Theorem about complexity measures of Boolean functions
In computational complexity, the sensitivity theorem, proved by Hao Huang in 2019,[1] states that the sensitivity of a Boolean function is at least the square root of its degree, thus settling a conjecture posed by Nisan and Szegedy in 1992.[2] The proof is notably succinct, given that prior progress had been limited.[3]
^Huang 2019.
^Nisan & Szegedy 1994.
^Klarreich 2019.
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In computational complexity, the sensitivitytheorem, proved by Hao Huang in 2019, states that the sensitivity of a Boolean function f : { 0 , 1 } n →...
calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names...
depend also on the prevalence. Both PPV and NPV can be derived using Bayes' theorem. Although sometimes used synonymously, a positive predictive value generally...
impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a...
Pierre Hohenberg in the framework of the two Hohenberg–Kohn theorems (HK). The original HK theorems held only for non-degenerate ground states in the absence...
this sensitivity. If we set G 2 = { k 2 } k = 1 ∞ {\displaystyle {\mathfrak {G}}^{2}=\{k^{2}\}_{k=1}^{\infty }} , then Lagrange's four-square theorem can...
Central limit theorem Central limit theorem (illustration) – redirects to Illustration of the central limit theorem Central limit theorem for directional...
Fourier amplitude sensitivity testing (FAST) is a variance-based global sensitivity analysis method. The sensitivity value is defined based on conditional...
cases, the last two properties above have been shown to actually imply sensitivity to initial conditions. In the discrete-time case, this is true for all...
concave sensitivity to stressors, leading to a negative sensitivity to increase in volatility. The relation between fragility, convexity, and sensitivity to...
of other parties. advertising elasticity of demand (AED) Measures the sensitivity of a good's demand to a change in advertising. agflation An increase...
the Jacobian determinant at p is non-zero. This is the inverse function theorem. Furthermore, if the Jacobian determinant at p is positive, then f preserves...
thought of as estimators of these quantities). The ROC curve is thus the sensitivity or recall as a function of false positive rate. Given the probability...
therefore connected by Bayes' theorem. There are various relationships between these ratios. If the prevalence, sensitivity, and specificity are known,...
for assessing the value of performing a diagnostic test. They use the sensitivity and specificity of the test to determine whether a test result usefully...
instances}}{\text{All retrieved instances}}}} Recall (also known as sensitivity) is the fraction of relevant instances that were retrieved. Written as...
p} equals the average sensitivity at p {\displaystyle p} . The Russo–Margulis formula is key for proving sharp threshold theorems such as Friedgut's. One...
almost all elements of X, even if it isn't an ultrafilter. The prime number theorem shows that the number of primes less than or equal to n is asymptotically...
as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic...
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