Acknowledgement: This research was in collaboration with Pedro Del Nido, MD, William E. Ladd Professor of Surgery, Chairman of Cardiac Surgery, and Tal Geva, MD, Director of Cardiac MRI Department, Children's Hospital Boston, Harvard Medical School, USA. It was supported in part by NIH R01 HL089269 (del Nido, Tang, Geva), NIH-R01 HL63095 (PJdN), and NIH- 5P50 HL074734 (Clinical Trial, PI-Geva).
* Numerical modeling. Bacteria are modeled as self-propelled point force dipoles subject to two types of forces: hydrodynamic interactions with the surrounding fluid and excluded volume interactions with other bacteria modeled by a Lennard-Jones-type potential. This model, allowing for numerical simulations of a large number of particles, is implemented on the Graphical Processing Units (GPU), and is in agreement with experiments.
* Analytical study of dilute suspensions. We introduced a model for swimming bacteria and obtained explicit asymptotic formula for the effective viscosity in terms of known physical parameters. This formula is compared with that derived in our PDE model for a dilute suspension of prolate spheroids driven by a stochastic torque, which models random reorientation of bacteria ("tumbling"). It is shown that the steady-state probability distributions of single particle configurations are identical for the dilute and semi-dilute models in the limiting case of particles becoming spheres. Thus, a deterministic system incorporating pairwise hydrodynamic interactions and excluded volume constraints behaves as a system with a random stochastic torque. This phenomenon of stochasticity arising from a deterministic system is referred to as self-induced noise.
* Kinetic collisional model-work in progress. Most of the previous work on bacterial suspensions ignores collisions. These inelastic interactions lead to an alignment of the nearby-swimming bacteria, which has been indeed observed experimentally. To understand the onset of collective motion in the above model, we investigate the correlation of bacterial velocities and orientations as a function of the interparticle distance. We seek to capture a phase transition in the bacterial suspension - an appearance of correlations and local preferential alignment with an increase of concentration. A probabilistic model for the distribution function for bacterial positions and orientations will be derived in the presence of self-induced noise.
Collaborators: PSU students S. Ryan and B. Haines, and DOE scientists I. Aronson and D. Karpeev (both Argonne Nat. Lab)
We review winner-loser models, the currently popular explanation for the occurrence of linear dominance hierarchies, via a three-part approach. 1) We isolate the two most significant components of the mathematical formulation of three of the most widely-cited models and rigorously evaluate the components' predictions against data collected on hierarchy formation in groups of hens. 2) We evaluate the experimental support in the literature for the basic assumptions contained in winner-loser models. 3) We apply new techniques to the hen data to uncover several behavioral dynamics of hierarchy formation not previously described. The mathematical formulations of these models do not show satisfactory agreement with the hen data, and key model assumptions have either little, or no conclusive, support from experimental findings in the literature. In agreement with the latest experimental results concerning social cognition, the new behavioral dynamics of hierarchy formation discovered in the hen data suggest that members of groups are intensely aware both of their own interactions as well as interactions occurring among other members of their group. We suggest that more adequate models of hierarchy formation should be based upon behavioral dynamics that reflect more sophisticated levels of social cognition.
Numerical models and observational data are critical in modern science and engineering. Since both of these information sources involve uncertainty, the use of statistical, probabilistic methods play a fundamental role. I discuss a general Bayesian framework for combining uncertain information and indicate how various approaches (ensemble forecasting, UQ, etc.) fit in this framework. A paleoclimate analysis illustrates the use of simple physics and statistical modeling to produce inferences. A second example involves glacial dynamics and illustrates how updating models and data can lead to estimates of model error. A third example involves the extraction of information from multi-model ensembles in climate projection studies.
A number of phenomena in visual perception involve wave-like propagation dynamics. Examples include perceptual filling-in, migraine aura, and the expansion of illusory contours. Another important example is the wave-like propagation of perceptual dominance during binocular rivalry. Binocular rivalry is the phenomenon where perception switches back and forth between different images presented to the two eyes. The resulting fluctuations in perceptual dominance and suppression provide a basis for non-invasive studies of the human visual system and the identification of possible neural mechanisms underlying conscious visual awareness. In this talk we present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one-dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are taken to be inhibitory (cross-inhibition). Slow adaptationis incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave-like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a "symmetry breaking mechanism" that allows waves to propagate. We end by discussing recent work on the effects of noise.
Odors are important cues for identification of many types of objects that animals need for survival. Natural odors are typically mixtures of up to a few dozen chemical components. Important information about odor 'objects' is often encoded in the ratio of components in the mixture. However, this odor mixture problem is complicated by two factors. First, many times the information channel is composed of a submixture of the overall mixture composition. Second, the ratios of components in the submixture can vary from one object to the next, which means that animals must learn to 'generalize' across a range of variation among objects that mean the same thing. Floral odors, for example, are important for honey bees to locate nectar and pollen sources that their colony needs for survival. Honey bees need to learn about the range of variation in odor composition so that they can optimally include flowers that have resources and exclude flowers with similar odors but which do not have nectar or pollen. I argue that nonassociative and associative plasticity in neural networks involved in early sensory coding is critical for extracting the relevant features of an odor mixture and setting up categories of odor objects. This plasticity can enhance decisions about pattern matching and multimodal associations in later processing in the brain.
The genetic differences that separate humans from other great apes seem modest, yet we are a prominent phenotypic outlier in several regards. Although little is known about the genetic and molecular bases underlying uniquely human traits, changes in gene regulation are likely an important component. My group is currently investigating changes in the transcriptomes of multiple tissues that accompanied human origins. We use genome-wide functional assays to identify the molecular mechanisms that mediate evolutionary changes in transcription, including the role of chromatin configuration and the function of noncoding RNAs. These assays highlight genomic regions of particular interest, where we have carried out focused functional analyses that provide insights into the evolution of human diet and brain size.