Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schr\"odinger equations

We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using Fast Fourier Transforms. To split the system into the quantum harmonic oscillator problem and the remaining part allows to get higher accuracies in many cases, but it requires to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build new methods which combine the advantages of using Fourier methods while solving the timedependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition).Comment: 12 pages of RevTex4-1, 8 figures; substantially revised and extended versio

Two Main Subtypes of Aldosterone-Producing Adrenocortical Adenomas by Morphological and Expression Phenotype

Background: Aldosteronism is still a considerable diagnostic challenge generally diagnosed in a 3-tiered system (initial screening, a confirmation of the diagnosis, and a determination of the specific subtype). Since the recognition that ¾ of cases are due to bilateral hyperplasia, the spectrum of adenomas needs further characterization to determine the origin of aldosterone secretion. Design: We selected unilateral aldosterone-producing adrenocortical adenomas (AP-ACA, 33) responsible of primary aldosteronism defined by WHO criteria from a consecutive series of 98 ACA. We analyzed the histological features (growth pattern, nuclear characteristics, cytoplasmic staining qualities) of the tumor and the expression profile by quantitative RT-PCR of key molecular players of glomerulosa differentiation (SFRP2, β-catenin, AT1R, CYP21 CYP11B2, NURR1 and NUR77) in both the tumor and the surrounding parenchyma. RNA was extracted, cleaned from normal and neoplastic tissues (RNeasy columns), first-strand cDNA synthesized using T7-(dT24)-oligomer and used as template for cRNA synthesis.. The peritumoral parenchyma was also evaluated for the cytohistological features of the glomurulosa and its extension into deep cortex/medulla and periadrenal soft tissues. Quantitative results were cross-validated (expression factor>2, significance<0.01). Variables were studied regarding morphological appearances of the tumor and the status of the peritumoral glomerulosa. Results: Two main groups of AP-ACA were identified morphologically with a corresponding molecular profile. AP-ACA composed predominantly of clear foamy cells (10) that revealed minimal expression of AT1R, CYP21 and CYP11B2 and AP-ACA composed predominantly of eosinophilic cells (23) expressing significantly high AT1R, CYP21 and CYP11B2. The peritumoral parenchyma revealed functional hyperplastic glomerulosa in 31 cases, more prominent and with extra-adrenal extension in clear cell AP-ACA. Conclusions: The common presence of peritumoral hyperplasia suggests a proliferative response of cells to unidentified paracrine/autocrine factor as main mechanism in AP-ACA, which are not involved in glomerulosa differentiation in the clear cell subtype. Clear cell AP-ACA causes a syndrome of aldosteronism characterized by histologic features intermediate between adrenal adenoma and adrenal hyperplasia. Category: Endocrine PathologyUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Histological Risk Classification Predicts Malignancy and Recurrence in Paragangliomas

Background: Mid-term outcome information in risk stratified patient cohort is needed to inform prognosis in individual patients with paragangliomas (PGL), adjuvant therapy choice and future research. The objective is to define the outcome relevance of a novel risk stratification scheme for PGLs. Design: A classification scheme for PGLs was devised and specimen were assessed for invasion capacity (infiltrative edges with broad fibrous bands, extra-adrenal extension [recording capsular, microscopic periadrenal and gross periadrenal], capsular and peritumoral vascular invasion [recording thin- and thick-walled blood vessels]), tumorigenic expansion (expansile nodules with diffuse areas, hypercellular homogenous areas, necrosis [recording multifocal and confluent subtypes]) and mitogenic activity (MFC/10HPF, presence of atypical mitotic figures). Patients were prospectively stratified as low risk or high risk (presence of at least one feature of invasive capacity and two features of tumorigenic expansion). Patients underwent systematic treatment and follow up for their PGLs in a tertiary referral center. Results: The multilevel analysis based on 78 patients identified statistically significant differences in clinical and biochemical presentation between low risk and high risk patients for gender (p<0.05), noradrenalin (4.6±8.5 vs 11.6±16.9), dopamine (0.6±0.3 vs 1.7±2.4), size of lesion (49.8±19.5 vs 89.2±45.8) and malignancy, 0% vs 21.6% (p<0.01), treatment modalities for MIBG therapy, 0% vs 40.5% (p<.0001), MVR, 0% vs 23.3% (p<.001) and lymph node dissection, 13.5% vs 40.5% (p<0.01) and distant metastases, 0% vs 21.6% (p<0.01). Disease free survival was significantly lower in HR patients 0% vs 78.4% (p=0.004). Histological risk stratification predicts DFS with AUC of 0.8 (95% CI: 0.69-0.90; p<0.01). 7/37 patients with HR had a synchronous diagnosis of malignancy based on other criteria and 4 patients suffered local recurrence. Conclusions: Stratification as low risk excluded a synchronous diagnosis of malignancy and disease recurrence of a follow-up interval of 1-75 months (median 12 months). A high-risk status is associated with high risk of malignancy and disease recurrence.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

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

Symmetrically Processed Splitting Integrators for Enhanced Hamiltonian Monte Carlo Sampling

[EN] We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals as standard leapfrog/Verlet without impairing in any way the quality of the samples. They are based on a suitable modification of the processing technique first introduced by Butcher. The idea of modified processing may also be useful for other purposes, like the construction of high-order splitting integrators with positive coefficients.The first, third, and fourth authors were supported by project PID2019-104927GB-C21 (AEI/FEDER, UE) . The second author was supported by projects PID2019-104927GB-C22 (GNI-QUAMC) , (AEI/FEDER, UE) VA105G18, and VA169P20 (Junta de Castilla y Leon, ES) co-financed by FEDER funds.Blanes Zamora, S.; Calvo, M.; Casas, F.; Sanz-Serna, JM. (2021). Symmetrically Processed Splitting Integrators for Enhanced Hamiltonian Monte Carlo Sampling. SIAM Journal on Scientific Computing. 43(5):A3357-A3371. https://doi.org/10.1137/20M137940X30SA3357A337143

High-throughput variable-to-fixed entropy codec using selective, stochastic code forests

Efficient high-throughput (HT) compression algorithms are paramount to meet the stringent constraints of present and upcoming data storage, processing, and transmission systems. In particular, latency, bandwidth and energy requirements are critical for those systems. Most HT codecs are designed to maximize compression speed, and secondarily to minimize compressed lengths. On the other hand, decompression speed is often equally or more critical than compression speed, especially in scenarios where decompression is performed multiple times and/or at critical parts of a system. In this work, an algorithm to design variable-to-fixed (VF) codes is proposed that prioritizes decompression speed. Stationary Markov analysis is employed to generate multiple, jointly optimized codes (denoted code forests). Their average compression efficiency is on par with the state of the art in VF codes, e.g., within 1% of Yamamoto et al.\u27s algorithm. The proposed code forest structure enables the implementation of highly efficient codecs, with decompression speeds 3.8 times faster than other state-of-the-art HT entropy codecs with equal or better compression ratios for natural data sources. Compared to these HT codecs, the proposed forests yields similar compression efficiency and speeds

"Literatura y cine: lecturas cruzadas sobre las “Memorias del subdesarrollo”" [Reseña]

Reseña de Santana-Fernández de Castro, A. "Literatura y cine: lecturas cruzadas sobre las “Memorias del subdesarrollo”". Biblioteca de la Cátedra de Cultura Cubana Alejo Carpentier. Santiago de Compostela: Universidade, 2010. 276 pp

New families of symplectic splitting methods for numerical integration in dynamical astronomy

We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We derive in a systematic way an independent set of necessary and sufficient conditions to be satisfied by the coefficients of splitting methods to achieve a prescribed order of accuracy. Splitting methods satisfying such (generalized) order conditions are appropriate in particular for the numerical simulation of the Solar System described in Jacobi coordinates. We show that, when using Poincar\'e Heliocentric coordinates, the same order of accuracy may be obtained by imposing an additional polynomial equation on the coefficients of the splitting method. We construct several splitting methods appropriate for each of the two sets of coordinates by solving the corresponding systems of polynomial equations and finding the optimal solutions. The experiments reported here indicate that the efficiency of our new schemes is clearly superior to previous integrators when high accuracy is required.Comment: 24 pages, 2 figures. Revised version, accepted for publication in Applied Numerical Mathematic

EFFECTS OF TWO DIFFERENT COMPRESSION STOCKINGS IN VENOUS RETURN BEFORE AND AFTER RUNNING

In this study it analyse venous return with different compression stockings (CS). 10 experienced runners ran in two experimental test during 35 minutes in a treadmill at 75% of their maximal aerobic speed. Venous blood flow was measured before/after test with magnetic resonance (RMN). Results indicated that fatigue increased venous blood flow in all conditions (p\u3c0.05), but larger differences were found without stocking condition (WS) (right=1,63 ml/s; left=1,66 ml/s). No significant differences (p\u3e0.05) were found with medium compression stocking (MS). Results suggest that CS didn´t increase venous return and decrease comparing to WS. Nevertheless, if compression stockings lead faster recovery, we couldn’t measure because RMN isn’t faster like other methods