Related papers: How predictable is technological progress?
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
We consider an energy storage problem involving a wind farm with a forecasted power output, a stochastic load, an energy storage device, and a connection to the larger power grid with stochastic prices. Electricity prices and wind power…
Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a…
Numerical weather prediction (NWP) and machine learning (ML) methods are popular for solar forecasting. However, NWP models have multiple possible physical parameterizations, which requires site-specific NWP optimization. This is further…
Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble…
In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of supervised machine learning algorithms is introduced. The method relies on the notion of…
We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each…
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean,…
This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…
Considering a broad family of technologies where a measure of performance (MoP) is difficult or impossible to formulate, we seek an alternative measure that exhibits a regular pattern of evolution over time, similar to how a MoP may follow…
A fundamental problem in technological studies is how to measure the evolution of technology. The literature has suggested several approaches to measuring the level of technology (or state-of-the-art) and changes in technology. However, the…
Meteorological forecasting provides reliable prediction about the future weather within a given interval of time. Meteorological forecasting can be viewed as a form of hybrid diagnostic reasoning and can be mapped onto an integrated…
The masking-one-out (MOO) procedure, masking an observed entry and comparing it versus its imputed values, is a very common procedure for comparing imputation models. We study the optimum of this procedure and generalize it to a missing…
Diffusion models have shown promise in forecasting future data from multivariate time series. However, few existing methods account for recurring structures, or patterns, that appear within the data. We present Pattern-Guided Diffusion…
Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts…
Prognostics is a process of assessing the extent of deviation or degradation of a product from its expected normal operating condition, and then, based on continuous monitoring, predicting the future reliability of the product. By being…
The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…
Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the…