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Добірка наукової літератури з теми "Condition numbers of matrices"

Автор: Grafiati
Опубліковано: 28 вересня 2022
Оновлено: 28 січня 2023

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Зміст

  1. Статті в журналах
  2. Дисертації
  3. Книги
  4. Частини книг
  5. Тези доповідей конференцій
  6. Звіти організацій

Статті в журналах з теми "Condition numbers of matrices":

1

Szarek, Stanislaw J. "Condition numbers of random matrices." Journal of Complexity 7, no. 2 (June 1991): 131–49. http://dx.doi.org/10.1016/0885-064x(91)90002-f.

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2

Chen, Zizhong, and Jack J. Dongarra. "Condition Numbers of Gaussian Random Matrices." SIAM Journal on Matrix Analysis and Applications 27, no. 3 (January 2005): 603–20. http://dx.doi.org/10.1137/040616413.

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3

Andersen, L. S., and J. L. Volakis. "Condition Numbers for Various Fem Matrices." Journal of Electromagnetic Waves and Applications 13, no. 12 (January 1999): 1663–79. http://dx.doi.org/10.1163/156939399x00105.

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4

Viswanath, D., and L. N. Trefethen. "Condition Numbers of Random Triangular Matrices." SIAM Journal on Matrix Analysis and Applications 19, no. 2 (April 1998): 564–81. http://dx.doi.org/10.1137/s0895479896312869.

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5

Gohberg, I., and I. Koltracht. "Condition numbers for functions of matrices." Applied Numerical Mathematics 12, no. 1-3 (May 1993): 107–17. http://dx.doi.org/10.1016/0168-9274(93)90114-7.

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6

Edelman, Alan. "Eigenvalues and Condition Numbers of Random Matrices." SIAM Journal on Matrix Analysis and Applications 9, no. 4 (October 1988): 543–60. http://dx.doi.org/10.1137/0609045.

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7

Cheung, Dennis, and Felipe Cucker. "Componentwise Condition Numbers of Random Sparse Matrices." SIAM Journal on Matrix Analysis and Applications 31, no. 2 (January 2009): 721–31. http://dx.doi.org/10.1137/080729463.

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8

Charpentier, S., K. Fouchet, O. Szehr, and R. Zarouf. "Condition numbers of matrices with given spectrum." Analysis and Mathematical Physics 9, no. 3 (May 21, 2019): 971–90. http://dx.doi.org/10.1007/s13324-019-00328-4.

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9

Böttcher, A., and S. M. Grudsky. "Structured condition numbers of large Toeplitz matrices are rarely better than usual condition numbers." Numerical Linear Algebra with Applications 12, no. 2-3 (September 29, 2004): 95–102. http://dx.doi.org/10.1002/nla.401.

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10

De Terán, Fernando, Froilán M. Dopico, and Javier Pérez. "Condition numbers for inversion of Fiedler companion matrices." Linear Algebra and its Applications 439, no. 4 (August 2013): 944–81. http://dx.doi.org/10.1016/j.laa.2012.09.020.

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Статті в журналах Дисертації Книги

Дисертації з теми "Condition numbers of matrices":

1

Edelman, Alan. "Eigenvalues and condition numbers of random matrices." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14322.

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2

Uwamariya, Denise. "Large deviations of condition numbers of random matrices." Licentiate thesis, Linköpings universitet, Tillämpad matematik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-175751.

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Random matrix theory has found many applications in various fields such as physics, statistics, number theory and so on. One important approach of studying random matrices is based on their spectral properties. In this thesis, we investigate the limiting behaviors of condition numbers of suitable random matrices in terms of large deviations. The thesis is divided into two parts. Part I, provides to the readers an short introduction on the theory of large deviations, some spectral properties of random matrices, and a summary of the results we derived, and in Part II, two papers are appended. In the first paper, we study the limiting behaviors of the 2-norm condition number of p x n random matrix in terms of large deviations for large n and p being fixed or p = p(n) → ∞ with p(n) = o(n). The entries of the random matrix are assumed to be i.i.d. whose distribution is quite general (namely sub- Gaussian distribution). When the entries are i.i.d. normal random variables, we even obtain an application in statistical inference. The second paper deals with the β-Laguerre (or Wishart) ensembles with a general parameter β > 0. There are three special cases β = 1, β = 2 and β = 4 which are called, separately, as real, complex and quaternion Wishart matrices. In the paper, large deviations of the condition number are achieved as n → ∞, while p is either fixed or p = p(n) → ∞ with p(n) = o(n/ln(n)).
3

Böttcher, A., and S. M. Grudsky. "Estimates for the condition numbers of large semi-definite Toeplitz matrices." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801238.

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This paper is devoted to asymptotic estimates for the condition numbers $\kappa(T_n(a))=||T_n(a)|| ||T_n^(-1)(a)||$ of large $n\cross n$ Toeplitz matrices $T_N(a)$ in the case where $\alpha \element L^\infinity$ and $Re \alpha \ge 0$ . We describe several classes of symbols $\alpha$ for which $\kappa(T_n(a))$ increases like $(log n)^\alpha, n^\alpha$ , or even $e^(\alpha n)$ . The consequences of the results for singular values, eigenvalues, and the finite section method are discussed. We also consider Wiener-Hopf integral operators and multidimensional Toeplitz operators.
4

Arslan, Bahar. "Functions of structured matrices." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/functions-of-structured-matrices(75511801-f8b8-4ac3-9434-35f88b1d0bb0).html.

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The growing interest in computing structured matrix functions stems from the fact that preserving and exploiting the structure of matrices can help us gain physically meaningful solutions with less computational cost and memory requirement. The work presented here is divided into two parts. The first part deals with the computation of functions of structured matrices. The second part is concerned with the structured error analysis in the computation of matrix functions. We present algorithms applying the inverse scaling and squaring method and using the Schur-like form of the symplectic matrices as an alternative to the algorithms using the Schur decomposition to compute the logarithm of symplectic matrices. There are two main calculations in the inverse scaling and squaring method: taking a square root and evaluating the Padé approximants. Numerical experiments suggest that using the Schur-like form with the structure preserving iterations for the square root helps us to exploit the Hamiltonian structure of the logarithm of symplectic matrices. Some type of matrices are nearly structured. We discuss the conditions for using the nearest structured matrix to the nearly structured one by analysing the forward error bounds. Since the structure preserving algorithms for computing the functions of matrices provide advantages in terms of accuracy and data storage we suggest to compute the function of the nearest structured matrix. The analysis is applied to the nearly unitary, nearly Hermitian and nearly positive semi-definite matrices for the matrix logarithm, square root, exponential, cosine and sine functions. It is significant to investigate the effect of the structured perturbations in the sensitivity analysis of matrix functions. We study the structured condition number of matrix functions defined between smooth square matrix manifolds. We develop algorithms computing and estimating the structured condition number. We also present the lower and upper bounds on the structured condition number, which are cheaper to compute than the "exact" structured condition number. We observe that the lower bounds give a good estimation for the structured condition numbers. Comparing the structured and unstructured condition number reveals that they can differ by several orders of magnitude. Having discussed how to compute the structured condition number of matrix functions defined between smooth square matrix manifolds we apply the theory of structured condition numbers to the structured matrix factorizations. We measure the sensitivity of matrix factors to the structured perturbations for the structured polar decomposition, structured sign factorization and the generalized polar decomposition. Finally, we consider the unstructured perturbation analysis for the canonical generalized polar decomposition by using three different methods. Apart from theoretical aspect of the perturbation analysis, perturbation bounds obtained from these methods are compared numerically and our findings show an improvement on the sharpness of the perturbation bounds in the literature.
5

Nagata, Munehiro. "Studies on Accurate Singular Value Decomposition for Bidiagonal Matrices." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215686.

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原著論文リスト[A1]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9607-5.”. [A2]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s10092-013-0085-5.”, [A3]: DOI“10.1016/j.camwa.2015.11.022”
Kyoto University (京都大学)
0048
新制・課程博士
博士(情報学)
甲第19859号
情博第610号
新制||情||106(附属図書館)
32895
京都大学大学院情報学研究科数理工学専攻
(主査)教授 中村 佳正, 教授 矢ｹ崎 一幸, 教授 山下 信雄
学位規則第4条第1項該当
6

Meinke, Ashley Marie. "Fibonacci Numbers and Associated Matrices." Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1310588704.

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7

Segura, ugalde Esteban. "Computation of invariant pairs and matrix solvents." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0045/document.

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Cette thèse porte sur certains aspects symboliques-numériques du problème des paires invariantes pour les polynômes de matrices. Les paires invariantes généralisent la définition de valeur propre / vecteur propre et correspondent à la notion de sous-espaces invariants pour le cas nonlinéaire. Elles trouvent leurs applications dans le calcul numérique de plusieurs valeurs propres d’un polynôme de matrices; elles présentent aussi un intérêt dans le contexte des systèmes différentiels. En utilisant une approche basée sur les intégrales de contour, nous déterminons des expressions du nombre de conditionnement et de l’erreur rétrograde pour le problème du calcul des paires invariantes. Ensuite, nous adaptons la méthode des moments de Sakurai-Sugiura au calcul des paires invariantes et nous étudions le comportement de la version scalaire et par blocs de la méthode en présence de valeurs propres multiples. Le résultats obtenus à l’aide des approches directes peuvent éventuellement être améliorés numériquement grâce à une méthode itérative: nous proposons ici une comparaison de deux variantes de la méthode de Newton appliquée aux paires invariantes. Le problème des solvants de matrices est très proche de celui des paires invariants. Le résultats présentés ci-dessus sont donc appliqués au cas des solvants pour obtenir des expressions du nombre de conditionnement et de l’erreur, et un algorithme de calcul basé sur la méthode des moments. De plus, nous étudions le lien entre le problème des solvants et la transformation des polynômes de matrices en forme triangulaire
In this thesis, we study some symbolic-numeric aspects of the invariant pair problem for matrix polynomials. Invariant pairs extend the notion of eigenvalue-eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. They have applications in the numeric computation of several eigenvalues of a matrix polynomial; they also present an interest in the context of differential systems. Here, a contour integral formulation is applied to compute condition numbers and backward errors for invariant pairs. We then adapt the Sakurai-Sugiura moment method to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues, and we analyze the behavior of the scalar and block versions of the method in presence of different multiplicity patterns. Results obtained via direct approaches may need to be refined numerically using an iterative method: here we study and compare two variants of Newton’s method applied to the invariant pair problem. The matrix solvent problem is closely related to invariant pairs. Therefore, we specialize our results on invariant pairs to the case of matrix solvents, thus obtaining formulations for the condition number and backward errors, and a moment-based computational approach. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials
8

Fouchet, Karine. "Powers of Blaschke factors and products : Fourier coefficients and applications." Thesis, Aix-Marseille, 2021. http://www.theses.fr/2021AIXM0647.

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Dans cette thèse, nous calculons les formules asymptotiques pour n grand, des coefficients de Fourier de la puissance n ième d'un facteur de Blaschke, permettant de prolonger et d'affiner les estimations déjà existantes. Pour cela, nous utilisons des outils classiques d'analyse asymptotique: la méthode de la phase stationnaire et celle de la descente la plus raide. Puis en application, nous construisons des fonctions fortement annulaires dont les coefficients de Taylor satisfont des propriétés de sommation nous permettant de généraliser et d'affiner les résultats de D.D. Bonar, F.W. Carroll et G. Piranian (1977). En utilisant des polynômes plats, nous élaborons aussi une autre construction de telles fonctions à partir d'un théorème de E. Bombieri et J. Bourgain (2009). Par ailleurs, nous obtenons une majoration asymptotiquement exacte, pour n grand, de la suite (\widehat{B^n} (k))_{k \geq 0} des coefficients de Fourier de la puissance n ième d'un produit de Blaschke fini quelconque B, que nous appliquerons dans la dernière partie de la thèse à une question d'analyse matricielle/théorie des opérateurs, énoncée par J. J. Schäffer en 1970. Nous élaborons aussi des exemples constructifs de produits de Blaschke finis qui atteignent nos majorants. Enfin nous étudions le conditionnement de matrices T \in \mathcal{M}_n(\mathbb{C}) pour n grand, matrices dont le spectre est donné et qui agissent sur un espace de Hilbert ou de Banach, en particulier pour les matrices de Kreiss. Dans le cas banachique, nous utilisons notre majoration des \widehat{B^n}(k) pour construire des matrices de spectres donnés arbitraires réfutant la conjecture de Schäffer
In this thesis we first compute asymptotic formulas for Fourier coefficients of the n th-power of a Blaschke factor as n gets large which extend and sharpen known estimates on those coefficients. To perform this study we use standard tools of asymptotic analysis: the so-called method of the stationary phase and the method of the steepest descent. Next as an application of our asymptotic formulas we construct strongly annular functions with Taylor coefficients satisfying sharp summation properties. This allows us to generalize and sharpen results by D.D. Bonar, F.W. Carroll and G. Piranian (1977). Making use of properties of flat polynomials, we also present another construction of such functions built on a theorem by E. Bombieri and J. Bourgain (2009). In another part of the thesis we obtain sharp upper bounds as n gets large, on the sequence (\widehat{B^{n}}(k))_{k\geq0} of the Fourier coefficients of the n th-power of an arbitrary finite Blaschke product B, which we apply in the last part of the thesis to a question raised by J.J. Schäffer (1970) in matrix analysis/operator theory. We also provide constructive examples of finite Blaschke products that achieve our upper bounds. The last chapter is dedicated to the study of the condition numbers of large matrices T\in\mathcal{M}_{n}(\mathbb{C}) with given spectrum acting on a Hilbert space or on a Banach space, espacially for some specific classes of matrices, the so-called Kreiss matrices. In the Banach case, we use our upper bound on (\widehat{B^{n}}(k))_{k\geq0} where B is arbitrary to exhibit matrices with arbitrary given spectrum refuting Schäffer's conjecture
9

Hofmann, B., and G. Fleischer. "Stability Rates for Linear Ill-Posed Problems with Convolution and Multiplication Operators." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800987.

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In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.
10

Núñez, Araya Manuel A. (Manuel Adolfo) 1964. "Condition numbers and properties of central trajectories in convex programming." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/10214.

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Книги з теми "Condition numbers of matrices":

1

Guattery, Stephen. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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2

Smyth, W. Franklin. Analytical chemistry of complex matrices. Chichester [England]: Wiley, 1996.

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3

Vavasis, Stephen A. Condition numbers for polyhedra with real number data. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1993.

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4

Papillon, Vincent. Vecteurs, matrices et nombres complexes. Mont-Royal, Québec: Modulo, 1993.

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5

Demmel, James. On condition numbers and the distance to the nearest ill-posed problem. New York: Courant Institute of Mathematical Sciences, New York University, 1985.

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6

Demmel, James W. On condition numbers and the distance to the nearest ill-posed problem. New York: Courant Institute of Mathematical Sciences, New York University, 1987.

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7

Benjamin, Arthur. Discrete mathematics. Chantilly, VA: The Teaching Company, 2009.

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8

Charles, Nordhoff. The communistic societies of the United States: From personal visit and observation : including detailed accounts of the Economists, Zoarites, Shakers, the Amana, Oneida, Bethel, Aurora, Icarian and other existing societies : their religis creeds, social practices, numbers, industries, and present condition. New York: Harper, 1990.

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9

Canada. Parliament. House of Commons. Standing Committee on Human Resources Development and the Status of Persons with Disabilities. Beyond the numbers : the future of the social insurance number system in Canada : report of the Standing Committee on Human Resources Development and the Status of Persons with Disabilities =: Au-delà des chiffres : l'avenir du numéro d'assurance sociale au Canada : rapport du Comité permanent du développement des ressources humaines et de la condition des personnes handicapées. Ottawa, Ont: Minister of Public Works and Government Services Canada = Ministre des travaux publics et services gouvernementaux Canada, 1999.

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10

Moore, Emily H. Difference sets: Connecting algebra, combinatorics and geometry. Providence, Rhode Island: American Mathematical Society, 2013.

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Частини книг з теми "Condition numbers of matrices":

1

Böttcher, Albrecht, and Sergei M. Grudsky. "Condition Numbers." In Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis, 52–77. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8395-5_4.

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2

Böttcher, Albrecht, and Sergei M. Grudsky. "Condition Numbers." In Toeplitz Matrices, Asymptotic Linear Algebra and Functional Analysis, 52–77. Gurgaon: Hindustan Book Agency, 2000. http://dx.doi.org/10.1007/978-93-86279-04-0_4.

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3

Branham, Richard L. "Matrices, Norms, and Condition Numbers." In Scientific Data Analysis, 20–33. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-3362-6_2.

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4

Koltracht, I., and P. Lancaster. "Condition Numbers of Toeplitz and Block Toeplitz Matrices." In I. Schur Methods in Operator Theory and Signal Processing, 271–300. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5483-2_11.

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5

Seidel, Markus. "Norms, Condition Numbers and Pseudospectra of Convolution Type Operators on Intervals." In Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics, 663–80. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49182-0_27.

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6

Zlatev, Zahari. "Condition Number Estimators in a Sparse Matrix Software." In Computational Methods for General Sparse Matrices, 155–72. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-017-1116-6_9.

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7

Rump, Siegfried M., and Hiroshi Sekigawa. "The Ratio Between the Toeplitz and the Unstructured Condition Number." In Numerical Methods for Structured Matrices and Applications, 397–419. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-8996-3_18.

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8

McArthur, Kelly M. "Condition Numbers for the Sinc Matrices Associated with Discretizing the Second-Order Differential Operator." In Computation and Control III, 285–99. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0321-6_21.

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9

Litvak, Alexander E., Konstantin Tikhomirov, and Nicole Tomczak-Jaegermann. "Small Ball Probability for the Condition Number of Random Matrices." In Lecture Notes in Mathematics, 125–37. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46762-3_5.

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10

Diao, Huaian, and Yimin Wei. "On the Level-2 Condition Number for Moore–Penrose Inverse in Hilbert Space." In Combinatorial Matrix Theory and Generalized Inverses of Matrices, 159–69. India: Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1053-5_13.

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Тези доповідей конференцій з теми "Condition numbers of matrices":

1

Mishachev, Nikolai, Anatoly Shmyrin, and Roman Popov. "Three Versions of Sequential Projection Algorithm and Condition Numbers of Large Random Matrices." In 2020 2nd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA). IEEE, 2020. http://dx.doi.org/10.1109/summa50634.2020.9280606.

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2

Chan, Stanley H., Ankit K. Jain, Truong Q. Nguyen, and Edmund Y. Lam. "Bounds for the Condition Numbers of Spatially-variant Convolution Matrices in Image Restoration Problems." In Signal Recovery and Synthesis. Washington, D.C.: OSA, 2011. http://dx.doi.org/10.1364/srs.2011.sma4.

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3

Nishi, Tetsuo, Siegfried Rump, and Shin'ichi Oishi. "A consideration on the condition number of extremely ill-conditioned matrices." In 2013 European Conference on Circuit Theory and Design (ECCTD). IEEE, 2013. http://dx.doi.org/10.1109/ecctd.2013.6662260.

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4

Ferreira, P. J. S. G. "The condition number of certain matrices and applications." In 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258). IEEE, 1999. http://dx.doi.org/10.1109/icassp.1999.758331.

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5

Zhong, Caijun, Matthew R. McKay, Tharm Ratnarajah, and Kai-Kit Wong. "Distribution of the Demmel Condition Number of Complex Wishart Matrices." In GLOBECOM 2010 - 2010 IEEE Global Communications Conference. IEEE, 2010. http://dx.doi.org/10.1109/glocom.2010.5684238.

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6

Lu Wei and Olav Tirkkonen. "Approximation to the condition number distribution of almost square matrices." In Workshops (ICUMT). IEEE, 2009. http://dx.doi.org/10.1109/icumt.2009.5345445.

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7

Moitra, Ankur. "Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices." In STOC '15: Symposium on Theory of Computing. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2746539.2746561.

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8

Wei, Lu, and Olav Tirkkonen. "Approximate Condition Number Distribution of Complex Non-Central Correlated Wishart Matrices." In ICC 2011 - 2011 IEEE International Conference on Communications. IEEE, 2011. http://dx.doi.org/10.1109/icc.2011.5962954.

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9

Matthaiou, M., M. R. McKay, P. J. Smith, and J. A. Nossek. "Exact Expressions for the Condition Number Distribution of Complex Wishart Matrices." In ICC 2010 - 2010 IEEE International Conference on Communications. IEEE, 2010. http://dx.doi.org/10.1109/icc.2010.5502235.

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10

Danczyk, Josh, and Krishnan Suresh. "Improving the Condition Number of Finite Element Stiffness Matrices via Inverted Elements." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47328.

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In the finite element method, poor quality elements typically increase the condition number of the underlying stiffness matrix, thereby potentially: (1) degrading the computed solution, and (2) slowing the convergence of iterative solvers. Current mesh improvement strategies rely on node movement and edge-flipping to alleviate these problems. However, these methods cannot guarantee a lower-bound on mesh quality, especially in 3-D. In this paper we propose the concept, and use, of inverted elements to improve mesh quality and condition number. Inverted elements are standard finite elements, but with negative Jacobian. After establishing the mathematical properties of these elements we show how they can be used to dramatically improve the quality of a mesh through the use of an ‘element cover’. Further, we show that a lower-bound on the mesh quality can be easily achieved, as supported by numerical experiments and case-studies.

Звіти організацій з теми "Condition numbers of matrices":

1

Zhang, Cheng, and Yue Yang. Impact of adaptive design on reducing the duration of clinical trials in rare cancers: a meta-analysis. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, February 2022. http://dx.doi.org/10.37766/inplasy2022.2.0081.

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Review question / Objective: Whether the application of adaptive design in clinical trials of rare cancers can shorten the duration of clinical trials? Condition being studied: Currently, the development of innovative drug products (InMPs) for rare cancers faces many challenges, including the difficulty of enrolling sufficient numbers of patients from small and heterogeneous patient populations for clinical trials, and the significant risks of high financial investment, long development times and potential failure from a pharmaceutical company's perspective for rare cancer drugs due to limited knowledge of the natural history of the disease. Therefore, alternative approaches to clinical trial design are needed to conduct cost-effective, well-controlled analyses that can assess treatment effects in small, heterogeneous populations within shorter time frames. Adaptive trials, on the other hand, may be an effective solution to this problem. Adaptive clinical trials are designed to accelerate the clinical trial process by making predefined adjustments to key parameters through data accumulated at predefined time points during the trial without compromising the integrity and validity of the results.This study aims to examine the value of adaptive design in reducing the duration of clinical trials in rare cancers and encourage their wider implementation.
2

Gillor, Osnat, Stefan Wuertz, Karen Shapiro, Nirit Bernstein, Woutrina Miller, Patricia Conrad, and Moshe Herzberg. Science-Based Monitoring for Produce Safety: Comparing Indicators and Pathogens in Water, Soil, and Crops. United States Department of Agriculture, May 2013. http://dx.doi.org/10.32747/2013.7613884.bard.

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Using treated wastewater (TWW) for crop irrigation represents an important opportunity for ensuring adequate food production in light of growing freshwater scarcity worldwide. However, the environmentally sustainable approach of using TWW for irrigation can lead to contamination of produce with fecal pathogens that may remain in treated water. The overall goal of this research was to evaluate the correlation between the presence of fecal indicator bacteria (FIB) and that of a suite of human pathogens in TWW, the irrigated soil, and crops. Field experiments were conducted to compare secondary and tertiary TWW with dechlorinated tap water for irrigation of tomatoes, a typical commercial crop, in Israel, a semi-arid country. Human pathogens including bacteria (Salmonella), protozoa (Cryptosporidiumand Giardia), and viruses (Adenovirus [AV Types A, B, C & 40/41] and Enterovirus [EV71 subtypes]) were monitored in two field trials using a combination of microscopic, cultivation-based, and molecular (qPCR) techniques. Results from the field trials indicate that microbial contamination on the surface of tomatoes did not appear to be associated with the source of irrigated waters; FIB contamination was not statistically different on tomatoes irrigated with TWW as compared to tomatoes irrigated with potable water. In fact, Indicator bacteria testing did not predict the presence of pathogens in any of the matrices tested. High concentrations of FIB were detected in water and on tomato surfaces from all irrigation treatment schemes, while pathogen contamination on tomato surfaces (Cryptosporidiumand Salmonella) was only detected on crops irrigated with TWW. These results suggest that regular monitoring for pathogens should take place to accurately detect presence of harmful microorganisms that could threaten consumer safety. A notable result from our study is that the large numbers of FIB in the water did not appear to lead to FIB accumulation in the soil. With the exception of two samples, E. coli that was present at 10³ to 10⁴ cells/100 mL in the water, was not detected in the soil. Other bacterial targets associated with the enteric environment (e. g., Proteusspp.) as well as protozoal pathogens were detected in the TWW, but not in the soil. These findings suggest that significant microbial transfer to the soil from TWW did not occur in this study. The pattern of FIB contamination on the surfaces of tomatoes was the same for all treatment types, and showed a temporal effect with more contamination detected as the duration of the field trial increased. An important observation revealed that water quality dramatically deteriorated between the time of its release from the wastewater treatment plant and the time it was utilized for irrigation, highlighting the importance of performing water quality testing throughout the growing season at the cultivation site.
3

Wolfenson, David, William W. Thatcher, and James E. Kinder. Regulation of LH Secretion in the Periovulatory Period as a Strategy to Enhance Ovarian Function and Fertility in Dairy and Beef Cows. United States Department of Agriculture, December 2003. http://dx.doi.org/10.32747/2003.7586458.bard.

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The general research objective was to increase herd pregnancy rates by enhancing corpus luteum (CL) function and optimizing follicle development, in order to increase conception rate and embryo survival. The specific objectives were: to determine the effect of the duration of the preovulatory LH surge on CL function; to determine the function of LH during the postovulatory period on CL development; to optimize CL differentiation and follicle development by means of a biodegradable GnRH implant; to test whether optimization of CL development and follicle dynamics in timed- insemination protocols would improve fertility in high-yielding dairy cows. Low fertility in cattle results in losses of hundreds of millions of dollars in the USA and Israel. Two major causes of low fertility are formation of a functionally impaired CL, and subsequent enhanced ovarian follicle development. A functionally impaired CL may result from suboptimal LH secretion. The two major causes of low fertility in dairy cattle in US and Israel are negative energy status and summer heat stress; in both situations, low fertility is associated with reductions in LH secretion and impaired development of the ovulatory follicle and of the CL. In Florida, the use of 450-mg deslorelin (GnRH analogue) implants to induce ovulation, under the Ovsynch protocol resulted in a higher pregnancy rates than use of 750-mg implants, and pregnancy losses tended to decrease compared to controls, due probably to decrease in follicular development and estradiol secretion at the time of conceptus signaling to maintain the CL. An alternative strategy to enhance progesterone concentrations involved induction of an accessory CL by injection of hCG on day 5 after the cows were inseminated. Treatment with hCG resulted in 86% of the cows having two CLs, compared with 23% of the control cows. Conception rates were higher among the hCG-treated cows than among the controls. Another approach was to replace the second injection of GnRH analogue, in a timed-insemination protocol, with estradiol cypionate (ECP) injected 24 h after the injection of PGF₂ₐ Pregnancy rates were comparable with those obtained under the regular Ovsynch (timed- AI) program. Use of ECP induced estrus, and cows inseminated at detected estrus are indeed more fertile than those not in estrus at the time of insemination. Collectively, the BARD-supported programs at the University of Florida have improved timed insemination programs. In Ohio, the importance of the frequency of LH episodes during the early stages of the estrous cycle of cattle, when the corpus luteum is developing, was studied in an in vivo experiment in which cows were subjected to various episodic exposures to exogenous bovine LH. Results indicate that the frequent LH episodes immediately following the time of ovulation are important in development of the corpus luteum, from the points of view of both size and functionality. In another study, rates of cell proliferation and numbers of endothelial cells were examined in vitro in CLs collected from cows that received post-ovulation pulsatile LH treatment at various frequencies. The results indicate that the corpora lutea growth that results from luteal cell proliferation is enhanced by the episodes of LH release that occur immediately after the time of ovulation in cattle. The results also show that luteal endothelial cell numbers did not differ among cows treated with different LH doses. In Israel. a longer duration of the preovulatory LH surge stimulated the steroidogenic capacity of granulosa-derived luteal cells, and might, thereby, contribute to a higher progesterone output from the bovine corpus luteum. In an in vivo study, a subgroup of high-yielding dairy cows with extended estrus to ovulation interval was identified. Associated with this extended interval were: low plasma progesterone and estradiol concentrations and a low preovulatory LH surge prior to ovulation, as well as low post- ovulation progesterone concentration. In experiments based on the above results, we found that injection of GnRH at the onset of estrus increased the LHpeak, prevented late ovulation, decreased the variability between cows and elicited high and uniform progesterone levels after ovulation. GnRH at estrus onset increased conception rates, especially in the summer, and among primiparous cows and those with low body condition. Another study compared ovarian functions in multiparous lactating cows with those in nulliparous non-lactating heifers. The results revealed differences in ovarian follicular dynamics, and in plasma concentrations of steroids and gonadotropins that may account for the differences in fertility between heifers and cows.
4

Fluhr, Robert, and Maor Bar-Peled. Novel Lectin Controls Wound-responses in Arabidopsis. United States Department of Agriculture, January 2012. http://dx.doi.org/10.32747/2012.7697123.bard.

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Innate immune responses in animals and plants involve receptors that recognize microbe-associated molecules. In plants, one set of this defense system is characterized by large families of TIR–nucleotide binding site–leucine-rich repeat (TIR-NBS-LRR) resistance genes. The direct interaction between plant proteins harboring the TIR domain with proteins that transmit and facilitate a signaling pathway has yet to be shown. The Arabidopsis genome encodes TIR-domain containing genes that lack NBS and LRR whose functions are unknown. Here we investigated the functional role of such protein, TLW1 (TIR LECTIN WOUNDRESPONSIVE1). The TLW1 gene encodes a protein with two domains: a TIR domain linked to a lectin-containing domain. Our specific aim in this proposal was to examine the ramifications of the TL1-glycan interaction by; A) The functional characterization of TL1 activity in the context of plant wound response and B) Examine the hypothesis that wounding induced specific polysaccharides and examine them as candidates for TL-1 interactive glycan compounds. The Weizmann group showed TLW1 transcripts are rapidly induced by wounding in a JA-independent pathway and T-DNA-tagged tlw1 mutants that lack TLW1 transcripts, fail to initiate the full systemic wound response. Transcriptome methodology analysis was set up and transcriptome analyses indicates a two-fold reduced level of JA-responsive but not JA-independent transcripts. The TIR domain of TLW1 was found to interact directly with the KAT2/PED1 gene product responsible for the final b-oxidation steps in peroxisomal-basedJA biosynthesis. To identify potential binding target(s) of TL1 in plant wound response, the CCRC group first expressed recombinant TL1 in bacterial cells and optimized conditions for the protein expression. TL1 was most highly expressed in ArcticExpress cell line. Different types of extraction buffers and extraction methods were used to prepare plant extracts for TL1 binding assay. Optimized condition for glycan labeling was determined, and 2-aminobenzamide was used to label plant extracts. Sensitivity of MALDI and LC-MS using standard glycans. THAP (2,4,6- Trihydroxyacetophenone) showed minimal background peaks at positive mode of MALDI, however, it was insensitive with a minimum detection level of 100 ng. Using LC-MS, sensitivity was highly increased enough to detect 30 pmol concentration. However, patterns of total glycans displayed no significant difference between different extraction conditions when samples were separated with Dionex ICS-2000 ion chromatography system. Transgenic plants over-expressing lectin domains were generated to obtain active lectin domain in plant cells. Insertion of the overexpression construct into the plant genome was confirmed by antibiotic selection and genomic DNA PCR. However, RT-PCR analysis was not able to detect increased level of the transcripts. Binding ability of azelaic acid to recombinant TL1. Azelaic acid was detected in GST-TL1 elution fraction, however, DHB matrix has the same mass in background signals, which needs to be further tested on other matrices. The major findings showed the importance of TLW1 in regulating wound response. The findings demonstrate completely novel and unexpected TIR domain interactions and reveal a control nexus and mechanism that contributes to the propagation of wound responses in Arabidopsis. The implications are to our understanding of the function of TIR domains and to the notion that early molecular events occur systemically within minutes of a plant sustaining a wound. A WEB site (http://genome.weizmann.ac.il/hormonometer/) was set up that enables scientists to interact with a collated plant hormone database.

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