Related papers: Fracture strength of disordered media: Universalit…
We investigate the size scaling of the macroscopic fracture strength of heterogeneous materials when microscopic disorder is controlled by fat-tailed distributions. We consider a fiber bundle model where the strength of single fibers is…
The random fiber bundle (RFB) model, with the strength of the fibers distributed uniformly within a finite interval, is studied under the assumption of global load sharing among all unbroken fibers of the bundle. At any fixed value of the…
In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random…
We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has…
Disordered networks of fragile elastic elements have been proposed as a model for inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221]. In numerical studies, weakening of such networks is seen to be accompanied by…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect…
We apply the formalism of amplitude symmetries to the angular distribution of the decays $B \to D^* \ell \nu$ for $\ell=e,\mu,\tau$. We show that the angular observables used to describe the distribution of this class of decays are not…
We consider the problem of learning the interaction strength between the nodes of a network based on dependent binary observations residing on these nodes, generated from a Markov Random Field (MRF). Since these observations can possibly be…
Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…
We investigate the upper tail distribution of the partition function of the directed polymer in a random environment on $\mathbb Z^d$ in the weak disorder phase. We show that the distribution of the infinite volume partition function…
We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random…
We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load…
Molecular-dynamics simulations of fracture in metallic glass-like systems are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a…
Quasi-brittle behavior where macroscopic failure is preceded by stable damaging and intensive cracking activity is a desired feature of materials because it makes fracture predictable. Based on a fiber bundle model with global load sharing…
Nanoscale materials display enhanced strength and toughness but also larger fluctuations and more pronounced size effects with respect to their macroscopic counterparts. Here we study the system size-dependence of the failure strength…
Disordered networks of fragile elastic elements have been proposed as a model of inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221, http://xyz.lanl.gov]. It is shown that the ratio $\Gamma$ of responses of such a…
The nonparametric maximum likelihood estimator (NPMLE) in monotone binary regression models is studied when the impact of the features on the labels is weak. Here, weakness is colloquially understood as "close to flatness" of the…