Relevant bibliographies by topics / Other theoretical computer science and computational mathematics, n.e.c

Academic literature on the topic 'Other theoretical computer science and computational mathematics, n.e.c'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Other theoretical computer science and computational mathematics, n.e.c"

1

OUYANG, YONGZHONG, ZHONGHAI TANG, and YIZENG LIANG. "DENSITY FUNCTIONAL THEORY STUDY ON THE DECOMPOSITION MECHANISMS OF POLYNITROTRIPRISMANES: C6H6-n (NO2)n (n = 2, 4, 6)." Journal of Theoretical and Computational Chemistry 09, no. 03 (June 2010): 561–71. http://dx.doi.org/10.1142/s0219633610005852.

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Density functional theory (DFT) has been carried out to predict some possible decomposition pathways of polynitrotriprismanes C 6 H 6-n ( NO 2)n (n = 2, 4, 6) at B3LYP/6-31 + G (d, p) level. The calculated results (BDE298) suggest that the most preferred dissociation reaction for these compounds involves an initial rupture of C–C bond in the triprismane cage skeleton, followed by an opening of the second C–C bond of the intermediate to form nitro Dewar benzene, which has a similar reaction pathway as that of octanitrocubane. In addition, the predicted reaction energy shows that the whole decomposition reaction is exothermic, and the rupture of the second C–C bond is mainly the energy origin of these compounds. The predicted dissociation route for three selected PNNPs will be very helpful not only for synthesis of PNNPs, but also for characterization of other nitro-substituted high energy density materials (HEDMs).
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2

Flajolet, Philippe, Zhicheng Gao, Andrew Odlyzko, and Bruce Richmond. "The Distribution of Heights of Binary Trees and Other Simple Trees." Combinatorics, Probability and Computing 2, no. 2 (June 1993): 145–56. http://dx.doi.org/10.1017/s0963548300000560.

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The number, , of rooted plane binary trees of height ≤ h with n internal nodes is shown to satisfyuniformly for δ−1(log n)−1/2 ≤ β ≤ δ(log n)1/2, where and δ is a positive constant. An asymptotic formula for is derived for h = cn, where 0 < c < 1. Bounds for are also derived for large and small heights. The methods apply to any simple family of trees, and the general asymptotic results are stated.
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3

HARRINGTON, PAUL, COLM Ó. DÚNLAING, and CHEE K. YAP. "OPTIMAL VORONOI DIAGRAM CONSTRUCTION WITH n CONVEX SITES IN THREE DIMENSIONS." International Journal of Computational Geometry & Applications 17, no. 06 (December 2007): 555–93. http://dx.doi.org/10.1142/s0218195907002483.

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This paper presents a worst-case optimal algorithm for constructing the Voronoi diagram for n disjoint convex and rounded semi-algebraic sites in 3 dimensions. Rather than extending optimal 2-dimensional methods,32,16,20,2 we base our method on a suboptimal 2-dimensional algorithm, outlined by Lee and Drysdale and modified by Sharir25,30 for computing the diagram of circular sites. For complexity considerations, we assume the sites have bounded complexity, i.e., the algebraic degree is bounded as is the number of algebraic patches making up the site. For the sake of simplicity we assume that the sites are what we call rounded. This assumption simplifies the analysis, though it is probably unnecessary. Our algorithm runs in time O(C(n)) where C(n) is the worst-case complexity of an n-site diagram. For spherical sites C(n) is θ(n2), but sharp estimates do not seem to be available for other classes of site.
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Łuczak, Tomasz, and László Pyber. "On Random Generation of the Symmetric Group." Combinatorics, Probability and Computing 2, no. 4 (December 1993): 505–12. http://dx.doi.org/10.1017/s0963548300000869.

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We prove that the probability i(n, k) that a random permutation of an n element set has an invariant subset of precisely k elements decreases as a power of k, for k ≤ n/2. Using this fact, we prove that the fraction of elements of Sn belong to transitive subgroups other than Sn or An tends to 0 when n → ∞, as conjectured by Cameron. Finally, we show that for every ∈ > 0 there exists a constant C such that C elements of the symmetric group Sn, chosen randomly and independently, generate invariably Sn with probability at least 1 − ∈. This confirms a conjecture of McKay.
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5

BARLOW, MARTIN T., JIAN DING, ASAF NACHMIAS, and YUVAL PERES. "The Evolution of the Cover Time." Combinatorics, Probability and Computing 20, no. 3 (February 15, 2011): 331–45. http://dx.doi.org/10.1017/s0963548310000489.

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The cover time of a graph is a celebrated example of a parameter that is easy to approximate using a randomized algorithm, but for which no constant factor deterministic polynomial time approximation is known. A breakthrough due to Kahn, Kim, Lovász and Vu [25] yielded a (log logn)2 polynomial time approximation. We refine the upper bound of [25], and show that the resulting bound is sharp and explicitly computable in random graphs. Cooper and Frieze showed that the cover time of the largest component of the Erdős–Rényi random graph G(n, c/n) in the supercritical regime with c > 1 fixed, is asymptotic to ϕ(c)nlog2n, where ϕ(c) → 1 as c ↓ 1. However, our new bound implies that the cover time for the critical Erdős–Rényi random graph G(n, 1/n) has order n, and shows how the cover time evolves from the critical window to the supercritical phase. Our general estimate also yields the order of the cover time for a variety of other concrete graphs, including critical percolation clusters on the Hamming hypercube {0, 1}n, on high-girth expanders, and on tori ℤdn for fixed large d. This approach also gives a simpler proof of a result of Aldous [2] that the cover time of a uniform labelled tree on k vertices is of order k3/2. For the graphs we consider, our results show that the blanket time, introduced by Winkler and Zuckerman [45], is within a constant factor of the cover time. Finally, we prove that for any connected graph, adding an edge can increase the cover time by at most a factor of 4.
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6

BUCKNUM, MICHAEL J., CHRIS J. PICKARD, IOAN STAMATIN, and EDUARDO A. CASTRO. "ON THE STRUCTURE OF i-CARBON." Journal of Theoretical and Computational Chemistry 05, no. 02 (June 2006): 175–85. http://dx.doi.org/10.1142/s0219633606002209.

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In the carbon science literature, there have been various reports over the past few decades of potentially novel crystalline forms of carbon emerging as nanometer scale fragments recovered from the explosive remnants of heated, shock compressed graphite and other precursors of C . Two nanometric and crystalline forms of C that are particularly prominent in these studies are known as n-diamond and i-carbon forms. In our previous work, we have shown that the commonly observed diffraction pattern of n-diamond nanocrystals, recorded by several research groups around the world, is consistent with the calculated diffraction pattern of a novel form of carbon that we propose to call glitter. Glitter is a tetragonal allotrope of carbon with a calculated density of ~3.08g/cm3, and the density functional theory (DFT) optimized lattice parameters given as a = 0.2560 nm and c = 0.5925 nm. In addition to the diffraction evidence for n-diamond having the glitter structure, the DFT calculated band structure of glitter shows it to be metallic, like the observed electrical characteristics of n-diamond. In this communication, we report on a comparison of the diffraction pattern observed for nanocrystalline i-carbon by the investigative team of Yamada et al. in 1994, with the calculated diffraction pattern of glitter based upon the optimized lattice parameters. The close fit of the latter dataset to that observed for i-carbon, as reported herein, suggests that indeed i-carbon may be of the same structure as n-diamond, and that they both may have the tetragonal glitter structure.
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7

JU, XUE-HAI, and HE-MING XIAO. "A DENSITY FUNCTIONAL THEORY INVESTIGATION ON THE TAUTOMERS AND CRYSTAL OF 2-DIAZO-4,6-DINITROPHENOL." Journal of Theoretical and Computational Chemistry 03, no. 04 (December 2004): 599–607. http://dx.doi.org/10.1142/s0219633604001239.

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Density functional method was applied to the study of the highly efficient primary explosive 2-diazo-4,6-dinitrophenol (DDNP) in both gaseous tautomers and its bulk state. Two stable tautomers were located. It was found that the structure (I) with open diazo, i.e. with linear CNN, is more stable than that with diazo ring tautomer (II) of DDNP. The structure I is in good agreement with the structure in the bulk. The lattice energy is -89.01 kJ/mol, and this value drops to -83.29 kJ/mol when a 50% correction of the basis set superposition error was adopted. The frontier bands are quite flat. The carbon atoms in DDNP make up the upper valence bands. While the lower conduction bands mainly consist of carbon and diazo N atoms. The bond populations of C–N bonds (both C–Nitro and C–Diazo) are much less than those of the other bonds and the detonation may be initiated through the breakdown of C–N bonds.
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8

Arunachalam, Srinivasan, Sourav Chakraborty, Michal Koucký, Nitin Saurabh, and Ronald De Wolf. "Improved Bounds on Fourier Entropy and Min-entropy." ACM Transactions on Computation Theory 13, no. 4 (December 31, 2021): 1–40. http://dx.doi.org/10.1145/3470860.

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Given a Boolean function f:{ -1,1} ^{n}→ { -1,1, define the Fourier distribution to be the distribution on subsets of [n], where each S ⊆ [n] is sampled with probability f ˆ (S) 2 . The Fourier Entropy-influence (FEI) conjecture of Friedgut and Kalai [28] seeks to relate two fundamental measures associated with the Fourier distribution: does there exist a universal constant C > 0 such that H(f ˆ2 ) ≤ C ⋅ Inf (f), where H (fˆ2) is the Shannon entropy of the Fourier distribution of f and Inf(f) is the total influence of f In this article, we present three new contributions toward the FEI conjecture: (1) Our first contribution shows that H(f ˆ2 ) ≤ 2 ⋅ aUC ⊕ (f), where aUC ⊕ (f) is the average unambiguous parity-certificate complexity of f . This improves upon several bounds shown by Chakraborty et al. [20]. We further improve this bound for unambiguous DNFs. We also discuss how our work makes Mansour's conjecture for DNFs a natural next step toward resolution of the FEI conjecture. (2) We next consider the weaker Fourier Min-entropy-influence (FMEI) conjecture posed by O'Donnell and others [50, 53], which asks if H ∞ fˆ2) ≤ C ⋅ Inf(f), where H ∞ fˆ2) is the min-entropy of the Fourier distribution. We show H ∞ (fˆ2) ≤ 2⋅C min ⊕ (f), where C min ⊕ (f) is the minimum parity-certificate complexity of f . We also show that for all ε≥0, we have H ∞ (fˆ2) ≤2 log⁡(∥f ˆ ∥1,ε/(1−ε)), where ∥f ˆ ∥1,ε is the approximate spectral norm of f . As a corollary, we verify the FMEI conjecture for the class of read- k DNFs (for constant k ). (3) Our third contribution is to better understand implications of the FEI conjecture for the structure of polynomials that 1/3-approximate a Boolean function on the Boolean cube. We pose a conjecture: no flat polynomial (whose non-zero Fourier coefficients have the same magnitude) of degree d and sparsity 2 ω(d) can 1/3-approximate a Boolean function. This conjecture is known to be true assuming FEI, and we prove the conjecture unconditionally (i.e., without assuming the FEI conjecture) for a class of polynomials. We discuss an intriguing connection between our conjecture and the constant for the Bohnenblust-Hille inequality, which has been extensively studied in functional analysis.
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9

ADDARIO-BERRY, LOUIGI, SVANTE JANSON, and COLIN McDIARMID. "On the Spread of Random Graphs." Combinatorics, Probability and Computing 23, no. 4 (June 13, 2014): 477–504. http://dx.doi.org/10.1017/s0963548314000248.

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The spread of a connected graph G was introduced by Alon, Boppana and Spencer [1], and measures how tightly connected the graph is. It is defined as the maximum over all Lipschitz functions f on V(G) of the variance of f(X) when X is uniformly distributed on V(G). We investigate the spread for certain models of sparse random graph, in particular for random regular graphs G(n,d), for Erdős–Rényi random graphs Gn,p in the supercritical range p>1/n, and for a ‘small world’ model. For supercritical Gn,p, we show that if p=c/n with c>1 fixed, then with high probability the spread of the giant component is bounded, and we prove corresponding statements for other models of random graphs, including a model with random edge lengths. We also give lower bounds on the spread for the barely supercritical case when p=(1+o(1))/n. Further, we show that for d large, with high probability the spread of G(n,d) becomes arbitrarily close to that of the complete graph $\mathsf{K}_n$.
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10

Jiang, Tao, and Liana Yepremyan. "Supersaturation of even linear cycles in linear hypergraphs." Combinatorics, Probability and Computing 29, no. 5 (June 23, 2020): 698–721. http://dx.doi.org/10.1017/s0963548320000206.

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AbstractA classical result of Erdős and, independently, of Bondy and Simonovits [3] says that the maximum number of edges in an n-vertex graph not containing C2k, the cycle of length 2k, is O(n1+1/k). Simonovits established a corresponding supersaturation result for C2k’s, showing that there exist positive constants C,c depending only on k such that every n-vertex graph G with e(G)⩾ Cn1+1/k contains at least c(e(G)/v(G))2k copies of C2k, this number of copies tightly achieved by the random graph (up to a multiplicative constant).In this paper we extend Simonovits' result to a supersaturation result of r-uniform linear cycles of even length in r-uniform linear hypergraphs. Our proof is self-contained and includes the r = 2 case. As an auxiliary tool, we develop a reduction lemma from general host graphs to almost-regular host graphs that can be used for other supersaturation problems, and may therefore be of independent interest.
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