Here τ is an experimental time scale that is long compared to molecular time scales, and in consequence the average is independent of the starting position of the trajectory. The second line assumes that the temporal probability density is uniform, ℘(t)=1/τ. In other words, the weight ...
This work begins by looking at how logical consequence and probabilistic conditioning relate, and we observe that both can be described in terms of projections, allowing for a compact description of them. In turn, this leads to a general version of consequence, a relation extended from binary to...
Risk is the product of two key factors: probability (likelihood of occurrence) and impact (consequence if exploited). If there is a high likelihood of a vulnerability occurring and large impact in the scenario it does, that vulnerability would be of high or even critical risk....
A consequence of this definition is that the probability of an event is affected by the knowledge of probability of another event. We see from the expression above that if A and B are mutually exclusive, the conditional probability is zero because P(A·B) = 0. If A and B are independent...
are not too close. as a consequence, the entire spectra of \(h^x\) and \(h^{x'}\) are essentially uncorrelated. to establish this effect of eigenbasis rotation , we use a multi-resolvent local law for the resolvents of \(h^x\) and \(h^{x'}\) ; this method currently requires...
Probability density function provides the probability that a random variable will fall between a given interval. Understand probability density function using solved examples.
In other words, the information stored between the system and the reference spreads to the environment. The consequence is that the information between the system and the reference decreases, which gives $$\Delta {{{\mathcal{I}}}(S;R)\ge 0,$$ (1) with \(\Delta {{{\mathcal{I}}}...
1.In the end,according to the fuzzy evaluation matrix and the weighting coefficient of each factor,the failure probability and the failure consequence for the development risk are evaluated by the fuzzy-based assessment method,and the development risk value is obtained from the failure probability an...
Integrating precursor data with probability adapting of BN could revise generic prior probabilities of basic events, safety barriers and consequence states to be more case-specific updated probabilities. Such dynamic probabilities of consequence states can be used to predict the development trend of the ...
As covariates are regarded as fixed values in the modeling, it is of no material consequence if their values are spatially correlated or not. How to incorporate covariates into the modeling of species occurrence has been a central theme of this book and covered elsewhere. Autologistic models ...