Autobiography of Olga Taussky-Todd

This autobiographical essay was written for the Archives in 1979-80 by Olga Taussky-Todd, emeritus professor of mathematics. In it she recalls her childhood and early education in the Austro-Hungarian Empire, in Vienna and Linz; her early interest in mathematics; her studies at the University of Vienna; and her interest in algebraic number theory (PhD 1930). Recollections of her thesis advisor Philip Furtwängler, Hans Hahn, Kurt Gödel, Karl Menger; her appointment in Göttingen as one of the editors of Hilbert's collected works; colleagues at Göttingen; friendship with Emmy Noether. She spends the 1934-35 academic year at Bryn Mawr, with Emmy Noether, then moves to Girton College, Cambridge. The next year she moves to London University; meets and marries fellow mathematician John (Jack) Todd. After World War II breaks out, they move to Queens University in Belfast, then back to London; their war work; their move to U.S.A. in 1947. Her interest in matrix theory; their stay at the Institute for Advanced Study, in Princeton. Their appointment at the Institute for Numerical Analysis, UCLA. Return to London. Their work at the National Bureau of Standards, in Washington, in early 1950s. 1957 appointments at Caltech: John Todd as professor of mathematics, Olga Taussky-Todd as research associate. Recollections of her mathematical research, her colleagues, and her work with students at Caltech

Uncertainty quantification for nonlinear difference equations with dependent random inputs via a stochastic Galerkin projection technique

[EN] Discrete stochastic systems model discrete response data on some phenomenon with inherent uncertainty. The main goal of uncertainty quantification is to derive the probabilistic features of the stochastic system. This paper deals with theoretical and computational aspects of uncertainty quantification for nonlinear difference equations with dependent random inputs. When the random inputs are independent random variables, a generalized Polynomial Chaos (gPC) approach has been usually used to computationally quantify the uncertainty of stochastic systems. In the gPC technique, the stochastic Galerkin projections are done onto linear spans of orthogonal polynomials from the Askey-Wiener scheme or from Gram-Schmidt orthonormalization procedures. In this regard, recent results have established the algebraic or exponential convergence of these Galerkin projections to the solution process. In this paper, as the random inputs of the difference equation may be dependent, we perform Galerkin projections directly onto linear spans of canonical polynomials. The main contribution of this paper is to study the spectral convergence of these Galerkin projections for the solution process of general random difference equations. Spectral convergence is important to derive the main statistics of the response process at a cheap computational expense. In this regard, the numerical experiments bring to light the theoretical discussion of the paper.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. The co-author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). Uncertainty quantification for nonlinear difference equations with dependent random inputs via a stochastic Galerkin projection technique. Communications in Nonlinear Science and Numerical Simulation. 72:108-120. https://doi.org/10.1016/j.cnsns.2018.12.011S1081207

Adding 6 months of androgen deprivation therapy to postoperative radiotherapy for prostate cancer: a comparison of short-course versus no androgen deprivation therapy in the RADICALS-HD randomised controlled trial

Background Previous evidence indicates that adjuvant, short-course androgen deprivation therapy (ADT) improves metastasis-free survival when given with primary radiotherapy for intermediate-risk and high-risk localised prostate cancer. However, the value of ADT with postoperative radiotherapy after radical prostatectomy is unclear. Methods RADICALS-HD was an international randomised controlled trial to test the efficacy of ADT used in combination with postoperative radiotherapy for prostate cancer. Key eligibility criteria were indication for radiotherapy after radical prostatectomy for prostate cancer, prostate-specific antigen less than 5 ng/mL, absence of metastatic disease, and written consent. Participants were randomly assigned (1:1) to radiotherapy alone (no ADT) or radiotherapy with 6 months of ADT (short-course ADT), using monthly subcutaneous gonadotropin-releasing hormone analogue injections, daily oral bicalutamide monotherapy 150 mg, or monthly subcutaneous degarelix. Randomisation was done centrally through minimisation with a random element, stratified by Gleason score, positive margins, radiotherapy timing, planned radiotherapy schedule, and planned type of ADT, in a computerised system. The allocated treatment was not masked. The primary outcome measure was metastasis-free survival, defined as distant metastasis arising from prostate cancer or death from any cause. Standard survival analysis methods were used, accounting for randomisation stratification factors. The trial had 80% power with two-sided α of 5% to detect an absolute increase in 10-year metastasis-free survival from 80% to 86% (hazard ratio [HR] 0·67). Analyses followed the intention-to-treat principle. The trial is registered with the ISRCTN registry, ISRCTN40814031, and ClinicalTrials.gov, NCT00541047. Findings Between Nov 22, 2007, and June 29, 2015, 1480 patients (median age 66 years [IQR 61–69]) were randomly assigned to receive no ADT (n=737) or short-course ADT (n=743) in addition to postoperative radiotherapy at 121 centres in Canada, Denmark, Ireland, and the UK. With a median follow-up of 9·0 years (IQR 7·1–10·1), metastasis-free survival events were reported for 268 participants (142 in the no ADT group and 126 in the short-course ADT group; HR 0·886 [95% CI 0·688–1·140], p=0·35). 10-year metastasis-free survival was 79·2% (95% CI 75·4–82·5) in the no ADT group and 80·4% (76·6–83·6) in the short-course ADT group. Toxicity of grade 3 or higher was reported for 121 (17%) of 737 participants in the no ADT group and 100 (14%) of 743 in the short-course ADT group (p=0·15), with no treatment-related deaths. Interpretation Metastatic disease is uncommon following postoperative bed radiotherapy after radical prostatectomy. Adding 6 months of ADT to this radiotherapy did not improve metastasis-free survival compared with no ADT. These findings do not support the use of short-course ADT with postoperative radiotherapy in this patient population

Duration of androgen deprivation therapy with postoperative radiotherapy for prostate cancer: a comparison of long-course versus short-course androgen deprivation therapy in the RADICALS-HD randomised trial

Background Previous evidence supports androgen deprivation therapy (ADT) with primary radiotherapy as initial treatment for intermediate-risk and high-risk localised prostate cancer. However, the use and optimal duration of ADT with postoperative radiotherapy after radical prostatectomy remains uncertain. Methods RADICALS-HD was a randomised controlled trial of ADT duration within the RADICALS protocol. Here, we report on the comparison of short-course versus long-course ADT. Key eligibility criteria were indication for radiotherapy after previous radical prostatectomy for prostate cancer, prostate-specific antigen less than 5 ng/mL, absence of metastatic disease, and written consent. Participants were randomly assigned (1:1) to add 6 months of ADT (short-course ADT) or 24 months of ADT (long-course ADT) to radiotherapy, using subcutaneous gonadotrophin-releasing hormone analogue (monthly in the short-course ADT group and 3-monthly in the long-course ADT group), daily oral bicalutamide monotherapy 150 mg, or monthly subcutaneous degarelix. Randomisation was done centrally through minimisation with a random element, stratified by Gleason score, positive margins, radiotherapy timing, planned radiotherapy schedule, and planned type of ADT, in a computerised system. The allocated treatment was not masked. The primary outcome measure was metastasis-free survival, defined as metastasis arising from prostate cancer or death from any cause. The comparison had more than 80% power with two-sided α of 5% to detect an absolute increase in 10-year metastasis-free survival from 75% to 81% (hazard ratio [HR] 0·72). Standard time-to-event analyses were used. Analyses followed intention-to-treat principle. The trial is registered with the ISRCTN registry, ISRCTN40814031, and ClinicalTrials.gov , NCT00541047 . Findings Between Jan 30, 2008, and July 7, 2015, 1523 patients (median age 65 years, IQR 60–69) were randomly assigned to receive short-course ADT (n=761) or long-course ADT (n=762) in addition to postoperative radiotherapy at 138 centres in Canada, Denmark, Ireland, and the UK. With a median follow-up of 8·9 years (7·0–10·0), 313 metastasis-free survival events were reported overall (174 in the short-course ADT group and 139 in the long-course ADT group; HR 0·773 [95% CI 0·612–0·975]; p=0·029). 10-year metastasis-free survival was 71·9% (95% CI 67·6–75·7) in the short-course ADT group and 78·1% (74·2–81·5) in the long-course ADT group. Toxicity of grade 3 or higher was reported for 105 (14%) of 753 participants in the short-course ADT group and 142 (19%) of 757 participants in the long-course ADT group (p=0·025), with no treatment-related deaths. Interpretation Compared with adding 6 months of ADT, adding 24 months of ADT improved metastasis-free survival in people receiving postoperative radiotherapy. For individuals who can accept the additional duration of adverse effects, long-course ADT should be offered with postoperative radiotherapy. Funding Cancer Research UK, UK Research and Innovation (formerly Medical Research Council), and Canadian Cancer Society

Discrete analogs of inequalities of Wirtinger

In the theory of inequalities there are often encountered inequalities which are first proved for finite series and then established for infinite series or integrals. We shall discuss here the finite analogs of several integral inequalities which appear to have been established directly. There is often the added interest in the finite case of considering whether or not an improvement in the constants is possible (cf. H. Frazer [7])

Discrete analogs of inequalities of Wirtinger

In the theory of inequalities there are often encountered inequalities which are first proved for finite series and then established for infinite series or integrals. We shall discuss here the finite analogs of several integral inequalities which appear to have been established directly. There is often the added interest in the finite case of considering whether or not an improvement in the constants is possible (cf. H. Frazer [7])

On Non-Vanishing Of Twisted Symmetric And Exterior Square L-Functions For GL(n)

this paper is to prove