A Task-Parallel Approach for Localized Topological Data Structures.

Unstructured meshes are characterized by data points irregularly distributed in the Euclidian space. Due to the irregular nature of these data, computing connectivity information between the mesh elements requires much more time and memory than on uniformly distributed data. To lower storage costs, dynamic data structures have been proposed. These data structures compute connectivity information on the fly and discard them when no longer needed. However, on-the-fly computation slows down algorithms and results in a negative impact on the time performance. To address this issue, we propose a new task-parallel approach to proactively compute mesh connectivity. Unlike previous approaches implementing data-parallel models, where all threads run the same type of instructions, our task-parallel approach allows threads to run different functions. Specifically, some threads run the algorithm of choice while other threads compute connectivity information before they are actually needed. The approach was implemented in the new Accelerated Clustered TOPOlogical (ACTOPO) data structure, which can support any processing algorithm requiring mesh connectivity information. Our experiments show that ACTOPO combines the benefits of state-of-the-art memory-efficient (TTK CompactTriangulation) and time-efficient (TTK ExplicitTriangulation) topological data structures. It occupies a similar amount of memory as TTK CompactTriangulation while providing up to 5x speedup. Moreover, it achieves comparable time performance as TTK ExplicitTriangulation while using only half of the memory space.

TopoCluster: A Localized Data Structure for Topology-Based Visualization.

Unstructured data are collections of points with irregular topology, often represented through simplicial meshes, such as triangle and tetrahedral meshes. Whenever possible such representations are avoided in visualization since they are computationally demanding if compared with regular grids. In this work, we aim at simplifying the encoding and processing of simplicial meshes. The article proposes TopoCluster, a new localized data structure for tetrahedral meshes. TopoCluster provides efficient computation of the connectivity of the mesh elements with a low memory footprint. The key idea of TopoCluster is to subdivide the simplicial mesh into clusters. Then, the connectivity information is computed locally for each cluster and discarded when it is no longer needed. We define two instances of TopoCluster. The first instance prioritizes time efficiency and provides only a modest savings in memory, while the second instance drastically reduces memory consumption up to an order of magnitude with respect to comparable data structures. Thanks to the simple interface provided by TopoCluster, we have been able to integrate both data structures into the existing Topological Toolkit (TTK) framework. As a result, users can run any plugin of TTK using TopoCluster without changing a single line of code.

Locus coeruleus and dorsal cingulate morphology contributions to slowed processing speed.

Slowed information processing speed is a defining feature of cognitive aging. Nucleus locus coeruleus (LC) and medial prefrontal regions are targets for understanding slowed processing speed because these brain regions influence neural and behavioral response latencies through their roles in optimizing task performance. Although structural measures of medial prefrontal cortex have been consistently related to processing speed, it is unclear if 1) declines in LC structure underlie this association because of reciprocal connections between LC and medial prefrontal cortex, or 2) if LC declines provide a separate explanation for age-related changes in processing speed. LC and medial prefrontal structural measures were predicted to explain age-dependent individual differences in processing speed in a cross-sectional sample of 43 adults (19-79 years; 63% female). Higher turbo-spin echo LC contrast, based on a persistent homology measure, and greater dorsal cingulate cortical thickness were significantly and each uniquely related to faster processing speed. However, only dorsal cingulate cortical thickness appeared to statistically mediate age-related differences in processing speed. The results suggest that individual differences in cognitive processing speed can be attributed, in part, to structural variation in nucleus LC and medial prefrontal cortex, with the latter key to understanding why older adults exhibit slowed processing speed.

Relating individual cell division events to single-cell ERK and Akt activity time courses.

Biochemical correlates of stochastic single-cell fates have been elusive, even for the well-studied mammalian cell cycle. We monitored single-cell dynamics of the ERK and Akt pathways, critical cell cycle progression hubs and anti-cancer drug targets, and paired them to division events in the same single cells using the non-transformed MCF10A epithelial line. Following growth factor treatment, in cells that divide both ERK and Akt activities are significantly higher within the S-G2 time window (~ 8.5-40 h). Such differences were much smaller in the pre-S-phase, restriction point window which is traditionally associated with ERK and Akt activity dependence, suggesting unappreciated roles for ERK and Akt in S through G2. Simple metrics of central tendency in this time window are associated with subsequent cell division fates. ERK activity was more strongly associated with division fates than Akt activity, suggesting Akt activity dynamics may contribute less to the decision driving cell division in this context. We also find that ERK and Akt activities are less correlated with each other in cells that divide. Network reconstruction experiments demonstrated that this correlation behavior was likely not due to crosstalk, as ERK and Akt do not interact in this context, in contrast to other transformed cell types. Overall, our findings support roles for ERK and Akt activity throughout the cell cycle as opposed to just before the restriction point, and suggest ERK activity dynamics may be more important than Akt activity dynamics for driving cell division in this non-transformed context.

Cortical asymmetries at different spatial hierarchies relate to phonological processing ability.

The ability to map speech sounds to corresponding letters is critical for establishing proficient reading. People vary in this phonological processing ability, which has been hypothesized to result from variation in hemispheric asymmetries within brain regions that support language. A cerebral lateralization hypothesis predicts that more asymmetric brain structures facilitate the development of foundational reading skills like phonological processing. That is, structural asymmetries are predicted to linearly increase with ability. In contrast, a canalization hypothesis predicts that asymmetries constrain behavioral performance within a normal range. That is, structural asymmetries are predicted to quadratically relate to phonological processing, with average phonological processing occurring in people with the most asymmetric structures. These predictions were examined in relatively large samples of children (N = 424) and adults (N = 300), using a topological asymmetry analysis of T1-weighted brain images and a decoding measure of phonological processing. There was limited evidence of structural asymmetry and phonological decoding associations in classic language-related brain regions. However, and in modest support of the cerebral lateralization hypothesis, small to medium effect sizes were observed where phonological decoding accuracy increased with the magnitude of the largest structural asymmetry across left hemisphere cortical regions, but not right hemisphere cortical regions, for both the adult and pediatric samples. In support of the canalization hypothesis, small to medium effect sizes were observed where phonological decoding in the normal range was associated with increased asymmetries in specific cortical regions for both the adult and pediatric samples, which included performance monitoring and motor planning brain regions that contribute to oral and written language functions. Thus, the relevance of each hypothesis to phonological decoding may depend on the scale of brain organization.

Persistence Cycles for Visual Exploration of Persistent Homology.

Persistent homology is a fundamental tool in topological data analysis used for the most diverse applications. Information captured by persistent homology is commonly visualized using scatter plots representations. Despite being widely adopted, such a visualization technique limits user understanding and is prone to misinterpretation. This article proposes a new approach for the efficient computation of persistence cycles, a geometric representation of the features captured by persistent homology. We illustrate the importance of rendering persistence cycles when analyzing scalar fields, and we discuss the advantages that our approach provides compared to other techniques in topology-based visualization. We provide an efficient implementation of our approach based on discrete Morse theory, as a new module for the Topology Toolkit. We show that our implementation has comparable performance with respect to state-of-the-art toolboxes while providing a better framework for visually analyzing persistent homology information.

The Topology of Pediatric Structural Asymmetries in Language-Related Cortex.

Structural asymmetries in language-related brain regions have long been hypothesized to underlie hemispheric language laterality and variability in language functions. These structural asymmetries have been examined using voxel-level, gross volumetric, and surface area measures of gray matter and white matter. Here we used deformation-based and persistent homology approaches to characterize the three-dimensional topology of brain structure asymmetries within language-related areas that were defined in functional neuroimaging experiments. Persistence diagrams representing the range of values for each spatially unique structural asymmetry were collected within language-related regions of interest across 212 children (mean age (years) = 10.56, range 6.39-16.92; 39% female). These topological data exhibited both leftward and rightward asymmetries within the same language-related regions. Permutation testing demonstrated that age and sex effects were most consistent and pronounced in the superior temporal sulcus, where older children and males had more rightward asymmetries. While, consistent with previous findings, these associations exhibited small effect sizes that were observable because of the relatively large sample. In addition, the density of rightward asymmetry structures in nearly all language-related regions was consistently higher than the density of leftward asymmetric structures. These findings guide the prediction that the topological pattern of structural asymmetries in language-related regions underlies the organization of language.