Evolutionary dynamical models for cyclic competitions of three species (e.g., rock, paper, and scissors, or RPS) provide a paradigm, at the microscopic level of individual interactions, to address many issues in coexistence and biodiversity. Real ecosystems often involve competitions among more than three species. By extending the RPS game model to five (rock-paper-scissors-lizard-Spock, or RPSLS) mobile species, we uncover a fundamental type of mesoscopic interactions among subgroups of species. In particular, competitions at the microscopic level lead to the emergence of various local groups in different regions of the space, each involving three species. It is the interactions among the groups that fundamentally determine how many species can coexist. In fact, as the mobility is increased from zero, two transitions can occur: one from a five- to a three-species coexistence state and another from the latter to a uniform, single-species state. We develop a mean-field theory to show that, in order to understand the first transition, group interactions at the mesoscopic scale must be taken into account. Our findings suggest, more broadly, the importance of mesoscopic interactions in coexistence of great many species.

A structurally and compositionally well-defined and spectrally tunable artificial light-harvesting system has been constructed in which multiple organic dyes attached to a three-arm-DNA nanostructure serve as an antenna conjugated to a photosynthetic reaction center isolated from Rhodobacter sphaeroides 2.4.1. The light energy absorbed by the dye molecules is transferred to the reaction center, where charge separation takes place. The average number of DNA three-arm junctions per reaction center was tuned from 0.75 to 2.35. This DNA-templated multichromophore system serves as a modular light-harvesting antenna that is capable of being optimized for its spectral properties, energy transfer efficiency, and photostability, allowing one to adjust both the size and spectrum of the resulting structures. This may serve as a useful test bed for developing nanostructured photonic systems.

We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.

Background: Immunosignaturing is a new peptide microarray based technology for profiling of humoral immune responses. Despite new challenges, immunosignaturing gives us the opportunity to explore new and fundamentally different research questions. In addition to classifying samples based on disease status, the complex patterns and latent factors underlying immunosignatures, which we attempt to model, may have a diverse range of applications.

Methods: We investigate the utility of a number of statistical methods to determine model performance and address challenges inherent in analyzing immunosignatures. Some of these methods include exploratory and confirmatory factor analyses, classical significance testing, structural equation and mixture modeling.

Results: We demonstrate an ability to classify samples based on disease status and show that immunosignaturing is a very promising technology for screening and presymptomatic screening of disease. In addition, we are able to model complex patterns and latent factors underlying immunosignatures. These latent factors may serve as biomarkers for disease and may play a key role in a bioinformatic method for antibody discovery.

Conclusion: Based on this research, we lay out an analytic framework illustrating how immunosignatures may be useful as a general method for screening and presymptomatic screening of disease as well as antibody discovery.

Background: Microarray image analysis processes scanned digital images of hybridized arrays to produce the input spot-level data for downstream analysis, so it can have a potentially large impact on those and subsequent analysis. Signal saturation is an optical effect that occurs when some pixel values for highly expressed genes or peptides exceed the upper detection threshold of the scanner software (2¹⁶ - 1 = 65, 535 for 16-bit images). In practice, spots with a sizable number of saturated pixels are often flagged and discarded. Alternatively, the saturated values are used without adjustments for estimating spot intensities. The resulting expression data tend to be biased downwards and can distort high-level analysis that relies on these data. Hence, it is crucial to effectively correct for signal saturation.

Results: We developed a flexible mixture model-based segmentation and spot intensity estimation procedure that accounts for saturated pixels by incorporating a censored component in the mixture model. As demonstrated with biological data and simulation, our method extends the dynamic range of expression data beyond the saturation threshold and is effective in correcting saturation-induced bias when the lost information is not tremendous. We further illustrate the impact of image processing on downstream classification, showing that the proposed method can increase diagnostic accuracy using data from a lymphoma cancer diagnosis study.

Conclusions: The presented method adjusts for signal saturation at the segmentation stage that identifies a pixel as part of the foreground, background or other. The cluster membership of a pixel can be altered versus treating saturated values as truly observed. Thus, the resulting spot intensity estimates may be more accurate than those obtained from existing methods that correct for saturation based on already segmented data. As a model-based segmentation method, our procedure is able to identify inner holes, fuzzy edges and blank spots that are common in microarray images. The approach is independent of microarray platform and applicable to both single- and dual-channel microarrays.

Background: High-throughput technologies such as DNA, RNA, protein, antibody and peptide microarrays are often used to examine differences across drug treatments, diseases, transgenic animals, and others. Typically one trains a classification system by gathering large amounts of probe-level data, selecting informative features, and classifies test samples using a small number of features. As new microarrays are invented, classification systems that worked well for other array types may not be ideal. Expression microarrays, arguably one of the most prevalent array types, have been used for years to help develop classification algorithms. Many biological assumptions are built into classifiers that were designed for these types of data. One of the more problematic is the assumption of independence, both at the probe level and again at the biological level. Probes for RNA transcripts are designed to bind single transcripts. At the biological level, many genes have dependencies across transcriptional pathways where co-regulation of transcriptional units may make many genes appear as being completely dependent. Thus, algorithms that perform well for gene expression data may not be suitable when other technologies with different binding characteristics exist. The immunosignaturing microarray is based on complex mixtures of antibodies binding to arrays of random sequence peptides. It relies on many-to-many binding of antibodies to the random sequence peptides. Each peptide can bind multiple antibodies and each antibody can bind multiple peptides. This technology has been shown to be highly reproducible and appears promising for diagnosing a variety of disease states. However, it is not clear what is the optimal classification algorithm for analyzing this new type of data.

Results: We characterized several classification algorithms to analyze immunosignaturing data. We selected several datasets that range from easy to difficult to classify, from simple monoclonal binding to complex binding patterns in asthma patients. We then classified the biological samples using 17 different classification algorithms. Using a wide variety of assessment criteria, we found ‘Naïve Bayes’ far more useful than other widely used methods due to its simplicity, robustness, speed and accuracy.

Conclusions: ‘Naïve Bayes’ algorithm appears to accommodate the complex patterns hidden within multilayered immunosignaturing microarray data due to its fundamental mathematical properties.

It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control.