Linear Algebra I
... where f˜ej +1 (wj0 ) = 0 for j = 1, . . . , `. We now lift wj0 to an element vj0 ∈ V (i.e., we pick vj0 ∈ V that maps to wj0 under the canonical epimorphism V → W ). Then v10 , f (v10 ), . . . , f e1 (v10 ), v20 , f (v20 ), . . . , f e2 (v20 ), . . . , v`0 , f (v`0 ), . . . , f e` (v`0 ) are linearl ...
... where f˜ej +1 (wj0 ) = 0 for j = 1, . . . , `. We now lift wj0 to an element vj0 ∈ V (i.e., we pick vj0 ∈ V that maps to wj0 under the canonical epimorphism V → W ). Then v10 , f (v10 ), . . . , f e1 (v10 ), v20 , f (v20 ), . . . , f e2 (v20 ), . . . , v`0 , f (v`0 ), . . . , f e` (v`0 ) are linearl ...
Random Involutions and the Distinct Prime Divisor Function
... where f (a, b) is fraction from the previous slide which represents the probability of an involution on Fn2 being isomorphic to F2 [Z/2]a x Fb2 , and the sum is being taken over all (a0 , b0 ) such that 2a0 + b0 = n. ...
... where f (a, b) is fraction from the previous slide which represents the probability of an involution on Fn2 being isomorphic to F2 [Z/2]a x Fb2 , and the sum is being taken over all (a0 , b0 ) such that 2a0 + b0 = n. ...
Hankel Matrices: From Words to Graphs
... Weighted RMSOL vs. MSOLEVAL, II In contrast to these disadvantages, MSOLEVALF has the following advantages: (i) The expressions are natural and intuitive. (ii) The expressions are defined for all formulas of MSOL without any restrictions. (iii) If we replace formulas occurring in an expression by eq ...
... Weighted RMSOL vs. MSOLEVAL, II In contrast to these disadvantages, MSOLEVALF has the following advantages: (i) The expressions are natural and intuitive. (ii) The expressions are defined for all formulas of MSOL without any restrictions. (iii) If we replace formulas occurring in an expression by eq ...
Efficiently Decodable Compressed Sensing by List-Recoverable Codes and Recursion Hung Q. Ngo
... O(d) non-zero entries for some parameter 1 ≤ d N ) such that the following conditions holds: kx − x̂kp ≤ C · kx − x∗d kp + C 0 · kνkp , where x∗d is the vector x with all but its d highest-magnitude components zeroed out. In the above C ≥ 1 is the approximation factor. Ideally, we would like to ac ...
... O(d) non-zero entries for some parameter 1 ≤ d N ) such that the following conditions holds: kx − x̂kp ≤ C · kx − x∗d kp + C 0 · kνkp , where x∗d is the vector x with all but its d highest-magnitude components zeroed out. In the above C ≥ 1 is the approximation factor. Ideally, we would like to ac ...
Large Graphs and Graph Limits
... We consider sequences of large graphs which have certain convergent graph parameters. Many important graph parameters like the edge density may be represented asymptotically as homomorphism densities. I turns out that convergence of homomorphism densities of a graph sequence gives rise to distance b ...
... We consider sequences of large graphs which have certain convergent graph parameters. Many important graph parameters like the edge density may be represented asymptotically as homomorphism densities. I turns out that convergence of homomorphism densities of a graph sequence gives rise to distance b ...