Inertia-based spectrum slicing for symmetric quadratic eigenvalue problems

[EN] In the quadratic eigenvalue problem (QEP) with all coefficient matrices symmetric, there can be complex eigenvalues. However, some applications need to compute real eigenvalues only. We propose a Lanczos-based method for computing all real eigenvalues contained in a given interval of large-scale symmetric QEPs. The method uses matrix inertias of the quadratic polynomial evaluated at different shift values. In this way, for hyperbolic problems, it is possible to make sure that all eigenvalues in the interval have been computed. We also discuss the general nonhyperbolic case. Our implementation is memory-efficient by representing the computed pseudo-Lanczos basis in a compact tensor product representation. We show results of computational experiments with a parallel implementation in the SLEPc library.Agencia Estatal de Investigacion, Grant/Award Number: TIN2016-75985-PCampos, C.; Román Moltó, JE. (2020). Inertia-based spectrum slicing for symmetric quadratic eigenvalue problems. Numerical Linear Algebra with Applications. 27(4):1-17. https://doi.org/10.1002/nla.2293S117274Tisseur, F., & Meerbergen, K. (2001). The Quadratic Eigenvalue Problem. SIAM Review, 43(2), 235-286. doi:10.1137/s0036144500381988Veselić, K. (2011). Damped Oscillations of Linear Systems. Lecture Notes in Mathematics. doi:10.1007/978-3-642-21335-9Grimes, R. G., Lewis, J. G., & Simon, H. D. (1994). A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems. SIAM Journal on Matrix Analysis and Applications, 15(1), 228-272. doi:10.1137/s0895479888151111Campos, C., & Roman, J. E. (2012). Strategies for spectrum slicing based on restarted Lanczos methods. Numerical Algorithms, 60(2), 279-295. doi:10.1007/s11075-012-9564-zLi, R., Xi, Y., Vecharynski, E., Yang, C., & Saad, Y. (2016). A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems. SIAM Journal on Scientific Computing, 38(4), A2512-A2534. doi:10.1137/15m1054493Guo, C.-H., Higham, N. J., & Tisseur, F. (2010). An Improved Arc Algorithm for Detecting Definite Hermitian Pairs. SIAM Journal on Matrix Analysis and Applications, 31(3), 1131-1151. doi:10.1137/08074218xNiendorf, V., & Voss, H. (2010). Detecting hyperbolic and definite matrix polynomials. Linear Algebra and its Applications, 432(4), 1017-1035. doi:10.1016/j.laa.2009.10.014NakatsukasaY NoferiniV. Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems;2017. Preprint arXiv:1711.00495.Parlett, B. N., & Chen, H. C. (1990). Use of indefinite pencils for computing damped natural modes. Linear Algebra and its Applications, 140, 53-88. doi:10.1016/0024-3795(90)90222-xCampos, C., & Roman, J. E. (2016). Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems. 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R., & van der Vorst, H. A. (1996). Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT Numerical Mathematics, 36(3), 595-633. doi:10.1007/bf01731936Bai, Z., & Su, Y. (2005). SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem. SIAM Journal on Matrix Analysis and Applications, 26(3), 640-659. doi:10.1137/s0895479803438523Güttel, S., & Tisseur, F. (2017). The nonlinear eigenvalue problem. Acta Numerica, 26, 1-94. doi:10.1017/s0962492917000034Yang, L., Sun, Y., & Gong, F. (2018). The inexact residual iteration method for quadratic eigenvalue problem and the analysis of convergence. Journal of Computational and Applied Mathematics, 332, 45-55. doi:10.1016/j.cam.2017.10.003Keçeli, M., Corsetti, F., Campos, C., Roman, J. E., Zhang, H., Vázquez-Mayagoitia, Á., … Wagner, A. F. (2018). SIESTA-SIPs: Massively parallel spectrum-slicing eigensolver for an ab initio molecular dynamics package. Journal of Computational Chemistry, 39(22), 1806-1814. doi:10.1002/jcc.25350Voss, H., Werner, B., & Hadeler, K. P. (1982). A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems. Mathematical Methods in the Applied Sciences, 4(1), 415-424. doi:10.1002/mma.1670040126Higham, N. J., Mackey, D. S., & Tisseur, F. (2009). Definite Matrix Polynomials and their Linearization by Definite Pencils. SIAM Journal on Matrix Analysis and Applications, 31(2), 478-502. doi:10.1137/080721406Al-Ammari, M., & Tisseur, F. (2012). Hermitian matrix polynomials with real eigenvalues of definite type. Part I: Classification. Linear Algebra and its Applications, 436(10), 3954-3973. doi:10.1016/j.laa.2010.08.035Gohberg, I., Lancaster, P., & Rodman, L. (1980). Spectral Analysis of Selfadjoint Matrix Polynomials. The Annals of Mathematics, 112(1), 33. doi:10.2307/1971320RozložnÍk, M., Okulicka-DŁużewska, F., & Smoktunowicz, A. (2015). Cholesky-Like Factorization of Symmetric Indefinite Matrices and Orthogonalization with Respect to Bilinear Forms. SIAM Journal on Matrix Analysis and Applications, 36(2), 727-751. doi:10.1137/130947003Lu, D., Su, Y., & Bai, Z. (2016). Stability Analysis of the Two-level Orthogonal Arnoldi Procedure. SIAM Journal on Matrix Analysis and Applications, 37(1), 195-214. doi:10.1137/151005142Campos, C., & Roman, J. E. (2016). Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc. SIAM Journal on Scientific Computing, 38(5), S385-S411. doi:10.1137/15m1022458Higham, N. J., Mackey, D. S., Mackey, N., & Tisseur, F. (2007). Symmetric Linearizations for Matrix Polynomials. SIAM Journal on Matrix Analysis and Applications, 29(1), 143-159. doi:10.1137/050646202BalayS AbhyankarS AdamsM et al. PETSc users manual. ANL‐95/11 ‐ Revision 3.10. Argonne National Laboratory;2018.Betcke, T., Higham, N. J., Mehrmann, V., Schröder, C., & Tisseur, F. (2013). NLEVP. ACM Transactions on Mathematical Software, 39(2), 1-28. doi:10.1145/2427023.2427024Assink, J., Waxler, R., & Velea, D. (2017). A wide-angle high Mach number modal expansion for infrasound propagation. The Journal of the Acoustical Society of America, 141(3), 1781-1792. doi:10.1121/1.497757

Ecologically acceptable usage of derivatives of essential oil of sweet basil, Ocimum basilicum, as antifeedants against larvae of the gypsy moth, Lymantria dispar

Ethanol solutions of five fractions obtained from essential oil of sweet basil Ocimum basilicum L. (Lamiales: Lamiaceae) (F1-F5) were tested for their antifeedant properties against 2nd instar gypsy moth larvae, Lymantria dispar L. (Lepidoptera: Lymantriidae), in laboratory non-choice and feeding-choice experiments. Prior to bioassays, the chemical composition of each fraction was determined by gas chromatography analyses. Significant larval deterrence from feeding was achieved by application of tested solutions to fresh leaves of the host plant. The most effective were F1 (0.5%), F4 (0.05, 0.1, and 0.5%), and F5 (0.1 and 0.5%), which provided an antifeedant index > 80% after five days. A low rate of larval mortality was observed in no-choice bioassay. In situ screening of chlorophyll fluorescence as an indicator of plant stress level (assessed by the induced fluorometry) confirmed that the tested compounds did not cause alternations in the photosynthetic efficiency of treated leaves

Poboljšani metodi za merenje sigurnosnih karakteristika sistema uzemljenja u visokonaponskim postrojenjima

The grounding system has an important role to maintain safe and reliable operation of highvoltage (HV) power facility (usually substation). The main task of a grounding system is to discharge maximum ground fault current expected into the soil, without exceeding safety limits for touch and step voltages within the substation and the surrounding area. It is desirable that the substation grounding provides a near zero resistance to remote earth. The prevailing practice is to install a grounding grid of horizontal ground electrodes (buried bare copper conductors) supplemented by a number of vertical ground rods connected to the grid, and by a number of equipment grounding mats and interconnecting cables. The grounding grid provides a common ground for the electrical equipment and for all metallic structures at the substation. It also limits the surface potential gradient. Grounding is traditionally modeled as a pure resistance. This is a good approximation at low frequencies, but as the frequency gets higher, inductance starts to play an important role. National and international standards give detailed guidelines for grounding system design, as well as for testing, under power frequency conditions, but only limited recommendations for high frequency and transient conditions are available. The main performance metrics of the grounding system are: grounding grid integrity, grounding system impedance, and touch and step voltage. The performance metrics should be periodically tested. The goal is to perform the test when the substation is in-service (to avoid interruption of service and costly downtime). Due to conductive interference in the grounding system (usually several amperes, up to about 15 A), caused by power frequency, its harmonics and background noise, the active HV substation is an extremely challenging environment for the measurement on grounding system. This is further compounded by the impact of very low impedance of the grounding system (typically less than 0.5 Ω). Essential data to calculate safety risks in advance is often not available. Measurements are therefore an essential supplement to the theory. Unlike the theoretical approaches, empirical approaches are not widely available in the literature due to the arduous work involved, the difficulty to obtain permissions, and safety restrictions. There is a continual interest in scientific community and standardization bodies to improve the measurement of performance metrics of the grounding system. The drawbacks of actual measurement methods are related to less or more subjectivity and requirements for high level of test current (up to 100 A AC and up to 300 A DC). In this thesis, in order to avoid mentioning drawbacks, we elaborated and experimentally verified the efficient methods. The overall contribution of this thesis is the substantial enhancement of the grounding system measurement by eliminating the current restrictions found in the IEEE standards 80 and 81, respectively. The original works, that constitute the core of this thesis, have been published in referring publications. This thesis is divided into three parts. Part I includes Chapters 2 and 3. Part II includes Chapters 4 to 7. Part III contains Chapter 8. Part I gives an extensive review of published literature related to the analytical and simulation investigations of earth electrode systems. Part I also analyzes the existing methods for measurement performance metrics of the grounding system. Critical review of the constraints inherent in existing methods was given. Part II includes original contributions of the thesis: new method for measurement of grounding grid integrity (Ch.4); an effective method (so called FSM) for eliminating the effect of conductive interference at power frequency (Ch. 5); new method for grounding system impedance measurement (so called FOP-FSM) (Ch.6); new method for measurement of touch and step voltage (so called FEM-FSM) (Ch.7). Our experiment-driven verification approach of the proposed measurement methods is based on totally 49 power facilities (voltage range: 110 kV, 220 kV and 400 kV) in Serbia. Part III gives an extensive review of thesis results. Part III also proposes and elaborates directions for further automation of the proposed measurement methods

Prognostical factors and corelation with the survival of patients with amyotrophic lateral sclerosis

УВОД: Aмиoтрофична латерална склероза (ALS) је прогресивно неуродегенеративно оболење са просечним средњим временом преживљавања од 3 године. Код појединих болесника је, међутим, преживљавање дуже. С обзиром на брз и фаталан ток болести, значајно је идентификовати прогностичке факторе преживљавања у циљу оптималне употребе медицинских и друштвених ресурса. ЦИЉ РАДА: установити могуће факторе дужег преживљавања болесника са ALS у тренутку постављања дијагнозе, током 17 –огодишњег праћења на територији Београда. MEТОДЕ РАДА: испитивано је 325 болесника са пребивалиштем у Београду који су дијагностиковани у периоду од јануара 1992. до децембра 2009. године. Преживљавање је процењивано Kaplan-Meier-овом методом. Прогностичке факторе смо издвојили применом Cox-ог пропорционалног регресионог модела. REЗУЛТАТИ: До краја децембра 2009.г. укупно је 267 болесника са ALS умрло (82.2%). Mедиана времена преживљавања је 3 године (95%CI 2.86-3.14). Средње време трајања болести од почетка првих симптома је 4.35 ± 0.20 година. Средње животно доба на почетку болести је 57.74 ± 11.46 година док је средње животно доба приликом постављања дијагнозе 59.21 ± 11.26 година. Булбарни почетак је регистрован код 84 (25.8%) болесника, спинални почетак код 241 (74.1%). Код болесника са спиналним почетком је средње време трајања ALS 4.5 ± 0.2 година, било значајно дуже у односу на болеснике са булбарним почетком (3.7 ± 0.4 година, p=0.016). Иако је дуже средње време трајања болести код мушкараца (4.40 ± 0.3 година) у односу на жене (4.2 ± 0.3 година), пол нема утицаја на преживљавање у нашој кохорти (p>0.05). Cox-овом поцедуром је утврђено да су: млађе животно доба на почетку болести, дуже дијагностичко кашњење, виши ALSFRS скор приликом дијагностиковања и рана примена рилузола у статистички значајној корелацији са дужим преживљавањем. ЗАКЉУЧАК: Млађе животно доба на почетку болести и дуже дијагностичко кашњење су прогностички фактори дужег преживљавања болесника са ALS који су регистровани и у студијама других аутора. Већа вредност ALSFRS скора у моменту постављања дијагнозе и рана примена рилузола су додатни прогностички фактори дужег преживљавања. Старије животно доба на почетку болести и булбарни почетак болести су фактори лошије прогнозе у нашој кохорти болесника.BACKGROUND: Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disorder. Median survival from symptom onset is 3 years, but some patients live longer. Identification of prognostic factors will facilitate optimal use of medical and social resources. OBJECTIVE: In order to define the prognostic factor for survival, at the first visit, we investigated our ALS database of patients residents in Belgrade, the last 17 years. MATERIAL AND METHODS: In the period 1992.-2009. 325 patients with the diagnosis of definite or probable ALS were discovered in the Belgrade district. The survival were assessed with the Kaplan-Meier method. The prognostic value of each factor was estimated using Cox proportional hazard analyses. RESULTS: As of December 2009. 267 ALS patients (82.2%) ALS have died. The median survival time was 3 years, (95%CI: 2.86-3.14). Mean survival time from symptoms onset was 4.35 ± 0.20 years. The mean age at onset was 57.74 ± 11.46 years and the mean age at diagnosis was 59.21 ± 11.26 years. Eighty four patients (25.8%) had a bulbar onset and 241 (74.1%) had spinal onset of the disease. Mean survival time from onset for patients with spinal onset was 4.5 ± 0.2 years and 3.7 ± 0.4 years for patients with bulbar onset (p=0.016). Mean survival time for men was 4.40 ± 0.3 years and 4.2 ± 0.3 years for women (p>0.05). In the Cox multivariable model, the factors independently related to a longer survival were younger age, longer diagnostic delay, higher ALSFRS score at first examination and early riluzole treatment. CONCLUSIONS: The identification of younger age, longer diagnostic delay as predictors of prolonged survival in ALS clinic population supports the findings of several, earlier studies. Several additional variables assessed at the first examination predict longer survival: higher ALSFRS score and early riluzole treatment. Gender had no effect on survival. Advanced age and bulbar signs at onset indicated poorer prognosis in our population

Supplementary data for the article: Jevtić, I. I.; Savić Vujović, K.; Srebro, D.; Vučković, S.; Ivanović, M. D.; Kostić-Rajačić, S. V. Synthesis and Pharmacological Evaluation of Novel Cis and Trans 3-Substituted Anilidopiperidines. Pharmacol. Rep 2020, 72 (4), 1069–1075. https://doi.org/10.1007/s43440-020-00121-2

Supplementary material for: [ https://doi.org/10.1007/s43440-020-00121-2]Related to published version: [https://cherry.chem.bg.ac.rs/handle/123456789/4211

Development of a spectroscopic diagnostic tool for electric field measurements in IShTAR (Ion cyclotron Sheath Test ARrangement)

A

μ-opioid/D2 dopamine receptor pharmacophore containing ligands: Synthesis and pharmacological evaluation

Herein, the synthesis and pharmacological evaluation of 13 novel compounds, designed as potential heterobivalent ligands for μ-opioid receptor (MOR) and dopamine D2 receptors (D2DAR), are reported. The compounds consisted of anilido piperidine and N-aryl piperazine moieties, joined by a variable-length methylene linker. The two moieties represent MOR and D2DAR pharmacophores, respectively. The synthesis encompassed four steps, securing the final products in 28–42 % overall yields. The approach has a considerable synthetic potential, providing access to various related structures. Pharmacological tests involved in vitro competitive assay for D2DAR using [3H] spiperon, as a standard radioligand, and in vivo antinociceptive tests for MOR. The measured dopamine affinities were modest to low, while antinociceptive activity was completely absent. Therefore, the compounds of the general structure prepared in this research are unlikely to be useful as opioid–dopamine receptor heterobivalent ligands

Investigations of the Changes in the Bentonite Structure Caused by the Different Treatments

Abstract: Th