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The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural network models have proved to be adept at modeling processes with spatial-temporal complexity.…
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it…
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…
We give a new characterisation of the unparametrised geodesics, or distinguished curves, for affine, pseudo-Riemannian, conformal, and projective geometry. This is a type of moving incidence relation. The characterisation is used to provide…
Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure…
The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by…
Quantum non-demolition measurements define a non-invasive protocol to extract information from a quantum system that we aim to monitor. They exploit an additional quantum system that is sequentially coupled to the system. Eventually, by…
We use 1-dimensional numerical simulations to study spherical collapse in the f(R) gravity models. We include the nonlinear coupling of the gravitational potential to the scalar field in the theory and use a relaxation scheme to follow the…
Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities, and multi-physics…
Motivation of our work is to present a new methodology for symbol recognition. We support structural methods for representing visual associations in graphic documents. The proposed method employs a structural approach for symbol…
Supercritical collisionless perpendicular shocks have an average macrostructure determined primarily by the dynamics of ions specularly reflected at the magnetic ramp. Within the overall macrostructure, instabilities, both linear and…
We propose a nonparametric parameter estimation of confidence intervals when the underlying has large or infinite variance. We explain the method by a simple numerical example and provide an application to estimate the coupling strength in…
Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…
Guided by recent advances in the understanding of nucleation and propagation of fracture in elastic brittle materials, this paper proposes a suite of three simple experiments that permit the measurement of the three macroscopic material…
Natural Disasters like hurricanes, floods or earthquakes can damage power grid devices and create cascading blackouts and islands. The nature of failure propagation and extent of damage is dependent on the structural features of the grid,…
Decision trees and their ensembles are endowed with a rich set of diagnostic tools for ranking and screening variables in a predictive model. Despite the widespread use of tree based variable importance measures, pinning down their…
Predicting region-wide structural responses under seismic shaking is essential for enhancing the effectiveness of earthquake engineering task forces such as earthquake early warning and regional seismic risk and resilience assessments.…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
Predictions are often probabilities; e.g., a prediction could be for precipitation tomorrow, but with only a 30% chance. Given such probabilistic predictions together with the actual outcomes, "reliability diagrams" help detect and diagnose…
Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely…