1 Overview We continue discussing the distinct elements problem. Recall that in this problem, you receive as input a stream S = (x 1 , x 2 ,. . .), with each x i ∈ [n], and you are supposed to compute k = #{v ∈ [n] : v appears in S}. Topics for today: • Review of the algorithm from last lecture. • The LogLog algorithm, which is more space efficient. • Generalizing the algorithm from last lectur...

Phonetics attempts to describe and understand how speech is produced and perceived; phonology attempts to understand the patterning—in general, the behavior—of speech sounds in particular languages and in all languages. Is phonetics part of phonology? This straightforward question has received various answers at different points in the history of linguistics. In this paper I attempt to document...

◈ well-known keystream generator ◈ proposed by Coppersmith, Krawczyk and Mansour [Crypto 93] ◈ use two LFSRs A and S. – Let a 0 , a 1 , … denote the sequence generated by A. – Let s 0 , s 1 , … denote the sequence generated by S. ◈ The resultant sequence is a " shrunken " version of the first one. ◈ modified version of Shrinking Generator ◈ proposed by Meier and Staffelbach [Eurocrypt 94] ◈ use...

Suppose that N is a diffuse, property T von Neumann algebra and X is an arbitrary finite generating set of selfadjoint elements for N. By using rigidity/deformation arguments applied to representations of N in ultraproducts of full matrix algebras, we deduce that the microstate spaces of X are asymptotically discrete up to unitary conjugacy. We use this description to show that the free entropy...

Proof. Let us assume that G is planar but not free planar. Then there exists an edge xy not belonging to the graph whom adding to the graph it becomes non-planar. Then in G for an arbitrary cycle C through x, y there exists a pair of screening bridges Bx and By x from y with respect to C, i. e. either Bx and By are not placeable on one side against C or they are connected [i.e. not placeable to...