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In this paper we present the application of a novel methodology to scientific citation and collaboration networks. This methodology is designed for understanding the governing dynamics of evolving networks and relies on an attachment kernel, a scalar function of node properties, which stochastically drives the addition and deletion of vertices and edges. We illustrate how the kernel function of a given network can be extracted from the history of the network and discuss other possible applications.

This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From data on more than 2 million patents and their citations, we extract an attractiveness function, A(k, l), which determines the likelihood that a patent will be cited. A(k, l) is approximately separable into a product of a function A k (k) and a function A l (l), where k is the number of citations already received (in-degree) and l is the age measured in patent number units. A l (l) displays a peak at low l and a long power law tail, suggesting that some patented technologies have very long-term effects. A k (k) exhibits super-linear preferential attachment. The preferential attachment exponent has been increasing since 1991, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. The overall average probability that a new patent will be cited by a given patent has increased slightly during the same period. We discuss some possible implications of our results for patent policy.

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Associative learning is a central building block of human cognition and in large part depends on mechanisms of synaptic plasticity, memory capacity and fronto-hippocampal interactions. A disorder like schizophrenia is thought to be characterized by altered plasticity, and impaired frontal and hippocampal function. Understanding the expression of this dysfunction through appropriate experimental studies, and understanding the processes that may give rise to impaired behavior through biologically plausible computational models will help clarify the nature of these deficits. We present a preliminary computational model designed to capture learning dynamics in healthy control and schizophrenia subjects. Experimental data was collected on a spatial-object paired-associate learning task. The task evinces classic patterns of negatively accelerated learning in both healthy control subjects and patients, with patients demonstrating lower rates of learning than controls. Our rudimentary computational model of the task was based on biologically plausible assumptions, including the separation of dorsal/spatial and ventral/object visual streams, implementation of rules of learning, the explicit parameterization of learning rates (a plausible surrogate for synaptic plasticity), and learning capacity (a plausible surrogate for memory capacity). Reductions in learning dynamics in schizophrenia were well-modeled by reductions in learning rate and learning capacity. The synergy between experimental research and a detailed computational model of performance provides a framework within which to infer plausible biological bases of impaired learning dynamics in schizophrenia.

Cognition is based on the integrated functioning of hierarchically organized cortical processing streams in a manner yet to be clarified. Because integration fundamentally depends on convergence and the complementary notion of divergence of the neuronal connections, we analysed integration by measuring the degree of convergence/divergence through the connections in the network of cortical areas. By introducing a new index, we explored the complementary convergent and divergent nature of connectional reciprocity and delineated the backward and forward cortical sub-networks for the first time. Integrative properties of the areas defined by the degree of convergence/divergence through their afferents and efferents exhibited distinctive characteristics at different levels of the cortical hierarchy. Areas previously identified as hubs exhibit information bottleneck properties. Cortical networks largely deviate from random graphs where convergence and divergence are balanced at low reciprocity level. In the cortex, which is dominated by reciprocal connections, balance appears only by further increasing the number of reciprocal connections. The results point to the decisive role of the optimal number and placement of reciprocal connections in large-scale cortical integration. Our findings also facilitate understanding of the functional interactions between the cortical areas and the information flow or its equivalents in highly recurrent natural and artificial networks.

In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects k possible partners from the existing network and joins them with probability δ by undirected edges. The 'activity' of the node ends here; it will get new partners only if it is selected by a newcomer. The model produces an infinite-order phase transition when a giant component appears at a specific value of δ, which depends on k. The average component size is discontinuous at the transition. In contrast, the network behaves significantly different for k = 1. There is no giant component formed for any δ and thus in this sense there is no phase transition. However, the average component size diverges for δ ≥ 1 2 .

We develop a general theory of budgetary politics and examine its implications on a new data set on U.S. government expenditures from 1791 to 2010. We draw on three major approaches to budgeting: decision-making theories, primarily incrementalism and serial processing; policy process models; and path dependency. We show that the incrementalist budget model is recursive and that its solution is exponential growth, and isolate three periods in which it operates in pure form. The equilibrium periods are separated by critical junctures, associated with wars or economic collapse. We assess policy process dynamics by examining the deviations within equilibrium periods. We offer three takeaways: (1) exponential incrementalism is fundamental to a theory of budgeting; (2) disjoint shifts in the level of exponential incrementalism are caused only by critical moments; (3) temporally localized dynamics cause bends in the exponential path, longer returns to the path within budgetary eras, and annual punctuations in budget changes. Decision-Making TheoriesDecision-making theories focus on how budget actors decide allocations. Actors themselves are grouped by institutional role, so the decision-making theories focus both on institutional interactions and the cognitive capacities