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Maurice Rojas, Mounir Nisse","submitted_at":"2017-10-02T04:44:52Z","abstract_excerpt":"Suppose $c_1,\\ldots,c_{n+k}$ are real numbers, $\\{a_1,\\ldots,a_{n+k}\\}\\!\\subset\\!\\mathbb{R}^n$ is a set of points not all lying in the same affine hyperplane, $y\\!\\in\\!\\mathbb{R}^n$, $a_j\\cdot y$ denotes the standard real inner product of $a_j$ and $y$, and we set $g(y)\\!:=\\!\\sum^{n+k}_{j=1} c_j e^{a_j\\cdot y}$. We prove that, for generic $c_j$, the number of connected components of the real zero set of $g$ is $O\\!\\left(n^2+\\sqrt{2}^{k^2}(n+2)^{k-2}\\right)$. 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