ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.

Parameter-free extraction of the functional network topology from intracranial EEG recordings: a time-resolved study of graph properties in focal onset seizures

Rationale: Focal onset epileptic seizures are due to abnormal interactions between distributed brain areas. By estimating the cross-correlation matrix of multi-site intra-cerebral EEG recordings (iEEG), one can quantify these interactions. To assess the topology of the underlying functional network, the binary connectivity matrix has to be derived from the cross-correlation matrix by use of a threshold. Classically, a unique threshold is used that constrains the topology [1]. Our method aims to set the threshold in a data-driven way by separating genuine from random cross-correlation. We compare our approach to the fixed threshold method and study the dynamics of the functional topology. Methods: We investigate the iEEG of patients suffering from focal onset seizures who underwent evaluation for the possibility of surgery. The equal-time cross-correlation matrices are evaluated using a sliding time window. We then compare 3 approaches assessing the corresponding binary networks. For each time window: * Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. * The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. * The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. * Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: *topologies that are different in terms of c, k, Eg and El. *from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a ‘‘U-curve’’ underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks.

Genetic Distance between Species Predicts Novel Trait Expression in Their Hybrids

Interspecific hybridization can generate transgressive hybrid phenotypes with extreme trait values exceeding the combined range of the parental species. Such variation can enlarge the working surface for natural selection, and may facilitate the evolution of novel adaptations where ecological opportunity exists. The number of quantitative trait loci fixed for different alleles in different species should increase with time since speciation. If transgression is caused by complementary gene action or epistasis, hybrids between more distant species should be more likely to display transgressive phenotypes. To test this prediction we collected data on transgression frequency from the literature, estimated genetic distances between the hybridizing species from gene sequences, and calculated the relationship between the two using phylogenetically controlled methods. We also tested if parental phenotypic divergence affected the occurrence of transgression. We found a highly significant positive correlation between transgression frequency and genetic distance in eudicot plants explaining 43% of the variance in transgression frequency. In total, 36% of the measured traits were transgressive. The predicted effect of time since speciation on transgressive segregation was unconfounded by the potentially conflicting effects of phenotypic differentiation between species. Our analysis demonstrates that the potential impact hybridization may have on phenotypic evolution is predictable from the genetic distance between species.

Phenotypic novelty in experimental hybrids is predicted by the genetic distance between species of cichlid fish

Background: Transgressive segregation describes the occurrence of novel phenotypes in hybrids with extreme trait values not observed in either parental species. A previously experimentally untested prediction is that the amount of transgression increases with the genetic distance between hybridizing species. This follows from QTL studies suggesting that transgression is most commonly due to complementary gene action or epistasis, which become more frequent at larger genetic distances. This is because the number of QTLs fixed for alleles with opposing signs in different species should increase with time since speciation provided that speciation is not driven by disruptive selection. We measured the amount of transgression occurring in hybrids of cichlid fish bred from species pairs with gradually increasing genetic distances and varying phenotypic similarity. Transgression in multi-trait shape phenotypes was quantified using landmark-based geometric morphometric methods. Results: We found that genetic distance explained 52% and 78% of the variation in transgression frequency in F1 and F2 hybrids, respectively. Confirming theoretical predictions, transgression when measured in F2 hybrids, increased linearly with genetic distance between hybridizing species. Phenotypic similarity of species on the other hand was not related to the amount of transgression. Conclusion: The commonness and ease with which novel phenotypes are produced in cichlid hybrids between unrelated species has important implications for the interaction of hybridization with adaptation and speciation. Hybridization may generate new genotypes with adaptive potential that did not reside as standing genetic variation in either parental population, potentially enhancing a population's responsiveness to selection. Our results make it conceivable that hybridization contributed to the rapid rates of phenotypic evolution in the large and rapid adaptive radiations of haplochromine cichlids.

Phenotypic divergence but not genetic distance predicts assortative mating among species of a cichlid fish radiation

The hypothesis of ecological divergence giving rise to premating isolation in the face of gene flow is controversial. However, this may be an important mechanism to explain the rapid multiplication of species during adaptive radiation following the colonization of a new environment when geographical barriers to gene flow are largely absent but underutilized niche space is abundant. Using cichlid fish, we tested the prediction of ecological speciation that the strength of premating isolation among species is predicted by phenotypic rather than genetic distance. We conducted mate choice experiments between three closely related, sympatric species of a recent radiation in Lake Mweru (Zambia/DRC) that differ in habitat use and phenotype, and a distantly related population from Lake Bangweulu that resembles one of the species in Lake Mweru. We found significant assortative mating among all closely related, sympatric species that differed phenotypically, but none between the distantly related allopatric populations of more similar phenotype. Phenotypic distance between species was a good predictor of the strength of premating isolation, suggesting that assortative mating can evolve rapidly in association with ecological divergence during adaptive radiation. Our data also reveals that distantly related allopatric populations that have not diverged phenotypically, may hybridize when coming into secondary contact, e.g. upon river capture because of diversion of drainage systems.