"A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an (implicit) model of the environmental variables. The system's state retains information about past environmental fluctuations, and a fraction of this information is predictive of future ones. The remaining nonpredictive information reflects model complexity that does not improve predictive power, and represents the ineffectiveness of the model. We expose the fundamental equivalence between this model inefficiency and thermodynamic inefficiency, measured by the energy dissipated during the interaction between system and environment. Our results hold arbitrarily far from thermodynamic equilibrium and are applicable to a wide range of systems, including biomolecular machines. They highlight a profound connection between the effective use of information and efficient thermodynamic operation: any system constructed to keep memory about its environment and to operate energetically efficiently has to be predictive."

"Using frequency distributions of daily closing price sequences of several stock markets, we investigate whether the bias away from an equiprobable sequence distribution, predicted by algorithmic probability, may account for some of the deviation of financial markets from log-normal, and if so for how much of said deviation and over what sequence lengths. Our discussion might constitute a potential starting point for a further investigation of the market as a rule-based system with an 'algorithmic' component, despite its apparent randomness. The use of the theory of algorithmic complexity may supply a set of probing new tools that can be applied to the study of the market price phenomenon. Moreover, the main discussion is cast in terms of assumptions common to areas of economics consistent with an algorithmic view of the market."

"We introduce a simple criterion, the CAR score, for ranking and selecting variables in linear regression. The CAR score arises naturally in the best predictor formulation of the linear model, offers a canonical decomposition of the proportion of explained variance, and also takes account of correlation and grouping structure among explanatory variables. As population quantity the CAR score is not tied to any specific inference paradigm. Variable selection based on AIC, $C_p$, BIC, and other information criteria is shown to be equivalent to thresholding CAR scores at a fixed level, whereas using false discovery rates corresponds to an adaptive cutoff. In computer simulations we show that CAR scores are highly effective for variable selection with a prediction error that compares favorable with the elastic net and similar regression procedures. We illustrate the approach by analyzing diabetes data as well as gene expression data from the human frontal cortex."

"Recovery of the sparsity pattern (or support) of a sparse vector from a small number of noisy linear samples is a common problem that arises in signal processing and statistics. In the high dimensional setting, it is known that recovery with a vanishing fraction of errors is impossible if the sampling rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector. In this paper, it is shown that recovery with an arbitrarily small but constant fraction of errors is, however, possible, and that in some cases a computationally simple thresholding estimator is near-optimal.…"

"…The intrinsic underlying structure of the system is modeled by an epsilon-machine and its causal states. The decisional states are the emerging patterns corresponding to the utility function. In a complex systems perspective, these patterns thus form a partition of the lower-level system states that is defined according to the higher-level user's knowledge. The transitions between these decisional states correspond to events that lead to a change of decision. An algorithm is provided so as to estimate the states and their transitions from data. Application examples are given for hidden model reconstruction, cellular automata filtering, and edge detection in images."

"We present a method for estimating the complexity of an image based on the concept of logical depth. Unlike the application of the concept of algorithmic complexity by itself, the addition of the concept of logical depth results in a characterization of objects by organizational (physical) complexity. We use this measure to classify images by their information content. The method provides a means for evaluating and classifying objects by way of their visual representations."

"We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints.…"

"[Open Questions] Most of the encoding schemes considered in this paper use randomness and therefore are not given explicitly. As a result, the encoding and decoding schemes are not efficient. Finding explicit and efficient encoding and decoding schemes for the scenarios described in the paper remains open."