RESUMO
WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum-classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available.
RESUMO
We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fröhlich-Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low-rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach that directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in the case of homogeneous systems, the tensor-train ranks of state vectors only marginally depend on the chain length, which results in a linear growth of the storage consumption. However, the central processing unit time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wave packet width and the corresponding stabilization energy on the exciton-phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fröhlich-Holstein type Hamiltonians.
RESUMO
Clonal evolution is believed to be a main driver for progression of various types of cancer and implicated in facilitating resistance to drugs. However, the hierarchical organization of malignant clones in the hematopoiesis of myelodysplastic syndromes (MDS) and its impact on response to drug therapy remain poorly understood. Using high-throughput sequencing of patient and xenografted cells, we evaluated the intratumoral heterogeneity (n= 54) and reconstructed mutational trajectories (n = 39) in patients suffering from MDS (n = 52) and chronic myelomonocytic leukemia-1 (n = 2). We identified linear and also branching evolution paths and confirmed on a patient-specific level that somatic mutations in epigenetic regulators and RNA splicing genes frequently constitute isolated disease-initiating events. Using high-throughput exome- and/or deep-sequencing, we analyzed 103 chronologically acquired samples from 22 patients covering a cumulative observation time of 75 years MDS disease progression. Our data revealed highly dynamic shaping of complex oligoclonal architectures, specifically upon treatment with lenalidomide and other drugs. Despite initial clinical response to treatment, patients' marrow persistently remained clonal with rapid outgrowth of founder-, sub-, or even fully independent clones, indicating an increased dynamic rate of clonal turnover. The emergence and disappearance of specific clones frequently correlated with changes of clinical parameters, highlighting their distinct and far-reaching functional properties. Intriguingly, increasingly complex mutational trajectories are frequently accompanied by clinical progression during the course of disease. These data substantiate a need for regular broad molecular monitoring to guide clinical treatment decisions in MDS.