Local cluster aggregation models of explosive percolation

We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step of the process one edge is selected from a small set of potential edges sharing common vertices and added to the graph. We show that the evolution can be accurately described by a system of differential equations and that such models exhibit the discontinuous emergence of the giant component. Yet, they also obey scaling behaviors characteristic of continuous transitions, with scaling exponents that differ from the classic Erdos-Renyi model.Comment: Final version as appearing in PR

Environmental and genetic influences on neurocognitive development: the importance of multiple methodologies and time-dependent intervention

Genetic mutations and environmental factors dynamically influence gene expression and developmental trajectories at the neural, cognitive, and behavioral levels. The examples in this article cover different periods of neurocognitive development—early childhood, adolescence, and adulthood—and focus on studies in which researchers have used a variety of methodologies to illustrate the early effects of socioeconomic status and stress on brain function, as well as how allelic differences explain why some individuals respond to intervention and others do not. These studies highlight how similar behaviors can be driven by different underlying neural processes and show how a neurocomputational model of early development can account for neurodevelopmental syndromes, such as autism spectrum disorders, with novel implications for intervention. Finally, these studies illustrate the importance of the timing of environmental and genetic factors on development, consistent with our view that phenotypes are emergent, not predetermined

Strongly discontinuous explosive percolation with multiple giant components

We generalize the random graph evolution process of Bohman, Frieze, and Wormald [T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algorithms, 25, 432 (2004)]. Potential edges, sampled uniformly at random from the complete graph, are considered one at a time and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function asymptotically approaching the value alpha = 1/2. We show that multiple giant components appear simultaneously in a strongly discontinuous percolation transition and remain distinct. Furthermore, tuning the value of alpha determines the number of such components with smaller alpha leading to an increasingly delayed and more explosive transition. The location of the critical point and strongly discontinuous nature are not affected if only edges which span components are sampled.Comment: Final version appearing in PR

Teachers developing assessment for learning: impact on student achievement

While it is generally acknowledged that increased use of formative assessment (or assessment for learning) leads to higher quality learning, it is often claimed that the pressure in schools to improve the results achieved by students in externally-set tests and examinations precludes its use. This paper reports on the achievement of secondary school students who worked in classrooms where teachers made time to develop formative assessment strategies. A total of 24 teachers (2 science and 2 mathematics teachers, in each of six schools in two LEAs) were supported over a six-month period in exploring and planning their approach to formative assessment, and then, beginning in September 1999, the teachers put these plans into action with selected classes. In order to compute effect sizes, a measure of prior attainment and at least one comparison group was established for each class (typically either an equivalent class taught in the previous year by the same teacher, or a parallel class taught by another teacher). The mean effect size was 0.32

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Scaffolds for Dental Pulp Tissue Engineering

For tissue engineering strategies, the choice of an appropriate scaffold is the first and certainly a crucial step. A vast variety of biomaterials is available: natural or synthetic polymers, extracellular matrix, self-assembling systems, hydrogels, or bioceramics. Each material offers a unique chemistry, composition and structure, degradation profile, and possibility for modification. The role of the scaffold has changed from passive carrier toward a bioactive matrix, which can induce a desired cellular behavior. Tailor-made materials for specific applications can be created. Recent approaches to generate dental pulp rely on established materials, such as collagen, polyester, chitosan, or hydroxyapatite. Results after transplantation show soft connective tissue formation and newly generated dentin. For dentinpulp- complex engineering, aspects including vascularization, cell-matrix interactions, growth-factor incorporation, matrix degradation, mineralization, and contamination control should be considered. Self-assembling peptide hydrogels are an example of a smart material that can be modified to create customized matrices. Rational design of the peptide sequence allows for control of material stiffness, induction of mineral nucleation, or introduction of antibacterial activity. Cellular responses can be evoked by the incorporation of cell adhesion motifs, enzymecleavable sites, and suitable growth factors. The combination of inductive scaffold materials with stem cells might optimize the approaches for dentin-pulp complex regeneration

Modular horizontal network within mouse primary visual cortex

Interactions between feedback connections from higher cortical areas and local horizontal connections within primary visual cortex (V1) were shown to play a role in contextual processing in different behavioral states. Layer 1 (L1) is an important part of the underlying network. This cell-sparse layer is a target of feedback and local inputs, and nexus for contacts onto apical dendrites of projection neurons in the layers below. Importantly, L1 is a site for coupling inputs from the outside world with internal information. To determine whether all of these circuit elements overlap in L1, we labeled the horizontal network within mouse V1 with anterograde and retrograde viral tracers. We found two types of local horizontal connections: short ones that were tangentially limited to the representation of the point image, and long ones which reached beyond the receptive field center, deep into its surround. The long connections were patchy and terminated preferentially in M2 muscarinic acetylcholine receptor-negative (M2-) interpatches. Anterogradely labeled inputs overlapped in M2-interpatches with apical dendrites of retrogradely labeled L2/3 and L5 cells, forming module-selective loops between topographically distant locations. Previous work showed that L1 of M2-interpatches receive inputs from the lateral posterior thalamic nucleus (LP) and from a feedback network from areas of the medial dorsal stream, including the secondary motor cortex. Together, these findings suggest that interactions in M2-interpatches play a role in processing visual inputs produced by object-and self-motion

Bond percolation on a class of correlated and clustered random graphs

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via different types of hyperedges, edges that can link more than 2 nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviors of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network.Comment: 16 pages and 4 figure