STENCIL-NET for equation-free forecasting from data.

We present an artificial neural network architecture, termed STENCIL-NET, for equation-free forecasting of spatiotemporal dynamics from data. STENCIL-NET works by learning a discrete propagator that is able to reproduce the spatiotemporal dynamics of the training data. This data-driven propagator can then be used to forecast or extrapolate dynamics without needing to know a governing equation. STENCIL-NET does not learn a governing equation, nor an approximation to the data themselves. It instead learns a discrete propagator that reproduces the data. It therefore generalizes well to different dynamics and different grid resolutions. By analogy with classic numerical methods, we show that the discrete forecasting operators learned by STENCIL-NET are numerically stable and accurate for data represented on regular Cartesian grids. A once-trained STENCIL-NET model can be used for equation-free forecasting on larger spatial domains and for longer times than it was trained for, as an autonomous predictor of chaotic dynamics, as a coarse-graining method, and as a data-adaptive de-noising method, as we illustrate in numerical experiments. In all tests, STENCIL-NET generalizes better and is computationally more efficient, both in training and inference, than neural network architectures based on local (CNN) or global (FNO) nonlinear convolutions.

Stability selection enables robust learning of differential equations from limited noisy data.

We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data. Our stability selection approach, termed PDE-STRIDE, can be combined with any sparsity-promoting regression method and provides an interpretable criterion for model component importance. We show that the particular combination of stability selection with the iterative hard-thresholding algorithm from compressed sensing provides a fast and robust framework for equation inference that outperforms previous approaches with respect to accuracy, amount of data required, and robustness. We illustrate the performance of PDE-STRIDE on a range of simulated benchmark problems, and we demonstrate the applicability of PDE-STRIDE on real-world data by considering purely data-driven inference of the protein interaction network for embryonic polarization in Caenorhabditis elegans. Using fluorescence microscopy images of C. elegans zygotes as input data, PDE-STRIDE is able to learn the molecular interactions of the proteins.

Parallel Discrete Convolutions on Adaptive Particle Representations of Images.

We present data structures and algorithms for native implementations of discrete convolution operators over Adaptive Particle Representations (APR) of images on parallel computer architectures. The APR is a content-adaptive image representation that locally adapts the sampling resolution to the image signal. It has been developed as an alternative to pixel representations for large, sparse images as they typically occur in fluorescence microscopy. It has been shown to reduce the memory and runtime costs of storing, visualizing, and processing such images. This, however, requires that image processing natively operates on APRs, without intermediately reverting to pixels. Designing efficient and scalable APR-native image processing primitives, however, is complicated by the APR's irregular memory structure. Here, we provide the algorithmic building blocks required to efficiently and natively process APR images using a wide range of algorithms that can be formulated in terms of discrete convolutions. We show that APR convolution naturally leads to scale-adaptive algorithms that efficiently parallelize on multi-core CPU and GPU architectures. We quantify the speedups in comparison to pixel-based algorithms and convolutions on evenly sampled data. We achieve pixel-equivalent throughputs of up to 1TB/s on a single Nvidia GeForce RTX 2080 gaming GPU, requiring up to two orders of magnitude less memory than a pixel-based implementation.

Learning physically consistent differential equation models from data using group sparsity.

We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring differential-equation models from data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn biologically plausible and physically consistent models rather than models that simply fit the data best. We present the group iterative hard thresholding algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling.

Adaptive particle representation of fluorescence microscopy images.

Modern microscopes create a data deluge with gigabytes of data generated each second, and terabytes per day. Storing and processing this data is a severe bottleneck, not fully alleviated by data compression. We argue that this is because images are processed as grids of pixels. To address this, we propose a content-adaptive representation of fluorescence microscopy images, the Adaptive Particle Representation (APR). The APR replaces pixels with particles positioned according to image content. The APR overcomes storage bottlenecks, as data compression does, but additionally overcomes memory and processing bottlenecks. Using noisy 3D images, we show that the APR adaptively represents the content of an image while maintaining image quality and that it enables orders of magnitude benefits across a range of image processing tasks. The APR provides a simple and efficient content-aware representation of fluosrescence microscopy images.

Stochastic clonal expansion of "superstars" enhances the reserve capacity of enteric nervous system precursor cells.

We quantified cell population increase in the quail embryo enteric nervous system (ENS) from E2.5 (about 1500 cells) to E12 (about 8 million cells). We then probed ENS proliferative capacity by grafting to the chorio-allantoic membrane large (600 cells) and small (40 cells) populations of enteric neural crest (ENC) cells with aneural gut. This demonstrated that ENC cells show an extremely high capacity to regulate their proliferation while forming the ENS. Previous mathematical models and clonal label experiments revealed that a few dominant ENS "superstar" cell clones emerge but most clones are small. The model implied that "superstars" arise stochastically, but the same outcome could arise if "superstars" were pre-determined. We investigated these two modes mathematically and by grafting experiments with large and small numbers of ENCs, each including one EGFP-labelled ENC cell. The stochastic model predicts that the frequency of "superstar" detection increases as the ENC population decreases, the pre-determined model does not. Experimentally, as predicted by the stochastic model, the frequency of "superstar" detection increased with small ENC cell number. We conclude that ENS "superstar" clones achieve this status stochastically. Clonal dominance implies that clonal diversity is greatly reduced and in this case, somatic mutations may affect the phenotype. We suggest that somatic mutations coupled with loss of clonal diversity may contribute to variable penetrance and expressivity in individuals with genetically identical ENS pathologies.

Dynamic stepwise opening of integron attC DNA hairpins by SSB prevents toxicity and ensures functionality.

Biologically functional DNA hairpins are found in archaea, prokaryotes and eukaryotes, playing essential roles in various DNA transactions. However, during DNA replication, hairpin formation can stall the polymerase and is therefore prevented by the single-stranded DNA binding protein (SSB). Here, we address the question how hairpins maintain their functional secondary structure despite SSB's presence. As a model hairpin, we used the recombinogenic form of the attC site, essential for capturing antibiotic-resistance genes in the integrons of bacteria. We found that attC hairpins have a conserved high GC-content near their apical loop that creates a dynamic equilibrium between attC fully opened by SSB and a partially structured attC-6-SSB complex. This complex is recognized by the recombinase IntI, which extrudes the hairpin upon binding while displacing SSB. We anticipate that this intriguing regulation mechanism using a base pair distribution to balance hairpin structure formation and genetic stability is key to the dissemination of antibiotic resistance genes among bacteria and might be conserved among other functional hairpins.

Improving the appropriateness of antipsychotic prescribing in nursing homes: a mixed-methods process evaluation of an academic detailing intervention.

BACKGROUND: In 2014, nursing home administration and government officials were facing increasing public and media scrutiny around the variation of antipsychotic medication (APM) prescribing across Ontario nursing homes. In response, policy makers partnered to test an academic detailing (AD) intervention to address appropriate prescribing of APM in nursing homes in a cluster-randomized trial. This mixed-methods study aimed to explore how and why the AD intervention may have resulted in changes in the nursing home context. The objectives were to understand how the intervention was implemented, explore contextual factors associated with implementation, and examine impact of the intervention on prescribing. METHODS: Administrative data for the primary outcome of the full randomized trial will not be available for a minimum of 1 year. Therefore, this paper reports the findings of a planned, quantitative interim trial analysis assessed mean APM dose and prescribing prevalence at baseline and 3 and 6 months across 40 nursing homes (18 intervention, 22 control). Patient-level administrative data regarding prescribing were analyzed using generalized linear mixed effects regression. Semi-structured interviews were conducted with nursing home staff from the intervention group to explore opinions and experiences of the AD intervention. Interviews were analyzed using the framework method, with constructs from the Consolidated Framework for Implementation Research (CFIR) applied as pre-defined deductive codes. Open coding was applied when emerging themes did not align with CFIR constructs. Qualitative and quantitative findings were triangulated to examine points of divergence to understand how the intervention may work and to identify areas for future opportunities and areas for improvement. RESULTS: No significant differences were observed in prescribing outcomes. A total of 22 interviews were conducted, including four academic detailers and 18 nursing home staff. Constructs within the CFIR domains of Outer Setting, Inner Setting, and Characteristics of Individuals presented barriers to antipsychotic prescribing. Intervention Source, Evidence Strength and Quality, and Adaptability explained participant engagement in the AD intervention; nursing homes that exhibited a Tension for Change and Leadership Engagement reported positive changes in processes and communication. CONCLUSIONS: Participants described their experiences with the intervention against the backdrop of a range of factors that influence APM prescribing in nursing homes that exist at the system, facility, provider, and resident levels. In this context, the perceived credibility and flexibility of the intervention were critical features that explained engagement with and potential impact of the intervention. Development of a common language across the team to enable communication was reported as a proximal outcome that may eventually have an effect on APM prescribing rates. Process evaluations may be useful during early stages of evaluation to understand how the intervention is working and how it might work better. Qualitative results suggest the lack of early changes observed in prescribing may reflect the number of upstream factors that need to change for APM rates to decrease. TRIAL REGISTRATION: ClinicalTrials.gov, NCT02604056.

Differential Clonal Expansion in an Invading Cell Population: Clonal Advantage or Dumb Luck?

In neoplastic cell growth, clones and subclones are variable both in size and mutational spectrum. The largest of these clones are believed to represent those cells with mutations that make them the most "fit," in a Darwinian sense, for expansion in their microenvironment. Thus, the degree of quantitative clonal expansion is regarded as being determined by innate qualitative differences between the cells that originate each clone. Here, using a combination of mathematical modelling and clonal labelling experiments applied to the developmental model system of the forming enteric nervous system, we describe how cells which are qualitatively identical may consistently produce clones of dramatically different sizes: most clones are very small while a few clones we term "superstars" contribute most of the cells to the final population. The basis of this is minor stochastic variations ("luck") in the timing and direction of movement and proliferation of individual cells, which builds a local advantage for daughter cells that is cumulative. This has potentially important consequences. In cancers, especially before strongly selective cytotoxic therapy, the assumption that the largest clones must be the cells with deterministic proliferative ability may not always hold true. In development, the gradual loss of clonal diversity as "superstars" take over the population may erode the resilience of the system to somatic mutations, which may have occurred early in clonal growth.

Spatial and temporal dynamics of cell generations within an invasion wave: a link to cell lineage tracing.

Mathematical models of a cell invasion wave have included both continuum partial differential equation (PDE) approaches and discrete agent-based cellular automata (CA) approaches. Here we are interested in modelling the spatial and temporal dynamics of the number of divisions (generation number) that cells have undergone by any time point within an invasion wave. In the CA framework this is performed from agent lineage tracings, while in the PDE approach a multi-species generalized Fisher equation is derived for the cell density within each generation. Both paradigms exhibit qualitatively similar cell generation densities that are spatially organized, with agents of low generation number rapidly attaining a steady state (with average generation number increasing linearly with distance) behind the moving wave and with evolving high generation number at the wavefront. This regularity in the generation spatial distributions is in contrast to the highly stochastic nature of the underlying lineage dynamics of the population. In addition, we construct a method for determining the lineage tracings of all agents without labelling and tracking the agents, but through either a knowledge of the spatial distribution of the generations or the number of agents in each generation. This involves determining generation-dependent proliferation probabilities and using these to define a generation-dependent Galton-Watson (GDGW) process. Monte-Carlo simulations of the GDGW process are used to determine the individual lineage tracings. The lineages of the GDGW process are analyzed using Lorenz curves and found to be similar to outcomes generated by direct lineage tracing in CA realizations. This analysis provides the basis for a potentially useful technique for deducing cell lineage data when imaging every cell is not feasible.

Cell lineage tracing in the developing enteric nervous system: superstars revealed by experiment and simulation.

Cell lineage tracing is a powerful tool for understanding how proliferation and differentiation of individual cells contribute to population behaviour. In the developing enteric nervous system (ENS), enteric neural crest (ENC) cells move and undergo massive population expansion by cell division within self-growing mesenchymal tissue. We show that single ENC cells labelled to follow clonality in the intestine reveal extraordinary and unpredictable variation in number and position of descendant cells, even though ENS development is highly predictable at the population level. We use an agent-based model to simulate ENC colonization and obtain agent lineage tracing data, which we analyse using econometric data analysis tools. In all realizations, a small proportion of identical initial agents accounts for a substantial proportion of the total final agent population. We term these individuals superstars. Their existence is consistent across individual realizations and is robust to changes in model parameters. This inequality of outcome is amplified at elevated proliferation rate. The experiments and model suggest that stochastic competition for resources is an important concept when understanding biological processes which feature high levels of cell proliferation. The results have implications for cell-fate processes in the ENS.

Associations between force and fatigue in fast-twitch motor units of a cat hindlimb muscle.

Associations were quantified between the control force and fatigue-induced force decline in 22 single fast-twitch-fatigable motor units of 5 deeply anesthetized adult cats. The units were subjected to intermittent stimulation at 1 train/s for 360 s. Two stimulation patterns were delivered in a pseudo-random manner. The first was a 500-ms train with constant interpulse intervals. The second pattern had the same number of stimuli, mean stimulus rate, and stimulus duration, but the stimulus pulses were rearranged to increase the force produced by the units in the control (prefatigue) state. The associations among the control peak tetanic force of these units, 3 indices of fatigue, and total cumulative force during fatiguing contractions were dependent, in part, on the stimulation pattern used to produce fatigue. The associations were also dependent, albeit to a lesser extent, on the force measure (peak vs. integrated) and the fatigue index used to quantify fatigue. It is proposed that during high-force fatiguing contractions, neural mechanisms are potentially available to delay and reduce the fatigue of fast-twitch-fatigable units for brief, but functionally relevant, periods. In contrast, the fatigue of slow-twitch fatigue-resistant units seems more likely to be controlled largely, if not exclusively, by metabolic processes within their muscle cells.

A prospective audit of stomas--analysis of risk factors and complications and their management.

AIM: To prospectively audit stomas and to determine the nature and rate of complications and their relationship with various risk factors and their management. MATERIALS AND METHODS: The study was performed prospectively on 97 consecutive patients who had stomas formed between January 2000 to August 2000. Patients were followed up for one year. Risk factors including age, body mass index (BMI), preoperative siting, contour of the abdominal wall, smoking, grade of operating surgeon, emergency or elective procedure, diabetes, type of stoma and suture material used were noted. The type of surgery, and indications for surgery were also recorded. The complications were documented by two qualified stoma nurses and a photographic record taken. Statistical analysis comprising both univariate and multivariate methods, was performed by SPSS 10. RESULTS: The mean age was 65 years (standard deviation 16.01, range 16-99) and mean body mass index was 24.5 (standard deviation 4.66, range 15-37). Forty-nine of 97 (50.5%) stomas developed one or more complications. Twenty-three patients experienced retraction, 18 had stomas sited in a skin crease, 16 had early and 12 had late skin excoriation, 12 had detachments and a further 12 had parastomal hernia. Eleven further stoma complications were noted including prolapse, necrosis, ischaemia and sloughing. None of the risk factors achieved statistical significance when analysed against the overall complication rate. However, when the risk factors were analysed against individual complications using univariate logistic regression, a high body mass index was associated with more retractions (P = 0.003), early skin excoriation (P = 0.036) and poor siting (stoma in crease) occurred more commonly in emergencies (P = 0.022). Diabetes was associated with late skin excoriation (P = 0.02). Multivariate logistic regressions confirmed an independent association of body mass index, diabetes and emergency surgery with complications. Forty-five of 49 patients who had complications needed some conservative management such as a convexity appliance. Four patients needed refashioning. CONCLUSION: Body mass index, diabetes and emergency surgery were the significant risk factors identified in our study. Overall complications compare favourably with other series. We found that preoperative siting by stoma nurses and the grade of operating surgeon did not affect the outcome.

Mutagenicity in lung of big Blue((R)) mice and induction of tandem-base substitutions in Salmonella by the air pollutant peroxyacetyl nitrate (PAN): predicted formation of intrastrand cross-links.

Peroxyacetyl nitrate (PAN) is a ubiquitous air pollutant formed from NO(2) reacting with acetoxy radicals generated from ambient aldehydes in the presence of sunlight and ozone. It contributes to eye irritation associated with photochemical smog and is present in most urban air. PAN was generated in a chamber containing open petri dishes of Salmonella TA100 (gas-phase exposure). After subtraction of the background mutation spectrum, the spectrum of PAN-induced mutants selected at 3.1-fold above the background mutant yield was 59% GC-->TA, 29% GC-->AT, 2% GC-->CG, and 10% multiple mutations - primarily GG-->TT tandem-base substitutions. Using computational molecular modeling methods, a mechanism was developed for producing this unusual tandem-base substitution. The mechanism depends on the protonation of PAN near the polyanionic DNA to release NO(2)(+) resulting in intrastrand dimer formation. Insertion of AA opposite the dimerized GG would account for the tandem GG-->TT transversions. Nose-only exposure of Big Blue((R)) mice to PAN at 78ppm (near the MTD) was mutagenic at the lacI gene in the lung (mutant frequency +/-S.E. of 6.16+/-0.58/10(5) for controls versus 8.24+/-0.30/10(5) for PAN, P=0.016). No tandem-base mutations were detected among the 40 lacI mutants sequenced. Dosimetry with 3H-PAN showed that 24h after exposure, 3.9% of the radiolabel was in the nasal tissue, and only 0.3% was in the lung. However, based on the molecular modeling considerations, the labeled portion of the molecule would not have been expected to have been bound covalently to DNA. Our results indicate that PAN is weakly mutagenic in the lungs of mice and in Salmonella and that PAN produces a unique signature mutation (a tandem GG-->TT transversion) in Salmonella that is likely due to a GG intrastrand cross-link. Thus, PAN may pose a mutagenic and possible carcinogenic risk to humans, especially at the high concentrations at which it is present in some urban environments.

The effect of rearfoot eversion on maximal hallux dorsiflexion. A preliminary study.

Functional hallux limitus has been recently described as an etiologic factor in postural complaints. Eversion of the rearfoot has been theoretically linked to decreased hallux dorsiflexion, although there have been no scientific studies on this subject to date. This study was undertaken to investigate the relationship between rearfoot eversion and hallux dorsiflexion; the results show that hallux dorsiflexion is decreased with rearfoot eversion in a static setting.

Determinants of bone mineral density in older men.

Although osteoporosis in men is increasingly recognized as an important health issue and bone mass appears to be a major determinant of fracture, there remain few data concerning the determinants of bone mass in men. To determine the correlates of bone density in men, we studied a large group of older subjects recruited from three rural communities in the northwestern United States. Three hundred and fifty-five men over the age of 60 years (mean 71.5 +/- 7.4 years) without known disorders of mineral metabolism were recruited by community advertising. Bone mineral density was measured at the lumbar spine, proximal femur and radius by dual-energy X-ray absorptiometry, and factors potentially related to skeletal status were assessed by direct measurements or questionnaire. In univariate analyses weight (positively) and age (negatively) were associated with bone density. After adjustment for these two factors, alcohol intake, osteoarthritis and thiazide use were associated with higher bone density, while previous fractures, gastrectomy, peptic ulcer disease, rheumatoid arthritis, glucocorticoid use, hypertension, previous hyperthyroidism, height loss since age 20 years, chronic lung disease and smoking were related to lower density. In multivariate models, only weight and a history of cancer were related to higher bone mass, and age, previous fracture, rheumatoid arthritis, gastrectomy and hypertension were associated with lower density. These data contribute to the emerging field of osteoporosis in men, and may help in the clinical identification of men at higher risk of osteopenia.