相关论文: St. Petersburg paradox and failure probability

The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…

Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…

The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum…

The effect of geometrical shape of eroding absolutely rigid particles on the threshold rate of failure has been studied. The Shtaerman-Kilchevsky theory of quasi-static blunt impact, which generalizes Hertz's classical impact theory, is…

This paper is concerned with difficulties encountered by engineers when they attempt to predict the orientation of fibers in the creation of injection molded plastic parts. It is known that Jeffery's equation, which was designed to model a…

We analyze a 19-year time series of North American electric power transmission system blackouts. Contrary to previously reported results we find a fatter than exponential decay in the distribution of inter-occurrence times and evidence of…

We formulate the problem of probabilistic predictions of global failure in the simplest possible model based on site percolation and on one of the simplest model of time-dependent rupture, a hierarchical fiber bundle model. We show that…

The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium…

For over a decade, researchers in formal methods tried to create formalisms that permit natural specification of systems and allow mathematical reasoning about their correctness. The availability of fully-automated reasoning tools enables…

We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…

Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the dynamics of crack propagation…

The remaining travel time of a plane shortens with every minute that passes from its departure, and a flame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun…

The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected…

The fermi paradox uses an appeal to the mediocrity principle to make it seem counter-intuitive that humanity has not been contacted by extraterrestrial intelligence. A numerical, statistical analysis was conducted to determine whether this…

By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter ($\epsilon$) which eliminates the assumption of complete…

The probability of rare and extreme events is an important quantity for design purposes. However, computing the probability of rare events can be expensive because only a few events, if any, can be observed. To this end, it is necessary to…

Simpson's paradox, a long-standing statistical phenomenon, describes the reversal of an observed association when data are disaggregated into sub-populations. It has critical implications across statistics, epidemiology, economics, and…

As a serious attempt for constructing a new foundation for describing micro-incidents from a local causal standpoint, I explained before that each micro-entity can be assumed to be composed of a probability field joined to a particle…

Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…

The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between…