On max-k-sums
نویسنده
چکیده
The max-k-sum of a set of real scalars is the maximum sum of a subset of size k, or alternatively the sum of the k largest elements. We study two extensions: First, we show how to obtain smooth approximations to functions that are pointwise max-k-sums of smooth functions. Second, we discuss how the max-k-sum can be defined on vectors in a finite-dimensional real vector space ordered by a closed convex cone.
منابع مشابه
Maximal inequalities for centered norms of sums of independent random vectors
Let X1, X2, . . . , Xn be independent random variables and Sk = Pk i=1 Xi. We show that for any constants ak, P( max 1≤k≤n ||Sk| − ak| > 11t) ≤ 30 max 1≤k≤n P(||Sk| − ak| > t). We also discuss similar inequalities for sums of Hilbert and Banach space valued random vectors.
متن کاملA fast numerical method for max-convolution and the application to efficient max-product inference in Bayesian networks
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in ...
متن کاملAn Application of Hermitian K-Theory: Sums-of-Squares Formulas
By using Hermitian K-theory, we improve D. Dugger and D. Isaksen’s condition (some powers of 2 dividing some binomial coefficients) for the existence of sums-of-squares formulas. 2010 Mathematics Subject Classification: 19G38; 11E25; 15A63
متن کاملStepanov’s Method Applied to Binomial Exponential Sums
For a prime p and binomial axk+bxl with 1 ≤ l < k < 1 32 (p−1) 2 3 , we use Stepanov’s method to obtain the bound ∣∣∣∣∣ p−1 ∑ x=1 ep(ax k + bx) ∣∣∣∣∣ max { 1, l∆− 1 3 } 1 4 k 1 4 p 3 4 , where ∆ = k−l (k,l,p−1) .
متن کاملConvex geometry of max-stable distributions
It is shown that max-stable random vectors in [0,∞)d with unit Fréchet marginals are in one to one correspondence with convex sets K in [0,∞)d called max-zonoids. The max-zonoids can be characterised as sets obtained as limits of Minkowski sums of cross-polytopes or, alternatively, as the selection expectation of a random crosspolytope whose distribution is controlled by the spectral measure of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016