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Networks, Evolution, Science & Neural Systems
Alex Bäcker

Abstract. Recent times have seen the advent of large amounts of data on networks of diverse kinds, from the WWW and citation networks to protein and gene expression networks. Part of my work has been aimed at extracting insight out of these massive collections of data. We show, for example, that recent years have seen an expansion in the memory of science and a homogenization of citation distributions. In parallel, I have been developing mathematical methods to extract information from multi-neuron recordings of brain activity. More generally, I am addressing a variety of open questions at the interface of biology, math and computation.

Research Summary

Software as Networks
I have developed a software tool that constructs graphs to represent a collection of software programs, where each node represents a program and each edge represents a call from one program to another. I have calculated statistical properties of several of these graphs.

A Revolution in Scientific Production (with Kevin Boyack)
Analyzing data from the entire Science Citation Index (SCI) and historic science funding levels, Kevin Boyack and I discovered that scientific production, measured in published papers indexed by the SCI, underwent a dramatic change in growth pattern shortly after 1960, changing from exponential growth to linear growth with a slope much higher than that of the exponential at the discontinuity point. We have traced this change to a rather abrupt increase in U.S. science funding that has continued to increase linearly to this day. The slow exponential growth of the early days is consistent with growth driven by each professor taking on a fixed number of apprentices in his life. Modern science shows instead growth that appears to be limited by the funding levels rather than by the number of academicians available to teach the profession.

The Expanding Memory of Science (with Kevin Boyack)
Kevin Boyack and I discovered that the memory of science, measured by the age of citations, has been growing in the past several years. We have further disambiguated the effects of memory expansion due to aging of the scientific literature, that due to growth of science, and that which cannot be explained by either growth or aging.

The Socializing Effect of the WWW on Citation Distributions
I have obtained interesting results analyzing the structure of citation graphs, using appropriate normalizations to show that the Internet has a socializing or equalizing effect on citation distributions, and that articles available online are 5 times as likely to be cited as those which are not, even within the same journal. I hope to submit this to a general-interest journal soon.

A Mathematical Formulation for Curiosity
I have developed a mathematical formulation for curiosity that may be useful to guide exploration of robots and machine learning algorithms to solve a well-known problem that autonomous robots tend to cluster around what they know best after they have found rewarding stimuli. The formulation remains to be tested in simulations or robot runs. The basic idea is the following: Learning behavior should seek to maximize not prediction success, but change of predictions. To do this, it should venture into spaces where it has very poor accuracy of prediction. This can be stimulated automatically by rewarding positive increases in prediction confidence. Confidence can be modeled simply by abs(predicted prob. of event occurring - 0.5).

Higher-order Correlations (with Elebeoba May)
Correlation, like distance, has remained largely a measure defined between two variables ever since Sir Francis Galton introduced the concept in 1888 (Galton, 1888). Even multivariate correlational analysis relies on computing the correlation between two (and only two) variables: an unmodified variable and a composite variable consisting of the weighted sum of 2 or more variates (DuBois, 1957). And yet pairwise correlations do not uniquely characterize the interactions between a set of N variables, and it is an important problem in data mining and many fields of science to determine whether additional interactions exist. I aim to provide a computationally tractable definition or approximation of the N-way independence (maximum entropy or lack of structure beyond lower-order correlations) between N variables, with particular emphasis on binary variables such as neuronal spike trains. Iterative algorithms for the calculation of the maximum entropy distributions exist (Gokhale and Kullback, 1978), but their implementation for N>20 is out of reach for even the fastest supercomputers (Bohte et al., 2000). We are implementing a fast algorithm for the detection of higher order correlations, using a generalization of the cross-product ratio.

Earthshine: A Visual Illusion
I have described a novel visual illusion concerning the Moon – observers perceive the illuminated part as belonging to a circle of greater diameter than the dark part (Earthshine).

Cellular automata and Randomness
Proved wrong a contention of Stephen Wolfram’s new book, A New Kind of Science, about the generation of apparent randomness by simple automata with simple initial conditions by showing statistical regularities exist in the binary sequence produced by rule 30 in the central column.

A Robust Measure for Spike Timing Jitter
Measuring the precision of spike timing under dynamic conditions is problematic due to the difficulty of ascribing matches between spikes in the face of dropped spikes. Existing methods draw an arbitrary cutoff for the maximum allowed separation between matching spikes. We have developed a measure robust to variations in the choice of such maximum separation.

A Measure for Collective Synchronization
Our previous work has shown neuronal synchronization is crucial to the decoding of information in neural assemblies. Yet methods to measure non-oscillatory synchronization in multineuron recordings are lacking. We propose the variance of the spike count across a neuronal assembly as a measure for collective synchronization.

Ecological Determinants of Stable Equilibria with Multiple Coexisting Genotypes
Perhaps the oldest mystery of evolution and ecology is the origin of biodiversity. Different species can co-exist stably in the same niche for ages. In contrast, all intermediates between our last common ancestor with the great apes have disappeared. Additionally, all species examined exhibit a striking abundance of polymorphisms. We have put forth a theory to explain biodiversity.