We consider the problem of supporting several different path queries over a tree on n nodes, each having a weight drawn from a set of σ distinct values, where σ ≤ n. One query we support is the path median query, which asks for the median weight on a path between two given nodes. For this and the more general path selection query, we present a linear space data structure that answers queries in...

We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string S[1, n] over alphabet [1..σ] in time O(lgn/ lg lgn), which is optimal. The time is worst-case for the queries and amortized for the updates. This complexity is better than the best previous ones by a Θ(1 + lg σ/ lg lgn) factor. Our structure uses nH0(S) + O(n + σ(l...

This data article contains complementary results related to the paper "Effect of metal ions on the binding reaction of (-)-epigallocatechin gallate to β-lactoglobulin" (Zhang et al., 2017) [1]. Data was obtained by circular dichroism (CD) spectroscopy to investigate potential β-lactoglobulin (β-Lg) conformational changes with different concentrations of EGCg and Cu2+ or Al3+ added to β-Lg. 500 ...

We prove an (lg 2 n= lg lg n) lower bound for the depth of n-input sorting networks based on the shuue permutation. The best previously known lower bound was the trivial (lg n) bound, while the best upper bound is given by Batcher's (lg 2 n)-depth bitonic sorting network. The proof technique employed in the lower bound argument may be of independent interest.

The goal of this work is to construct a perverse t-structure on the ∞-category ℓ-adic LG-equivariant sheaves loop Lie algebra Lg and show that affine Grothendieck–Springer sheaf S perverse. Moreover, an intermediate extension its restriction locus “compact” elements with regular semi-simple reduction. Note classical methods do not apply in our situation because LG are infinite-dimensional ind-s...

The skyline of a set of points in the plane is the subset of maximal points, where a point (x, y) is maximal if no other point (x′, y′) satisfies x′ ≥ x and y′ ≥ x. We consider the problem of preprocessing a set P of n points into a space efficient static data structure supporting orthogonal skyline counting queries, i.e. given a query rectangle R to report the size of the skyline of P ∩ R. We ...

We give an algorithm to nd a minimum spanning tree in the k-dimensional space under rectilinear metric. The running time is O(8 k p k n(lg n) k?2 lg lg n) for k 3. This improves the previous bound by a factor p k lg 2 n=4 k .

Molecular interactions between β-lactoglobulin (β-LG) and sugar beet pectin (SBP) were studied using online multi-detection high performance size exclusion chromatography (HPSEC) at neutral pH and 50mM ionic strength. The hydrodynamic properties of various interacting polymer fractions were characterized in detail and compared with those of β-LG and SBP. Results showed that ∼6.5% (w/w) of nativ...

The generalized conductance ϕ(G,H) between two weighted graphs G and H on the same vertex set V is defined as ratioϕ(G,H)=minS⊆V⁡capG(S,S¯)capH(S,S¯), where capG(S,S¯) total weight of edges crossing from S⊆V to S¯=V−S. We show that minimum eigenvalue λ(LG,LH) pair Laplacians LG LH satisfiesϕ(G,H)≥λ(LG,LH)≥ϕ(G,H)ϕ(G)/16, ϕ(G) standard G. A cut meets this bound can be obtained eigenvector corresp...