Poster Session

Mathematical Models of Emergence: Proposals from George Ellis' Physics and the Real World

Author: Stephen Harnish

In a recent series of articles, George Ellis (University of Cape Town) proposed several mathematical models relating to strong and weak emergence. This poster outlines his thought and models, focusing especially on connections to broader work on network motifs, modularity and evolutionary game theory. It features simple mathematical tools contrasting spatial, temporal and structural coarse-graining and modularity. Mathematical models of multi-scale motifs in hierarchical networks are also considered.

Self-organization and patterns of glioma cells: effects of cell-cell adhesion

Authors: Evgeniy Khain, Michal O. Nowicki, E. Antonio Chiocca, S.E. Lawler and Leonard M. Sander

One of the key still unsolved problems in the biology of cancer is the formation of secondary tumors. We consider here Glioblastoma Multiforme (GBM), a form of highly malignant brain tumor. It is well known that one of the reasons that GBM is resistant to treatment is that it is highly invasive due to the large motility of the tumor cells. For one cell line invading cells do not cluster, for another one the cells cluster to form secondary tumors, rendering the resection of the primary tumor essentially futile. Being motivated by these observations, we consider the growth of clusters of glioma cells from a low density preparation. Our simulations show that the growth of cell clusters is sensitively dependent on adhesion. In fact, there is a critical value of the strength of adhesion; above the critical strength phase separation occurs and large clusters grow due to coarsening (and proliferation), whereas below the threshold the system remains homogeneous. We verified the predictions of the model in a separate experiment in which we followed the clustering dynamics of glioma cells on a surface. The results suggest a mechanism of clustering and eventual formation of secondary tumors in brain.

Conformity and Consistency in a Voter Model

Author: Casey Schneider-Mizell

In many cultural and political interactions, an individual is influenced to take on similar values as his peers. A person will also have opinions about many different topics which tend to cluster into self-consistent groups, even when seemingly unrelated. Political party platforms are an example of this phenomenon. We describe these dynamics as a force for external conformity and a force for internal consistency and consider the relative weight for each force a system parameter. We investigate the effect of this parameter on consensus time of a large group of fully connected individuals. The social forces are represented in the topology of a weighted network on which we consider voter model dynamics.

Mathematical Modeling Applied to Cancer Progression:
Understanding the role of RHOC GTP-ase in Aggressive Phenotypes of Breast Cancer

Authors: Alejandra C. Ventura, Jacques-A. Sepulchre, Mei Wu, Zhi-Fen Wu, Jorge R. Tredicce, Sofia D. Merajver

The most damaging change during cancer progression is the growth of metastases. The protein RhoC GTPase was found to be crucial in that process in different cancers, particularly, in a highly aggressive form of breast cancer. RhoC is a molecular switch cycling between inactive (GDP-bound) and active (GTP-bound) states, tightly regulated by several regulatory proteins. We have developed a dual mathematical-experimental approach to understand this cycle and its deregulation in breast cancer cells in comparison with normal ones. A major impact of this work is to quantitatively predict the effects of drugs targeted against RhoC in cancer.

A New Analysis Tool for Citation Networks

Authors: Elizabeth Leicht

The study of networks has attracted a large amount of attention from the complex systems community in recent years. A wide range of networks have been studied, including social networks, biological networks, information networks, and others. Many of these networks have long histories of study in other fields. A citation network is an information network in which the vertices represent documents of some kind and the edges betweeen them represent the citation of one document by another. The nature of citations forces these networks to have a temporal dimension. Previous work has not made the temporal dimension of citation networks a major focus. We explore this issue using the specific citation network of United States Supreme Court decisions as our example.

Network Structure, Nural Synchrony and Plasticity

Authors: Jack Waddell, Rhonda Dzakpasu, Victoria Booth, Brett Riley, Jonathan Reasor, Gina Poe, Michal Zochowski

We propose a novel measure to detect temporal ordering in the activity of individual neurons in a local network, which is thought to be a hallmark of activity-dependent synaptic modifications during learning. The measure, called Causal Entropy, is based on the adaptive detection of asymmetries in the relative temporal patterning between neuronal pairs. We show that our measure could more readily detect those asymmetries than standard cross correlation- based techniques, especially since the temporal sensitivity of causal entropy can detect such changes rapidly and dynamically. We show the behavior of the measure on both simulated and experimental data experimental data of multiple hippocampal neurons simultaneously recorded from a rat exploring its environment.

Furthermore, we simulate two forms of plasticity based on synchrony, as measured by our measure. They are: adaptation, under which the initially different properties of the units converge, and rewiring, in which clusters of interconnected elements are formed based on the temporal correlations. We show how those processes lead to different network structures and investigate their optimal characteristics from the point of view of resulting network properties.

Growth Matters: How Modification in the Rates of Growth can Influence Performance Outcomes in Coordination Problems

Author: Erik Johnston

Studies of group coordination problems show that as the size of a group increases the ability to coordinate the actions of key participants decreases significantly. One recent research contribution showed that growing collaborations from a small group to a large group through the sequential addition of new participants to the existing group is a unique mechanism for achieving success (Weber, 2006). In the lab, Weber found that a small sized group has a higher likelihood for coordination than larger groups. By then adding people to successfully coordinated small groups, larger coordinated groups can be successfully grown. Results of the current work will help researchers recognize the importance of the rate of growth in the process of building collaborations. The research also grounds Weber's experimental findings within a collection of field studies of civic collaboration in Colorado. The research demonstrates the value of combining laboratory studies, field studies, theoretical modeling, and agent-based modeling to create a rich description of the research space and increase confidence in the findings. Using this research, practitioners can increase the effectiveness of collaboration outcomes of civic collaborations.

Coupled Networks and Burst Propagation in the Evolution of Seizure Dynamics

Authors:M. ZOCHOWSKI(1), B.H. SINGER (1), M. DERCHANSKY(2), and P.L. CARLEN(2).

Affiliations:
(1)Neurosci. Prog., Dept of Physics, and Biophysics Res. Dev., Univ. of Michigan, Ann Arbor, MI 48109.
(2)Division of Cell. and Mol. Bio., Toronto Western Res. Inst., Ontario, Toronto, Canada.

We present an analysis of seizure-like events (SLEs) in an ex vivo whole hippocampus, as well as a modeling study that sheds light on the network dynamics underlying the activity. We observe that during SLEs, the internal frequency of spiking activity during bursts varies across the hippocampus. Early in the SLE, bursting activity is led by the region with the highest internal frequency, while late in the SLE, activity is led by the region with the lowest internal frequency. Using a heuristic computational model, we examine the influences of local changes in excitability and connectivity on the dynamic relationship of coupled neural networks. We propose that each SLE can be divided into two phases. During the first, seizure dynamics are driven by the activity of a local network autonomously generating bursting activity. The second phase marks the decline of the seizure and is characterized by the mutual interaction of multiple local networks, none of which have an intrinsic drive to bursting activity. This work was supported by a UM Research Incentives Grant (MZ) and CIHR research grant MT14447, as well as the Krembil Scientist Development Seed Fund, and Savoy Epilepsy Foundation (PLC). BHS is supported by the UMMS Medical Scientist Training Program (NIH T32-GM007863) and Hearing, Balance, and Chemical Senses Training Program (NIH T32-DC-00011).

Dynamics of Networking Agents Competing for High Centrality and Low Degree

Author: Gourab Ghoshal

We model a system of networking agents that seek a trade-off between high centrality and low degree. Unlike other game-theory based models for network evolution, the success of the agents is thus only related to their network position. The agents use strategies based on local information to improve their score. Both the evolution of strategies and network structure are investigated. We find a dramatic time evolution with cascades of strategy change accompanied by a change in network structure. On average the network self-organizes to a state close to the transition between a fragmented state and a state with a giant component. With increasing system size both the average degree and the level of fragmentation decreases.