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The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in learning theory, differential privacy, and algorithm design in general.
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Self-reciprocal polynomials and coterm polynomials [PDF]
We classify all self-reciprocal polynomials arising from reversed Dickson polynomials over $\mathbb{Z}$ and $\mathbb{F}_p$, where $p$ is prime. As a consequence, we also obtain coterm polynomials arising from reversed Dickson polynomials.
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Isomorphisms of algebras of symmetric functions on spaces $\ell_p$
The work is devoted to the study of algebras of entire symmetric functions on some Banach spaces of sequences. A function on a vector space is called symmetric with respect to some fixed group $G$ of operators acting on this space, or $G$-symmetric, if ...
T. V. Vasylyshyn
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Lightweight noncommutative key exchange protocol for IoT environments
Network communications are expanding rapidly in many fields, including telecommunications, the Internet of Things, space, consumer electronics, and the military, with different privacy and security issues at stake in each of these areas.
Shamsa Kanwal +5 more
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The polynomial and the Poisson measurement error models: some further results on quasi score and corrected score estimation [PDF]
The asymptotic covariance matrices of the corrected score, the quasi score, and the simple score estimators of a polynomial measurement error model have been derived in the literature.
Schneeweiß, Hans
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To improve the visual quality of noisy medical images acquired by low radiation dose imaging, medical image denoising is highly desirable for clinical disease diagnosis.
Linlin Ji, Qiang Guo, Mingli Zhang
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Safety Margin Prediction Algorithms Based on Linear Regression Analysis Estimates
In this paper, we consider the problem of approximating the safety margin of a single instance of a technical system based on inaccurate observations at specified time points.
Gurami Tsitsiashvili, Alexandr Losev
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wytsai8/polynomial-regression:
polynomial-regression Our analysis is divided into two parts, Photoacoustic/optical imaging features: Signal analysis process by MATLAB. The data and scripts are in the folder of "image_features".
wytsai8
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Polynomial invariants are polynomial
AMSLaTeX+epic.sty+eepic.sty, 7 ...
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In this paper, we study polynomial norms, i.e. norms that are the $d^{\text{th}}$ root of a degree-$d$ homogeneous polynomial $f$. We first show that a necessary and sufficient condition for $f^{1/d}$ to be a norm is for $f$ to be strictly convex, or equivalently, convex and positive definite.
Amir Ali Ahmadi +2 more
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