Pretend play has been claimed to be crucial to children's healthy development. Here we examine evidence for this position versus 2 alternatives: Pretend play is 1 of many routes to positive developments (equifinality), and pretend play is an epiphenomenon of other factors that drive development. Evidence from several domains is considered. For language, narrative, and emotion regulation, the research conducted to date is consistent with all 3 positions but insufficient to draw conclusions. For executive function and social skills, existing research leans against the crucial causal position but is insufficient to differentiate the other 2. For reasoning, equifinality is definitely supported, ruling out a crucially causal position but still leaving open the possibility that pretend play is epiphenomenal. For problem solving, there is no compelling evidence that pretend play helps or is even a correlate. For creativity, intelligence, conservation, and theory of mind, inconsistent correlational results from sound studies and nonreplication with masked experimenters are problematic for a causal position, and some good studies favor an epiphenomenon position in which child, adult, and environment characteristics that go along with play are the true causal agents. We end by considering epiphenomenalism more deeply and discussing implications for preschool settings and further research in this domain. Our take-away message is that existing evidence does not support strong causal claims about the unique importance of pretend play for development and that much more and better research is essential for clarifying its possible role.

Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyze it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand vs. price, the bid-ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a nondimensional granularity parameter, is in most cases a more significant determinant of market behavior than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero-intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic-zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable. Contents

The topology of the proteome map revealed by recent large-scale hybridization methods has shown that the distribution of protein-protein interactions is highly heterogeneous, with many proteins having few links while a few of them are heavily connected. This particular topology is shared by other cellular networks, such as metabolic pathways, and it has been suggested to be responsible for the high mutational homeostasis displayed by the genome of some organisms. In this paper we explore a recent model of proteome evolution that has been shown to reproduce many of the features displayed by its real counterparts. The model is based on gene duplication plus re-wiring of the newly created genes. The statistical features displayed by the proteome of well-known organisms are reproduced, suggesting that the overall topology of the protein maps naturally emerges from the two leading mechanisms considered by the model.

We analyze the stoichiometry, energetics, and reaction concentration dependence of the reductive tricarboxylic acid (rTCA) cycle as a universal and possibly primordial metabolic core. The rTCA reaction sequence is a network-autocatalytic cycle along the relaxation pathway for redox couples in nonequilibrium reducing environments, which provides starting organic compounds for the synthesis of all major classes of biomolecules. The concentration dependence of its reactions suggests it as a precellular bulk process. We propose that rTCA is statistically favored among competing redox relaxation pathways under early-earth conditions and that this feature drove its emergence and also accounts for its evolutionary robustness and universality. The ability to enhance the rate of core reactions creates an energetic basis for selection of subsequent layers of biological complexity.