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In this work we introduce a spatio-temporal bounded noise derived by the sine-Wiener noise and by the spatially colored unbounded noise proposed by GarcASHa-Ojalvo, Sancho, and RamASHrez-Piscina (GSR noise). We characterize the behavior of the equilibrium distribution of this novel noise by showing its dependence on both the temporal and the spatial autocorrelation lengths. In particular, we show that the distribution experiences a stochastic transition from bimodality to trimodality.

Functions to calculate measures of spatial association, especially measures of spatial autocorrelation, have been made available in many software applications. Measures may be global, applying to the whole data set under consideration, or local, applying to each observation in the data set. Methods of statistical inference may also be provided, but these will, like the measures themselves, depend on the support of the observations, chosen assumptions, and the way in which spatial association is represented; spatial weights are often used as a representational technique. In addition, assumptions may be made about the underlying mean model, and about error distributions. Different software implementations may choose to expose these choices to the analyst, but the sets of choices available may vary between these implementations, as may default settings. This comparison will consider the implementations of global Moran’s I, Getis–Ord G and Geary’s C, local \\[I_i\\] and \\[G_i\\], available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.

We expect luminous (M 1450 ≲ −26.5) high-redshift quasars to trace the highest-density peaks in the early Universe. Here, we present observations of four z ≳ 6 quasar fields using JWST/NIRCam in the imaging and wide-field slitless spectroscopy mode and report a wide range in the number of detected [O iii]-emitting galaxies in the quasars’ environments, ranging between a density enhancement of δ ≈ 65 within a 2 cMpc radius—one of the largest protoclusters during the Epoch of Reionization discovered to date—to a density contrast consistent with zero, indicating the presence of a UV-luminous quasar in a region comparable to the average density of the Universe. By measuring the two-point cross-correlation function of quasars and their surrounding galaxies, as well as the galaxy autocorrelation function, we infer a correlation length of quasars at 〈z〉 = 6.25 of r0QQ=22.0−2.9+3.0cMpch−1 , while we obtain a correlation length of the [O iii]-emitting galaxies of r0GG=4.1±0.3cMpch−1 . By comparing the correlation functions to dark-matter-only simulations we estimate the minimum mass of the quasars’ host dark matter halos to be log10(Mhalo,min/M⊙)=12.43−0.15+0.13 (and log10(Mhalo,min[OIII]/M⊙)=10.56−0.03+0.05 for the [O iii] emitters), indicating that (a) luminous quasars do not necessarily reside within the most overdense regions in the early Universe, and that (b) the UV-luminous duty cycle of quasar activity at these redshifts is f duty ≪ 1. Such short quasar activity timescales challenge our understanding of early supermassive black hole growth and provide evidence for highly dust-obscured growth phases or episodic, radiatively inefficient accretion rates.

The characteristics of subdiffusion are influenced by hydrodynamic fluctuations, not the scaling of the mean square displacement (MSD) at the long time limit, but rather the transition of this property from ballistic behaviour at early times to its final scaling at large times. Additionally, since a significant portion of the normalised velocity autocorrelation function (NVAF), a widely used motion descriptor, no longer adequately describes the antipersistent character that is typical of a subdiffusive motion, it is also impacted by these fluctuations. The combined findings can lead to misleading conclusions if hydrodynamic fluctuations are not taken into account. Diffusing and vorticity time scales are crucial for the way the motion turns into the final subdiffusion dynamics, whose exponent is determined by the scaling of the friction.

Dark-field imaging probes the projected autocorrelation function at the autocorrelation length of the grating interferometer and quantitatively accesses the parameters of a microstructure model. The National Institute of Standards and Technology has developed a novel far-field grating interferometer to study hierarchical materials in various fields such as polymer science, geology, additive manufacturing under the INFER project. In this work, we detail the simulation of dark-field imaging which is one of the goals of INFER.

A number of spatial statistic measurements such as Moran’s I and Geary’s C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with the time lag in time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by using the Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary’s coefficient and Getis’ index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation.

Spatial autocorrelation is inherent to remotely sensed data. Nearby pixels are more similar than distant ones. This property can help to improve the classification performance, by adding spatial or contextual features into the model. However, it can also lead to overestimation of generalisation capabilities, if the spatial dependence between training and test sets is ignored. In this paper, we review existing approaches that deal with spatial autocorrelation for image classification in remote sensing and demonstrate the importance of bias in accuracy metrics when spatial independence between the training and test sets is not respected. We compare three spatial and non-spatial cross-validation strategies at pixel and object levels and study how performances vary at different sample sizes. Experiments based on Sentinel-2 data for mapping two simple forest classes show that spatial leave-one-out cross-validation is the better strategy to provide unbiased estimates of predictive error. Its performance metrics are consistent with the real quality of the resulting map contrary to traditional non-spatial cross-validation that overestimates accuracy. This highlight the need to change practices in classification accuracy assessment. To encourage it we developped Museo ToolBox, an open-source python library that makes spatial cross-validation possible.

Streamflow prediction is an important matter for the water resources management and the design of hydraulic structures that can be built on rivers. Recently, it has become a widely studied research field where data obtained from stream gauge stations can be utilized for creating estimating models by resorting to different methods such as machine and deep learning techniques. In this study, we performed monthly streamflow predictions by using the following data-driven methods of machine learning: linear regression, support vector regression, random forest and deep learning (DL) models to compare the performances of ML's and DL's techniques. A general workflow that can be applied to similar regions is presented. An estimating model containing six-input combinations and time-lagged streamflow data is improved by means of the autocorrelation function (ACF) and partial autocorrelation function (PACF). Furthermore, moving average is used as a smoothing technique to make the dataset more stable and reduce the effects of noise data. A comparative evaluation has been conducted to determine the performances of the above-mentioned methods. In this study, we proposed four different DL models and compared them with existing techniques. For the comparison of the results, we used evaluation criteria such as Nash–Sutcliffe efficiency (NSE), mean square error (MSE) and percent bias (PBIAS). The experimental results indicate that our bidirectional gated recurrent units (BiGRU) model outperforms both ML algorithms and existing solutions with 0.971 NSE, 0.001 MSE and − 1.536 PBIAS scores.

SpinSpotter is a robust and automated algorithm designed to extract stellar rotation periods from large photometric data sets with minimal supervision. Our approach uses the autocorrelation function (ACF) to identify stellar rotation periods up to one-third the observational baseline of the data. Our algorithm also provides a suite of diagnostics that describe the features in the ACF, which allows the user to fine-tune the tolerance with which to accept a period detection. We apply it to approximately 130,000 main-sequence stars observed by the Transiting Exoplanet Survey Satellite at 2-minute cadence during Sectors 1–26 and identify rotation periods for 13,504 stars ranging from 0.4 to 14 days. We demonstrate good agreement between our sample and known values from the literature and note key differences between our population of rotators and those previously identified in the Kepler field, most notably a large population of fast-rotating M dwarfs. Our sample of rotating stars provides a data set with coverage of nearly the entire sky that can be used as a basis for future gyrochronological studies and, when combined with proper motions and distances from Gaia, to search for regions with high densities of young stars, thus identifying areas of recent star formation and undiscovered moving group members. Our algorithm is publicly available for download and use on GitHub at https://github.com/rae-holcomb/SpinSpotter.

The Snow Microwave Radiative Transfer (SMRT) thermal emission and backscatter model was developed to determine uncertainties in forward modeling through intercomparison of different model ingredients. The model differs from established models by the high degree of flexibility in switching between different electromagnetic theories, representations of snow microstructure, and other modules involved in various calculation steps. SMRT v1.0 includes the dense media radiative transfer theory (DMRT), the improved Born approximation (IBA), and independent Rayleigh scatterers to compute the intrinsic electromagnetic properties of a snow layer. In the case of IBA, five different formulations of the autocorrelation function to describe the snow microstructure characteristics are available, including the sticky hard sphere model, for which close equivalence between the IBA and DMRT theories has been shown here. Validation is demonstrated against established theories and models. SMRT was used to identify that several former studies conducting simulations with in situ measured snow properties are now comparable and moreover appear to be quantitatively nearly equivalent. This study also proves that a third parameter is needed in addition to density and specific surface area to characterize the microstructure. The paper provides a comprehensive description of the mathematical basis of SMRT and its numerical implementation in Python. Modularity supports model extensions foreseen in future versions comprising other media (e.g., sea ice, frozen lakes), different scattering theories, rough surface models, or new microstructure models.