Further, there is a similar equivalency between material implication and set inclusion (indeed, often it is represented with the same symbol). This leads us to the above view that, for the purposes of developing abstractions of logical consequence, one possible direction is to treat these ...
As a consequence, the entire spectra of and are essentially uncorrelated. To establish this effect of eigenbasis rotation, we use a multi-resolvent local law for the resolvents of and ; this method currently requires for typical choices of . To ensure this, we assume that where is an N-...
Unlike most other branches of mathematics, frequentist methods of statistical inference suffer from the lack of an axiomatic basis; as a consequence, their proposed desiderata are often mutually incompatible, and the analysis of the same data may well lead to incompatible results when different, appar...
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...
One consequence of this is that convergence in distribution does not produce unique limits: if converges in distribution to , and has the same distribution as , then also converges in distribution to . However, limits are unique up to equivalence in distribution (this is a consequence of the ...
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}}}...
root. We prove that $\ln Z_{\geq D}$ grows as $\ln n$ asymptotically and obtain its limiting behavior in probability. Moreover, we obtain that the kth moment of $\ln Z_{\geq D}$ is proportional to $(\!\ln n)^k$. As a consequence, we obtain that the first-order growth of...
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 ...
In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the spectator...