Related papers: Characterising lognormal fractional-Brownian-motio…
We investigate conditional neural fields (CNFs), mesh-agnostic, coordinate-based decoders conditioned on a low-dimensional latent, for spatial dimensionality reduction of turbulent flows. CNFs are benchmarked against Proper Orthogonal…
We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
The repeating behavior of fast radio bursts (FRBs) is regarded as a key clue to understanding their physical origin, yet reliably distinguishing repeaters from apparent non-repeaters with current observations remains challenging. Here we…
A new reconstruction method of complex-valued fractional Brownian motion (CV-fBm) field based on Compressive Sampling (CS) is proposed. The decay property of Fourier coefficients magnitude of the fBm signals/ fields indicates that fBms are…
Using functional magnetic resonance imaging (fMRI) and deep learning to explore functional brain networks (FBNs) has attracted many researchers. However, most of these studies are still based on the temporal correlation between the sources…
We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an…
Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations <x(t)x(s)> ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with 0<H<1 is called the Hurst exponent. For H = 1/2, x(t) is a Brownian motion, while for H…
Spatial patterns and processes of cities can be described with various entropy functions. However, spatial entropy always depends on the scale of measurement, and it is difficult to find a characteristic value for it. In contrast, fractal…
Spatial patterning is common in ecological systems and has been extensively studied via different modeling approaches. Individual-based models (IBMs) accurately describe nonlinear interactions at the organism level and the stochastic…
For equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d=2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…
Spectral density functions are central to the simulation of complex many body systems. Their determination requires to make approximations not only to the dynamics but also to the underlying electronic structure theory. Here, blending…
This paper proposes FractalNet, a framework based on fractal design principles that automatically generates and evaluates convolutional neural network (CNN) architectures using recursive template patterns. Rather than relying on…
Predictions of nuclear properties far from measured data are inherently imprecise because of uncertainties in our knowledge of nuclear forces and in our treatment of quantum many-body effects in strongly-interacting systems. While the model…
Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other…
The possibility of determining cosmological parameters on the basis of a wide set of observational data including the Abell-ACO cluster power spectrum and mass function, peculiar velocities of galaxies, the distribution of Ly-$\alpha$…
This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…