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. Here, we show that operator-theoretic techniques previously developed to identify slowly decorrelating observables of autonomous dynamical systems provide a powerful means for identifying nonlinear trends and persistent cycles of non-autonomous systems using data from a single trajectory of the system. We apply our framework to real-world examples from climate dynamics: Variability of sea surface temperature over the industrial era and the mid-Pleistocene transition of Quaternary glaciation cycles.

Investigation of Clinically Significant Molecular Aberrations in Patients with Prostate Cancer: Implications for Personalized Treatment, Prognosis and Genetic Testing.

The data on tumor molecular profiling of European patients with prostate cancer is limited. Our aim was to evaluate the prevalence and prognostic and predictive values of gene alterations in unselected patients with prostate cancer. The presence of gene alterations was assessed in patients with histologically confirmed prostate cancer using the ForeSENTIA® Prostate panel (Medicover Genetics), targeting 36 clinically relevant genes and microsatellite instability testing. The primary endpoint was the prevalence of gene alterations in homologous recombination repair (HRR) genes. Overall, 196 patients with prostate cancer were evaluated (median age 72.2 years, metastatic disease in 141 (71.9%) patients). Gene alterations were identified in 120 (61%) patients, while alteration in HRR genes were identified in 34 (17.3%) patients. The most commonly mutated HRR genes were ATM (17, 8.7%), BRCA2 (9, 4.6%) and BRCA1 (4, 2%). The presence of HRR gene alterations was not associated with advanced stage (p = 0.21), age at diagnosis (p = 0.28), Gleason score (p = 0.17) or overall survival (HR 0.72; 95% CI: 0.41-1.26; p = 0.251). We identified clinically relevant somatic gene alterations in European patients with prostate cancer. These molecular alterations have prognostic significance and therapeutic implications and/or may trigger genetic testing in selected patients. In the era of precision medicine, prospective research on the predictive role of these alterations for innovative treatments or their combinations is warranted.

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. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.

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. The objective and robust characterization of this and other important phenomena presents a long-standing challenge in Earth system science, the resolution of which would lead to improved scientific understanding and prediction of climate dynamics, as well as assessment of their impacts on human and natural systems. Here, we show that the spectral theory of dynamical systems, combined with techniques from data science, provides an effective means for extracting coherent modes of climate variability from high-dimensional model and observational data, requiring no frequency prefiltering, but recovering multiple timescales and their interactions. Lifecycle composites of ENSO are shown to improve upon results from conventional indices in terms of dynamical consistency and physical interpretability. In addition, the role of combination modes between ENSO and the annual cycle in ENSO diversity is elucidated.

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. To resolve this limitation, here we employ a new nonparametric statistical approach based on analog forecasting, called kernel analog forecasting (KAF), which avoids assumptions on the underlying dynamics through the use of nonlinear kernel methods for machine learning and dimension reduction of high-dimensional datasets. Through a rigorous connection with Koopman operator theory for dynamical systems, KAF yields statistically optimal predictions of future ENSO states as conditional expectations, given noisy and potentially incomplete data at forecast initialization. Here, using industrial-era Indo-Pacific sea surface temperature (SST) as training data, the method is shown to successfully predict the Niño 3.4 index in a 1998-2017 verification period out to a 10-month lead, which corresponds to an increase of 3-8 months (depending on the decade) over a benchmark linear inverse model (LIM), while significantly improving upon the ENSO predictability "spring barrier". In particular, KAF successfully predicts the historic 2015/16 El Niño at initialization times as early as June 2015, which is comparable to the skill of current dynamical models. An analysis of a 1300-yr control integration of a comprehensive climate model (CCSM4) further demonstrates that the enhanced predictability afforded by KAF holds over potentially much longer leads, extending to 24 months versus 18 months in the benchmark LIM. Probabilistic forecasts for the occurrence of El Niño/La Niña events are also performed and assessed via information-theoretic metrics, showing an improvement of skill over LIM approaches, thus opening an avenue for environmental risk assessment relevant in a variety of contexts.

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. An averaging approach is also introduced, rendering the spectrum of the assimilated observables discrete and thus amenable to numerical approximation. We present a data-driven formulation of the quantum mechanical data assimilation approach, utilizing kernel methods from machine learning and delay-coordinate maps of dynamical systems to represent the evolution and measurement operators via matrices in a data-driven basis. The data-driven formulation is structurally similar to its infinite-dimensional counterpart and shown to converge in a limit of large data under mild assumptions. Applications to periodic oscillators and the Lorenz 63 system demonstrate that the framework is able to naturally handle highly non-Gaussian statistics, complex state space geometries, and chaotic dynamics.

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. More generally, the boundary conditions impose restrictions on the choice of basis sets. We demonstrate how an alternative basis can be constructed using ideas from diffusion maps. In our numerical experiments, this basis gives results of comparable or better accuracy to Markov state models. Additionally, we show that delay embedding can reduce the information lost when projecting the system's dynamics for model construction; this improves estimates of dynamical statistics considerably over the standard practice of increasing the lag time.

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. P-selectin membrane expression was evaluated using monoclonal antibodies. RESULTS: The platelet response to adenosine diphosphate 5 µΜ and 20 µΜ at T0 were 42 ± 15 and 60 ± 14%, respectively. After discontinuation of clopidogrel, corresponding maximum aggregation values at T1 were 60 ± 16 and 74 ± 14%, and increased to 69 ± 16 and 79 ± 18% at T2. No significant difference in platelet aggregation values were noted between T1 and T2, while similar aggregation values were recorded at T3. CONCLUSIONS: Our findings indicate that in patients undergoing transurethral resection of the prostate, platelet activation is similar 3 and 7 days from clopidogrel cessation. These results may be of relevance in subjects at increased thrombotic risk prior to a surgical procedure carrying a high-bleeding risk.

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. Comparison between the ADC and FA of normal testis, malignant and benign testicular lesions was performed. RESULTS: No significant differences of the ADC and FA in normal testis between the cranial, middle and lower thirds and between the bilateral testicular thirds were found. ADC was significantly lower in malignancies compared to normal testis (P=0.006) and benign testicular lesions (P=0.006). FA was significantly higher both in malignancies (P=0.001) and benign lesions (P<0.001) compared to normal testis. FA in malignancies did not differ from FA in benign lesions (P=0.221) CONCLUSIONS: This study shows the feasibility of testis DTI. Both ADC and FA significantly differ between testicular lesions and normal testis, although FA did not show an incremental diagnostic value compared to ADC in lesion differentiation.

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). Material and Methods The normal testes from 106 men were included. Testicular volume (TV) was calculated by using the ellipsoid formula: length × width × height × 0.52. Diffusion-weighted imaging was performed using a SS EPI diffusion pulse sequence and b-values of 0 and 900 s/mm-2. Magnetization transfer imaging was obtained using a 3D GRE sequence both with and without an off-resonance radiofrequency pulse. MTR maps were obtained by the following formula: (SIo-SIm) / (SIo) × 100%, where SIo and SIm represent the signal intensity in the baseline image and that in the corresponding image acquired with an off-resonance MT pulse, respectively. The mean and standard deviation of testicular volume (TV), ADC, and MTR of both testes was calculated and compared using a paired sample t-test. Results The mean TV (mL) was greater ( P = 0.006) for the right testis (16.77 ± 4.84) compared to the left (15.97 ± 4.45). ADC of the right testis (1.09 ± 0.12 × 10 - 3 mm2 s-1) was not different ( P = 0.064) from that of the left testis (1.07 ± 0.12 × 10-3 mm2 s-1). Differences ( P = 0.032) were observed between MTR of the right (46.6 ± 2.1%) and left testis (46.0 ± 2.2%). Conclusion The reported differences in paired testes size was confirmed, introducing a possible relationship with structural and functional asymmetry of normal testes, based on MTR.

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. An accurate preoperative diagnosis is challenging. Magnetic resonance imaging examination of the scrotum has been reported as a valuable adjunct modality in the investigation of scrotal pathology. The technique by providing both structural and functional information is useful in the differentiation between extratesticular and intratesticular diseases and in the preoperative characterization of the histologic nature of various scrotal lesions. There are few reports in the English literature addressing the magnetic resonance imaging findings of cellular angiofibroma of the scrotum and no reports on functional magnetic resonance imaging data. Here we present the first case of a cellular angiofibroma arising from the tunica vaginalis of the testis and we discuss the value of a multiparametric magnetic resonance protocol, including diffusion-weighted imaging, magnetization transfer imaging and dynamic contrast-enhanced magnetic resonance imaging in the preoperative diagnosis of this rare neoplasm. CASE PRESENTATION: A 47-year Greek man presented with a painless left scrotal swelling, which had gradually enlarged during the last 6 months. Magnetic resonance imaging of his scrotum displayed a left paratesticular mass, in close proximity to the tunica vaginalis, with heterogeneous high signal intensity on T2-weighted images and no areas of restricted diffusion. The tumor was hypointense on magnetization transfer images, suggestive for the presence of macromolecules. On dynamic contrast-enhanced magnetic resonance imaging the mass showed intense heterogeneous enhancement with a type II curve. Magnetic resonance imaging findings were strongly suggestive of a benign paratesticular tumor, which was confirmed on pathology following lesion excision. CONCLUSIONS: Magnetic resonance imaging of the scrotum by combining conventional and functional magnetic resonance data provides useful diagnostic information in the preoperative characterization of scrotal masses. A possible diagnosis of a benign paratesticular tumor based on magnetic resonance imaging features may improve patient care and decrease the number of unnecessary radical surgical explorations.

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.

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. Immunohistochemical methods were applied in order to evaluate the expression of VEGF and its receptors (VEGFR-1, VEGFR-2), while microvascular density (MVD) was determined using CD105. In Pca samples, we recorded stage, differentiation, perineural invasion, adjuvant radiotherapy and their correlation with angiogenesis. RESULTS: 225 The expression of VEGF, VEGFR-1 and VEGFR-2 was significantly higher in Pca than compared to BPH (p <0.001, p <0.001 and p <0.001, respectively) and HGPIN (p <0.001, p <0.001 and p = 0.04, respectively), while there was no difference between BPH and HGPIN. MVD was higher in Pca compared to BPH (p <0.001) and HGPIN (p <0.01), while there was no difference between BPH and HGPIN. VEGF expression and MVD were significantly greater in Pca samples with poor differentiation (p = 0.044 and p = 0.038, respectively) and perineural invasion (p <0.001 and p = 0.019, respectively), while overexpression of VEGF was associated with advanced pathological stage (p = 0.047). CONCLUSIONS: Angiogenesis is more prominent in Pca than in BPH and HGPIN, while there is no difference between BPH and HGPIN. Pharmaceutical inhibition of angiogenesis could be a valuable therapeutic option for Pca in the near future.

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. The volume of interest was placed to include the majority of normal testicular parenchyma. Association between normalized metabolite concentrations, defined as ratios of the calculated metabolite concentrations relative to creatine concentration, and age was assessed. RESULTS: Quantified metabolites of the spectra were choline (Cho), creatine (Cr), myo-inositol (mI), scyllo-inositol, taurine, lactate, GLx compound, glucose, lipids, and macromolecules resonating at 0.9 ppm (LM09), around 20 ppm (LM20), and at 13 ppm (LM13). Most prominent peaks were Cho, Cr, mI, and lipids. A weak negative correlation between mI and age (P = 0.015) was observed. Higher normalized concentrations of Cho (P = 0.03), mI (P = 0.08), and LM13 (P = 0.05) were found in group I than in group II. CONCLUSIONS: 1H-MR spectra of a normal adult testis showed several metabolite peaks. A decrease of levels of Cho, mI, and LM13 was observed with advancing age. KEY POINTS: • Single-voxel PRESS MRS of a normal testis is feasible. • 1H-MR spectra of a normal testis showed several metabolite peaks. • Most prominent peaks were Cho, Cr, mI, and lipids. • A decrease of Cho, mI, and LM13 was seen with advancing age.

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. This approach allows one to quantify uncertainties (in fact, evolve the probability distribution) for nontrivial dynamical systems with equation-free modeling. We verify our approach on various examples, ranging from an inhomogeneous anisotropic stochastic differential equation on a torus, the chaotic Lorenz three-dimensional model, and the Niño-3.4 data set which is used as a proxy of the El Niño Southern Oscillation.

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. An accurate estimation of the local extent of testicular carcinomas in patients for whom testis-sparing surgery is planned is possible.

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). DWI was performed along the axial plane, using a single shot, multislice spin-echo planar diffusion pulse sequence and b-values of 0 and 900 s mm-2 . The mean and standard deviation of the ADC values of normal testicular parenchyma were calculated for each age group separately. Analysis of variance (ANOVA) followed by post hoc analysis (Dunnett T3) was used for statistical purposes. The ADC values (× 10-3 mm 2 s-1 ) of normal testicular tissue were different among age groups (group 1: 1.08 ± 0.13; group 2: 1.15 ± 0.15 and group 3: 1.31 ± 0.22). ANOVA revealed differences in mean ADC among age groups (F = 11.391, P < 0.001). Post hoc analysis showed differences between groups 1 and 2 (P = 0.008) and between groups 1 and 3 (P = 0.043), but not between groups 2 and 3 (P = 0.197). Our findings suggest that ADC values of normal testicular tissue increase with advancing age.

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. Patients were divided into three groups according to the final diagnosis: benign intratesticular lesions, malignant intratesticular lesions, and normal testes. The patterns of contrast enhancement of both the normal testes and the intratesticular lesions were evaluated. Time-signal intensity plots were created and classified according to shape: Type I presented a linear increase of contrast enhancement throughout the examination, type II showed an initial upstroke followed by either a plateau or a gradual increase in the late contrast-enhanced phase, and type III presented an initial upstroke followed by gradual washout of the contrast medium. The relative percentages of peak height, maximum time, and mean slope were also calculated. RESULTS: Normal testes enhanced homogeneously with a type I curve. Most benign intratesticular lesions showed inhomogeneous or homogeneous contrast enhancement and a type II curve. Testicular carcinomas showed heterogeneous contrast enhancement with a type III curve. The relative percentages of maximum time to peak proved the most important discriminating factor in differentiating malignant from benign intratesticular masses (p < 0.001). CONCLUSION: Dynamic contrast-enhanced MRI may be used to distinguish between benign and malignant intratesticular mass lesions.

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. Augmented with graph-theoretic means, this approach can recover the three-dimensional structure of objects from random snapshots of unknown orientation at four orders of magnitude higher complexity than previously demonstrated. This is critical for the burgeoning field of structure recovery by X-ray Free Electron Lasers, as well as the more established electron microscopic techniques, including cryo-electron microscopy of biological systems. In a subsequent paper, we demonstrate the recovery of structure and dynamics from experimental, ultralow-signal random sightings of systems with X-rays, electrons, and photons, with no orientational or timing information.

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. We also show that ultra-low-signal, random sightings of dynamically evolving systems can be sequenced into high quality movies to reveal their evolution. Our approach offers a route to recovering timing information in time-resolved experiments, and extracting 3D movies from two-dimensional random sightings of dynamic systems.