Qudits of composite dimension, mutually unbiased bases and projective ring geometry

The $d^2$ Pauli operators attached to a composite qudit in dimension $d$ may be mapped to the vectors of the symplectic module $\mathcal{Z}_d^{2}$ ($\mathcal{Z}_d$ the modular ring). As a result, perpendicular vectors correspond to commuting operators, a free cyclic submodule to a maximal commuting set, and disjoint such sets to mutually unbiased bases. For dimensions $d=6,~10,~15,~12$, and 18, the fine structure and the incidence between maximal commuting sets is found to reproduce the projective line over the rings $\mathcal{Z}_{6}$, $\mathcal{Z}_{10}$, $\mathcal{Z}_{15}$, $\mathcal{Z}_6 \times \mathbf{F}_4$ and $\mathcal{Z}_6 \times \mathcal{Z}_3$, respectively.Comment: 10 pages (Fast Track communication). Journal of Physics A Mathematical and Theoretical (2008) accepte

The MLL recombinome of acute leukemias in 2017

Chromosomal rearrangements of the human MLL/KMT2A gene are associated with infant, pediatric, adult and therapy-induced acute leukemias. Here we present the data obtained from 2345 acute leukemia patients. Genomic breakpoints within the MLL gene and the involved translocation partner genes (TPGs) were determined and 11 novel TPGs were identified. Thus, a total of 135 different MLL rearrangements have been identified so far, of which 94 TPGs are now characterized at the molecular level. In all, 35 out of these 94 TPGs occur recurrently, but only 9 specific gene fusions account for more than 90% of all illegitimate recombinations of the MLL gene. We observed an age-dependent breakpoint shift with breakpoints localizing within MLL intron 11 associated with acute lymphoblastic leukemia and younger patients, while breakpoints in MLL intron 9 predominate in AML or older patients. The molecular characterization of MLL breakpoints suggests different etiologies in the different age groups and allows the correlation of functional domains of the MLL gene with clinical outcome. This study provides a comprehensive analysis of the MLL recombinome in acute leukemia and demonstrates that the establishment of patient-specific chromosomal fusion sites allows the design of specific PCR primers for minimal residual disease analyses for all patients

The MLL recombinome of acute leukemias in 2017

Chromosomal rearrangements of the human MLL/KMT2A gene are associated with infant, pediatric, adult and therapy-induced acute leukemias. Here we present the data obtained from 2345 acute leukemia patients. Genomic breakpoints within the MLL gene and the involved translocation partner genes (TPGs) were determined and 11 novel TPGs were identified. Thus, a total of 135 different MLL rearrangements have been identified so far, of which 94 TPGs are now characterized at the molecular level. In all, 35 out of these 94 TPGs occur recurrently, but only 9 specific gene fusions account for more than 90% of all illegitimate recombinations of the MLL gene. We observed an age-dependent breakpoint shift with breakpoints localizing within MLL intron 11 associated with acute lymphoblastic leukemia and younger patients, while breakpoints in MLL intron 9 predominate in AML or older patients. The molecular characterization of MLL breakpoints suggests different etiologies in the different age groups and allows the correlation of functional domains of the MLL gene with clinical outcome. This study provides a comprehensive analysis of the MLL recombinome in acute leukemia and demonstrates that the establishment of patient-specific chromosomal fusion sites allows the design of specific PCR primers for minimal residual disease analyses for all patients.</p

The MLL recombinome of acute leukemias in 2017

Chromosomal rearrangements of the human MLL/KMT2A gene are associated with infant, pediatric, adult and therapy-induced acute leukemias. Here we present the data obtained from 2345 acute leukemia patients. Genomic breakpoints within the MLL gene and the involved translocation partner genes (TPGs) were determined and 11 novel TPGs were identified. Thus, a total of 135 different MLL rearrangements have been identified so far, of which 94 TPGs are now characterized at the molecular level. In all, 35 out of these 94 TPGs occur recurrently, but only 9 specific gene fusions account for more than 90% of all illegitimate recombinations of the MLL gene. We observed an age-dependent breakpoint shift with breakpoints localizing within MLL intron 11 associated with acute lymphoblastic leukemia and younger patients, while breakpoints in MLL intron 9 predominate in AML or older patients. The molecular characterization of MLL breakpoints suggests different etiologies in the different age groups and allows the correlation of functional domains of the MLL gene with clinical outcome. This study provides a comprehensive analysis of the MLL recombinome in acute leukemia and demonstrates that the establishment of patient-specific chromosomal fusion sites allows the design of specific PCR primers for minimal residual disease analyses for all patients

Cladistical analysis of the Jovian and Saturnian satellite systems

Jupiter and Saturn each have complex systems of satellites and rings. These satellites can be classified into dynamical groups, implying similar formation scenarios. Recently, a larger number of additional irregular satellites have been discovered around both gas giants that have yet to be classified. The aim of this paper is to examine the relationships between the satellites and rings of the gas giants, using an analytical technique called cladistics. Cladistics is traditionally used to examine relationships between living organisms, the 'tree of life.' In this work, we perform the first cladistical study of objects in a planetary science context. Our method uses the orbital, physical, and compositional characteristics of satellites to classify the objects in the Jovian and Saturnian systems. We find that the major relationships between the satellites in the two systems, such as families, as presented in previous studies, are broadly preserved. In addition, based on our analysis of the Jovian system, we identify a new retrograde irregular family, the Iocaste family, and suggest that the Phoebe family of the Saturnian system can be further divided into two subfamilies. We also propose that the Saturnian irregular families be renamed, to be consistent with the convention used in Jovian families. Using cladistics, we are also able to assign the new unclassified irregular satellites into families. Taken together, the results of this study demonstrate the potential use of the cladistical technique in the investigation of relationships between orbital bodies