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.

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.

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.

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.

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.

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. The method employs Laplacian eigenmaps, evaluated after suitable time-lagged embedding, to produce a reduced representation of the observed samples, where standard tools of matrix algebra can be used to perform truncated singular-value decomposition despite the nonlinear geometrical structure of the dataset. We illustrate the utility of the technique in capturing intermittent modes associated with the Kuroshio current in the North Pacific sector of a general circulation model and dimensional reduction of a low-order atmospheric model featuring chaotic intermittent regime transitions, where classical singular spectrum analysis is already known to fail dramatically.

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.

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.

Development and validation of a direct headspace GC-FID method for the determination of sevoflurane, desflurane and other volatile compounds of forensic interest in biological fluids: application on clinical and post-mortem samples.

A simple and reliable headspace GC-flame ionization detection (HS-GC-FID) method has been developed and validated for the simultaneous determination of seven volatile compounds of forensic interest: sevoflurane, desflurane, ethanol, methanol, 1-propanol, acetone and acetaldehyde. All seven compounds including acetonitrile (internal standard) eluted within 10 min and were well resolved with no endogenous interference. Good linearity was observed in the range of 1-12 mg/dL for both anesthetics and 2.5-40 mg/dL for the other five analytes. The method showed good precision, sensitivity and repeatability. Most of the analytes remained stable during the storage of samples at 4°C. Desflurane and acetone degraded (>10%), when the samples remained on the autosampler for more than 2 and 3 h, respectively. The method was finally applied on clinical and post-mortem blood and urine samples. The clinical samples were collected both from patients who underwent surgery, as well as from the occupationally exposed medical and nursing staff of the university hospital, working in the operating rooms. The hospital staff samples were found negative for all compounds, while the patients' samples were found positive for the anesthetic administered to the patient. The post-mortem blood samples were found positive for ethanol and acetaldehyde.

Disposable pipette extraction for gas chromatographic determination of codeine, morphine, and 6-monoacetylmorphine in vitreous humor.

The availability of a sensitive and rapid analytical method for the determination of opiates, and other substances of forensic interest, in a variety of biological specimens is of utmost importance to forensic laboratories. Solid-phase extraction is very popular in the pre-treatment of forensic samples. Nevertheless, a new approach, disposable pipette extraction (DPX), is gaining increasing interest in sample preparation. DPX has already been applied to the analysis of drugs of abuse in common biological matrices, such as urine and blood, but has not yet been evaluated on alternative biological samples, such as vitreous humor. The objective of this study was to evaluate the applicability of DPX on the analysis of opiates in vitreous humor. The currently developed method is fast, reliable, and easy to perform. The sensitivity, precision, and accuracy are satisfactory. Recoveries obtained are within the range of 72-91%, whereas the sample volume of vitreous humor required is only 100 µL.

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.

MRI in the characterization and local staging of testicular neoplasms.

OBJECTIVE: The purpose of this study was to assess the role of MRI in the preoperative characterization and local staging of testicular neoplasms. SUBJECTS AND METHODS: MRI was performed on 33 patients referred because a testicular mass had been detected clinically and sonographically. Both T1- and T2-weighted sequences were performed with a 1.5-T MRI unit. Gadolinium chelate was administered IV in all cases. We recorded the presence of a lesion and whether the histologic diagnosis of testicular malignancy could have been predicted on the basis of MRI features. For testicular neoplasms, local extension of disease was studied. The MRI findings were correlated with the surgical and histopathologic results. RESULTS: Histologic examination revealed 36 intratesticular lesions, 28 (78%) of which were malignant and eight benign. Thirteen malignant testicular tumors (46%) were confined within the testis, 12 (43%) had invaded the testicular tunicae or epididymis, and three (11%) had invaded the spermatic cord. The sensitivity and specificity of MRI in differentiating benign from malignant intratesticular lesions were 100% (95% CI, 87.9-100%) and 87.5% (95% CI, 52.9-97.7%). The rate of correspondence between MRI and histologic diagnosis in the local staging of testicular tumors was 92.8% (26/28). CONCLUSION: MRI is a good diagnostic tool for the evaluation of testicular disease. It is highly accurate in the preoperative characterization and local staging of testicular neoplasms.

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.

Post-fertilization effects of chronic renal failure in male rats.

We evaluated the potential for growth and intrauterine development of embryos generated from the fertilization of oocytes with spermatozoa recovered from animals with chronic renal failure (CRF). Group A included sham-operated rats (n = 28), group B1 involved CRF rats that had undergone erythropoietin plus bromocryptine treatment (n = 28), and group B2 included CRF rats that had received normal saline. Embryos derived from the in vitro fertilization of oocytes with spermatozoa recovered from rats of group A or group B1 or group B2 were transferred to female recipients. We induced CRF in a group of rats (group B; n = 56; the total kidney volume was reduced to one-sixth with two operations). One week after the second operation, the rats of group B were randomly divided into group B1 (they subsequently received bromocryptine plus erythropoietin) and group B2 (they received injections of saline). Nine weeks after the second operation, the fertility of each male rat was assessed by mating tests and in vitro fertilization of oocytes. The mean litter size was significantly smaller in the subpopulation of fertile animals in group B2 than in the fertile rats of group B1 and in the fertile rats of group B1 than in the fertile rats of group A. Per cent of transferred blastocysts that developed into alive offspring were significantly lower in group B2 than in group B1 and in group B1 than in group A. Epididymal spermatozoa demonstrated a significantly larger DNA-oxidative damage in group B2 than in group B1 and in group B1 than in group A. These findings demonstrate that sperm-DNA damage because of CRF development is accompanied by a defect in the development of embryos generated in vitro. We may suggest that bromocryptine and erythropoietin protecting sperm DNA from oxidative damage improve reproductive potential in rats with CRF.

Development and validation of an HPLC method for the determination of seven penicillin antibiotics in veterinary drugs and bovine blood plasma.

Herein a quantitative method for the determination of seven penicillins in bovine plasma and veterinary drugs has been developed. Amoxicillin (AMO), ampicillin (AMP), penicillin G (PENG), penicillin V (PENV), oxacillin (OXA), cloxacillin (CLO) and dicloxacillin (DICLO) were separated on a Perfectsil ODS-2 (250 x 4 mm, 5 microm) column, using gradient elution, with a mobile phase of 0.1% v/v TFA and ACN-methanol (90:10 v/v). PDA detection was used at 240 nm. Penicillins were isolated from bovine plasma by SPE on Lichrolut RP-18 cartridges with mean recoveries from 85.7 to 113.5%. Colchicine (3 ng/microL) was used as an internal standard. The developed method was validated in terms of selectivity, linearity, accuracy, precision, stability and sensitivity. Repeatability (n = 5) and between-day precision (n = 5) revealed RSD < 12%. The detection limits in the bovine plasma were estimated as 18 ng for AMO and AMP, 25 for PENG, PENV and OXA, 3 ng for CLO and 12 ng for DICLO. Spiked plasma samples were stable for 1 wk, except for AMP and CLO, which were stable for 3 wk and OXA for 4 wk. AMO, PENG and PENV were stable for two freeze-thaw cycles, OXA, CLO and DICLO for four, while AMP only for one.

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.

Hormonal regulation of spermatogenesis and spermiogenesis.

Normal testicular function is dependent upon hormones acting through endocrine and paracrine pathways both in vivo and in vitro. Sertoli cells provide factors necessary for the successful progression of spermatogonia into spermatozoa. Sertoli cells have receptors for follicle stimulating hormone (FSH) and testosterone which are the main hormonal regulators of spermatogenesis. Hormones such as testosterone, FSH and luteinizing hormone (LH) are known to influence the germ cell fate. Their removal induces germ cell apoptosis. Proteins of the Bcl-2 family provide one signaling pathway which appears to be essential for male germ cell homeostasis. In addition to paracrine signals, germ cells also depend upon signals derived from Sertoli by direct membrane contact. Somatostatin is a regulatory peptide playing a role in the regulation of the proliferation of the male gametes. Activin A, follistatin and FSH play a role in germ cell maturation during the period when gonocytes resume mitosis to form the spermatogonial stem cells and differentiating germ cell populations. In vitro cultures systems have provided evidence that spermatogonia in advance stage of differentiation have specific regulatory mechanisms that control their fate. This review article provides an overview of the literature concerning the hormonal pathways regulating spermatogenesis.

16-MDCT cystoscopy in the evaluation of neoplasms of the urinary bladder.

OBJECTIVE: The purpose of this study was to evaluate the utility of 16-MDCT cystoscopy in the detection of urinary bladder neoplasms in a high-risk population. SUBJECTS AND METHODS: Fifty patients who presented with hematuria and a recent diagnosis or a history of bladder carcinoma underwent CT cystoscopy. All patients were examined in the supine and prone positions after bladder distention with room air. A detector configuration of 16 x 0.75 mm and a pitch of 1.2 was used. Virtual images were obtained with volume-rendered algorithms. Transverse tomographic slices, multiplanar reformatted images, and virtual images were prospectively evaluated separately and in combination. Conventional cystoscopy was considered the standard of reference for assessing the efficacy of MDCT cystoscopy in the detection of urinary bladder tumors. RESULTS: Fifty-five (96%) of 57 urinary bladder lesions recognized at conventional cystoscopy were detected with MDCT cystoscopy. The size of the lesions ranged from 0.3 to 9.7 cm in diameter, including 18 lesions with a diameter of 0.5 cm or less. Transverse, multiplanar reformatted, and virtual images proved complementary for lesion detection. CONCLUSION: MDCT cystoscopy is an accurate technique for the detection of urinary bladder neoplasms in patients at high risk, yielding satisfactory results in the identification of lesions smaller than 0.5 cm.