DSSAE: Deep stacked sparse autoencoder analytical model for COVID-19 diagnosis by fractional Fourier entropy
(Aim) COVID-19 has caused more than 2.28 million deaths till 4/Feb/2021 while it is still
spreading across the world. This study proposed a novel artificial intelligence model to …
spreading across the world. This study proposed a novel artificial intelligence model to …
Complexity of quantum circuits via sensitivity, magic, and coherence
Quantum circuit complexity—a measure of the minimum number of gates needed to
implement a given unitary transformation—is a fundamental concept in quantum …
implement a given unitary transformation—is a fundamental concept in quantum …
Degree and sensitivity: tails of two distributions
The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of
sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan …
sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan …
Low-sensitivity functions from unambiguous certificates
We provide new query complexity separations against sensitivity for total Boolean functions:
a power $3 $ separation between deterministic (and even randomized or quantum) query …
a power $3 $ separation between deterministic (and even randomized or quantum) query …
Improved bounds on Fourier entropy and min-entropy
Given a Boolean function f:{-1, 1}^{n}→{-1, 1, define the Fourier distribution to be the
distribution on subsets of [n], where each S⊆[n] is sampled with probability f ˆ (S) 2. The …
distribution on subsets of [n], where each S⊆[n] is sampled with probability f ˆ (S) 2. The …
Towards a proof of the fourier-entropy conjecture?
The total influence of a function is a central notion in analysis of Boolean functions, and
characterizing functions that have small total influence is one of the most fundamental …
characterizing functions that have small total influence is one of the most fundamental …
On the Analysis of Boolean Functions and Fourier-Entropy-Influence Conjecture
X Han - arXiv preprint arXiv:2308.00509, 2023 - arxiv.org
This manuscript includes some classical results we select apart from the new results we've
found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We …
found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We …
On the Fourier Entropy Influence conjecture for extremal classes
G Shalev - arXiv preprint arXiv:1806.03646, 2018 - arxiv.org
The Fourier Entropy-Influence (FEI) Conjecture of Friedgut and Kalai states that ${\bf H}[f]\leq
C\cdot {\bf I}[f] $ holds for every Boolean function $ f $, where ${\bf H}[f] $ denotes the …
C\cdot {\bf I}[f] $ holds for every Boolean function $ f $, where ${\bf H}[f] $ denotes the …
Decision trees, protocols and the entropy-influence conjecture
A Wan, J Wright, C Wu - Proceedings of the 5th conference on …, 2014 - dl.acm.org
Given ƒ:{--1, 1} n→{--1, 1}, define the spectral distribution of ƒ to be the distribution on
subsets of [n] in which the set S is sampled with probability ƒ (S) 2. Then the Fourier Entropy …
subsets of [n] in which the set S is sampled with probability ƒ (S) 2. Then the Fourier Entropy …
A lower bound on the constant in the Fourier min-entropy/influence conjecture
We describe a new construction of Boolean functions. A specific instance of our construction
provides a 30-variable Boolean function having min-entropy/influence ratio to be 128/45≈ …
provides a 30-variable Boolean function having min-entropy/influence ratio to be 128/45≈ …