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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 29 січня 2023

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1

CHEN, Zi-Yun, Jian-Ning SUN, Ren-Ming YUAN, and Wei-Mei JIANG. "Analysis Study on Convective Boundy Layer Eddy Structure in Water Tank by Orthonormal Wavelet." Chinese Journal of Geophysics 47, no. 6 (November 2004): 1085–92. http://dx.doi.org/10.1002/cjg2.591.

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2

Dijk, Nico M. Van. "An Error-Bound Theorem for Approximate Markov Chains." Probability in the Engineering and Informational Sciences 6, no. 3 (July 1992): 413–24. http://dx.doi.org/10.1017/s026996480000262x.

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Анотація:

Recently an error-bound theorem was reported to conclude analytic error bounds for approximate Markov chains. The theorem required a uniform bound for marginal expectations of the approximate model. This note will relax this bound to steady state rather than marginal expectations as of practical interest(i) to simplify verification and/or(ii) to obtain a more accurate error bound.A communication model is studied in detail to support the results.

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3

BLANCHARD, PH, and J. STUBBE. "BOUND STATES FOR SCHRÖDINGER HAMILTONIANS: PHASE SPACE METHODS AND APPLICATIONS." Reviews in Mathematical Physics 08, no. 04 (May 1996): 503–47. http://dx.doi.org/10.1142/s0129055x96000172.

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Properties of bound states for Schrödinger operators are reviewed. These include: bounds on the number of bound states and on the moments of the energy levels, existence and nonexistence of bound states, phase space bounds and semi-classical results, the special case of central potentials, and applications of these bounds in quantum mechanics of many particle systems and dynamical systems. For the phase space bounds relevant to these applications we improve the explicit constants.

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4

Paulavičius, Remigijus, and Julius Žilinskas. "INFLUENCE OF LIPSCHITZ BOUNDS ON THE SPEED OF GLOBAL OPTIMIZATION." Technological and Economic Development of Economy 18, no. 1 (April 10, 2012): 54–66. http://dx.doi.org/10.3846/20294913.2012.661170.

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Global optimization methods based on Lipschitz bounds have been analyzed and applied widely to solve various optimization problems. In this paper a bound for Lipschitz function is proposed, which is computed using function values at the vertices of a simplex and the radius of the circumscribed sphere. The efficiency of a branch and bound algorithm with proposed bound and combinations of bounds is evaluated experimentally while solving a number of multidimensional test problems for global optimization. The influence of different bounds on the performance of a branch and bound algorithm has been investigated.

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5

Pereira, Rajesh, and Mohammad Ali Vali. "Generalizations of the Cauchy and Fujiwara Bounds for Products of Zeros of a Polynomial." Electronic Journal of Linear Algebra 31 (February 5, 2016): 565–71. http://dx.doi.org/10.13001/1081-3810.3333.

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The Cauchy bound is one of the best known upper bounds for the modulus of the zeros of a polynomial. The Fujiwara bound is another useful upper bound for the modulus of the zeros of a polynomial. In this paper, compound matrices are used to derive a generalization of both the Cauchy bound and the Fujiwara bound. This generalization yields upper bounds for the modulus of the product of $m$ zeros of the polynomial.

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6

Anade, Dadja, Jean-Marie Gorce, Philippe Mary, and Samir M. Perlaza. "An Upper Bound on the Error Induced by Saddlepoint Approximations—Applications to Information Theory." Entropy 22, no. 6 (June 20, 2020): 690. http://dx.doi.org/10.3390/e22060690.

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This paper introduces an upper bound on the absolute difference between: ( a ) the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables with finite absolute third moment; and ( b ) a saddlepoint approximation of such CDF. This upper bound, which is particularly precise in the regime of large deviations, is used to study the dependence testing (DT) bound and the meta converse (MC) bound on the decoding error probability (DEP) in point-to-point memoryless channels. Often, these bounds cannot be analytically calculated and thus lower and upper bounds become particularly useful. Within this context, the main results include, respectively, new upper and lower bounds on the DT and MC bounds. A numerical experimentation of these bounds is presented in the case of the binary symmetric channel, the additive white Gaussian noise channel, and the additive symmetric α -stable noise channel.

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7

Kılıçer, Pınar, Elisa Lorenzo García, and Marco Streng. "Primes Dividing Invariants of CM Picard Curves." Canadian Journal of Mathematics 72, no. 2 (May 7, 2019): 480–504. http://dx.doi.org/10.4153/s0008414x18000111.

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AbstractWe give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus 3, our bound is sharp enough for use in explicit constructions of Picard curves.

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8

Ipsen, Ilse C. F. "Relative perturbation results for matrix eigenvalues and singular values." Acta Numerica 7 (January 1998): 151–201. http://dx.doi.org/10.1017/s0962492900002828.

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Анотація:

It used to be good enough to bound absolute of matrix eigenvalues and singular values. Not any more. Now it is fashionable to bound relative errors. We present a collection of relative perturbation results which have emerged during the past ten years.No need to throw away all those absolute error bound, though. Deep down, the derivation of many relative bounds can be based on absolute bounds. This means that relative bounds are not always better. They may just be better sometimes – and exactly when depends on the perturbation.

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9

Li, Yating, and Yaqiang Wang. "Schur Complement-Based Infinity Norm Bounds for the Inverse of GDSDD Matrices." Mathematics 10, no. 2 (January 7, 2022): 186. http://dx.doi.org/10.3390/math10020186.

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Анотація:

Based on the Schur complement, some upper bounds for the infinity norm of the inverse of generalized doubly strictly diagonally dominant matrices are obtained. In addition, it is shown that the new bound improves the previous bounds. Numerical examples are given to illustrate our results. By using the infinity norm bound, a lower bound for the smallest singular value is given.

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10

Ambainis, Andris, Martins Kokainis, Krišjānis Prūsis, Jevgēnijs Vihrovs, and Aleksejs Zajakins. "All Classical Adversary Methods Are Equivalent for Total Functions." ACM Transactions on Computation Theory 13, no. 1 (March 2021): 1–20. http://dx.doi.org/10.1145/3442357.

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We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions and are equal to the fractional block sensitivity fbs( f ). That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. This equivalence also implies that for total functions, the relational adversary is equivalent to a simpler lower bound, which we call rank-1 relational adversary. For partial functions, we show unbounded separations between fbs( f ) and other adversary bounds, as well as between the adversary bounds themselves. We also show that, for partial functions, fractional block sensitivity cannot give lower bounds larger than √ n ⋅ bs( f ), where n is the number of variables and bs( f ) is the block sensitivity. Then, we exhibit a partial function f that matches this upper bound, fbs( f ) = Ω (√ n ⋅ bs( f )).

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11

GATHERAL, JIM, IVAN MATIĆ, RADOŠ RADOIČIĆ, and DAN STEFANICA. "TIGHTER BOUNDS FOR IMPLIED VOLATILITY." International Journal of Theoretical and Applied Finance 20, no. 05 (August 2017): 1750035. http://dx.doi.org/10.1142/s0219024917500352.

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We establish bounds on Black–Scholes implied volatility that improve on the uniform bounds previously derived by Tehranchi. Our upper bound is uniform, while the lower bound holds for most options likely to be encountered in practical applications. We further demonstrate the practical effectiveness of our new bounds by showing how the efficiency of the bisection algorithm is improved for a snapshot of SPX option quotes.

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12

Liu, Qilong, and Yaotang Li. "Bounds for the Z-eigenpair of general nonnegative tensors." Open Mathematics 14, no. 1 (January 1, 2016): 181–94. http://dx.doi.org/10.1515/math-2016-0017.

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AbstractIn this paper, we consider the Z-eigenpair of a tensor. A lower bound and an upper bound for the Z-spectral radius of a weakly symmetric nonnegative irreducible tensor are presented. Furthermore, upper bounds of Z-spectral radius of nonnegative tensors and general tensors are given. The proposed bounds improve some existing ones. Numerical examples are reported to show the effectiveness of the proposed bounds.

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13

Kumabe, Masahiro. "Minimal complementation below uniform upper bounds for the arithmetical degrees." Journal of Symbolic Logic 61, no. 4 (December 1996): 1158–92. http://dx.doi.org/10.2307/2275810.

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Анотація:

This paper was inspired by Lerman [15] in which he proved various properties of upper bounds for the arithmetical degrees. We discuss the complementation property of upper bounds for the arithmetical degrees. In Lerman [15], it is proved that uniform upper bounds for the arithmetical degrees are jumps of upper bounds for the arithmetical degrees. So any uniform upper bound for the arithmetical degrees is not a minimal upper bound for the arithmetical degrees. Given a uniform upper bound a for the arithmetical degrees, we prove a minimal complementation theorem for the upper bounds for the arithmetical degrees below a. Namely, given such a and b < a which is an upper bound for the arithmetical degrees, there is a minimal upper bound for the arithmetical degrees c such that b ∪ c = a. This answers a question in Lerman [15]. We prove this theorem by different methods depending on whether a has a function which is not dominated by any arithmetical function. We prove two propositions (see §1), of which the theorem is an immediate consequence.Our notation is almost standard. Let A ⊕ B = {2n∣n ∈ A} ∪ {2n + 1∣n + 1∣n ∈ B} for any sets A and B. Let ω be the set of nonnegative natural numbers.

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14

Lu, Cheng, Jianxin Chen, and Runyao Duan. "Some bounds on the minimum number of queries required for quantum channel perfect discrimination." Quantum Information and Computation 12, no. 1&2 (January 2012): 138–48. http://dx.doi.org/10.26421/qic12.1-2-9.

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Анотація:

We prove a lower bound on the $q$-maximal fidelities between two quantum channels $\E_0$ and $\E_1$ and an upper bound on the $q$-maximal fidelities between a quantum channel $\E$ and an identity $\I$. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguishability between $\E$ and $\I$ and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating $\E$ and $\I$. Interestingly, in the $2$-dimensional case, both bounds coincide. Based on the optimal perfect discrimination protocol presented in \cite{DFY09}, we can further generalize the lower bound and upper bound to the minimum number of queries to perfectly discriminating $\E$ and $I$ over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels $\E_0$ and $\E_1$ in sequential scheme and over all possible discrimination schemes respectively.

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15

Eichfelder, Gabriele, Peter Kirst, Laura Meng, and Oliver Stein. "A general branch-and-bound framework for continuous global multiobjective optimization." Journal of Global Optimization 80, no. 1 (January 19, 2021): 195–227. http://dx.doi.org/10.1007/s10898-020-00984-y.

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AbstractCurrent generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and by the corresponding termination criteria and node selection steps. In particular, our branch-and-bound concept employs a new enclosure of the set of nondominated points by a union of boxes. On this occasion we also suggest a new discarding test based on a linearization technique. We provide a convergence proof for our general branch-and-bound framework and illustrate the results with numerical examples.

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16

CHITTURI, BHADRACHALAM. "UPPER BOUNDS FOR SORTING PERMUTATIONS WITH A TRANSPOSITION TREE." Discrete Mathematics, Algorithms and Applications 05, no. 01 (March 2013): 1350003. http://dx.doi.org/10.1142/s1793830913500031.

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An upper bound for sorting permutations with an operation estimates the diameter of the corresponding Cayley graph and an exact upper bound equals the diameter. Computing tight upper bounds for various operations is of theoretical and practical (e.g., interconnection networks, genetics) interest. Akers and Krishnamurthy gave a Ω(n! n2) time method that examines n! permutations to compute an upper bound, f(Γ), to sort any permutation with a given transposition tree T, where Γ is the Cayley graph corresponding to T. We compute two intuitive upper bounds γ and δ′ each in O(n2) time for the same, by working solely with the transposition tree. Recently, Ganesan computed β, an estimate of the exact upper bound for the same, in O(n2) time. Our upper bounds are tighter than f(Γ) and β, on average and in most of the cases. For a class of trees, we prove that the new upper bounds are tighter than β and f(Γ).

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17

Murgatroyd, P. N., B. J. Donoghue, and C. D. Pudney. "Reversal of bounds in some dual-bound resistance calculations." IEE Proceedings - Science, Measurement and Technology 141, no. 6 (November 1, 1994): 429–31. http://dx.doi.org/10.1049/ip-smt:19941375.

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18

Moursli, Omar. "Branch and Bound Lower Bounds for the Hybrid Flowshop." IFAC Proceedings Volumes 30, no. 14 (July 1997): 31–36. http://dx.doi.org/10.1016/s1474-6670(17)42693-0.

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19

Hu, Zisheng, and Senlin Xu. "Bounds on the fundamental groups with integral curvature bound." Geometriae Dedicata 134, no. 1 (April 19, 2008): 1–16. http://dx.doi.org/10.1007/s10711-008-9235-3.

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20

Castañeda, Armando, and Sergio Rajsbaum. "New combinatorial topology bounds for renaming: the lower bound." Distributed Computing 22, no. 5-6 (June 9, 2010): 287–301. http://dx.doi.org/10.1007/s00446-010-0108-2.

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21

Marmorino, M. G., J. C. Schug, and C. A. Beattie. "Lower bound problems and bounds to atomic ionization energies." International Journal of Quantum Chemistry 77, no. 4 (2000): 779–84. http://dx.doi.org/10.1002/(sici)1097-461x(2000)77:4<779::aid-qua9>3.0.co;2-j.

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22

Ashbaugh, Mark S., and Pavel Exner. "Lower bounds to bound state energies in bent tubes." Physics Letters A 150, no. 3-4 (November 1990): 183–86. http://dx.doi.org/10.1016/0375-9601(90)90118-8.

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23

Buzdalov, Maxim, Benjamin Doerr, and Mikhail Kever. "The Unrestricted Black-Box Complexity of Jump Functions." Evolutionary Computation 24, no. 4 (December 2016): 719–44. http://dx.doi.org/10.1162/evco_a_00185.

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Анотація:

We analyze the unrestricted black-box complexity of the Jump function classes for different jump sizes. For upper bounds, we present three algorithms for small, medium, and extreme jump sizes. We prove a matrix lower bound theorem which is capable of giving better lower bounds than the classic information theory approach. Using this theorem, we prove lower bounds that almost match the upper bounds. For the case of extreme jump functions, which apart from the optimum reveal only the middle fitness value(s), we use an additional lower bound argument to show that any black-box algorithm does not gain significant insight about the problem instance from the first [Formula: see text] fitness evaluations. This, together with our upper bound, shows that the black-box complexity of extreme jump functions is [Formula: see text].

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24

Moon, Sunyo, and Seungkook Park. "Upper Bound for the Number of Distinct Eigenvalues of a Perturbed Matrix." Electronic Journal of Linear Algebra 34 (February 21, 2018): 115–24. http://dx.doi.org/10.13001/1081-3810.3588.

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In 2016, Farrell presented an upper bound for the number of distinct eigenvalues of a perturbed matrix. Xu (2017), and Wang and Wu (2016) introduced upper bounds which are sharper than Farrell's bound. In this paper, the upper bounds given by Xu, and Wang and Wu are improved.

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25

Chung, Kai-Min, Wei-Chun Kao, Chia-Liang Sun, Li-Lun Wang, and Chih-Jen Lin. "Radius Margin Bounds for Support Vector Machines with the RBF Kernel." Neural Computation 15, no. 11 (November 1, 2003): 2643–81. http://dx.doi.org/10.1162/089976603322385108.

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An important approach for efficient support vector machine (SVM) model selection is to use differentiable bounds of the leave-one-out (loo) error. Past efforts focused on finding tight bounds of loo (e.g., radius margin bounds, span bounds). However, their practical viability is still not very satisfactory. Duan, Keerthi, and Poo (2003) showed that radius margin bound gives good prediction for L2-SVM, one of the cases we look at. In this letter, through analyses about why this bound performs well for L2-SVM, we show that finding a bound whose minima are in a region with small loo values may be more important than its tightness. Based on this principle, we propose modified radius margin bounds for L1-SVM (the other case) where the original bound is applicable only to the hard-margin case. Our modification for L1-SVM achieves comparable performance to L2-SVM. To study whether L1-or L2-SVM should be used, we analyze other properties, such as their differentiability, number of support vectors, and number of free support vectors. In this aspect, L1-SVM possesses the advantage of having fewer support vectors. Their implementations are also different, so we discuss related issues in detail.

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26

MEHRABIAN, ABBAS. "Lower Bounds for the Cop Number when the Robber is Fast." Combinatorics, Probability and Computing 20, no. 4 (April 19, 2011): 617–21. http://dx.doi.org/10.1017/s0963548311000101.

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We consider a variant of the Cops and Robbers game where the robber can movetedges at a time, and show that in this variant, the cop number of ad-regular graph with girth larger than 2t+2 is Ω(dt). By the known upper bounds on the order of cages, this implies that the cop number of a connectedn-vertex graph can be as large as Ω(n2/3) ift≥ 2, and Ω(n4/5) ift≥ 4. This improves the Ω($n^{\frac{t-3}{t-2}}$) lower bound of Frieze, Krivelevich and Loh (Variations on cops and robbers,J. Graph Theory, to appear) when 2 ≤t≤ 6. We also conjecture a general upper boundO(nt/t+1) for the cop number in this variant, generalizing Meyniel's conjecture.

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27

Poupart, Pascal, Kee-Eung Kim, and Dongho Kim. "Closing the Gap: Improved Bounds on Optimal POMDP Solutions." Proceedings of the International Conference on Automated Planning and Scheduling 21 (March 22, 2011): 194–201. http://dx.doi.org/10.1609/icaps.v21i1.13467.

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POMDP algorithms have made significant progress in recent years by allowing practitioners to find good solutions to increasingly large problems. Most approaches (including point-based and policy iteration techniques) operate by refining a lower bound of the optimal value function. Several approaches (e.g., HSVI2, SARSOP, grid-based approaches and online forward search) also refine an upper bound. However, approximating the optimal value function by an upper bound is computationally expensive and therefore tightness is often sacrificed to improve efficiency (e.g., sawtooth approximation). In this paper, we describe a new approach to efficiently compute tighter bounds by i) conducting a prioritized breadth first search over the reachable beliefs, ii) propagating upper bound improvements with an augmented POMDP and iii) using exact linear programming (instead of the sawtooth approximation) for upper bound interpolation. As a result, we can represent the bounds more compactly and significantly reduce the gap between upper and lower bounds on several benchmark problems.

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28

Sargolzahi, Iman, Sayyed Yahya Mirafzali, and Mohsen Sarbishaei. "Measurable lower bounds on concurrence." Quantum Information and Computation 11, no. 1&2 (January 2011): 79–94. http://dx.doi.org/10.26421/qic11.1-2-6.

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Анотація:

We derive measurable lower bounds on concurrence of arbitrary mixed states, for both bipartite and multipartite cases. First, we construct measurable lower bonds on the \textit{purely algebraic} bounds of concurrence [F. Mintert \textit{et al.} (2004), Phys. Rev. lett., 92, 167902]. Then, using the fact that the sum of the square of the algebraic bounds is a lower bound of the squared concurrence, we sum over our measurable bounds to achieve a measurable lower bound on concurrence. With two typical examples, we show that our method can detect more entangled states and also can give sharper lower bonds than the similar ones.

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29

Chen, Yuansi. "An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture." Geometric and Functional Analysis 31, no. 1 (February 2021): 34–61. http://dx.doi.org/10.1007/s00039-021-00558-4.

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AbstractWe prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency $$d^{-o_d(1)}$$ d - o d ( 1 ) . When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency $$d^{-1/4}$$ d - 1 / 4 . Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many implications, including improvements of the current best bounds in Bourgain’s slicing conjecture and in the thin-shell conjecture, better concentration inequalities for Lipschitz functions of log-concave measures and better mixing time bounds for MCMC sampling algorithms on log-concave measures.

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30

JOHNSON, CHARLES R., and YULIN ZHANG. "ON THE POSSIBLE RANKS AMONG MATRICES WITH A GIVEN PATTERN." Discrete Mathematics, Algorithms and Applications 02, no. 03 (September 2010): 363–77. http://dx.doi.org/10.1142/s1793830910000711.

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Анотація:

Given are tight upper and lower bounds for the minimum rank among all matrices with a prescribed zero–nonzero pattern. The upper bound is based upon solving for a matrix with a given null space and, with optimal choices, produces the correct minimum rank. It leads to simple, but often accurate, bounds based upon overt statistics of the pattern. The lower bound is also conceptually simple. Often, the lower and an upper bound coincide, but examples are given in which they do not.

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31

Liu, Tongliang, Dacheng Tao, and Dong Xu. "Dimensionality-Dependent Generalization Bounds for k-Dimensional Coding Schemes." Neural Computation 28, no. 10 (October 2016): 2213–49. http://dx.doi.org/10.1162/neco_a_00872.

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Анотація:

The k-dimensional coding schemes refer to a collection of methods that attempt to represent data using a set of representative k-dimensional vectors and include nonnegative matrix factorization, dictionary learning, sparse coding, k-means clustering, and vector quantization as special cases. Previous generalization bounds for the reconstruction error of the k-dimensional coding schemes are mainly dimensionality-independent. A major advantage of these bounds is that they can be used to analyze the generalization error when data are mapped into an infinite- or high-dimensional feature space. However, many applications use finite-dimensional data features. Can we obtain dimensionality-dependent generalization bounds for k-dimensional coding schemes that are tighter than dimensionality-independent bounds when data are in a finite-dimensional feature space? Yes. In this letter, we address this problem and derive a dimensionality-dependent generalization bound for k-dimensional coding schemes by bounding the covering number of the loss function class induced by the reconstruction error. The bound is of order [Formula: see text], where m is the dimension of features, k is the number of the columns in the linear implementation of coding schemes, and n is the size of sample, [Formula: see text] when n is finite and [Formula: see text] when n is infinite. We show that our bound can be tighter than previous results because it avoids inducing the worst-case upper bound on k of the loss function. The proposed generalization bound is also applied to some specific coding schemes to demonstrate that the dimensionality-dependent bound is an indispensable complement to the dimensionality-independent generalization bounds.

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32

Nedovic, M., and Lj Cvetkovic. "Norm bounds for the inverse and error bounds for linear complementarity problems for {P1,P2}-Nekrasov matrices." Filomat 35, no. 1 (2021): 239–50. http://dx.doi.org/10.2298/fil2101239n.

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Анотація:

{P1,P2}-Nekrasov matrices represent a generalization of Nekrasov matrices via permutations. In this paper, we obtained an error bound for linear complementarity problems for fP1; P2g-Nekrasov matrices. Numerical examples are given to illustrate that new error bound can give tighter results compared to already known bounds when applied to Nekrasov matrices. Also, we presented new max-norm bounds for the inverse of {P1,P2}-Nekrasov matrices in the block case, considering two different types of block generalizations. Numerical examples show that new norm bounds for the block case can give tighter results compared to already known bounds for the point-wise case.

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33

Obradovic, Milutin, Derek Thomas, and Nikola Tuneski. "On the difference of coefficients of univalent functions." Filomat 35, no. 11 (2021): 3653–61. http://dx.doi.org/10.2298/fil2111653o.

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For f ? S, the class of normalized functions, analytic and univalent in the unit disk D and given by f(z)=z+?? n=2 an Zn for z ? D, we give an upper bound for the coefficient difference |a4|-|a3| when f ? S. This provides an improved bound in the case n = 3 of Grinspan?s 1976 general bound ||an+1|-|an|| ?3.61.... Other coefficients bounds, and bounds for the second and third Hankel determinants when f ? S are found when either a2 = 0, or a3 = 0.

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34

Bertsimas, Dimitris, Karthik Natarajan, and Chung-Piaw Teo. "TIGHT BOUNDS ON EXPECTED ORDER STATISTICS." Probability in the Engineering and Informational Sciences 20, no. 4 (September 19, 2006): 667–86. http://dx.doi.org/10.1017/s0269964806060414.

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In this article, we study the problem of finding tight bounds on the expected value of the kth-order statistic E [Xk:n] under first and second moment information on n real-valued random variables. Given means E [Xi] = μi and variances Var[Xi] = σi2, we show that the tight upper bound on the expected value of the highest-order statistic E [Xn:n] can be computed with a bisection search algorithm. An extremal discrete distribution is identified that attains the bound, and two closed-form bounds are proposed. Under additional covariance information Cov[Xi,Xj] = Qij, we show that the tight upper bound on the expected value of the highest-order statistic can be computed with semidefinite optimization. We generalize these results to find bounds on the expected value of the kth-order statistic under mean and variance information. For k < n, this bound is shown to be tight under identical means and variances. All of our results are distribution-free with no explicit assumption of independence made. Particularly, using optimization methods, we develop tractable approaches to compute bounds on the expected value of order statistics.

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35

Guo, Qianping, Jinsong Leng, Houbiao Li, and Carlo Cattani. "Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices." Mathematics 7, no. 2 (February 3, 2019): 147. http://dx.doi.org/10.3390/math7020147.

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In this paper, an upper bound on the spectral radius ρ ( A ∘ B ) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ ( C ★ D ) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results.

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36

Denys, Aurélie, Peter Brown, and Anthony Leverrier. "Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation." Quantum 5 (September 13, 2021): 540. http://dx.doi.org/10.22331/q-2021-09-13-540.

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Анотація:

We establish an analytical lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation of coherent states. Previously, such bounds were only available for protocols with a Gaussian modulation, and numerical bounds existed in the case of simple phase-shift-keying modulations. The latter bounds were obtained as a solution of convex optimization problems and our new analytical bound matches the results of Ghorai et al. (2019), up to numerical precision. The more relevant case of quadrature amplitude modulation (QAM) could not be analyzed with the previous techniques, due to their large number of coherent states. Our bound shows that relatively small constellation sizes, with say 64 states, are essentially sufficient to obtain a performance close to a true Gaussian modulation and are therefore an attractive solution for large-scale deployment of continuous-variable quantum key distribution. We also derive similar bounds when the modulation consists of arbitrary states, not necessarily pure.

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37

Corgini, M., and D. P. Sankovich. "Rigorous Estimates for Correlation Functions and Existence of Phase Transitions in Some Models of Interacting Bosons." International Journal of Modern Physics B 11, no. 28 (November 10, 1997): 3329–41. http://dx.doi.org/10.1142/s0217979297001635.

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Using the so-called method of infrared bounds and a Roepstorff's inequality we obtain a lower bound for the amount of condensate and derive an upper bound for the anomalous average [Formula: see text] of Huang–Davies (HD) model. A lower bound for the static structure factor is also obtained. We generalize the HD model and prove the existence of Bose condensation for this kind of model systems. Finally we derived upper and lower bounds for correlation functions associated to a system of Fermi-particles interacting with a field of phonons.

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38

Xiong, Ke, Yu Zhang, Shenghui Wang, Zhifei Zhang, and Zhengding Qiu. "Worst case performance bounds for multimedia flows in QoS-enhanced TNPOSS network." Computer Science and Information Systems 8, no. 3 (2011): 890–908. http://dx.doi.org/10.2298/csis101201033x.

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Network performance bounds, including the maximal end-toend (E2E) delay, the maximal jitter and the maximal buffer backlog amount, are very important for network QoS control, buffer management and network optimization. QoS-enhanced To Next-hop Port Sequence Switch (QTNPOSS) is a recently proposed transmission scheme to achieve scalable fast forwarding for multimedia applications. However, the existing E2E delay bound of QTNPOSS network is not tight. To this end, this paper presents a lower E2E delay bound for QTNPOSS networks by using the network calculus theory, where the inherent properties (e.g. packet length and peak rate) of the flow are taken into account. Besides, the buffer size bound and the jitter bound of QTNPOSS network are also presented. Moreover, by extensive numerical experiments, we discuss the influences of the Long Range Dependence (LDR) traffic property and the Weighted Fair Queuing (WFQ) weight on the proposed network performance bounds. The results show that the WFQ weight influences the bounds more greatly than the LRD property.

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39

Liao, Qunying, and Juan Zhu. "A Note on Optimal Constant Dimension Codes." International Journal of Foundations of Computer Science 26, no. 01 (January 2015): 143–52. http://dx.doi.org/10.1142/s0129054115500070.

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In this paper, we study bounds for optimal constant dimension codes further. By revising the construction for constant dimension codes in [4], we improve some bounds on q-ary constant dimension codes in some cases. By combinatorial method, we show that there exists no optimal constant dimension code Aq[n, 2δ, k] meeting both Wang-Xing-Safavi-Naini-Bound and the maximal distance separate bound simultaneously.

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40

Zhao, Jianxing, та Caili Sang. "New bounds for the minimum eigenvalue of 𝓜-tensors". Open Mathematics 15, № 1 (16 березня 2017): 296–303. http://dx.doi.org/10.1515/math-2017-0018.

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Abstract A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.

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41

Hashimoto, Kazunari, and Chikako Uchiyama. "Effect of Quantum Coherence on Landauer’s Principle." Entropy 24, no. 4 (April 13, 2022): 548. http://dx.doi.org/10.3390/e24040548.

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Landauer’s principle provides a fundamental lower bound for energy dissipation occurring with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound (entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy (thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system–reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system–reservoir correlation, which may cause an additional source of energetic cost for the erasure.

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42

Akhmanova, Dana M., Nazgul K. Shamatayeva, and L. Zh Kasymova. "On boundary value problems for essentially loaded parabolic equations in bounded domains." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, no. 2 (June 30, 2020): 6–14. http://dx.doi.org/10.31489/2020m2/6-14.

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43

Green, Ben, and Terence Tao. "NEW BOUNDS FOR SZEMERÉDI'S THEOREM, III: A POLYLOGARITHMIC BOUND FOR." Mathematika 63, no. 3 (January 2017): 944–1040. http://dx.doi.org/10.1112/s0025579317000316.

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44

Eldar, Yonina C. "MSE Bounds With Affine Bias Dominating the CramÉr–Rao Bound." IEEE Transactions on Signal Processing 56, no. 8 (August 2008): 3824–36. http://dx.doi.org/10.1109/tsp.2008.925584.

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45

UENO, KENYA. "BREAKING THE RECTANGLE BOUND BARRIER AGAINST FORMULA SIZE LOWER BOUNDS." International Journal of Foundations of Computer Science 24, no. 08 (December 2013): 1339–54. http://dx.doi.org/10.1142/s0129054113500378.

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Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, which gives a formula size lower bound by showing a feasible solution of the dual problem of its LP-relaxation. As extensions of the LP bound, we introduce novel general techniques proving formula size lower bounds, named a quasi-additive bound and the Sherali-Adams bound. While the Sherali-Adams bound is potentially strong enough to give a lower bound matching to the rectangle bound, we prove that the quasi-additive bound can surpass the rectangle bound. We also reveal that the quasi-additive bound is potentially strong enough to prove the matching formula size lower bound.

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46

Fletcher, Roger, and Sven Leyffer. "Numerical Experience with Lower Bounds for MIQP Branch-And-Bound." SIAM Journal on Optimization 8, no. 2 (May 1998): 604–16. http://dx.doi.org/10.1137/s1052623494268455.

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47

El-Yaniv, R., and D. Pechyony. "Transductive Rademacher Complexity and its Applications." Journal of Artificial Intelligence Research 35 (June 22, 2009): 193–234. http://dx.doi.org/10.1613/jair.2587.

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We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher averages for particular algorithms, in terms of their "unlabeled-labeled" representation. This technique is relevant to many advanced graph-based transductive algorithms and we demonstrate its effectiveness by deriving error bounds to three well known algorithms. Finally, we present a new PAC-Bayesian bound for mixtures of transductive algorithms based on our Rademacher bounds.

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48

Bakir, Ilke, Natashia Boland, Brian Dandurand, and Alan Erera. "Sampling Scenario Set Partition Dual Bounds for Multistage Stochastic Programs." INFORMS Journal on Computing 32, no. 1 (January 2020): 145–63. http://dx.doi.org/10.1287/ijoc.2018.0885.

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We consider multistage stochastic programming problems in which the random parameters have finite support, leading to optimization over a finite scenario set. There has been recent interest in dual bounds for such problems, of two types. One, known as expected group subproblem objective (EGSO) bounds, require solution of a group subproblem, which optimizes over a subset of the scenarios, for all subsets of the scenario set that have a given cardinality. Increasing the subset cardinality in the group subproblem improves bound quality, (EGSO bounds form a hierarchy), but the number of group subproblems required to compute the bound increases very rapidly. Another is based on partitions of the scenario set into subsets. Combining the values of the group subproblems for all subsets in a partition yields a partition bound. In this paper, we consider partitions into subsets of (nearly) equal cardinality. We show that the expected value of the partition bound over all such partitions also forms a hierarchy. To make use of these bounds in practice, we propose random sampling of partitions and suggest two enhancements to the approach: sampling partitions that align with the multistage scenario tree structure and use of an auxiliary optimization problem to discover new best bounds based on the values of group subproblems already computed. We establish the effectiveness of these ideas with computational experiments on benchmark problems. Finally, we give a heuristic to save computational effort by ceasing computation of a partition partway through if it appears unpromising.

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49

Wipf, A. "Upper and lower bounds for the bounce action." Journal of Physics A: Mathematical and General 18, no. 13 (September 11, 1985): 2521–29. http://dx.doi.org/10.1088/0305-4470/18/13/027.

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50

Nataraj, P. S. V., and Gautam Sardar. "Computation of QFT Bounds for Robust Sensitivity and Gain-Phase Margin Specifications." Journal of Dynamic Systems, Measurement, and Control 122, no. 3 (February 3, 1999): 528–34. http://dx.doi.org/10.1115/1.1286867.

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Algorithms are presented for generation of QFT controller bounds to achieve robust sensitivity reduction and gain-phase margin specifications. The proposed algorithms use quadratic constraints and interval plant templates to derive the bounds, and present several improvements over existing QFT bound generation algorithms: (1) The bounds can be generated over interval controller phases, as opposed to discrete controller phases in existing QFT algorithms. This feature essentially solves the safety problems associated with phase discretization process in QFT bound generation; (2) The generated bounds are guaranteed to be safe and reliable, even for very coarse interval templates (of poor accuracy), and despite all kinds of computational errors; (3) Inner as well as outer enclosures of the exact bound values can be obtained using the proposed algorithms. Such enclosures directly provide upper bounds on the error in the generated results for any given interval template; (4) A very significant reduction in computational effort—typically, reduction in flops by 2–3 orders of magnitude is achieved; (5) The vertical line (or rectangle) nature of plant templates exhibited in the low and high frequency ranges can be readily exploited to obtain bounds with very little effort; (6) The number of flops required to generate the bounds for any given template can be estimated closely a priori; (7) The (entire) algorithms can be programmed using vectorized operations, resulting in small execution times. [S0022-0434(00)02403-5]

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