Maturation of limbic corticostriatal activation and connectivity associated with developmental changes in temporal discounting

Temporal discounting (TD) matures with age, alongside other markers of increased impulse control, and coherent, self-regulated behaviour. Discounting paradigms quantify the ability to refrain from preference of immediate rewards, in favour of delayed, larger rewards. As such, they measure temporal foresight and the ability to delay gratification, functions that develop slowly into adulthood. We investigated the neural maturation that accompanies the previously observed age-related behavioural changes in discounting, from early adolescence into mid-adulthood. We used functional magnetic resonance imaging of a hypothetical discounting task with monetary rewards delayed in the week to year range. We show that age-related reductions in choice impulsivity were associated with changes in activation in ventromedial prefrontal cortex (vmPFC), anterior cingulate cortex (ACC), ventral striatum (VS), insula, inferior temporal gyrus, and posterior parietal cortex. Limbic frontostriatal activation changes were specifically associated with age-dependent reductions in impulsive choice, as part of a more extensive network of brain areas showing age-related changes in activation, including dorsolateral PFC, inferior parietal cortex, and subcortical areas. The maturational pattern of functional connectivity included strengthening in activation coupling between ventromedial and dorsolateral PFC, parietal and insular cortices during selection of delayed alternatives, and between vmPFC and VS during selection of immediate alternatives. We conclude that maturational mechanisms within limbic frontostriatal circuitry underlie the observed post-pubertal reductions in impulsive choice with increasing age, and that this effect is dependent on increased activation coherence within a network of areas associated with discounting behaviour and inter-temporal decision-making.

Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

Brain computer interface control via functional connectivity dynamics

The dynamics of inter-regional communication within the brain during cognitive processing – referred to as functional connectivity – are investigated as a control feature for a brain computer interface. EMDPL is used to map phase synchronization levels between all channel pair combinations in the EEG. This results in complex networks of channel connectivity at all time–frequency locations. The mean clustering coefficient is then used as a descriptive feature encapsulating information about inter-channel connectivity. Hidden Markov models are applied to characterize and classify dynamics of the resulting complex networks. Highly accurate levels of classification are achieved when this technique is applied to classify EEG recorded during real and imagined single finger taps. These results are compared to traditional features used in the classification of a finger tap BCI demonstrating that functional connectivity dynamics provide additional information and improved BCI control accuracies.

Connectivity measures for internet topologies on the level of autonomous systems

Classical measures of network connectivity are the number of disjoint paths between a pair of nodes and the size of a minimum cut. For standard graphs, these measures can be computed efficiently using network flow techniques. However, in the Internet on the level of autonomous systems (ASs), referred to as AS-level Internet, routing policies impose restrictions on the paths that traffic can take in the network. These restrictions can be captured by the valley-free path model, which assumes a special directed graph model in which edge types represent relationships between ASs. We consider the adaptation of the classical connectivity measures to the valley-free path model, where it is -hard to compute them. Our first main contribution consists of presenting algorithms for the computation of disjoint paths, and minimum cuts, in the valley-free path model. These algorithms are useful for ASs that want to evaluate different options for selecting upstream providers to improve the robustness of their connection to the Internet. Our second main contribution is an experimental evaluation of our algorithms on four types of directed graph models of the AS-level Internet produced by different inference algorithms. Most importantly, the evaluation shows that our algorithms are able to compute optimal solutions to instances of realistic size of the connectivity problems in the valley-free path model in reasonable time. Furthermore, our experimental results provide information about the characteristics of the directed graph models of the AS-level Internet produced by different inference algorithms. It turns out that (i) we can quantify the difference between the undirected AS-level topology and the directed graph models with respect to fundamental connectivity measures, and (ii) the different inference algorithms yield topologies that are similar with respect to connectivity and are different with respect to the types of paths that exist between pairs of ASs.

Multiscale evolving complex network model of functional connectivity in neuronal cultures

Cultures of cortical neurons grown on multielectrode arrays exhibit spontaneous, robust and recurrent patterns of highly synchronous activity called bursts. These bursts play a crucial role in the development and topological selforganization of neuronal networks. Thus, understanding the evolution of synchrony within these bursts could give insight into network growth and the functional processes involved in learning and memory. Functional connectivity networks can be constructed by observing patterns of synchrony that evolve during bursts. To capture this evolution, a modelling approach is adopted using a framework of emergent evolving complex networks and, through taking advantage of the multiple time scales of the system, aims to show the importance of sequential and ordered synchronization in network function.

Spatio-temporal dependencies in functional connectivity in rodent cortical cultures

Models of functional connectivity in cortical cultures on multi-electrodes arrays may aid in understanding how cognitive pathways form and improve techniques that aim to interface with neuronal systems. To enable research on such models, this study uses both data- and model-driven approaches to determine what dependencies are present in and between functional connectivity networks derived from bursts of extracellularly recorded activity. Properties of excitation in bursts were analysed using correlative techniques to assess the degree of linear dependence and then two parallel techniques were used to assess functional connectivity. Three models presenting increasing levels of spatio-temporal dependency were used to capture the dynamics of individual functional connections and their consistencies were verified using surrogate data. By comparing network-wide properties between model generated networks and functional networks from data, complex interdependencies were revealed. This indicates the persistent co-activation of neuronal pathways in spontaneous bursts, as can be found in whole brain structures.

Relationships between changes in sustained fronto-striatal connectivity and positive affect with antidepressant treatment in major depression

Objective: Deficits in positive affect and their neural bases have been associated with major depression. However, whether reductions in positive affect result solely from an overall reduction in nucleus accumbens activity and fronto-striatal connectivity or the additional inability to sustain engagement of this network over time is unknown. The authors sought to determine whether treatment-induced changes in the ability to sustain nucleus accumbens activity and fronto-striatal connectivity during the regulation of positive affect are associated with gains in positive affect. Method: Using fMRI, the authors assessed the ability to sustain activity in reward-related networks when attempting to increase positive emotion during per- formance of an emotion regulation para- digm in 21 depressed patients before and after 2 months of antidepressant treat- ment. Over the same interval, 14 healthy comparison subjects underwent scanning as well. Results: After 2 months of treatment, self-reported positive affect increased. The patients who demonstrated the largest increases in sustained nucleus accumbens activity over the 2 months were those who demonstrated the largest increases in positive affect. In addition, the patients who demonstrated the largest increases in sustained fronto-striatal connectivity were also those who demonstrated the largest increases in positive affect when control- ling for negative affect. None of these associations were observed in healthy comparison subjects. Conclusions: Treatment-induced change in the sustained engagement of fronto- striatal circuitry tracks the experience of positive emotion in daily life. Studies examining reduced positive affect in a va- riety of psychiatric disorders might benefit from examining the temporal dynamics of brain activity when attempting to under- stand changes in daily positive affect.