Data Structures & Algorithm Analysis in C++

This is the textbook for CSIS 215 at Liberty University.https://digitalcommons.liberty.edu/textbooks/1005/thumbnail.jp

c-Axis tunneling in YBa2Cu3O7-\delta/PrBa2Cu3O7-\delta superlattices

In this work we report c-axis conductance measurements done on a superlattice based on a stack of 2 layers YBa2Cu3O{7-\delta} and 7 layers PrBa2Cu3O{7-\delta} (2:7). We find that these quasi-2D structures show no clear superconducting coupling along the c-axis. Instead, we observe tunneling with a gap of \Delta_c=5.0\pm 0.5 meV for the direction perpendicular to the superconducting planes. The conductance spectrum show well defined quasi-periodic structures which are attributed to the superlattice structure. From this data we deduce a low temperature c-axis coherence length of \xi_c=0.24\pm 0.03 nm.Comment: 15 pages, 5 figures. To appear in Phys.Rev.

The mechanism regulating the dissociation of the centrosomal protein C-Nap1 from mitotic spindle poles

The centrosomal protein C-Nap1 is thought to play an important role in centrosome cohesion during interphase of the cell cycle. At the onset of mitosis, when centrosomes separate for bipolar spindle formation, C-Nap1 dissociates from centrosomes. Here we report the results of experiments aimed at determining whether the dissociation of C-Nap1 from mitotic centrosomes is triggered by proteolysis or phosphorylation. Specifically, we analyzed both the cell cycle regulation of endogenous C-Nap1 and the fate of exogenously expressed full-length C-Nap1. Western blot analyses suggested a reduction in the endogenous C-Nap1 level during M phase, but studies using proteasome inhibitors and destruction assays performed in Xenopus extracts argue against ubiquitin-dependent degradation of C-Nap1. Instead, our data indicate that the mitotic C-Nap1 signal is reduced as a consequence of M-phase-specific phosphorylation. Overexpression of full-length C-Nap1 in human U2OS cells caused the formation of large structures that embedded the centrosome and impaired its microtubule nucleation activity. Remarkably, however, these centrosome-associated structures did not interfere with cell division. Instead, centrosomes were found to separate from these structures at the onset of mitosis, indicating that a localized and cell-cycle-regulated activity can dissociate C-Nap1 from centrosomes. A prime candidate for this activity is the centrosomal protein kinase Nek2, as the formation of large C-Nap1 structures was substantially reduced upon co-expression of active Nek2. We conclude that the dissociation of C-Nap1 from mitotic centrosomes is regulated by localized phosphorylation rather than generalized proteolysis

Exact Distance Oracles for Planar Graphs

We present new and improved data structures that answer exact node-to-node distance queries in planar graphs. Such data structures are also known as distance oracles. For any directed planar graph on n nodes with non-negative lengths we obtain the following: * Given a desired space allocation $S\in[n\lg\lg n,n^2]$, we show how to construct in $\tilde O(S)$ time a data structure of size $O(S)$ that answers distance queries in $\tilde O(n/\sqrt S)$ time per query. As a consequence, we obtain an improvement over the fastest algorithm for k-many distances in planar graphs whenever $k\in[\sqrt n,n)$. * We provide a linear-space exact distance oracle for planar graphs with query time $O(n^{1/2+eps})$ for any constant eps>0. This is the first such data structure with provable sublinear query time. * For edge lengths at least one, we provide an exact distance oracle of space $\tilde O(n)$ such that for any pair of nodes at distance D the query time is $\tilde O(min {D,\sqrt n})$. Comparable query performance had been observed experimentally but has never been explained theoretically. Our data structures are based on the following new tool: given a non-self-crossing cycle C with $c = O(\sqrt n)$ nodes, we can preprocess G in $\tilde O(n)$ time to produce a data structure of size $O(n \lg\lg c)$ that can answer the following queries in $\tilde O(c)$ time: for a query node u, output the distance from u to all the nodes of C. This data structure builds on and extends a related data structure of Klein (SODA'05), which reports distances to the boundary of a face, rather than a cycle. The best distance oracles for planar graphs until the current work are due to Cabello (SODA'06), Djidjev (WG'96), and Fakcharoenphol and Rao (FOCS'01). For $\sigma\in(1,4/3)$ and space $S=n^\sigma$, we essentially improve the query time from $n^2/S$ to $\sqrt{n^2/S}$.Comment: To appear in the proceedings of the 23rd ACM-SIAM Symposium on Discrete Algorithms, SODA 201

Poisson structures on certain moduli spaces for bundles on a surface

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, and $\xi \colon P \to \Sigma$ a principal $G$-bundle. In earlier work we have shown that the moduli space $N(\xi)$ of central Yang- Mills connections, for appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a diffeomorphism from $N(\xi)$ onto a certain representation space \roman{Rep}_{\xi}(\Gamma,G), with reference to suitable smooth structures $C^{\infty}(N(\xi))$ and C^{\infty}(\roman{Rep}_{\xi}(\Gamma,G)) where $\Gamma$ denotes the universal central extension of the fundamental group of $\Sigma$. Given an invariant symmetric bilinear form on $g^*$, we construct here Poisson structures on $C^{\infty}(N(\xi))$ and C^{\infty}(\roman{Rep}_{\xi}(\Gamma,G)) in such a way that the mentioned diffeomorphism identifies them. When the form on $g^*$ is non-degenerate the Poisson structures are compatible with the stratifications where \roman{Rep}_{\xi}(\Gamma,G) is endowed with the corresponding stratification and, furthermore, yield structures of a {\it stratified symplectic space\/}, preserved by the induced action of the mapping class group of $\Sigma$.Comment: 22 pages, AMSTeX 2.

Library for advanced functions in algorithms, data structures and AI implemented in C/C++ - Olib

Developers of one of most popular languages used for scientific computations which is C, have a lot of libraries at their disposal. Many of those allows usage of modern platforms equipped with advanced multicore processors. Among them is BLAS (Basic Linear Algebra Subprograms) and LAPACK (Linear Algebra PACKage). They contain mainly high performance procedures operating on matrix and vectors