Jack Waddell

Functional clustering algorithm for the analysis of dynamic network data

We formulate a technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines data traces and derives the optimal clustering cutoff in a simple and intuitive manner through the use of surrogate data sets. In order to demonstrate the power of this algorithm to detect changes in network dynamics and connectivity, we apply it to both simulated neural spike train data and real neural data obtained from the mouse hippocampus during exploration and slow-wave sleep. Using the simulated data, we show that our algorithm performs better than existing methods. In the experimental data, we observe state-dependent clustering patterns consistent with known neurophysiological processes involved in memory consolidation.

The Implications of Stochastic Synthesis for the Conjugation of Functional Groups to Nanoparticles

Stochastic synthesis of a ligand coupled to a nanoparticle results in a distribution of populations with different numbers of ligands per nanoparticle. This distribution was resolved and quantified using HPLC and is in excellent agreement with the ligand/nanoparticle average measured by 1H NMR, gel permeation chromatography (GPC), and potentiometric titration, and yet significantly more disperse than commonly held perceptions of monodispersity. Two statistical models were employed to confirm that the observed heterogeneity is consistent with theoretical expectations.

Causal entropies—A measure for determining changes in the temporal organization of neural systems

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 time-adaptive detection of asymmetries in the relative temporal patterning between neuronal pairs. We characterize properties of the measure on both simulated data and experimental multiunit recordings of hippocampal neurons from the awake, behaving rat, and show that the metric can 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.

Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers.

Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population models predict that a species with a lower dispersal rate always drives a competing species to extinction in the presence of spatial variation of resources. However, the introduction of intrinsic demographic stochasticity can reverse this conclusion. We present a simple model in which competition between the exploitation of resources and stochastic fluctuations leads to victory by either the faster or slower of two species depending on the environmental parameters. A simplified limiting case of the model, analyzed by closing the moment and correlation hierarchy, quantitatively predicts which species will win in the complete model under given parameters of spatial variation and average carrying capacity.

Origin of broad polydispersion in functionalized dendrimers and its effects on cancer-cell binding affinity.

Nanoparticles with multiple ligands have been proposed for use in nanomedicine. The multiple targeting ligands on each nanoparticle can bind to several locations on a cell surface facilitating both drug targeting and uptake. Experiments show that the distribution of conjugated ligands is unexpectedly broad, and the desorption rate appears to depend exponentially upon the mean number of attached ligands. These two findings are explained with a model in which ligands conjugate to the nanoparticle with a positive cooperativity of ≈4 kT , and that nanoparticles bound to a surface by multiple bonds are permanently affixed. This drives new analysis of the data, which confirms that there is only one time constant for desorption, that of a nanoparticle bound to the surface by a single bond.

Network reorganization driven by temporal interdependence of its elements

We employ an adaptive parameter control technique based on detection of phase/lag synchrony between the elements of the system to dynamically modify the structure of a network of nonidentical, coupled Rossler oscillators. Two processes are simulated: 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.

Functional structure from dynamic clustering of spike train data

We propose a new algorithm for detecting functional structure in neuronal networks based solely upon the information derived from the spike timings of the neurons. Unlike traditional algorithms that depend on knowledge of the topological structure of the network to parse the network into communities, we dynamically cluster the neurons to build communities with similar functional interactions. We define means to derive optimal clustering parameters and investigate what conditions have to be fulfilled to obtain reasonable predictions of functional structures. The success of the algorithm is verified using simulated spike train data, and we provide examples of the application of our method to experimental data where it detects known changes in neural states.