"Since the 1990s chaotic cat maps are widely used in data encryption, for their very complicated dynamics within a simple model and desired characteristics related to requirements of cryptography. The number of cat map parameters and the map period length after discretization are two major concerns in many applications for security reasons. In this paper, we propose a new family of 36 distinctive 3D cat maps with different spatial configurations taking existing 3D cat maps [1]-[4] as special cases. Our analysis and comparisons show that this new 3D cat maps family has more independent map parameters and much longer averaged period lengths than existing 3D cat maps. The presented cat map family can be extended to higher dimensional cases."

(to_teach tags for clsses which use the cat map as an example)

"Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data with summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. Although these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and we then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate ABC analyses than the ad hoc choices of summary statistics that have been proposed in the literature. We also demonstrate advantages over two alternative methods of simulation-based inference."

"We present direct evidence of an activator-inhibitor system in the generation of the regularly spaced transverse ridges of the palate. We show that new ridges, called rugae, that are marked by stripes of expression of Shh (encoding Sonic hedgehog), appear at two growth zones where the space between previously laid rugae increases. However, inter-rugal growth is not absolutely required: new stripes of Shh expression still appeared when growth was inhibited. Furthermore, when a ruga was excised, new Shh expression appeared not at the cut edge but as bifurcating stripes branching from the neighboring stripe of Shh expression, diagnostic of a Turing-type reaction-diffusion mechanism. Genetic and inhibitor experiments identified fibroblast growth factor (FGF) and Shh as components of an activator-inhibitor pair in this system. These findings demonstrate a reaction-diffusion mechanism that is likely to be widely relevant in vertebrate development."

"This article examines a series of Schelling-like models of residential segregation, in which agents prefer to be in the minority. We demonstrate that as long as agents care about the characteristics of their wider community, they tend to end up in a segregated state. We then investigate the process that causes this and conclude that the result hinges on the similarity of informational states among agents of the same type. This is quite different from Schelling-like behavior and suggests (in his terms) that segregation is an instance of macrobehavior that can arise from a wide variety of micromotives."

Sweet. (Bayesian estimation seems like overkill here however, especially since predictions are just made from point estimates.)

"Machamer, Darden, and Craver’s account of the nature and role of mechanisms in the special sciences has been very influential. Unfortunately, a confusing array of ontic, epistemic, and pragmatic distinctions is required to individuate their mechanisms, mechanism schemata, and mechanism sketches. I diagnose this as a conflation of token-level causal relations with type-level relations. I propose instead that a mechanism is an abstraction that relates entity types and activity types on the model of a directed graph. Mechanisms have an ontic status distinct from the causal chains of token entities and token activities that instantiate them."

Examine carefully. God knows hairballs are not very useful. There's apparently an R package.

To many math symbols to copy the abstract. Shorter: iterating randomly chosen Lipschitz maps can lead to time-averges converging to a heavy-tailed distribution.

Assumes all homophilous traits are measured, I believe.

This cries out for simulation.

"In this work we propose an objective function to guide the search for a state space reconstruction of a dynamical system from a time series of measurements. These statistics can be evaluated on any reconstructed attractor, thereby allowing a direct comparison among different approaches: (uniform or nonuniform) delay vectors, PCA, Legendre coordinates, etc. It can also be used to select the most appropriate parameters of a reconstruction strategy. In the case of delay coordinates this translates into finding the optimal delay time and embedding dimension from the absolute minimum of the advocated cost function. Its definition is based on theoretical arguments on noise amplification, the complexity of the reconstructed attractor, and a direct measure of local stretch which constitutes an irrelevance measure. The proposed method is demonstrated on synthetic and experimental time series."

"Complex social networks have received increasing attention from researchers. Recent work has focused on mechanisms that produce scale-free networks. We theoretically and empirically characterize the buyer–supplier network of the US economy and find that purely scale-free models have trouble matching key attributes of the network. We construct an alternative model that incorporates realistic features of firms’ buyer–supplier relationships and estimate the model’s parameters using microdata on firms’ self-reported customers. This alternative framework is better able to match the attributes of the actual economic network and aids in further understanding several important economic phenomena."

Possibly suitable for adoption in the undergrad complex systems class?

The "to teach" tag is conditional...

"Desert locusts, Schistocerca gregaria, show extreme phenotypic plasticity, transforming between a little-seen solitarious phase and the notorious swarming gregarious phase depending on population density. An essential tipping point in the process of swarm formation is the initial switch from strong mutual aversion in solitarious locusts to coherent group formation and greater activity in gregarious locusts. We show here that serotonin, an evolutionarily conserved mediator of neuronal plasticity, is responsible for this behavioral transformation, being both necessary if behavioral gregarization is to occur and sufficient to induce it. Our data demonstrate a neurochemical mechanism linking interactions between individuals to large-scale changes in population structure and the onset of mass migration."

"We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks. Our results are also applicable to detection of functional modules, partitions, and colorings in noisy planted models. Using a cavity method analysis, we unveil a phase transition from a region where the original group assignment is undetectable to one where detection is possible. In some cases, the detectable region splits into an algorithmically hard region and an easy one. Our approach naturally translates into a practical algorithm for detecting modules in sparse networks, and learning the parameters of the underlying model." --- This is really an EM algorithm, not a Bayesian method.

"For a broad range single-seed contagion processes acting on generalized random networks, we derive a unifying analytic expression for the possibility of global spreading events in a straightforward, physically intuitive fashion. Our reasoning lays bare a direct mechanical understanding of an archetypal spreading phenomena that is not evident in circuitous extant mathematical approaches."  (Are they really that circuitous?)

Hmmm, do these assumptions hold for power law distributions?  (Now corresponding software: "ddst" on CRAN.)

"A novel paradigm was developed to study the behavior of groups of networked people searching a problem space. The authors examined how different network structures affect the propagation of information in laboratory-created groups. Participants made numerical guesses and received scores that were also made available to their neighbors in the network. The networks were compared on speed of discovery and convergence on the optimal solution. One experiment showed that individuals within a group tend to converge on similar solutions even when there is an equally valid alternative solution. Two additional studies demonstrated that the optimal network structure depends on the problem space being explored, with networks that incorporate spatially based cliques having an advantage for problems that benefit from broad exploration, and networks with greater long-range connectivity having an advantage for problems requiring less exploration."

"Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these ... sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. ... analyze the song syntax in a Bengalese finch. ... the Markov model fails ... Instead, ... include adaptation of the self-transition probabilities when states are repeatedly revisited ... more than one state to the same syllable. ... Mathematically, the model is a partially observable Markov model with adaptation (POMMA). ... supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC ..."

"In this review, we summarize recent developments in stochastic evolutionary game dynamics of finite populations." Looks decent, at first scan.

"This paper describes four methods for estimating autocorrelation time and evaluates these methods with a test set of seven series. Fitting an autoregressive process appears to be the most accurate method of the four. An R package is provided for extending the comparison to more methods and test series."

"depmixS4 implements a general framework for defining and estimating dependent mixture models in the R programming language. This includes standard Markov models, latent/hidden Markov models, and latent class and finite mixture distribution models. The models can be fitted on mixed multivariate data with distributions from the glm family, the (logistic) multinomial, or the multivariate normal distribution. Other distributions can be added easily, and an example is provided with the exgaus distribution. Parameters are estimated by the expectation-maximization (EM) algorithm or, when (linear) constraints are imposed on the parameters, by direct numerical optimization with the Rsolnp or Rdonlp2 routines."

"A Green’s function method is developed to approach the spatiotemporal equations describing the cAMP production in Dictyostelium discoideum, markedly reducing numerical calculations times: cAMP concentrations and gradients are calculated just at the amoeba locations. A single set of parameters is capable of reproducing the different observed behaviors, from cAMP synchronization, spiral waves and reaction-diffusion patterns to streaming and mound formation. After aggregation, the emergence of a circular motion of amoebas, breaking the radial cAMP field symmetry, is observed."

Since I teach about Martian polar ice canyons in 462...

for 462 and for STACS?

Review paper.

Mars! Mars!! Mars!!!!

"sociological theories consider murder an outcome of the differential distribution of individual, neighborhood, or social characteristics ... explain variation in aggregate homicide rates [but not] the social order of murder [:] who kills whom, when, where, and for what reason. ... gang murder is best understood not by ... its individual determinants but by ... the social networks of action and reaction that create it. ... the social structure of gang murder is defined by the manner in which social networks are constructed and by people's placement in them. ... uses a network approach and incident‐level homicide records to recreate and analyze the structure of gang murders in Chicago. ... individual murders between gangs create an institutionalized network of group conflict, net of any individual's participation or motive. Within this network, murders spread through an epidemic‐like process of social contagion ...."

I had nothing to do with this (but wish I did).

"time-average variance constants" = sum of covariances = 1/correlation time (roughly).

Understanding phase transitions probabilistically, as places where the failure of mixing makes the ordinary central limit theorem break down, and non-Gaussian, heavy-tailed distributions appear for macroscopic averages. (I think I bookmarked this in 2000 and then forgot about it... and making me find it again is the only good thing about refereeing this **** paper, grumble.)

Re-purposing standard epidemic models (SIR, etc.) as descriptions of zombie outbreaks. (Conclusion: we're DOOMED!)

"We offer a solution to a long-standing problem in the theory of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity—the propensity for two neighbors of a network node also to be neighbors of one another. We show how standard random-graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant component forms, and position of the phase transition for percolation on the network."

Kicking off a special issue that might have been titled "Artificial life and theoretical biology: fight!"

"The aim of this paper is to study whether a child's schooling choices are affected by the schooling choices of other children. Identification is based on a randomized targeted intervention that grants a cash subsidy conditional on school attendance to a subgroup of eligible children within small rural villages in Mexico (PROGRESA). This policy change spills over to ineligible children if social interactions are relevant. Results indicate that the eligible children tend to attend school more frequently, and the ineligible children acquire more schooling when the subsidy is introduced in their local village. Moreover, the overall effect of PROGRESA on eligible children is the sum of a direct effect due to cash transfers and an indirect effect due to changes in peer group schooling. Interestingly, the social interactions effect is almost as important as the direct effect."

"The scale-free distribution of cluster sizes in continuous phase transitions is linked to the law of proportional effect. A numerical study of a two-dimensional Ising model suggests that a cluster size undergoes a multiplicative birth-death process. At the transition the ratio between birth and death rates approaches unity for large clusters, and the resulting steady state shows a power-law behavior. The percolation dynamic, on the other hand, yields a geometric phase transition without ergodicity breaking, where large-scale merging and splitting of clusters dominate the distribution. Instead of short-range birth-death jumps, the percolation transition is characterized by Lévi [sic] flights along the cluster-size axis."

Not clear from their abstract if they realize that statisticians _have_ been looking at networks.

"For a statistician, an inverse problem is an inference or estimation problem. The data are finite in number and contain errors, as they do in classical ... problems, and the unknown typically is infinite-dimensional, as it is in nonparametric regression. The additional complication in an inverse problem is that the data are only indirectly related to the unknown. Canonical abstract formulations of statistical estimation problems subsume this complication by allowing probability distributions to be indexed in more-or-less arbitrary ways by parameters, which can be infinite-dimensional. Standard statistical concepts, questions, and considerations such as bias, variance, mean-squared error, identifiability, consistency, efficiency, and various forms of optimality, apply to inverse problems. This article discusses inverse problems as statistical estimation and inference problems, and points to the literature for a variety of techniques and results."

Review paper. From a _very_ superficial glance, looks good.

Very reasonable set of slides from Thomas Lumley. I wouldn't plan on actually using them in a course --- they don't quite fit my style --- but I would put them on a list of pointers for students.

Data available?

Data available?

Cool!
(But, note to the Times online people: why would you include a link to your archive of stories on _human_ suicide, but no link to the paper?!?)

How the establishment of chains of stores makes it easier to establish _other_ chains,

This is the Yule-Simon model with a limited memory effect. The rank-size plots (i.e., empirical CDFs) they show make me pretty sure they're not producing power laws, though they may be power laws with exponential truncation; since their stats are bad, it's hard to say. Should make good take-home-final fodder, however.

"If you are using R and you think you’re in hell, this is a map for you. "