MBI Publications

MBI Publications for 2014 (20)

  • F. Kloosterman, S. Layton, Z. Chen and M. Wilson
    Bayesian decoding of unsorted spikes in the rat hippocampus
    Journal of NeurophysiologyVol. 111 No. 1 (2014) pp. 217-227

    Abstract

  • A. Lam and Y. Lou
    Evolutionarily stable and convergent stable strategies in reaction-diffusion models for conditional dispersal.
    Bulletin of mathematical biologyVol. 76 No. 2 (2014) pp. 261-91

    Abstract

    We consider a mathematical model of two competing species for the evolution of conditional dispersal in a spatially varying, but temporally constant environment. Two species are different only in their dispersal strategies, which are a combination of random dispersal and biased movement upward along the resource gradient. In the absence of biased movement or advection, Hastings showed that the mutant can invade when rare if and only if it has smaller random dispersal rate than the resident. When there is a small amount of biased movement or advection, we show that there is a positive random dispersal rate that is both locally evolutionarily stable and convergent stable. Our analysis of the model suggests that a balanced combination of random and biased movement might be a better habitat selection strategy for populations.
  • K. Liao and Y. Lou
    The effect of time delay in a two-patch model with random dispersal.
    Bulletin of mathematical biologyVol. 76 No. 2 (2014) pp. 335-76

    Abstract

    We consider a two-patch model for a single species with dispersal and time delay. For some explicit range of dispersal rates, we show that there exists a critical value ?c for the time delay ? such that the unique positive equilibrium of the system is locally asymptotically stable for ? ?[0,?c) and unstable for ? > ?c .
  • J. Newby and M. Schwemmer
    Effects of moderate noise on a limit cycle oscillator: counterrotation and bistability.
    Physical review lettersVol. 112 No. 11 (2014) pp. 114101

    Abstract

    The effects of noise on the dynamics of nonlinear systems is known to lead to many counterintuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different dynamics. In particular, the system can appear bistable, rotate in the opposite direction of the deterministic limit cycle, or cease oscillating altogether. Utilizing standard techniques from stochastic calculus and recently developed stochastic phase reduction methods, we elucidate the mechanisms underlying the different dynamics and verify our analysis with the use of numerical simulations. Last, we show that similar bistable behavior is found when moderate noise is applied to the FitzHugh-Nagumo model, which is more commonly used in biological applications.
  • J. Chang and T. Chou
    Iterative graph cuts for image segmentation with a nonlinear statistical shape prior.
    Journal of mathematical imaging and visionVol. 49 No. 1 (2014) pp. 87-97

    Abstract

    Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification of a shape prior using kernel density estimation is a natural technique. Unfortunately, energy functionals arising from kernel density estimation are of a form that makes them impossible to directly minimize using efficient optimization algorithms such as graph cuts. Our main contribution is to show how one may recast the energy functional into a form that is minimizable iteratively and efficiently using graph cuts.
  • A. Lam and Y. Lou
    Evolution of conditional dispersal: evolutionarily stable strategies in spatial models.
    Journal of mathematical biologyVol. 68 No. 4 (2014) pp. 851-77

    Abstract

    We consider a two-species competition model in which the species have the same population dynamics but different dispersal strategies. Both species disperse by a combination of random diffusion and advection along environmental gradients, with the same random dispersal rates but different advection coefficients. Regarding these advection coefficients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we find that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be three or more evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of conditional dispersal of organisms depends upon the spatial heterogeneity of the environment in a subtle way.
  • V. Krivan
    Behavioral refuges and predator-prey coexistence
    Journal of Theoretical BiologyVol. 339 (2014) pp. 112-121

    Abstract

    The effects of a behavioral refuge caused either by the predator optimal foraging or prey adaptive antipredator behavior on the Gause predator-prey model are studied. It is shown that both of these mechanisms promote predator-prey coexistence either at an equilibrium, or along a limit cycle. Adaptive prey refuge use leads to hysteresis in prey antipredator behavior which allows predator-prey coexistence along a limit cycle. Similarly, optimal predator foraging leads to sigmoidal functional responses with a potential to stabilize predator-prey population dynamics at an equilibrium, or along a limit cycle.
  • P. Bressloff and J. Newby
    Path integrals and large deviations in stochastic hybrid systems.
    Physical review. E, Statistical, nonlinear, and soft matter physicsVol. 89 No. 4 (2014) pp. 042701

    Abstract

    We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.
  • A. Matzavinos, B. Shtylla, Z. Voller, S. Liu and M. Chaplain
    Stochastic modeling of chromosomal segregation: Errors can introduce correction
    Bulletin of Mathematical Biology (2014)

    Abstract

  • J. Kim, Z. Kilpatrick, M. Bennett and K. Josic
    Molecular mechanisms that regulate the coupled period of the mammalian circadian clock
    Biophysical JournalVol. 106 No. 9 (2014) pp. 2071–2081

    Abstract

  • L. Altenberg
    Evolvability and Robustness in Artificial Evolving Systems: Three Perturbations
    Genetic Programming and Evolvable Machines (2014) (In Press)

    Abstract

  • N. Beckman and H. Rogers
    Consequences of Seed Dispersal for Plant Recruitment in Tropical Forests: Interactions within the Seedscape
    BiotropicaVol. 45 No. 6 (2014) pp. 666-681

    Abstract

    Seed dispersal sets the stage for the suite of biotic and abiotic interactions that determine the fate of individual seeds. In this review, we first focus on how dispersal influences the "seedscape", or the combination of abiotic, biotic, and spatial factors that affect the probability of germination once a seed has reached its final location. We review recent papers that examine the effect of dispersers on (1) the quality of the habitat in which a seed lands; (2) the distance seeds are dispersed from the parent tree; and (3) the density and composition of plants within the neighborhood of a seed following deposition. Next, we explore methods used to scale these processes up to the level of populations. We highlight demographic models that integrate across multiple life history stages and predict the impact of dispersal in variable environments on population growth. We also review studies that analyze existing spatial patterns of trees within large forest plots and use various strategies to infer the processes that led to those patterns. We continue to scale up from populations to communities, and discuss three approaches that have been taken to understand how dispersal may affect diversity and abundance in the community. We finish by highlighting several areas of research that are particularly promising for future directions of study.
  • V. Billock and B. Tsou
    Bridging the divide between sensory integration and binding theory: Using a binding-like neural synchronization mechanism to model sensory enhancement during multisensory interactions.
    Journal of Cognitive NeuroscienceVol. 26 (2014) pp. 1587-1599 (In Press)

    Abstract

  • B. Ermentrout and V. Billock
    Flicker-induced phosphenes
    Encyclopedia of Computational Neuroscience. Springer-Verlag (2014) (In Press)

    Abstract

  • L. Comita, S. Queenborough, S. Murphy, J. Eck, K. Xu, M. Krishnadas, N. Beckman and Y. Zhu
    Testing predictions of the Janzen–Connell hypothesis: a meta-analysis of experimental evidence for distance- and density-dependent seed and seedling survival
    Journal of EcologyVol. 102 No. 4 (2014) pp. 845-856

    Abstract

  • J. Chang, V. Savage and T. Chou
    A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation
    Journal of Statistical PhysicsVol. 157 No. 3 (2014) pp. 582–602

    Abstract

  • J. Chang and T. Chou
    Iterative graph cuts for image segmentation with a nonlinear statistical shape prior
    Journal of Mathematical Imaging and VisionVol. 49 No. 1 (2014) pp. 87-97

    Abstract

  • K. Liao, X. Bai and A. Friedman
    Mathematical modeling of interleukin-27 induction of anti-tumor T cells response.
    PloS oneVol. 9 No. 3 (2014) pp. e91844

    Abstract

    Interleukin-12 is a pro-inflammatory cytokine which promotes Th1 and cytotoxic T lymphocyte activities, such as Interferon-[Formula: see text] secretion. For this reason Interleukin-12 could be a powerful therapeutic agent for cancer treatment. However, Interleukin-12 is also excessively toxic. Interleukin-27 is an immunoregulatory cytokine from the Interleukin-12 family, but it is not as toxic as Interleukin-12. In recent years, Interleukin-27 has been considered as a potential anti-tumor agent. Recent experiments in vitro and in vivo have shown that cancer cells transfected with IL-27 activate CD8+ T cells to promote the secretion of anti-tumor cytokines Interleukin-10, although, at the same time, IL-27 inhibits the secretion of Interferon-[Formula: see text] by CD8+ T cells. In the present paper we develop a mathematical model based on these experimental results. The model involves a dynamic network which includes tumor cells, CD8+ T cells and cytokines Interleukin-27, Interleukin-10 and Interferon-[Formula: see text]. Simulations of the model show how Interleukin-27 promotes CD8+ T cells to secrete Interleukin-10 to inhibit tumor growth. On the other hand Interleukin-27 inhibits the secretion of Interferon-[Formula: see text] by CD8+ T cells which somewhat diminishes the inhibition of tumor growth. Our numerical results are in qualitative agreement with experimental data. We use the model to design protocols of IL-27 injections for the treatment of cancer and find that, for some special types of cancer, with a fixed total amount of drug, within a certain range, continuous injection has better efficacy than intermittent injections in reducing the tumor load while the treatment is ongoing, although the decrease in tumor load is only temporary.
  • W. Hao and A. Friedman
    The LDL-HDL Profile Determines the Risk of Atherosclerosis: A Mathematical Model.
    PloS oneVol. 9 No. 3 (2014) pp. e90497

    Abstract

    Atherosclerosis, the leading death in the United State, is a disease in which a plaque builds up inside the arteries. As the plaque continues to grow, the shear force of the blood flow through the decreasing cross section of the lumen increases. This force may eventually cause rupture of the plaque, resulting in the formation of thrombus, and possibly heart attack. It has long been recognized that the formation of a plaque relates to the cholesterol concentration in the blood. For example, individuals with LDL above 190 mg/dL and HDL below 40 mg/dL are at high risk, while individuals with LDL below 100 mg/dL and HDL above 50 mg/dL are at no risk. In this paper, we developed a mathematical model of the formation of a plaque, which includes the following key variables: LDL and HDL, free radicals and oxidized LDL, MMP and TIMP, cytockines: MCP-1, IFN-?, IL-12 and PDGF, and cells: macrophages, foam cells, T cells and smooth muscle cells. The model is given by a system of partial differential equations with in evolving plaque. Simulations of the model show how the combination of the concentrations of LDL and HDL in the blood determine whether a plaque will grow or disappear. More precisely, we create a map, showing the risk of plaque development for any pair of values (LDL,HDL).
  • C. Diekman and M. Golubitsky
    Network symmetry and binocular rivalry experiments.
    Journal of mathematical neuroscienceVol. 4 (2014) pp. 12

    Abstract

    Hugh Wilson has proposed a class of models that treat higher-level decision making as a competition between patterns coded as levels of a set of attributes in an appropriately defined network (Cortical Mechanisms of Vision, pp. 399-417, 2009; The Constitution of Visual Consciousness: Lessons from Binocular Rivalry, pp. 281-304, 2013). In this paper, we propose that symmetry-breaking Hopf bifurcation from fusion states in suitably modified Wilson networks, which we call rivalry networks, can be used in an algorithmic way to explain the surprising percepts that have been observed in a number of binocular rivalry experiments. These rivalry networks modify and extend Wilson networks by permitting different kinds of attributes and different types of coupling. We apply this algorithm to psychophysics experiments discussed by Kovács et al. (Proc. Natl. Acad. Sci. USA 93:15508-15511, 1996), Shevell and Hong (Vis. Neurosci. 23:561-566, 2006; Vis. Neurosci. 25:355-360, 2008), and Suzuki and Grabowecky (Neuron 36:143-157, 2002). We also analyze an experiment with four colored dots (a simplified version of a 24-dot experiment performed by Kovács), and a three-dot analog of the four-dot experiment. Our algorithm predicts surprising differences between the three- and four-dot experiments.

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