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At least 1,675 records · Page 93

Entity Resolution at Large Scale: Benchmarking and Algorithmics

We seek scalable benchmarks for entity resolution problems. Solutions to these problems range from trivial approaches such as string sorting to sophisticated methods such as statistical relational learning. The theoretical and practical complexity of these approaches varies widely, so one of the primary purposes of a benchmark will be to quantify the trade-off between solution quality and runtime. We are motivated by the ubiquitous nature of entity resolution as a fundamental problem faced by any organization that ingests large amounts of noisy text data. A benchmark is typically a rigid specification that provides an objective measure usable for ranking implementations of an algorithm. For example the Top500 and HPCG500 bench- marks rank supercomputers based on their performance of dense and sparse linear algebra problems (respectively). These two benchmarks require participants to report FLOPS counts attainable on various machines. Our purpose is slightly different. Whereas the supercomputing benchmarks mentioned above hold algorithms constant and aim to rank machines, we are primarily interested in ranking algorithms. As mentioned above, entity resolution problems can be approached in completely different ways. We believe that users of our benchmarks must decide what sort of procedure to run before comparing implementations and architectures. Eventually, we also wish to provide a mechanism for ranking machines while holding algorithmic approach constant . Our primary contributions are parallel algorithms for computing solution quality mea- sures per entity. We find in some real datasets that many entities are quite easy to resolve while others are difficult, with a heavy skew toward the former case. Therefore, measures such as global confusion matrices, F measures, etc. do not meet our benchmarking needs. We design methods for computing solution quality at the granularity of a single entity in order to know when proposed solutions do well in difficult situations (perhaps justifying extra computational), or struggling in easy situations. We report on progress toward a viable benchmark for comparing entity resolution algo- rithms. Our work is incomplete, but we have designed and prototyped several algorithms to help evalute the solution quality of competing approaches to these problems. We envision a benchmark in which the objective measure is a ratio of solution quality to runtime.

97 MATHEMATICS AND COMPUTING↗

Experimental evidence of intermittent chaos in a glow discharge plasma without external forcing and its numerical modelling

Intermittent chaos was observed in a glow discharge plasma as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) as the discharge voltage was increased. Floating potential fluctuations were analyzed by different statistical and spectral methods. Features like a gradual change in the normal variance of the interpeak time intervals, a dip in the skewness, and a hump in the kurtosis with variation in the control parameter have been seen, which are strongly indicative of intermittent behavior in the system. Detailed analysis also suggests that the intrinsic noise level in the experiment increases with the increasing discharge voltage. An attempt has been made to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations for an unmagnetized plasma. Though the experiment had no external forcing, it was conjectured that the intrinsic noise in the experiment could be playing a vital role in the dynamics of the system. Hence, a constant bias and noise as forcing terms were included in the model. Results from the theoretical model are in close qualitative agreement with the experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility

Wind tunnel experiments will continue to be a primary source of validation data for many types of mathematical and computational models in the aerospace industry. The increased emphasis on accuracy of data acquired from these facilities requires understanding of the uncertainty of not only the measurement data but also any correction applied to the data. One of the largest and most critical corrections made to these data is due to wall interference. In an effort to understand the accuracy and suitability of these corrections, a statistical validation process for wall interference correction methods has been developed. This process is based on the use of independent cases which, after correction, are expected to produce the same result. Comparison of these independent cases with respect to the uncertainty in the correction process establishes a domain of applicability based on the capability of the method to provide reasonable corrections with respect to customer accuracy requirements. The statistical validation method was applied to the version of the Transonic Wall Interference Correction System (TWICS) recently implemented in the National Transonic Facility at NASA Langley Research Center. The TWICS code generates corrections for solid and slotted wall interference in the model pitch plane based on boundary pressure measurements. Before validation could be performed on this method, it was necessary to calibrate the ventilated wall boundary condition parameters. Discrimination comparisons are used to determine the most representative of three linear boundary condition models which have historically been used to represent longitudinally slotted test section walls. Of the three linear boundary condition models implemented for ventilated walls, the general slotted wall model was the most representative of the data. The TWICS code using the calibrated general slotted wall model was found to be valid to within the process uncertainty for test section Mach numbers less than or equal to 0.60. The scatter among the mean corrected results of the bodies of revolution validation cases was within one count of drag on a typical transport aircraft configuration for Mach numbers at or below 0.80 and two counts of drag for Mach numbers at or below 0.90.

Walker, Eric Lee↗

Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility

Wind tunnel experiments will continue to be a primary source of validation data for many types of mathematical and computational models in the aerospace industry. The increased emphasis on accuracy of data acquired from these facilities requires understanding of the uncertainty of not only the measurement data but also any correction applied to the data. One of the largest and most critical corrections made to these data is due to wall interference. In an effort to understand the accuracy and suitability of these corrections, a statistical validation process for wall interference correction methods has been developed. This process is based on the use of independent cases which, after correction, are expected to produce the same result. Comparison of these independent cases with respect to the uncertainty in the correction process establishes a domain of applicability based on the capability of the method to provide reasonable corrections with respect to customer accuracy requirements. The statistical validation method was applied to the version of the Transonic Wall Interference Correction System (TWICS) recently implemented in the National Transonic Facility at NASA Langley Research Center. The TWICS code generates corrections for solid and slotted wall interference in the model pitch plane based on boundary pressure measurements. Before validation could be performed on this method, it was necessary to calibrate the ventilated wall boundary condition parameters. Discrimination comparisons are used to determine the most representative of three linear boundary condition models which have historically been used to represent longitudinally slotted test section walls. Of the three linear boundary condition models implemented for ventilated walls, the general slotted wall model was the most representative of the data. The TWICS code using the calibrated general slotted wall model was found to be valid to within the process uncertainty for test section Mach numbers less than or equal to 0.60. The scatter among the mean corrected results of the bodies of revolution validation cases was within one count of drag on a typical transport aircraft configuration for Mach numbers at or below 0.80 and two counts of drag for Mach numbers at or below 0.90.

Walker, Eric L.↗

Data for Transposon Signatures of Allopolyploid Genome Evolution

Hybridization brings together chromosome sets from two or more distinct progenitor species. Genome duplication associated with hybridization, or allopolyploidy, allows these chromosome sets to persist as distinct subgenomes during subsequent meioses. Here, we present a general method for identifying the subgenomes of a polyploid based on shared ancestry as revealed by the genomic distribution of repetitive elements that were active in the progenitors. This subgenome-enriched transposable element signal is intrinsic to the polyploid, allowing broader applicability than other approaches that depend on the availability of sequenced diploid relatives. We develop the statistical basis of the method, demonstrate its applicability in the well-studied cases of tobacco, cotton, and Brassica napus, and apply it to several cases: allotetraploid cyprinids, allohexaploid false flax, and allooctoploid strawberry. These analyses provide insight into the origins of these polyploids, revise the subgenome identities of strawberry, and provide perspective on subgenome dominance in higher polyploids.

Genomics↗

Contactless Determination of Electrical Conductivity of One-Dimensional Nanomaterials by Solution-Based Electro-orientation Spectroscopy

For nanowires of the same composition, and even fabricated within the same batch, often exhibit electrical conductivities that can vary by orders of magnitude. Unfortunately, existing electrical characterization methods are time-consuming, making the statistical survey of highly variable samples essentially impractical. Here, we demonstrate a contactless, solution-based method to efficiently measure the electrical conductivity of 1D nanomaterials based on their transient alignment behavior in ac electric fields of different frequencies. In comparison with direct transport measurements by probe-based scanning tunneling microscopy shows that electro-orientation spectroscopy can quantitatively measure nanowire conductivity over a 5-order-of-magnitude range, 10–5–1 Ω–1 m–1 (corresponding to resistivities in the range 102–107 Ω·cm). With this method, we statistically characterize the conductivity of a variety of nanowires and find significant variability in silicon nanowires grown by metal-assisted chemical etching from the same wafer. We also find that the active carrier concentration of n-type silicon nanowires is greatly reduced by surface traps and that surface passivation increases the effective conductivity by an order of magnitude. Moreover, this simple method makes electrical characterization of insulating and semiconducting 1D nanomaterials far more efficient and accessible to more researchers than current approaches. Electro-orientation spectroscopy also has the potential to be integrated with other solution-based methods for the high-throughput sorting and manipulation of 1D nanomaterials for postgrowth device assembly.

36 MATERIALS SCIENCE↗

Field‐Induced Ferroelectric Phase Evolution During Polarization “Wake‐Up” in Hf 0.5 Zr 0.5 O 2 Thin Film Capacitors

Abstract As an emerging nonvolatile memory technology, HfO 2 ‐based ferroelectrics exhibit excellent compatibility with silicon CMOS process flows; however, the reliability of polarization switching in these materials remains a major challenge. During repeated field programming and erase of the polarization state of initially pristine HfO 2 ‐based ferroelectric capacitors, the magnitude of the measured polarization increases, a phenomenon known as “wake‐up”. In this study, the authors attempt to understand what causes the wake‐up effect in Hf 0.5 Zr 0.5 O 2 (HZO) capacitors using nondestructive methods that probe statistically significant sample volumes. Synchrotron X‐ray diffraction reveals a concerted shift in HZO Bragg peak position as a function of polarization switching cycle number in films prepared under conditions such that they exhibit extremely large (≈3000%) wake‐up. In contrast, a control sample with insignificant wake‐up shows no such peak shift. Capacitance – voltage measurements show evolution in the capacitance loop with switching cycle number for the wake‐up sample and no change for the control sample. Piezoresponse force microscopy measurements are utilized to visualize the domain switching with wake‐up. The combination of these observations clearly demonstrates that wake‐up is caused by a field‐driven phase transformation of the tetragonal phase to the metastable ferroelectric orthorhombic phase during polarization switching of HZO capacitors.

36 MATERIALS SCIENCE↗

A Novel Non‐Destructive Rapid Tool for Estimating Amino Acid Composition and Secondary Structures of Proteins in Solution

Abstract Amino‐acid protein composition plays an important role in biology, medicine, and nutrition. Here, a groundbreaking protein analysis technique that quickly estimates amino acid composition and secondary structure across various protein sizes, while maintaining their natural states is introduced and validated. This method combines multivariate statistics and the thermostable Raman interaction profiling (TRIP) technique, eliminating the need for complex preparations. In order to validate the approach, the Raman spectra are constructed of seven proteins of varying sizes by utilizing their amino acid frequencies and the Raman spectra of individual amino acids. These constructed spectra exhibit a close resemblance to the actual measured Raman spectra. Specific vibrational modes tied to free amino and carboxyl termini of the amino acids disappear as signals linked to secondary structures emerged under TRIP conditions. Furthermore, the technique is used inversely to successfully estimate amino acid compositions and secondary structures of unknown proteins across a range of sizes, achieving impressive accuracy ranging between 1.47% and 5.77% of root mean square errors (RMSE). These results extend the uses for TRIP beyond interaction profiling, to probe amino acid composition and structure.

Chemistry↗

A Bayesian Framework for Spectral Reprojection

Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

Li, Tongtong (ORCID:0000000276644764)↗

Determination of tungsten in geochemical reference material basalt Columbia River 2 by radiochemical neutron activation analysis and inductively coupled plasma mass spectrometry

Environmental tungsten (W) analyses are inhibited by a lack of reference materials and practical methods to remove isobaric and radiometric interferences. We present a method that evaluates the potential use of commercially available sediment, Basalt Columbia River-2 (BCR-2), as a reference material using neutron activation analysis (NAA) and mass spectrometry. Tungsten concentrations using both methods are in statistical agreement at the 95% confidence interval (92 ± 4 ng/g for NAA and 100 ±7 ng/g for mass spectrometry) with recoveries greater than 95%. These results indicate that BCR-2 may be suitable as a reference material for future studies.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Materials informatics: From the atomic-level to the continuum

We report that in recent years materials informatics, which is the application of data science to problems in materials science and engineering, has emerged as a powerful tool for materials discovery and design. This relatively new field is already having a significant impact on the interpretation of data for a variety of materials systems, including those used in thermoelectrics, ferroelectrics, battery anodes and cathodes, hydrogen storage materials, polymer dielectrics, etc. Its practitioners employ the methods of multivariate statistics and machine learning in conjunction with standard computational tools (e.g., density-functional theory) to, for example, visualize and dimensionally reduce large data sets, identify patterns in hyperspectral data, parse microstructural images of polycrystals, characterize vortex structures in ferroelectrics, design batteries and, in general, establish correlations to extract important physics and infer structure-property-processing relationships. In this Overview, we critically examine the role of informatics in several important materials subfields, highlighting significant contributions to date and identifying known shortcomings. We specifically focus attention on the difference between the correlative approach of classical data science and the causative approach of physical sciences. From this perspective, we also outline some potential opportunities and challenges for informatics in the materials realm in this era of big data.

36 MATERIALS SCIENCE↗

Impact of U-10Mo HALEU fuel element tolerances on the Massachusetts Institute of Technology reactor safety and operational performance – Thermal hydraulics

The U.S. is coordinating efforts for the conversion of six U.S. High Performance Research Reactors (USHPRR) including one critical facility from highly enriched uranium (HEU) to low-enriched uranium (LEU). In order to continue the mission of these reactors, including the Massachusetts of Institute of Technology Reactor (MITR), and achieve similar performance, high-assay low-enriched uranium (HALEU) with a high-density metallic alloy of uranium with 10 wt% molybdenum (U-10Mo) is being evaluated. The impact of the fabrication specification and tolerances was assessed following the preliminary design of the MITR LEU fuel elements using the U-10Mo monolithic alloy. This research focuses on the analysis of fabrication specification impact on thermal hydraulics (TH) characteristic of the MITR LEU core as a function of the variation of the relevant fuel specification parameters (e.g., coolant channel gap thickness, fuel plate thickness, etc.). The analyses are performed based on an all-fresh LEU fuel conversion plan identified in a preliminary safety analysis report submitted to the Nuclear Regulatory Commission. The reactor power margin to the onset of nucleate boiling (ONB) is assessed under the limiting safety system settings (LSSS), where a scram occurs, to ensure there is sufficient margin to the reactor safety limit, which is defined by the onset of flow instability that occurs after the ONB. The best estimate plus uncertainty approach is employed to analyze this TH characteristic, which yields realistic results while maintaining adequate conservatism, utilizing a statistical uncertainty propagation method with the STAT7 code. The TH characteristic is analyzed as a function of the variability of the specification parameters resulting from the fabrication process. The main findings of this study show that the MITR core can meet the TH safety and operational requirements at the all-LEU initial core startup (cycle 1), selected transition cycles (most reactive cycle and most limiting cycle: cycle 3 and 5, respectively) and equilibrium (cycle 14) cores under all limiting fabrication parameter combinations considered. In addition, the analyses show that the dependency of the core power margin to ONB on those specification parameters that have the most direct impact on TH performance is non-linear but monotonically decreasing within the specification tolerances. The third order polynomial fit curves are reported in detail for selected limiting cases and can serve as a powerful tool for future MITR fuel management in cases such as when HALEU supply is established that may allow additional cycle length or other operational benefits.

Conversion↗

Design of machine learning models with domain experts for automated sensor selection for energy fault detection

Data-driven techniques that extract insights from sensor data reduce the cost of improving system energy performance through fault detection and system health monitoring. To lower cost barriers to widespread deployment, a methodology is proposed that takes advantage of existing sensor data, encodes expert knowledge about the application system to create ‘virtual sensors’ and applies statistical and mathematical methods to reduce the time required for manual configurations. The approach combines sensor data points with encoded expert knowledge that is generic to the application system but independent of a particular deployment, thereby reducing the need to tailor to individual deployments. Additionally, this paper not only presents a method that detects faults from measured energy data, but also (1) describes an engagement method with experts in the energy system domain to identify data, (2) integrates domain knowledge with the data, (3) automatically selects from among the large pool of potential input data, and (4) uses machine learning to automatically build a data-driven fault detection model. Demonstration on a commercial building chiller plant shows that only a small number of virtual sensors is necessary for fault detection with high accuracy rates. This corresponds to the use of only five out of 52 original sensor data points features. With as few as four features, classification F1 scores exceed 90% on the training set and 80% on the testing set. The results are implementable and realizable using off-the-shelf tools. The goal is to design with domain experts an energy monitoring system that can be configured once and then widely deployed with little additional cost or effort.

47 OTHER INSTRUMENTATION↗

Load response of a floating wind turbine to turbulent atmospheric flow

The two turbulence-generation models [Kaimal Spectrum Exponential Coherence (KSEC) and Mann] specified in the international standard for wind turbine design assume neutral atmospheric conditions and are based on statistical and spectral methods. Mainly due to the lack of physics, the flow fields simulated with these models ultimately differ in their underlying structure, especially in terms of the spatial coherence of longitudinal velocity perturbations. While this may not be critical for smaller wind turbine rotors, it becomes important when rotor sizes increase. Furthermore, it might be especially important in the context of floating technologies as they are more sensitive to large turbulent coherent structures. Previous work found that these differences between KSEC and Mann can propagate to loads predictions and thereby affect the design space of the entire wind turbine system. It is therefore crucial to determine in which ways these two models are underperforming. Up until now, validation of these models had only been done in the vertical direction because it is extremely difficult to obtain atmospheric turbulence measurements separated laterally, and sampled at heights relevant to wind energy. In this work, we address the lack of measurements by using high-fidelity, high-resolution simulation data as a reference. We perform hour-long, large-eddy simulations of turbulent velocity fields that are stability-dependent and contain three-dimensional coherent structures. These flow fields are then used to investigate which stochastic model is a better predictor of loads on a realistic spar-system floating offshore wind turbine, and to quantify how the assumption of neutral stratification propagates to short-term load estimates. Both stochastic turbulence models are found to overpredict fatigue loading in high-wind scenarios (in some cases, by more than 25%) and underpredict it when the wind speed is low (by as much as 20%). The KSEC model matches the high-fidelity flow fields more closely than Mann at high wind speeds, and the opposite is true at low wind speeds. Finally, turbine loading is found to be sensitive to atmospheric stability even when the turbulence intensity remains fairly constant. This sensitivity is most pronounced at low wind speeds, when fatigue load estimates on the spar system can differ by 40%.

17 WIND ENERGY↗

Distribution of chemical elements in soils and stream sediments in the area of abandoned Sb–As–Tl Allchar mine, Republic of Macedonia

The aim of this study was to investigate the distribution of some toxic elements in topsoil and subsoil, focusing on the identification of natural and anthropogenic element sources in the small region of rare As–Sb–Tl mineralization outcrop and abandoned mine Allchar known for the highest natural concentration of Tl in soil worldwide. The samples of soil and sediments after total digestion were analyzed by inductively coupled plasma–mass spectrometry (ICP–MS) and inductively coupled plasma–atomic emission spectrometry (ICP–AES). Factor analysis (FA) was used to identify and characterize element associations. Six associations of elements were determined by the method of multivariate statistics: Rb–Ta–K–Nb–Ga–Sn–Ba–Bi–Li–Be–(La–Eu)–Hf–Zr–Zn–In–Pd–Ag–Pt–Mg; Tl–As–Sb–Hg; Te–S–Ag–Pt–Al–Sc–(Gd–Lu)–Y; Fe–Cu–V–Ge–Co–In; Pd–Zr–Hf–W–Be and Ni–Mn–Co–Cr–Mg. The purpose of the assessment was to determine the nature and extent of potential contamination as well as to broadly assess possible impacts to human health and the environment. The results from the analysis of the collected samples in the vicinity of the mine revealed that As and Tl elements have the highest median values. Higher median values for Sb are obviously as a result of the past mining activities and as a result of area surface phenomena in the past. - Highlights: • Soil and river sediments were analyzed from Sb–As–Tl Allchar locality. • An increased content of certain toxic elements for environment was determined. • Highest As and Tl contents are obtained in the close vicinity of Allchar mine. • River sediments portray 160 times higher content of Sb than EU values. • The results classify Allchar as probably the highest natural Tl-deposit worldwide.

54 ENVIRONMENTAL SCIENCES↗

Flexible, cluster-based analysis of the electronic medical record of sepsis with composite mixture models

The widespread adoption of electronic medical records (EMRs) in healthcare has provided vast new amounts of data for statistical machine learning researchers in their efforts to model and predict patient health status, potentially enabling novel advances in treatment. In the case of sepsis, a debilitating, dysregulated host response to infection, extracting subtle, uncataloged clinical phenotypes from the EMR with statistical machine learning methods has the potential to impact patient diagnosis and treatment early in the course of their hospitalization. However, there are significant barriers that must be overcome to extract these insights from EMR data. First, EMR datasets consist of both static and dynamic observations of discrete and continuous-valued variables, many of which may be missing, precluding the application of standard multivariate analysis techniques. Second, clinical populations observed via EMRs and relevant to the study and management of conditions like sepsis are often heterogeneous; properly accounting for this heterogeneity is critical. Here, we describe an unsupervised, probabilistic framework called a composite mixture model that can simultaneously accommodate the wide variety of observations frequently observed in EMR datasets, characterize heterogeneous clinical populations, and handle missing observations. In conclusion, we demonstrate the efficacy of our approach on a large-scale sepsis cohort, developing novel techniques built on our model-based clusters to track patient mortality risk over time and identify physiological trends and distinct subgroups of the dataset associated with elevated risk of mortality during hospitalization.

59 BASIC BIOLOGICAL SCIENCES↗

Comparison of experimental methods for estimating matrix diffusion coefficients for contaminant transport modeling

Here, diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.

54 ENVIRONMENTAL SCIENCES↗

Hybrid framework for the simulation of stochastic chemical kinetics

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗