus, these data are indicative of two independent age effects on reported AM content: a positive correlation with the age of the individual and a negative one with the age of the event. These findings confirm and extend prior studies (Janssen et al., 2011; Gardner et al., 2012).

Additionally, independent of age, almost all AMs were reported to have at least one detail related to location, and nine out of 10 memories were reported to include some information about people, objects, and feelings, suggesting that these features are quite remarkable and/or at the core of subjective recall. In contrast, less than two-thirds of memories were reported to include sequential events. The feature *People* was also relatively independent, further demonstrating its unique role in memory; among the proposed functions of AM, remembrance of the individuals associated with specific life experiences is essential to form and maintain social relationships (see Pillemer, 1992; Bluck et al., 2005; Bluck and Alea, 2011; Waters, 2014).

Combining the observed temporal distributions of AM retrieval with measure of reported AM content permits computation of detailed probability estimates of reporting an element from a given life period at a particular age (**Figure 5**). For instance, this approach quantifies how likely it is for a detail retrieved by a 60 year old to be associated with an episode from his or her 20s (∼1.7%). Moreover, we can address questions on how these probability distributions change with subject age. For instance, how does the previously computed probability compare with the likelihood that the same amount of content retrieved by a 20 year old stems from a relatively recent event?

Several factors are proposed to account for the high accessibility of memories that compose the reminiscence bump, e.g., neurocognitive development, cultural influence, and life span changes in encoding efficiency (Rubin et al., 1998; Schrauf and Rubin, 2000; Berntsen and Rubin, 2004; Rathbone et al., 2008; Bohn and Berntsen, 2010; Janssen et al., 2015). We add to an understanding of the bump by showing that neither reported counts of detail across all features nor counts within individual features explain or are explained by the relatively high probability of recollection associated with this life period. These data are in line with previous studies that have demonstrated that AMs within the bump do not have higher ratings of certain characteristics of recollection (e.g., vividness, rehearsal, reliving, novelty, emotionality; Rubin and Schulkind, 1997; Janssen et al., 2011).

Past approaches reporting counts of AM content have predominately focused on the distinction between episodic and semantic retrieval (Levine et al., 2002; Piolino et al., 2002; Addis et al., 2008, 2010; also see Tulving, 1972, 1985). Episodic memory recounts a unique personally experienced event, with some form of contextual information (e.g., spatiotemporal detail). Semantic memory recalls abstracted knowledge of the world or of oneself (generally acquired from repeated experiences) that does not describe or call to mind a unique episode. This distinction is highlighted by case reports of neurocognitive deficits following targeted brain damage (Rosenbaum et al., 2005) and is present in numerous theories of AM (e.g., Conway and Pleydell-Pearce, 2000). Using a narrative scoring technique of event-cued AMs specified to life periods, Levine et al. (2002) found that, compared to younger subjects, older adults report fewer episodic but a similar or greater number of semantic details from typical memories. This age effect on episodic detail appeared to be feature-dependent as it was absent (but never reversed) for some features (e.g., *Times*). Contrasting accounts, however, have been reported. Hashtroudi et al. (1990) found that older adults reported more content for feelings and thoughts (albeit these same individuals showed a reduction in sensory-perceptual recollection). In addition, Janssen et al. (2011) found that ratings of AM vividness and re-living, proposed indices of episodic remembering were higher in older subjects (also see Rubin and Schulkind, 1997; Rubin and Berntsen, 2009). Direct comparison of memory content scores obtained using a variety of quantitative and qualitative approaches will be a useful endeavor to reconcile the apparently discrepant findings in AM recollection across age groups.

We emphasize that CRAM was broadly designed to measure the details that a participant considers part of an AM, i.e., the subjective content associated with a remembered life event. As such, CRAM does not classify reported elements as episodic or semantic. However, each feature definition was worded to collect the details that compose a memory for a temporally specific event; likewise, the general guidance provided to subjects emphasized reporting of detail unique to

## References

the specified episode (see Materials and Methods; Gardner et al., 2012). As CRAM collects reports of retrieved subjective detail, this approach also contrasts with those that aim to collect "true" or verifiable detail or those which collect all potentially retrievable details associated with an event (e.g., Mello and Fisher, 1996; Levine et al., 2002). We further stress that as counts of memory details are provided by the subject, although the results are in line with several prior findings, content measures as reported here may systematically differ from the actual numbers of details that are successfully retrieved from a given event memory. As CRAM's instruction was identical between all subjects, however, relative measures between and within age groups should reflect genuine changes in subjective memory.

Altogether, the data presented here provide previously inaccessible fine-scale quantitative characterizations of the reported subjective content of AMs as a function of the age of an individual and the age of a memory. These characterizations point to a moderate but significant age-associated featurespecific shift in how one's life story is perceived and recounted.

## Acknowledgments

This research was supported in part by the Air Force Office of Scientific Research (Award No: FA9550-10-1-0385) and the Office of Naval Research (Award No:<PHONE_NUMBER>98). Publication of this article was funded in part by the George Mason University Libraries Open Access Publishing Fund.

## Supplementary Material

The Supplementary Material for this article can be found online at: http://journal*.*frontiersin*.*org/article/10*.*3389/fpsyg*.* 2015*.*00631/abstract

**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.

*Copyright © 2015 Gardner, Mainetti and Ascoli. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

# Semantic memory as the root of imagination

#### Anna Abraham1 \* and Andreja Bubic2

*1 School of Social, Psychological and Communication Sciences, Faculty of Health and Social Sciences, Leeds Beckett University, Leeds, UK, 2 Psychology Department, Faculty of Humanities and Social Sciences, University of Split, Split, Croatia*

Keywords: creativity, prospection, neurocognition, cognitive neuroscience, mental time travel, episodic memory, theory of mind, moral reasoning

"Imagination is what makes our sensory experience meaningful, enabling us to interpret and make sense of it, whether from a conventional perspective or from a fresh, original, individual one. It is what makes perception more than the mere physical stimulation of sense organs. It also produces mental imagery, visual and otherwise, which is what makes it possible for us to think outside the confines of our present perceptual reality, to consider memories of the past and possibilities for the future, and to weigh alternatives against one another. Thus, imagination makes possible all our thinking about what is, what has been, and, perhaps most important, what might be."—Nigel J. T. Thomas (2004, as cited in Manu, 2006, p. 47)1 .

Investigations of the information processing mechanisms that underlie imaginative thought typically focus on a single branch of imagination, such as prospection, mental imagery or creativity, and are often generalized as being insightful to understanding the workings of imagination in general. In reality, however, there is very little in the way of theoretical or empirical exchange between the scientific communities that conduct research within the different domains of imagination. As a result, the research impetus in each of the sub-domains may be skewed to the pursuit of hypotheses that are not particularly viable in terms of understanding imagination as a whole. An example of this is pegging the roots of imagination to the processes of episodic memory—a reasonable assumption to make based on studies of episodic prospection. However, the associated findings and theoretical conclusions that follow are not entirely consistent with the literature on the mechanisms underlying creativity (Bubic and Abraham, 2014 ´ ), which is another core realm of imagination.

In an effort to promote interchange across the frontiers of imagination, in this Opinion Article we put forward the idea that all aspects of imagination emerge from semantic memory with increasingly higher-order levels of imaginative information processing emanating from and interacting with existing systems, eventually expanding beyond these to form new systems (**Figure 1**). We compare the associated neurocognitive findings and assumptions in terms of their fit with current knowledge in other fields of imagination and discuss their implications for reformulating hypotheses regarding imagination as a whole.

## The What?

Our conceptual knowledge of the world is the foundation from which all imaginative thought emerges and, as such, constitutes "the what-system" within the information processing hub. Investigations of the manner in which concepts are acquired, represented, stored, and accessed fall within the field of semantic cognition. The brain networks that underlie the what-system include

#### Edited by:

*Jason D. Runyan, Indiana Wesleyan University, USA*

Reviewed by:

*Jessica Andrews-Hanna, University of Colorado Boulder, USA*

> \*Correspondence: *Anna Abraham<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Cognitive Science, a section of the journal Frontiers in Psychology*

> Received: *05 December 2014* Accepted: *06 March 2015* Published: *24 March 2015*

#### Citation:

*Abraham A and Bubic A (2015) Semantic memory as the root of imagination. Front. Psychol. 6:325. doi: 10.3389/fpsyg.2015.00325*

1http://archive.today/www.imagery-imagination.com or http://www.co-bw.com/BrainConciousness%20Update%20index. htm

modality-specific sensory and motor systems as well as multimodal or supramodal regions within the inferior parietal lobe, middle and inferior temporal gyri, fusiform and parahippocampal gyri, inferior frontal gyrus, dorsomedial and ventromedial prefrontal cortex and the posterior cingulate gyrus (Binder et al., 2009; Binder and Desai, 2011; Kiefer and Pulvermüller, 2012). Such insights have emerged from neuroscientific investigations into the brain basis of semantic memory, semantic aspects of language processing, and the organization of conceptual knowledge in the brain.

## The What–Where?

Determining the location of any object or person relative to oneself, some other person or object is only possible by accessing representations of spatial information such as direction, orientation, distance and position of that object or person. Such information is coded by means of reference frames relative to the observer (egocentric) and independent of the observer (allocentric) (Burgess, 2006). Tasks of spatial memory and navigation have shown that medial temporal lobe structures such as the hippocampal formation, parahippocampal gyrus, entorhinal and perirhinal cortices as well as medial parietal regions, such as the retrosplenial and posterior cingulate cortices (Burgess, 2008; Chrastil, 2013; Ekstrom et al., 2014), are critically involved in spatial information processing. Others tasks of spatial cognition, such as perspective taking, have indicated the involvement of additional regions within the posterior parietal cortex, particularly the inferior parietal and temporo-parietal areas (Byrne and Becker, 2007; Dhindsa et al., 2014).

## The What–Where–When?

An event is defined as a specific happening (what) that occurs at a certain place (where) and at a given time (when). During retrospection we access events from our personal past (episodic memory, autobiographical memory), whereas during prospection we contemplate events that could unfold in our personal future (episodic future thinking). Both fall within the umbrella concept of mental time travel (Tulving, 1985). Neuroscientific evidence has consistently revealed that the brain network that is engaged when we imagine personal events in the near or distant future overlaps considerably with the network that is activated when we ponder our episodic or autobiographical past (Schacter et al., 2007, 2012; Mullally and Maguire, 2013). Regions that comprise this brain network include the ventral and dorsal medial prefrontal cortex, retrosplenial and posterior cingulate regions within the medial parietal cortex, anterior lateral temporal cortex, inferior parietal cortex, and medial temporal lobe structures such as the hippocampus. Notably, the regions of the mental time travel brain network also closely correspond to those of the brain's default mode network (DMN). The DMN is active under conditions of rest and low task load, and is held to reflect processing demands associated with mind-wandering, internal mentation and stimulus-independent thought (Andrews-Hanna et al., 2014). DMN brain areas are also involved in other facets of higher order cognition, like mental state reasoning or theory of mind, moral cognition, and selfreferential thought (Buckner et al., 2008; Spreng et al., 2009), all of which involve reasoning about one's self and/or others.

## The What-If?

Our capacity to imagine possibilities is virtually unconstrained. Investigations on the information processing circuits involved in prospection address the question of "what if?" or "what might be?" within a specific temporal context of our personal lives (which covers the aforementioned episodic prospection of the what–when–where system). However, our cognitive capacity to explore hypothetical possibility spaces is neither limited only to our personal lives nor to any temporal factor (past/present/future). Other operations that fall under the category of what-if or hypothetical reasoning based cognitive processes include semantic prospection, semantic or episodic counterfactual reasoning and creativity. In addition to the partial conceptual overlap between the what-if system and the previously discussed what-where-when system, the two also share common underlying neural mechanisms. Although only a few neuroscientific studies have investigated semantic prospection or the propensity to think about the non-personal future, the limited evidence indicates that semantic prospection is reliant on similar parts of the brain's episodic mental time travel network, particularly with reference to the engagement of anterior and dorsal medial prefrontal regions, inferior parietal cortices, the hippocampus and related medial temporal lobe structures (Abraham et al., 2008; Race et al., 2013).

In contrast to semantic prospection, which is relatively unrestricted with regard to the types of imaginable alternatives, counterfactual thinking primarily involves exploring possibilities that are contrary to what has already come to pass. Research on brain correlates of counterfactual comparisons and emotions that often accompany such cognition, such as regret, indicates a key role for the orbitofrontal and ventromedial prefrontal cortices (Camille et al., 2004; Levens et al., 2014). Furthermore, studies that have assessed episodic past, episodic future and episodic counterfactual thinking have reported a common brain network, involving the hippocampal formation, temporal lobe structures, lateral parietal regions as well as medial and lateral prefrontal areas. Within the episodic cognition domain, counterfactual thinking recruits some of these areas more strongly than past and future thinking, and also additionally engages the bilateral inferior parietal lobe and posterior medial frontal cortex (Van Hoeck et al., 2013).

Semantic prospection and counterfactual reasoning are concerned with hypothetical reasoning linked to the future and the past, respectfully. However, one can also engage in hypothetical reasoning within temporally unspecific contexts such as those involving moral and mental state reasoning, which, as pointed out earlier, strongly overlap in terms of their implicated brain network with the what–when–where system (Buckner et al., 2008). While the contexts tapped in such hypothetical reasoning operations are decidedly social in nature, a non-socially based avenue within which we necessarily exercise our capacity to think hypothetically is that of creativity.

Our capacity to be creative is examined by assessing the extent to which we are able to generate original and relevant responses to a particular end (Stein, 1953; Runco and Jaeger, 2012). The underlying brain mechanisms of creative cognition are very complex (Abraham, 2014). Brain regions such as the dorsal and ventral medial prefrontal cortex, retrosplenial and posterior cingulate cortices as well as medial temporal lobe structures are strongly engaged during divergent thinking, or the generation of multiple responses in an open-ended situation (Abraham et al., 2012). This indicates that there is a considerable overlap in the neural correlates of divergent thinking and that of the what–when–where network. While divergent thinking certainly involves hypothetical reasoning and exploration of an abstract possibility space, it does not necessarily translate to creative thought. Having constraints on divergent thinking pushes the information processing system to be necessarily creative (both original and relevant) and this leads to the additional activation of the semantic cognition and cognitive control networks with the major contributions being provided by brain regions such as the inferior frontal gyrus, temporal pole, frontopolar cortex, and basal ganglia. So the neural correlates of creative cognition system overlap only partially with those associated with other aspects of the imagination system with common activations seen in the dorsomedial prefrontal cortex and inferior parietal lobe (the what–when– where system) as well as the inferior frontal gyrus (the whatsystem).

## Integrating the Disparate Systems of Imagination

In this Opinion Article, we explored the view that processes of imagination—the "where" of spatial cognition, the "whatwhen-where" of episodic retrospection and prospection, and the "what-if " of semantic prospection, counterfactual reasoning and creative thinking—emerge from a foundation provided by the "what" of semantic memory operations. The evidence thus far clearly indicates that the many processes of imagination, which have mostly been systematically investigated in isolation from one another, are neurally implemented in substantially overlapping brain networks and are also similar with respect to their underlying cognitive algorithms and mechanisms. This resonates with other proposals that have highlighted that semantic and episodic cognitive operations and their related brain systems are dynamically interlinked (Squire and Zola, 1998; Greenberg and Verfaellie, 2010), as well as with recent calls for de-emphasizing the episodic or autonoetic aspects of future oriented cognition and advocating the central role played by semantic memory in the same (Stocker, 2012; Irish and Piguet, 2013).

This does not mean that all imaginative processes are to be considered "atemporal" per definition. Many forms of mental time travel as well as counterfactual thinking patently involve the consideration of temporal factors as a core facet of the imaginative process. In taking this a step further, it may even be argued that such processes are necessarily linked to the brain's predictive systems due to the fact that they involve the generation of estimates concerning events that reliably unfold over a certain period of time, albeit with differing levels of certainty (Bubic et al., 2010). This position has rarely been considered in the literature on imagination-relevant operations but it would fit with a number of suggestions that posit prediction as the fundamental mechanism that modulates our general neural and cognitive processing (Friston and Stephan, 2007; Pezzulo, 2008).

So, although the issue of temporality is undoubtedly relevant, the more fundamental basis that underlies all of the aforementioned processes is the reliance on our experiences with the world, its objects and events. We therefore suggest that if the aim is to develop a comprehensive information processing model of imagination, the foundational elements should be discussed in terms

## References

of semantic memory operations. As semantic memory involves the abstraction of content from experiences that are specific to sensory, motor, or affective modalities, conceptualizing the processes of imagination as stemming from semantic operations allows for a more seamless integration of its theoretical models with that of the wider research realm of perception, action and cognition where concepts such as embodied cognition and predictive processing are revolutionizing our understanding of psychology.

We hope these ideas will stimulate future research and the development of novel paradigms as well as critical scientific exchange between the research communities involved in understanding different aspects of imagination. Some questions can be already anticipated such as the "chicken-and-egg" problem within which it appears impossible to clearly substantiate what came first, or concerns about how to reach a consensus about what can be considered an underlying foundational element. Through the process of this discussion though, we hope that building blocks and essential frameworks will be uncovered that will guide us through the incredibly rich world of human imagination.

Van Hoeck, N., Ma, N., Ampe, L., Baetens, K., Vandekerckhove, M., and Van Overwalle, F. (2013). Counterfactual thinking: an fMRI study on changing the past for a better future. Soc. Cogn. Affect. Neurosci. 8, 556–564. doi: 10.1093/scan/nss031

**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.

Copyright © 2015 Abraham and Bubic. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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**2. Connection from the inner core to the surface**

The central part of the Sun is composed of a core (about a fourth of its radius) where thermonuclear reactions generate energy. While its average density is about 10 times that of lead, its temperature is about 15 106 K. The core yields to the radiative zone of the Sun, which is about one-third of the Sun's radius. Both the core and the radiative zone transfer energy by radiative forces of photons following a random walk and seem to act as an apparent solid body [2].

The photosphere is 300–500Km deep, it is the part of the Sun from which the light is being emitted, before the plasma becomes opaque. The effective temperature of the Sun comes from the photosphere, at about 5.8 103 K, plasma convection is visible there under the form of granules of sizes measured in Mm (103 m). As any convective cell, granules [3, 4] have central heat upwelling and peripherial cool downwelling (**Figure 1**). Their life span is short, 8–20 minutes. Within the granules area, additionally to pores and magnetic flux tubes, sunspots may rise within mid-latitudes and converge to subequatorial latitudes. A sunspot is a cooler region and is measured in tens of Mm. It is composed of a central darkest part, the umbra, and surrounded by a less dark area called the penumbra made of radial acicularity (**Figure 1**). Its existence is inherently due to the Sun's magnetism.

Further parts outside of the Sun are referred to as part of its "atmosphere." They are the chromosphere and the corona (in that order).

The chromosphere is 2000 km deep, it is the Sun's eclipse "red ring of fire." It is characterized by a steep drop in material density, and an initial temperature drop from 5.8 103 K to 3.5 103 K to eventually reach 35 103 K. The chromosphere and its transition zone to the next zone are the subject of study of the Interface Region Imaging Spectrograph (http://www.nasa.gov/iris), especially the chromospheric jets associated with coronal heating (de Pontieu, 2011 @SETI Talks).

The corona is a very large volume above the chromosphere, vastly warmer too, made of ionized plasma of about 1 106 K, with a majority of emission coming from Fe-XIV and Fe-X. It is the origin of the *solar winds*. Some areas with open magnetic fields (**Figure 2**) yield faster *solar winds* (about 0.7 106 m/s). The Hinode mission

#### **Figure 2.**

*High-resolution image of the sun from solar orbiter, showing magnetically bound plasma. Credit: ESA & NASA/ solar orbiter/EUI team; data processing: E. Kraaikamp (ROB) [5].*

recorded the most sensitive information about the magnetism of the Sun (http:// www.nasa.gov/hinode/).

The interplay between convection and magnetic fields drives all the heating in the solar atmosphere and the space weather. The magneto-convective energy heats the corona, drives the *solar wind*, causes flares and coronal mass ejections (de Pontieu, 2011 @SETI Talks).

Thompson et al. [6] used continuous observations from the Global Oscillation Network Group (GONG) and inverse modeling (harmonics frequency splitting, inverting rotation kernels) to confirm that differential rotation on the surface is carrying through most of the convection zone, until the tachocline at 0.713 of the Sun's atmosphere radius (R), a zone (**Figure 3**) of strong shear where disassociation happens with the deeper part of the Sun [2], and where variations of rotations have been linked with the presumed depth of the solar dynamo. Howe [2] further found that temporal variations in the tachocline region extend in the radiative zone as far as 0.63R (blue overlay on **Figure 3**), which suggests complex physics properties at the shear zone converting from (apparent) nearly solid state to convective.

Thompson et al. [6] also observed a shear layer just below surface at lower latitudes. In the equatorial regions, as depth increases, the rotation rate first increases (orange overlay on **Figure 3**) and then decreases. This particularity is reducing with latitude (away from equator). Sunspots are forced by the differential rotation to "stretch" from their roots in the convection zone and below [7] following the equatorial convergence until their "elasticity" is reaching limits. At this point, they "snap" to release as a filament.

A filament eruption (http://science.nasa.gov/missions/trace/) is a magnetic line disconnecting from the underlying magnetic field after a too large disturbance, the Alfvén waves survive the Corona transfer and are depositing energy in the *solar wind* [8].

**Figure 3.** *Time-averaged rotation rates (Ω/2π) vs. partial sun radius (r/R) at different latitudes, redrawn from Howe [2].*


*3.1. Simulator*

The Monte Carlo suite ("simulator") consists of four different classes of algorithms: (1) Standard localized moves that entail the displacement of a single or a sequence of atoms, (2) chain-connectivity-altering moves (CCAMs), (3) cluster-based moves, and (4) identity exchange moves, all being executed at a constant volume. When shrinkage or NPT simulations are conducted, the regular volume fluctuation moves and/or the MRoB algorithm [75] undertake the task of changing the dimensions of the orthogonal simulation cell. This size alteration can be isotropic or anisotropic.

The local moves have been described exhaustively in numerous past publications. For single monomers, the simplest possible move is that of a displacement in a random direction and length within a preset amplitude [0, *ldisp*(*i*)], which again can be different for each dimension, *i*. With respect to chains, the corresponding set consists of: (i) Flip (internal libration), (ii) end-mer rotation, (iii) reptation, (iv) intermolecular reptation, and (v) end-segment re-arrangement (or CCB as in [76,77]; the reason we use a different notation here is to avoid confusion with the general scheme employed in all moves is explained next). All polymer-related moves can be executed in a configurational bias (CB) pattern (as seen in Figure 1 for the reptation move), with the number of trial configurations per attempted move, *ntrials*, being an input variable in the simulator. Due to the introduction of energetic bias in the forward transition, the reverse transition must be attempted *ntrials*-1 times to guarantee microscopic reversibility. In general, the number of attempts can be different for each local move, *ntrials*(*i*), where index *i* runs over all available polymer-based moves. This is because the individual MC moves are characterized by distinctly different acceptance rates, which are further heavily affected by simulation conditions, chain stiffness and especially by concentration (packing density). As intuitively expected, increasing the number of trial configurations leads to a significant increase in the computational time required per MC move. Setting *ntrials* = 1 enables the conventional execution of the local moves and eliminates the necessity to perform the reverse transition. The selection of *ntrials* is highly system dependent; for example, optimal values for hard-sphere chains in the bulk as a function of the volume fraction from dilute conditions up to the maximally random jammed (MRJ) state can be found in Table 1 of Ref. [59].

**Figure 1.** Schematic of the reptation move implemented through a configurational bias pattern with *ntrials* = 3. Different candidate positions could be picked by the selection of the bond length, bending, and torsion angles used for the re-construction of the monomer.

The set of chain-connectivity-altering moves consists of the simplified end-bridging (sEB), simplified intramolecular end-bridging (sIEB), and simplified double bridging (sDB) [59,75] moves. All constitute simplified versions of the original EB [74,78] and DB [79,80] algorithms, initially developed for the rapid equilibration of atomistically detailed polyethylene chains of high molecular weight. The main difference with respect to the original moves is that none of the simplified versions entails the displacement of atoms; rather they proceed by deleting and forming properly selected bonds in a pair (sEB, sDB) of chains or a single (sIEB) chain. The main advantage of the sDB algorithm is that it can be applied to strictly monodisperse systems and primarily to non-linear molecular architectures. Its main disadvantage is that it requires a bridgeable distance between two different pairs of atoms. For systems of very small bond gaps (*dl* → 0), this condition is very rarely met except very near the jammed state where the contact network is rich as a result of the isostaticity condition [65]. Additionally, all systems to be reported in the continuation are composed of linear chains. Furthermore, it has been found that dispersity in chain lengths has no effect on the universal static scaling laws [66,67] and phase behavior [71,72] of the simulated thermal and athermal polymer packings. Based on the above, sDB is excluded from the mix of moves for all cases studied here.

The third class of MC moves is that of cluster-based ones. The two variations, implemented in Simu-D, are cluster rotation (CluRot) and cluster displacement (CluDis) as first introduced in the home-made cluster code reported in [63]. The execution of the moves proceeds according to the schematic in Figure 2. In the first step, the cluster is identified. Group similarity for cluster detection is conducted first through a Euclidean distance criterion, independently of the identity of the constituent atoms (chain versus single monomers etc.). Further linkage criteria can include additional common elements such as the same crystal similarity (as detected for example by the CCE analysis, see below). Once the clusters are identified with the corresponding members labelled accordingly, one cluster is selected randomly. That cluster, as a whole (i.e., a single object made of the corresponding sites), can be displaced by a random amount in a random direction (CluDis) or be rotated randomly with respect to its center of mass (CluRot). The cluster-related moves can be optionally and automatically de-activated when a single cluster exists in the system.

The cluster detection is a computationally demanding step, so the CluDis and CluRot moves have low attempt probabilities, as also happens with the chain-connectivity-altering ones and the algorithms that alter cell dimensions.

The fifth and final set of moves consists of algorithms that change the identity of atoms and can be applied in the case of blends of monomers and polymers but also of polymers composed of different monomers. Figure 3 presents three such identity exchange (IdEx) moves, involving a single monomer and a single chain or a pair of chains. In the top panel of Figure 3, the execution of IdEx1 is shown once a single monomer (shown in red) is within a bridgeable distance to one of the ends of the chain molecule (shown in blue). The move proceeds by connecting, via a bond, the chain end and the single monomer so that the newly incorporated atom becomes the new chain end. In parallel, the last bond connecting the other end of the chain is deleted and the end is converted to a single monomer. By construction, the move does not entail atom displacement but rather the reconstruction of properly selected bonds. Accordingly, the change in energy entering the Metropolis criterion for acceptance or rejection of the move is due to the bonded term (variation of one bond length, one bending, and one torsion angle), along with any non-bonded change due to the swap of identities. The concept of IdEx2 (middle panel) is very similar. The single

monomer needs to be within a bridgeable distance from the second or penultimate atom of the chain. If the proximity condition is fulfilled, it becomes, through bond formation, the new chain end, and the corresponding chain end is converted into a single atom through bond deletion. Finally, IdEx3 (bottom panel) entails two chains. The difference with respect to the single-chain version is that the new single monomer is created by the deletion of a terminal bond of a randomly selected chain, different than the one that gains the monomer. Clearly, the implementation of IdEx3 requires dispersity in chain lengths.

**Figure 2.** Schematic representation of the cluster displacement (CluDis) and cluster rotation (CluRot) moves in a mixed system of chain (**blue**) and single (**red**) monomers. The initial step of cluster detection is performed based solely on proximity criterion. The identified cluster is shown by the contour line. The cluster, as a whole unified group of monomers, can then be displaced in a random direction and length (ClusDis) or be rotated by a random amount around its center of mass (ClusRot).

**Figure 3.** Schematic representation of (**top**) IdEx1 involving a chain and a single monomer within a bridgeable distance from a chain end, (**middle**) IdEx2 involving a chain and a single monomer within a bridgeable distance from the atom lying in the second of penultimate position in the chain, and (**bottom**) IdEx3, which includes a pair of chains and a single monomer. In IdEx3, the single monomer, lying within a bridgeable distance from an end of the blue chain becomes part of it, while a randomly selected chain (shown here in green) loses a randomly selected end, which becomes a single monomer. None of the moves depicted above include the displacement of atoms, rather only deletion and formation of bonds. IdEx3 requires dispersity in chain lengths in order to be applicable. In all cases, chain monomers are shown in blue (or green) and single monomers in red.

Based on the concept of identity exchange, as presented above, one can envision variations with monomers being incorporated into the inner segments of the polymer chains. However, such an approach would require the double fulfillment of the bridgeable distance and would therefore significantly reduce the pair of sites that could trigger such IdEx moves. For this reason, no further modifications have been incorporated in the present implementation of the simulator.