Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

Retrograde tracer injections in 29 of the 91 areas of the macaque cerebral cortex revealed 1,615 interareal pathways, a third of which have not previously been reported. A weight index (extrinsic fraction of labeled neurons [FLNe]) was determined for each area-to-area pathway. Newly found projections were weaker on average compared with the known projections; nevertheless, the 2 sets of pathways had extensively overlapping weight distributions. Repeat injections across individuals revealed modest FLNe variability given the range of FLNe values (standard deviation <1 log unit, range 5 log units). The connectivity profile for each area conformed to a lognormal distribution, where a majority of projections are moderate or weak in strength. In the G29 × 29 interareal subgraph, two-thirds of the connections that can exist do exist. Analysis of the smallest set of areas that collects links from all 91 nodes of the G29 × 91 subgraph (dominating set analysis) confirms the dense (66%) structure of the cortical matrix. The G29 × 29 subgraph suggests an unexpectedly high incidence of unidirectional links. The directed and weighted G29 × 91 connectivity matrix for the macaque will be valuable for comparison with connectivity analyses in other species, including humans. It will also inform future modeling studies that explore the regularities of cortical networks.

SUMMARY Recent advances in neuroscience have engendered interest in large-scale brain networks. Using a consistent database of corticocortical connectivity, generated from hemisphere-wide, retrograde tracing experiments in the macaque, we analyzed interareal weights and distances to reveal an important organizational principle of brain connectivity. Using appropriate graph theoretical measures, we show that although very dense (66%), the interareal network has strong structural specificity. Connection weights exhibit a heavy-tailed lognormal distribution spanning five orders of magnitude and conform to a distance rule reflecting exponential decay with interareal separation. A single-parameter random graph model based on this rule predicts numerous features of the cortical network: (1) the existence of a network core and the distribution of cliques, (2) global and local binary properties, (3) global and local weight-based communication efficiencies modeled as network conductance, and (4) overall wire-length minimization. These findings underscore the importance of distance and weight-based heterogeneity in cortical architecture and processing.

Small-world networks provide an appealing description of cortical architecture owing to their capacity for integration and segregation combined with an economy of connectivity. Previous reports of low-density interareal graphs and apparent small-world properties are challenged by data that reveal high-density cortical graphs in which economy of connections is achieved by weight heterogeneity and distance-weight correlations. These properties define a model that predicts many binary and weighted features of the cortical network including a core-periphery, a typical feature of self-organizing information processing systems. Feedback and feedforward pathways between areas exhibit a dual counterstream organization, and their integration into local circuits constrains cortical computation. Here, we propose a bow-tie representation of interareal architecture derived from the hierarchical laminar weights of pathways between the high-efficiency dense core and periphery.

To what extent cortical pathways show significant weight differences and whether these differences are consistent across animals (thereby comprising robust connectivity profiles) is an important and unresolved neuroanatomical issue. Here we report a quantitative retrograde tracer analysis in the cynomolgus macaque monkey of the weight consistency of the afferents of cortical areas across brains via calculation of a weight index (fraction of labeled neurons, FLN). Injection in 8 cortical areas (3 occipital plus 5 in the other lobes) revealed a consistent pattern: small subcortical input (1.3% cumulative FLN), high local intrinsic connectivity (80% FLN), high-input form neighboring areas (15% cumulative FLN), and weak long-range corticocortical connectivity (3% cumulative FLN). Corticocortical FLN values of projections to areas V1, V2, and V4 showed heavy-tailed, lognormal distributions spanning 5 orders of magnitude that were consistent, demonstrating significant connectivity profiles. These results indicate that 1) connection weight heterogeneity plays an important role in determining cortical network specificity, 2) high investment in local projections highlights the importance of local processing, and 3) transmission of information across multiple hierarchy levels mainly involves pathways having low FLN values.

Mammals show a wide range of brain sizes, reflecting adaptation to diverse habitats. Comparing interareal cortical networks across brains of different sizes and mammalian orders provides robust information on evolutionarily preserved features and species-specific processing modalities. However, these networks are spatially embedded, directed, and weighted, making comparisons challenging. Using tract tracing data from macaque and mouse, we show the existence of a general organizational principle based on an exponential distance rule (EDR) and cortical geometry, enabling network comparisons within the same model framework. These comparisons reveal the existence of network invariants between mouse and macaque, exemplified in graph motif profiles and connection similarity indices, but also significant differences, such as fractionally smaller and much weaker long-distance connections in the macaque than in mouse. The latter lends credence to the prediction that long-distance cortico-cortical connections could be very weak in the much-expanded human cortex, implying an increased susceptibility to disconnection syndromes such as Alzheimer disease and schizophrenia. Finally, our data from tracer experiments involving only gray matter connections in the primary visual areas of both species show that an EDR holds at local scales as well (within 1.5 mm), supporting the hypothesis that it is a universally valid property across all scales and, possibly, across the mammalian class.

We investigated the influence of interareal distance on connectivity patterns in a database obtained from the injection of retrograde tracers in 29 areas distributed over six regions (occipital, temporal, parietal, frontal, prefrontal, and limbic). One-third of the 1,615 pathways projecting to the 29 target areas were reported only recently and deemed new-found projections (NFPs). NFPs are predominantly long-range, low-weight connections. A minimum dominating set analysis (a graph theoretic measure) shows that NFPs play a major role in globalizing input to small groups of areas. Randomization tests show that ( i ) NFPs make important contributions to the specificity of the connectivity profile of individual cortical areas, and ( ii ) NFPs share key properties with known connections at the same distance. We developed a similarity index, which shows that intraregion similarity is high, whereas the interregion similarity declines with distance. For area pairs, there is a steep decline with distance in the similarity and probability of being connected. Nevertheless, the present findings reveal an unexpected binary specificity despite the high density (66%) of the cortical graph. This specificity is made possible because connections are largely concentrated over short distances. These findings emphasize the importance of long-distance connections in the connectivity profile of an area. We demonstrate that long-distance connections are particularly prevalent for prefrontal areas, where they may play a prominent role in large-scale communication and information integration.

We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium surface. Monte Carlo simulations and a coarse-grained approximation indicate that the macroscopic landscape in the steady state is governed by the EdwardsWilkinson Hamiltonian. Since the efficiency of the algorithm corresponds to the density of local minima in the associated surface, our results imply that the algorithm is asymptotically scalable.PACS numbers: 89.80.+h, 02.70.Lq, 68.35.Ct To efficiently utilize modern supercomputers requires massively parallel implementations of dynamic algorithms for various physical, chemical, and biological processes. For many of these there are well-known and routinely used serial Monte Carlo (MC) schemes which are based on the realistic assumption that attempts to update the state of the system form a Poisson process. The parallel implementation of these dynamic MC algorithms belongs to the class of parallel discrete-event simulations, which is one of the most challenging areas in parallel computing [1] and has numerous applications not only in the physical sciences, but also in computer science, queueing theory, and economics. For example, in lattice Ising models the discrete events are spin-flip attempts, while in queueing systems they are job arrivals. Since current special-or multi-purpose parallel computers can have 10 4 − 10 5 processing elements (PE) [2], it is essential to understand and estimate the scaling properties of these algorithms.In this Letter we introduce an approach to investigate the asymptotic scaling properties of an extremely robust parallel scheme [3]. This parallel algorithm is applicable to a wide range of stochastic cellular automata with local dynamics, where the discrete events are Poisson arrivals. Although attempts have been made to estimate its efficiency under some restrictive assumptions [4], the mechanism which ensures the scalability of the algorithm in the "steady state" was never identified. Here we accomplish this by noting that the simulated time horizon is analogous to a growing and fluctuating surface. The local random time increments correspond to the deposition of random amounts of "material" at the local minima of the surface. This correspondence provides a natural ground for cross-disciplinary application of wellknown concepts from non-equilibrium surface growth [5] and driven systems [6] to a certain class of massively parallel computational schemes. To estimate the efficiency of this algorithm one must understand the morphology of the surface associated with the simulated time horizon. In particular, the efficiency of this parallel implementation (the fraction of the non-idling processing elements) exactly corresponds to the density of local minima in the surface model. We show that the steady-state behavior of the macroscopic landscape is governed by the EdwardsWilkinson (EW) Hamiltonian [7],...