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Strong XOR Lemma for Communication with Bounded Rounds A strong XOR lemma asserts that to achieve 1 2 + exp(−O(n)) success probability, one must use Ω(n · s) resource — the trivial solution is essentially optimal Now suppose that we are given n · s 2 resource in total, and we want to compute f⊕n
Amplifying Hardness: XOR and Hardcore Lemmas The sum of this vector Y 0 will necessarily be 1 − δ and hence Y 0 is of the form (1 − δ)Y for some probability distribution Y In this case we say that X has density δ in {0, 1}n One example for such a distribution is the uniform distribution over some subset S of size δ2n
Assembly Language: IA-32 Instructions - Princeton University Bitwise Logic Instructions • Simple instructions and{b,w,l} source, dest or{b,w,l} source, dest xor{b,w,l} source, dest not{b,w,l} dest sal{b,w,l} source, dest (arithmetic) sar{b,w,l} source, dest (arithmetic) dest = source dest dest = source | dest dest = source ^ dest dest = ~dest dest = dest << source dest = dest >> source
Multiple Sequence Alignments I - Princeton University Here, we consider the case where we wish to align three or more entire sequences (i e , global multiple sequence alignments) Usually, local multiple sequence alignment methods only look for ungapped alignments, or motifs, and we will return to motif finding in a future lecture
[chapter] [chapter] - Princeton University From the exact sequence of sheaves (1 37) there follows as usual an associated exact sequence of cohomology groups, leading to the following result
Microsoft PowerPoint - MSA - Lec 7. ppt - Princeton University Similarity Measures For pairwise alignments, we aligned sequences to maximize the similarity score With multiple sequences, not obvious what best way to score an alignment is Sum-of-pairs (SP) is a commonly studied similarity measure for MSAs
Codes and Xor graph products - Princeton University We note that the definition of the Xor product and of xα applies to multi-graphs as well: indeed, since only the parity of the number of edges between two vertices dictates their adjacency, we can assume that there are no multiple edges, however there may be (self) loops in the graph
Monochromatic sums and products in N - Annals of Mathematics (After applying the correspondence principle, this special case corresponds essentially to Corollary 1 5 ) The idea is to construct a sequence (Bn) of nonempty open sets of X, each contained inside some member Un of the open cover, such that (5) 8 n < m; 9 y = y(n; m) 2 N; MyA yBn
Combinatorics and Hodge theory - Princeton University Before defining Lorentzian polynomials in Definition 4, we list three applications of the theory to demonstrate the usefulness and ubiquity of Lorentzian polynomials