Revealing trends and persistent cycles of non-autonomous systems with autonomous operator-theoretic techniques.

An important problem in modern applied science is to characterize the behavior of systems with complex internal dynamics subjected to external forcings. Many existing approaches rely on ensembles to generate information from the external forcings, making them unsuitable to study natural systems where only a single realization is observed. A prominent example is climate dynamics, where an objective identification of signals in the observational record attributable to natural variability and climate change is crucial for making climate projections for the coming decades.

Data assimilation in operator algebras.

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system.

Spectral analysis of climate dynamics with operator-theoretic approaches.

The Earth's climate system is a classical example of a multiscale, multiphysics dynamical system with an extremely large number of active degrees of freedom, exhibiting variability on scales ranging from micrometers and seconds in cloud microphysics, to thousands of kilometers and centuries in ocean dynamics. Yet, despite this dynamical complexity, climate dynamics is known to exhibit coherent modes of variability. A primary example is the El Niño Southern Oscillation (ENSO), the dominant mode of interannual (3-5 yr) variability in the climate system.

Simultaneous removal of ammonium nitrogen, dissolved chemical oxygen demand and color from sanitary landfill leachate using natural zeolite.

In this study, natural zeolite with maximum adsorption capacity of 3.59 mg g was used for the simultaneous removal of ammonium nitrogen (NH-N), dissolved chemical oxygen demand (d-COD) and color from raw sanitary landfill leachate (SLL). Saturation, desorption and regeneration tests of zeolite were performed.

Extended-range statistical ENSO prediction through operator-theoretic techniques for nonlinear dynamics.

Forecasting the El Niño-Southern Oscillation (ENSO) has been a subject of vigorous research due to the important role of the phenomenon in climate dynamics and its worldwide socioeconomic impacts. Over the past decades, numerous models for ENSO prediction have been developed, among which statistical models approximating ENSO evolution by linear dynamics have received significant attention owing to their simplicity and comparable forecast skill to first-principles models at short lead times. Yet, due to highly nonlinear and chaotic dynamics (particularly during ENSO initiation), such models have limited skill for longer-term forecasts beyond half a year.

Quantum mechanics and data assimilation.

A framework for data assimilation combining aspects of operator-theoretic ergodic theory and quantum mechanics is developed. This framework adapts the Dirac-von Neumann formalism of quantum dynamics and measurement to perform sequential data assimilation (filtering) of a partially observed, measure-preserving dynamical system, using the Koopman operator on the L^{2} space associated with the invariant measure as an analog of the Heisenberg evolution operator in quantum mechanics. In addition, the state of the data assimilation system is represented by a trace-class operator analogous to the quantum mechanical density operator, and the assimilated observables by self-adjoint multiplication operators.

Galerkin approximation of dynamical quantities using trajectory data.

Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion. A specific choice of basis set in the expansion corresponds to the estimation of dynamical quantities using a Markov state model.

Clopidogrel Therapy in Patients with Cardiovascular Disease Undergoing Transurethral Resection of the Prostate: A Step Towards Individualization.

Objectives: The objective of this study was to test platelet function pre- and peri-operatively in clopidogrel-treated patients undergoing transurethral resection of the prostate.

Methods: This was a pilot study involving 20 male patients treated with clopidogrel (75 mg/day) for the secondary prevention of cardiovascular disease and scheduled for elective transurethral resection of the prostate. Platelet function testing with light transmittance aggregometry in platelet-rich plasma of four samples (T0, T1, T2, and T3 drawn on the same day, 3 and 7 days of clopidogrel cessation and 24-h post-operatively, respectively) was performed and evaluated in each patient.

Magnetic resonance diffusion tensor imaging of the testis: Preliminary observations.

Introduction: To evaluate the feasibility of testis diffusion tensor imaging (DTI), to determine normative apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values and to assess the efficacy of DTI in characterizing testicular pathology.

Materials And Methods: Fifty-six men underwent MRI of the scrotum, including DTI. Parametric and non-parametric statistical tests were used to compare the ADC and FA between the cranial, middle and lower thirds of normal testis and between the bilateral testicular thirds.

Normal testes asymmetry evaluated by apparent diffusion coefficient and magnetization transfer ratio.

Background In humans, the left testis generally hangs lower than the right and the right is larger than the left. Magnetic resonance imaging (MRI) represents an important adjuvant modality in the investigation of testicular diseases. Purpose To assess if normal testes asymmetry is related to apparent diffusion coefficient (ADC) and magnetization transfer ratio (MTR).

Microvascular density and immunohistochemical expression of VEGF, VEGFR-1 and VEGFR-2 in benign prostatic hyperplasia, high-grade prostate intraepithelial neoplasia and prostate cancer.

Introduction: The aim of our study was to determine and compare angiogenesis in benign prostatic hyperplasia (BPH), high-grade prostate intraepithelial neoplasia (HGPIN) and prostate cancer (Pca). Moreover, we evaluated its role as a prognostic factor for Pca.

Material And Methods: We examined 39, 12 and 51 samples of BPH, HGPIN and Pca, respectively.

Reply to "Comment on 'Nonparametric forecasting of low-dimensional dynamical systems' ".

In this Reply we provide additional results which allow a better comparison of the diffusion forecast and the "past-noise" forecasting (PNF) approach for the El Niño index. We remark on some qualitative differences between the diffusion forecast and PNF, and we suggest an alternative use of the diffusion forecast for the purposes of forecasting the probabilities of extreme events.

Magnetic resonance imaging findings of cellular angiofibroma of the tunica vaginalis of the testis: a case report.

Background: Cellular angiofibroma represents a rare mesenchymal tumor typically involving the inguinoscrotal area in middle-aged men. Although the origin of this benign tumor is unknown, it is histologically classified as an angiomyxoid tumor. Cellular angiofibroma is characterized by a diversity of pathological and imaging features.

MR Spectra of Normal Adult Testes and Variations with Age: Preliminary Observations.

Objectives: The aim was to determine the proton MR (1H-MR) spectra of normal adult testes and variations with age.

Methods: Forty-one MR spectra of normal testes, including 16 testes from men aged 20-39 years (group I) and 25 testes from men aged 40-69 years (group II), were analyzed. A single-voxel point-resolved spectroscopy sequence (PRESS), with TR/TE: 2000/25 ms was used.

Nonparametric forecasting of low-dimensional dynamical systems.

This paper presents a nonparametric modeling approach for forecasting stochastic dynamical systems on low-dimensional manifolds. The key idea is to represent the discrete shift maps on a smooth basis which can be obtained by the diffusion maps algorithm. In the limit of large data, this approach converges to a Galerkin projection of the semigroup solution to the underlying dynamics on a basis adapted to the invariant measure.

MR imaging of scrotum.

Magnetic resonance (MR) imaging of the scrotum has been used as a valuable supplemental diagnostic modality in evaluating scrotal pathology, mostly recommended in cases of inconclusive sonographic findings. Because of the advantages of the technique, MR imaging of the scrotum may provide valuable information in the detection and characterization of various scrotal diseases. The technique may accurately differentiate intratesticular from extratesticular mass lesions and provide important information in the preoperative characterization of the histologic nature of scrotal masses.

Apparent diffusion coefficient values of normal testis and variations with age.

The usefulness of diffusion-weighted magnetic resonance imaging (DWI) in the evaluation of scrotal pathology has recently been reported. A standard reference of normal testicular apparent diffusion coefficient (ADC) values and their variations with age is necessary when interpreting normal testicular anatomy and pathology. We evaluated 147 normal testes using DWI, including 71 testes from 53 men aged 20-39 years (group 1), 67 testes from 42 men aged 40-69 years (group 2) and nine testes from six men older than 70 years (group 3).

Dynamic contrast-enhanced subtraction MRI for characterizing intratesticular mass lesions.

Objective: The objective of our study was to analyze the enhancement patterns of various intratesticular mass lesions at dynamic contrast-enhanced subtraction MRI and assess the value of the technique in distinguishing between benign and malignant lesions.

Materials And Methods: We retrospectively evaluated the records and images of 44 consecutive men (11 benign and 16 malignant intratesticular lesions) who presented to the department of urology with a variety of clinical symptoms and were referred for imaging. Dynamic contrast-enhanced subtraction MRI was performed using a 3D fast-field echo sequence after the administration of paramagnetic contrast medium.

The symmetries of image formation by scattering. II. Applications.

We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach constitutes a physically-based, computationally efficient, and noise-robust route to analyzing the large and varied datasets generated by existing and emerging methods for studying structure and dynamics by scattering. We demonstrate three-dimensional structure recovery from X-ray diffraction and cryo-electron microscope image snapshots of unknown orientation, the latter at 12 times lower dose than currently in use.

The symmetries of image formation by scattering. I. Theoretical framework.

We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe. Here, we present an approach to image formation based on the symmetry properties of operations in three-dimensional space.

Diffusion-weighted MR imaging of normal and abnormal scrotum: preliminary results.

Magnetic resonance (MR) imaging of the scrotum represents an important supplemental diagnostic tool in the evaluation of scrotal diseases. Diffusion-weighted (DW) MR imaging is a developing technique, proved to improve tissue characterization. We evaluated the feasibility and diagnostic performance of DW MR imaging in the detection and characterization of scrotal lesions.

Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability.

Many processes in science and engineering develop multiscale temporal and spatial patterns, with complex underlying dynamics and time-dependent external forcings. Because of the importance in understanding and predicting these phenomena, extracting the salient modes of variability empirically from incomplete observations is a problem of wide contemporary interest. Here, we present a technique for analyzing high-dimensional, complex time series that exploits the geometrical relationships between the observed data points to recover features characteristic of strongly nonlinear dynamics (such as intermittency and rare events), which are not accessible to classical singular spectrum analysis.

Penis auto-amputation and chasm of the lower abdominal wall due to advanced penile carcinoma: a case report.

Introduction: Penile cancer is uncommon. When penile cancer is left untreated, at an advanced stage it can have tragic consequences for the patient.

Case Presentation: Our case report does not concern a new manifestation of penile cancer, but an interesting presentation with clinical significance that emphasizes the need to diagnose and treat penile cancer early.

Primary diffuse large B-cell testicular lymphoma: magnetic resonance imaging findings.

Testicular lymphoma represents the commonest testicular malignancy in men older than 50 years. MR imaging of the scrotum is an efficient supplemental diagnostic tool in the evaluation of scrotal diseases. We report two cases of primary diffuse large B-cell testicular lymphoma, presented in men over the age of 50 years.