Related papers: Extrinsic faulting in $3C$ close packed crystal st…
This is a preprint of Chapter 2 in the following work: Marta Lewicka, A Course on Tug-of-War Games with Random Noise, 2020, Springer, reproduced with permission of Springer Nature Switzerland AG. We present the basic relation between the…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
Computational modeling of high entropy alloys (HEA) is challenging given the scalability issues of Density functional theory (DFT) and the non-availability of Interatomic potentials (IP) for molecular dynamics simulations (MD). This work…
A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…
Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
The prospects for a determination of the strong coupling constant $\alpha_s$ via scaling violations of fragmentation functions in deeply inelastic scattering are studied. The statistical error in the case of an integrated luminosity of $250…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set size. Secondly, there is a \emph{related curse} concerned…
Soft fracture in highly deformable solids involves both geometric and constitutive nonlinearities, necessitating advanced theoretical and computational frameworks for its accurate understanding. Tensile fractures subjected to mixed-mode…
When computer codes are used for modeling complex physical systems, their unknown parameters are tuned by calibration techniques. A discrepancy function may be added to the computer code in order to capture its discrepancy with the real…
In the following work, we described the problems of porosity analysis of cement materials using backscattered electron images. We noticed that despite its great utility, the overflow porosity segmentation method allows for the introduction…
Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds for a single triangular set in terms of intrinsic data of the…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
High energy hadronic scattering processes can be described in terms of partonic scattering processes and parton distribution and fragmentation functions. These are bilocal matrix elements of quark operators. Colour gauge-invariance requires…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
The presence of defects in solids formed by active particles breaks their discrete translational symmetry. As a consequence, many of their properties become space-dependent and different from those characterizing perfectly ordered…
In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…
Material failure is mediated by the propagation of cracks, which in realistic 3D materials typically involve multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures,…