On some extensions of the fkn theorem
Web18 de out. de 2024 · Our results are a generalization of the Friedgut-Kalai-Naor Theorem [FKN'02], which holds for functions f:{-1,1}^n->{-1,1} that are close to a linear combination of uniformly distributed Boolean ... WebTherefore, some extensions of the framework are proposed. First, a related method for binary variables is proposed. Second, it is shown how to estimate non-normalized models defined in the non-negative real domain, i.e. Rn +. As a further result, it is shown that the score matching estimator can be obtained in closed form for some exponential ...
On some extensions of the fkn theorem
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WebThe FKN theorem has numerous extensions (see [2, 14, 27, 29, 35, 37, 39, 42]) and many applications, to hardness-of-approximation [9], information theory [43], social choice … WebActually, Carathéodory's extension theorem can be slightly generalized by replacing ring by semi-field. [2] The definition of semi-ring may seem a bit convoluted, but the following example shows why it is useful (moreover it allows us to give an explicit representation of the smallest ring containing some semi-ring).
WebOn some extensions of the FKN theorem. Article. Dec 2015; Jacek Jendrej. Krzysztof Oleszkiewicz. Jakub O. Wojtaszczyk. Let S = a1r1+a2r2+_ _ _+anrn be a weighted Rademacher sum. Web5 de jun. de 2024 · Extension theorems. Theorems on the continuation (extension) of functions from one set to a larger set in such a way that the extended function satisfies …
WebIn this note we consider Boolean functions defined on the discrete cube {−γ,γ−1}n equipped with a product probability measure μ⊗n, where μ=βδ−γ+αδγ−1 and γ=√α/β. We prove that if the spectrum of such a function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Webthe so-called Frank-Wolfe theorem. In particular, we first prove a general continuity result for the solution set defined by a system of convex quadratic inequalities. This result …
WebTheorem 1 (Kronecker's Field Extension Theorem): Let be a field and let be a nonconstant polynomial. Then there exists a field extension of and an element such that . Proof: Let …
Web29 de dez. de 2015 · On some extensions of the FKN theorem Download Citation On some extensions of the FKN theorem Let S = a1r1+a2r2+_ _ _+anrn be a weighted … csi wall protectionWeb22 de jun. de 2016 · In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial P(Z =αnZn ... csi warehouse club incorporatedWeb29 de dez. de 2015 · The author has extended the Friedgut–Kalai–Naor theorem to the slice, the subset of the Boolean cube consisting of all vectors with fixed Hamming weight, and extends the theorem further, to the multislice, a multicoloured version of the slice. csi warehouseWeb•Hypercontractivity and a quantum FKN theorem. The Friedgut-Kalai-Naor (FKN) theorem [FKN02] states that boolean functions whose Fourier transform is concentrated on the first level approximately depend on a single variable. We prove a quantum analogue of this statement. In order to obtain this result, we state and csi warehouse clubWeb10 de set. de 2024 · When α n = ∑ i ∈ S κ i for some S ⊆ [ℓ], it is natural to conjecture that the sets of the form A = {u: u j ∈ S} minimize the expansion, and this is indeed the case. Using our FKN theorem, we are able to show a stability version of this result: if a set of size α n has almost minimal expansion, then it is close to a set with minimal ... eagle india air ticketseagle in chineseWebn are some real numbers) was proved in [4] by E. Friedgut, G. Kalai, and A. Naor, and was a part of the proof of their theorem on Boolean functions on the discrete cube with … csi warehouse club inc