Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups

Given an quantum dynamical semigroup expressed as an exponential superoperator acting on a space of N-dimensional density operators, eigenvalue methods are presented by which canonical Kraus and Lindblad operator sum representations can be computed. These methods provide a mathematical basis on which to develop novel algorithms for quantum process tomography, the statistical estimation of superoperators and their generators, from a wide variety of experimental data. Theoretical arguments and numerical simulations are presented which imply that these algorithms will be quite robust in the presence of random errors in the data.Comment: RevTeX4, 31 pages, no figures; v4 adds new introduction and a numerical example illustrating the application of these results to Quantum Process Tomograph

Frequency of heterozygous TET2 deletions in myeloproliferative neoplasms

The Philadelphia chromosome (Ph)-negative myeloproliferative neoplasms (MPNs), including polycythemia vera, essential thrombocythemia, and primary myelofibrosis, are a group of clonal hematopoietic stem cell disorders with overlapping clinical and cytogenetic features and a variable tendency to evolve into acute leukemia. These diseases not only share overlapping chromosomal abnormalities but also a number of acquired somatic mutations. Recently, mutations in a putative tumor suppressor gene, ten-eleven translocation 2 (TET2) on chromosome 4q24 have been identified in 12% of patients with MPN. Additionally 4q24 chromosomal rearrangements in MPN, including TET2 deletions, have also been observed using conventional cytogenetics. The goal of this study was to investigate the frequency of genomic TET2 rearrangements in MPN using fluorescence in situ hybridization as a more sensitive method for screening and identifying genomic deletions. Among 146 MPN patients, we identified two patients (1.4%) who showed a common 4q24 deletion, including TET2. Our observations also indicated that the frequency of TET2 deletion is increased in patients with an abnormal karyotype (5%)

Ring chromosome 18 abnormality in acute myelogenous leukemia: the clinical dilemma

The ring chromosome is a circular, structural abnormality composed of either multiple chromosomes or a single chromosome with loss of genetic material at one or both ends. This chromosomal rearrangement is often unstable with frequent recombinations and may be accompanied by either loss or amplification of genetic material[1]. Considering that ring chromosomes are rare in acute myelogenous leukemia (AML), it is difficult to risk stratify patient prognosis, particularly when the ring chromosome occurs as the sole abnormality. Here we report a case of a ring chromosome 18 abnormality in a patient with newly diagnosed AML with monocytic differentiation. Cytogenetic analysis demonstrated 46, XY, r(18)(p11q21) karyotype in 19 of 34 evaluated metaphase cells. The patient received induction chemotherapy and subsequent allogeneic cord blood transplant from a sex-matched donor, and remained in hematologic and cytogenetic remission for 120 days post transplant. Soon after, he developed post transplant lymphoproliferative disorder and died of multi-organ failure. Although r(18) chromosomal abnormalities were not classified in the recent updated evidence-and expert opinion-based recommendations for the diagnosis and management of AML (likely due to the small number of reported cases), the patient was treated as high risk with stem cell transplantation. This was based on the unstable nature of the ring chromosome and the poor outcomes described in the literature of patients with sole ring 18 abnormalities

Nowe stanowiska źródeł z martwicami wapiennymi na obszarze Beskidu Małego

The paper presents hydrological-hydrochemical characteristics of springs with limestones precipitations situated in the area of the Beskid Mały Mts. These springs with characteristic plant communities Cratoneurion commutati were included to priority NATURA 2000 habitat (code 7220). It was revealed that precipitation of limestone occurs in spring with diversified mineralization of waters. It is a periodic phenomenon with the maximum of the occur-rence in summer

Development of Myelodysplastic Syndrome and Acute Myeloid Leukemia 15 Years after Hydroxyurea Use in a Patient with Sickle Cell Anemia

We report a 41 year old male with sickle cell disease who developed a myelodysplastic syndrome and acute myeloid leukemia with complex karyotype involving chromosomes 5, 7 and 17 after 15 years of hydroxyurea treatment. He responded poorly to induction chemotherapy with cytarabine/idarubicin followed by high dose cytarabine and succumbed to neutropenic sepsis. Multiple systematic reviews, observational studies and clinical trials were conducted to identify the toxicity profile of hydroxurea. Only six cases of leukemia/myelodysplastic syndrome were identified in patients with sickle cell anemia treated with hydroxyurea. Subsequently, it was concluded that hydroxyurea is not leukemogenic. However, it was noted that most of the published studies had only up to 9 years of follow-up. Our patient was started on hydroxyurea in 1990, before the widespread use of the drug and took hydroxyurea for 15 years. His presentation may reflect an outcome otherwise not yet observed because of the short follow-up of prior studies. We believe that the leukemogenic risk of hydroxyurea should be discussed with the patients and their families. Studies evaluating the adverse effects of hydroxyurea should have longer follow-up before definitive conclusions are drawn

Computing matrix functions arising in engineering models with orthogonal matrix polynomials

NOTICE: this is the author’s version of a work that was accepted for publication in Mathematical and Computer Modelling. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematical and Computer Modelling Volume 57, Issues 7–8, April 2013, Pages 1738–1743 DOI: 10.1016/j.mcm.2011.11.022Trigonometric matrix functions play a fundamental role in the solution of second order differential equations. Hermite series truncation together with Paterson¿Stockmeyer method and the double angle formula technique allow efficient computation of the matrix cosine. A careful error bound analysis of the Hermite approximation is given and a theoretical estimate for the optimal value of its parameters is obtained. Based on the ideas above, an efficient and highly-accurate Hermite algorithm is presented. A MATLAB implementation of this algorithm has also been developed and made available online. This implementation has been compared to other efficient state-of-the-art implementations on a large class of matrices for different dimensions, obtaining higher accuracy and lower computational costs in the majority of cases.This work has been partially supported by the Spanish Ministerio de Educacion grant MTM2009-08587 and Universidad Poliltecnica de Valencia PAID-06-11-2020.Defez Candel, E.; Sastre, J.; Ibáñez González, JJ.; Ruiz Martínez, PA. (2013). Computing matrix functions arising in engineering models with orthogonal matrix polynomials. Mathematical and Computer Modelling. 57(7):1738-1743. https://doi.org/10.1016/j.mcm.2011.11.022S1738174357

Efficient orthogonal matrix polynomial based method for computing matrix exponential

The matrix exponential plays a fundamental role in the solution of differential systems which appear in different science fields. This paper presents an efficient method for computing matrix exponentials based on Hermite matrix polynomial expansions. Hermite series truncation together with scaling and squaring and the application of floating point arithmetic bounds to the intermediate results provide excellent accuracy results compared with the best acknowledged computational methods. A backward-error analysis of the approximation in exact arithmetic is given. This analysis is used to provide a theoretical estimate for the optimal scaling of matrices. Two algorithms based on this method have been implemented as MATLAB functions. They have been compared with MATLAB functions funm and expm obtaining greater accuracy in the majority of tests. A careful cost comparison analysis with expm is provided showing that the proposed algorithms have lower maximum cost for some matrix norm intervals. Numerical tests show that the application of floating point arithmetic bounds to the intermediate results may reduce considerably computational costs, reaching in numerical tests relative higher average costs than expm of only 4.43% for the final Hermite selected order, and obtaining better accuracy results in the 77.36% of the test matrices. The MATLAB implementation of the best Hermite matrix polynomial based algorithm has been made available online. © 2011 Elsevier Inc. All rights reserved.This work has been supported by the Programa de Apoyo a la Investigacion y el Desarrollo of the Universidad Politecnica de Valencia PAID-05-09-4338, 2009.Sastre, J.; Ibáñez González, JJ.; Defez Candel, E.; Ruiz Martínez, PA. (2011). Efficient orthogonal matrix polynomial based method for computing matrix exponential. Applied Mathematics and Computation. 217(14):6451-6463. https://doi.org/10.1016/j.amc.2011.01.004S645164632171

Results of Phase II Clinical Trial MPD-RC 101: Allogeneic Hematopoietic Stem Cell Transplantation Conditioned with Fludarabine/Melphalan in Patients with Myelofibrosis

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The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its applications to several physical problem