wordlesslyPythagoreantheoremWe wordlessly prove using the Pythagorean theorem.doi:10.4169/math.mag.90.2.134ROGER B. NELSENMathematics Magazine
The quantity \sum (\hat Y - \acute{Y})^2 is called the ___ sum of squares. a. least b. total c. explained d. unexplained Identify the following terms: (a) two-way design, (b) complete factorial, and (c) cell Define and give an example of the unit or identity matrix. In ho...
Sum-of-Squares Meets Program Obfuscation, Revisited 来自 Semantic Scholar 喜欢 0 阅读量: 13 作者:B Barak,SB Hopkins,A Jain,P Kothari,A Sahai 摘要: We develop attacks on the security of variants of pseudo-random generators computed by quadratic polynomials. In particular we give a general ...
We give an upper bound on the sum of squares of ℓ-degrees in a k-uniform hypergraph in terms of ℓ,k and the number of vertices and edges of the hypergraph, where a ℓ-degree is the number of edges of the hypergraph containing a fixed ℓ-element subset of the vertices. For ...
(Update: Jump to the end to see the result expressed as a couple of matrix multiplications.) I think you can greatly simplify the computation by using the identity: For instance, S_{k,l} Fu_{ku} Fv_{lv} Fx_{kx} Fy_{ly} = S_{k,l} Fu_{ku} Fx_{kx} Fv_{lv} Fy_{ly} -...
Let s ( n ) be the number of representations of n as the sum of three squares. We prove a remarkable new identity for s ( p 2 n ) p s ( n ) with p being a... A Berkovich,W Jagy - 《Journal of Number Theory》 被引量: 17发表: 2011年 On the representation of integers as...
public static T SumOfSquares<T> (ReadOnlySpan<T> x) where T : System.Numerics.IAdditionOperators<T,T,T>, System.Numerics.IAdditiveIdentity<T,T>, System.Numerics.IMultiplyOperators<T,T,T>; Type Parameters T Parameters x ReadOnlySpan<T> Returns T Applies to .NET 9 and .NET 8 ...
A symmetric positive semi-definite (PSD) tensor, which is not sum-of-squares (SOS), is called a PSD non-SOS (PNS) tensor. Is there a fourth order four dimensional PNS Hankel tensor? The answer for this question has both theoretical and practical significance. Under the assumptions that the...
Regression analysis picks ONE line in particular – The criteria used is to minimize the sum of squares of the errors (distance from the points in the scatter plot to the line constructed). If there is more than one variable on which the prediction depends, it is called “Multiple ...
By the way, there's a simple proof for the statement that for an arbitrary single-variable polynomial of even degrees which only takes non-negative values, it can be written as the sum of squares. (I think it may be helpful for the above problem, so I put the proof ...