Stable marriage with general preferences

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization is practically well-motivated, and as we show, encompasses the well studied hard variant of stable marriage where preferences are allowed to have ties and to be incomplete. As a result, we prove that deciding the existence of a stable matching in our model is NP-complete. Complementing this negative result we present a polynomial-time algorithm for the above decision problem in a significant class of instances where the preferences are asymmetric. We also present a linear programming formulation whose feasibility fully characterizes the existence of stable matchings in this special case. Finally, we use our model to study a long standing open problem regarding the existence of cyclic 3D stable matchings. In particular, we prove that the problem of deciding whether a fixed 2D perfect matching can be extended to a 3D stable matching is NP-complete, showing this way that a natural attempt to resolve the existence (or not) of 3D stable matchings is bound to fail.Comment: This is an extended version of a paper to appear at the The 7th International Symposium on Algorithmic Game Theory (SAGT 2014

Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales

We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: our results seem new and interesting even in the particular cases when the time scale is the set of real numbers or the set of integers.Comment: This is a preprint of a paper whose final and definite form will appear in Journal of Optimization Theory and Applications (JOTA). Paper submitted 17-Nov-2011; revised 24-March-2012 and 10-April-2012; accepted for publication 15-April-201

Transversality Conditions for Infinite Horizon Variational Problems on Time Scales

We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for publication in "Optimization Letters"

C-axis lattice dynamics in Bi-based cuprate superconductors

We present results of a systematic study of the c axis lattice dynamics in single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained by spectral ellipsometry on single crystals and theoretical calculations. The calculations are carried out within the framework of a classical shell model, which includes long-range Coulomb interactions and short-range interactions of the Buckingham form in a system of polarizable ions. Using the same set of the shell model parameters for Bi2201, Bi2212 and Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes of A2u symmetry and suggest the phonon mode eigenvector patterns. We achieve good agreement between the calculated A2u eigenfrequencies and the experimental values of the c axis TO phonon frequencies which allows us to make a reliable phonon mode assignment for all three Bi-based cuprate superconductors. We also present the results of our shell model calculations for the Gamma-point A1g symmetry modes in Bi2201, Bi2212 and Bi2223 and suggest an assignment that is based on the published experimental Raman spectra. The superconductivity-induced phonon anomalies recently observed in the c axis infrared and resonant Raman scattering spectra in trilayer Bi2223 are consistently explained with the suggested assignment.Comment: 29 pages, 13 figure

Acute biphenotypic leukaemia: immunophenotypic and cytogenetic analysis

The incidence of acute biphenotypic leukaemia has ranged from less than 1% to almost 50% in various reports in the literature. This wide variability may be attributed to a number of reasons including lack of consistent diagnostic criteria, use of various panels of antibodies, and the failure to recognize the lack of lineage specificity of some of the antibodies used. The morphology, cytochemistry, immunophenotype and cytogenetics of acute biphenotypic leukaemias from our institution were studied. The diagnostic criteria took into consideration the morphology of the analysed cells, light scatter characteristics, and evaluation of antibody fluorescence histograms in determining whether the aberrant marker expression was arising from leukaemic blasts or differentiated bone marrow elements. Fifty-two of 746 cases (7%) fulfilled our criteria for acute biphenotypic leukaemias. These included 30 cases of acute lymphoblastic leukaemia (ALL) expressing myeloid antigens, 21 cases of acute myelogenous leukaemia (AML) expressing lymphoid markers, and one case of ALL expressing both B- and T-cell associated antigens. The acute biphenotypic leukaemia cases consisted of four major immunophenotypic subgroups: CD2± AML (11), CD19± AML (8), CD13 and/or CD33± ALL (24), CD11b± ALL (5) and others (4). Chromosomal analysis was carried out in 42/52 of the acute biphenotypic leukaemia cases; a clonal abnormality was found in 31 of these 42 cases. This study highlights the problems encountered in the diagnosis of acute biphenotypic leukaemia, some of which may be reponsible for the wide variation in the reported incidence of this leukaemia. We suggest that the use of strict, uniform diagnostic criteria may help in establishing a more consistent approach towards diagnosis of this leukaemic entity. We also suggest that biphenotypic leukaemia is comprised of biologically different groups of leukaemia based on immunophenotypic and cytogenetic findings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73301/1/j.1365-2141.1993.tb03024.x.pd

Addition of docetaxel to hormonal therapy in low- and high-burden metastatic hormone sensitive prostate cancer : long-term survival results from the STAMPEDE trial

Background STAMPEDE has previously reported that the use of upfront docetaxel improved overall survival (OS) for metastatic hormone naïve prostate cancer patients starting long-term androgen deprivation therapy. We report on long-term outcomes stratified by metastatic burden for M1 patients. Methods We randomly allocated patients in 2 : 1 ratio to standard-of-care (SOC; control group) or SOC + docetaxel. Metastatic disease burden was categorised using retrospectively-collected baseline staging scans where available. Analysis used Cox regression models, adjusted for stratification factors, with emphasis on restricted mean survival time where hazards were non-proportional. Results Between 05 October 2005 and 31 March 2013, 1086 M1 patients were randomised to receive SOC (n = 724) or SOC + docetaxel (n = 362). Metastatic burden was assessable for 830/1086 (76%) patients; 362 (44%) had low and 468 (56%) high metastatic burden. Median follow-up was 78.2 months. There were 494 deaths on SOC (41% more than the previous report). There was good evidence of benefit of docetaxel over SOC on OS (HR = 0.81, 95% CI 0.69–0.95, P = 0.009) with no evidence of heterogeneity of docetaxel effect between metastatic burden sub-groups (interaction P = 0.827). Analysis of other outcomes found evidence of benefit for docetaxel over SOC in failure-free survival (HR = 0.66, 95% CI 0.57–0.76, P  0.5 in each case). There was no evidence that docetaxel resulted in late toxicity compared with SOC: after 1 year, G3-5 toxicity was reported for 28% SOC and 27% docetaxel (in patients still on follow-up at 1 year without prior progression). Conclusions The clinically significant benefit in survival for upfront docetaxel persists at longer follow-up, with no evidence that benefit differed by metastatic burden. We advocate that upfront docetaxel is considered for metastatic hormone naïve prostate cancer patients regardless of metastatic burden

Radiotherapy to the prostate for men with metastatic prostate cancer in the UK and Switzerland: Long-term results from the STAMPEDE randomised controlled trial

Background STAMPEDE has previously reported that radiotherapy (RT) to the prostate improved overall survival (OS) for patients with newly diagnosed prostate cancer with low metastatic burden, but not those with high-burden disease. In this final analysis, we report long-term findings on the primary outcome measure of OS and on the secondary outcome measures of symptomatic local events, RT toxicity events, and quality of life (QoL). Methods and findings Patients were randomised at secondary care sites in the United Kingdom and Switzerland between January 2013 and September 2016, with 1:1 stratified allocation: 1,029 to standard of care (SOC) and 1,032 to SOC+RT. No masking of the treatment allocation was employed. A total of 1,939 had metastatic burden classifiable, with 42% low burden and 58% high burden, balanced by treatment allocation. Intention-to-treat (ITT) analyses used Cox regression and flexible parametric models (FPMs), adjusted for stratification factors age, nodal involvement, the World Health Organization (WHO) performance status, regular aspirin or nonsteroidal anti-inflammatory drug (NSAID) use, and planned docetaxel use. QoL in the first 2 years on trial was assessed using prospectively collected patient responses to QLQ-30 questionnaire. Patients were followed for a median of 61.3 months. Prostate RT improved OS in patients with low, but not high, metastatic burden (respectively: 202 deaths in SOC versus 156 in SOC+RT, hazard ratio (HR) = 0·64, 95% CI 0.52, 0.79, p < 0.001; 375 SOC versus 386 SOC+RT, HR = 1.11, 95% CI 0.96, 1.28, p = 0·164; interaction p < 0.001). No evidence of difference in time to symptomatic local events was found. There was no evidence of difference in Global QoL or QLQ-30 Summary Score. Long-term urinary toxicity of grade 3 or worse was reported for 10 SOC and 10 SOC+RT; long-term bowel toxicity of grade 3 or worse was reported for 15 and 11, respectively. Conclusions Prostate RT improves OS, without detriment in QoL, in men with low-burden, newly diagnosed, metastatic prostate cancer, indicating that it should be recommended as a SOC. Trial registration ClinicalTrials.gov NCT00268476, ISRCTN.com ISRCTN78818544

First Sagittarius A* Event Horizon Telescope results. I. The shadow of the supermassive black hole in the center of the Milky Way

Galaxie