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At least 559 records · Page 31

MICCO: An Enhanced Multi-GPU Scheduling Framework for Many-Body Correlation Functions

Calculation of many-body correlation functions is one of the critical kernels utilized in many scientific computing areas, especially in Lattice Quantum Chromodynamics (Lattice QCD). It is formalized as a sum of a large number of contraction terms each of which can be represented by a graph consisting of vertices describing quarks inside a hadron node and edges designating quark propagations at specific time intervals. Due to its computation- and memory-intensive nature, real-world physics systems (e.g., multi-meson or multi-baryon systems) explored by Lattice QCD prefer to leverage multi-GPUs. Different from general graph processing, many-body correlation function calculations show two specific features: a large number of computation-/data-intensive kernels and frequently repeated appearances of original and intermediate data. The former results in expensive memory operations such as tensor movements and evictions. The latter offers data reuse opportunities to mitigate the data-intensive nature of many-body correlation function calculations. However, existing graph-based multi-GPU schedulers cannot capture these data-centric features, thus resulting in a sub-optimal performance for many-body correlation function calculations. To address this issue, this paper presents a multi-GPU scheduling framework, MICCO, to accelerate contractions for correlation functions particularly by taking the data dimension (e.g., data reuse and data eviction) into account. This work first performs a comprehensive study on the interplay of data reuse and load balance, and designs two new concepts: local reuse pattern and reuse bound to study the opportunity of achieving the optimal trade-off between them. Based on this study, MICCO proposes a heuristic scheduling algorithm and a machine-learning-based regression model to generate the optimal setting of reuse bounds. Specifically, MICCO is integrated into a real-world Lattice QCD system, Redstar, for the first time running on multiple GPUs. The evaluation demonstrates MICCO outperforms other state-of-art works, achieving up to 2.25× speedup in synthesized datasets, and 1.49× speedup in real-world correlation functions.

Wang, Qihan↗

Balanced stochastic versus deterministic assembly processes benefit diverse yet uneven ecosystem functions in representative agroecosystems

Ecological assembly processes, by influencing community composition, determine ecosystem functions of microbiomes. However, debate remains on how stochastic versus deterministic assembly processes influence ecosystem functions such as carbon and nutrient cycling. Towards a better understanding, we investigated three types of agroecosystems (the upland, paddy, and flooded) that represent a gradient of stochastic versus deterministic assembly processes. Carbon and nutrient cycling multifunctionality, characterized by nine enzymes associated with soil carbon, nitrogen, phosphorous and sulfur cycling, was evaluated and then associated with microbial assembly processes and cooccurrence patterns of vital ecological groups. Our results suggest that strong deterministic processes favour microorganisms with convergent functions (as in the upland agroecosystem), while stochasticity-dominated processes lead to divergent functions (as in the flooded agroecosystem). To benefit agroecosystems services, we speculate that it is critical for a system to maintain balance between its stochastic and deterministic assembly processes (as in the paddy agroecosystem). By doing so, the system can preserve a diverse array of functional traits and also allow for particular traits to flourish. To further confirm this speculation, it is necessary to develop a systematic knowledge beyond merely characterizing general patterns towards the associations among community assembly, composition, and ecosystem functions.

Liu, Wenjing↗

Linking Community‐Climate Disequilibrium to Ecosystem Function

Turnover in species composition often lags behind the pace of climate change, resulting in mismatches between climate and communities. However, the impact of these community‐climate disequilibria on ecosystem functions is rarely considered, and current methods for measuring disequilibria assume that species ranges were, until recently, in equilibrium with climate. Here, in this work, we develop a simple theoretical model to address both of these problems by linking community‐climate disequilibrium with ecosystem functioning. We show how disequilibrium can impair functioning in the near‐term even when climate change is expected to enhance functioning in the long‐term. Responses are most likely to change over time in communities where turnover is slow, the impact of disequilibrium counteracts the direct effects of climate on ecosystem function, and pre‐existing disequilibrium is large. These findings emphasise the importance of precise and unbiased estimates of community‐climate disequilibria for improving ecological forecasts. By fitting our model to time series of both climate and ecosystem function from a metacommunity simulation, we show the potential for community‐climate disequilibrium to be inferred without direct knowledge about species' distributions or climatic tolerances. We end by outlining a research agenda to apply dynamic disequilibrium concepts and test novel hypotheses across diverse ecosystems.

climate change↗

Functional Adaptation of LPS-affected Dentoalveolar Fibrous Joints in Rats

We report the functional interplay between cementum of the root and alveolar bone of the socket is tuned by a uniquely positioned 70–80 µm wide fibrous and lubricious ligament in a dentoalveolar joint (DAJ). In this study, structural and biomechanical properties of the DAJ, periodontal ligament space (PDL-space also known as the joint space), alveolar bone of the socket, and cementum of the tooth root that govern the biomechanics of a lipopolysaccharide (LPS)-affected DAJ were mapped both in space and time. The hemi-maxillae from 20 rats (4 control at 6 weeks of age, 4 control and 4 LPS-affected at 12 weeks of age, 4 control and 4 LPS-affected at 16 weeks of age) were investigated using a hybrid technique; micro-X-ray computed tomography (5 µm resolution) in combination with biomechanical testing in situ. Temporal variations in bone and cementum volume fractions were evaluated. Trends in mineral apposition rates (MAR) in additional six Sprague Dawley rats (3 controls, 3 LPS-affected) were revealed by transforming spatial fluorochrome signals to functional growth rates (linearity factor - RW) of bone, dentin, and cementum using a fast Fourier transform on fluorochrome signals from 100-µm hemi-maxillae sections. An overall change in LPS-affected DAJ biomechanics (a 2.5–4.5X increase in tooth displacement and 2X tooth rotation at 6 weeks, no increase in displacement and a 7X increase in rotation at 12 weeks; 27% increase in bone effective strain at 6 weeks and 11% at 12 weeks relative to control) was associated with structural changes in the coronal regions of the DAJ (15% increase in PDL-space from 0 to 6 weeks but only 5% from 6 to 12 weeks compared to control). A significant increase (p < 0.05) in PDL-space between ligated and age-matched control was observed. The bone fraction of ligated at 12 weeks was significantly lower than its age-matched control, and no significant differences (p > 0.05) between groups were observed at 6 weeks. Cementum in the apical regions grew faster but nonlinearly (11% and 20% increase in cementum fraction (CF) at 6 and 12 weeks) compared to control. Alveolar bone revealed site-specific nonlinear growth with an overall increase in MAR (108.5 µm/week to 126.7 µm/week after LPS treatment) compared to dentin (28.3 µm/week in control vs. 26.1 µm/week in LPS-affected) and cementum (126.5 µm/week in control vs. 119.9 µm/week in LPS-affected). A significant increase in CF (p < 0.05) in ligated specimens was observed at 6 weeks of age. Anatomy-specific responses of cementum and bone to the mechano-chemo stimuli, and their collective temporal contribution to observed changes in PDL-space were perpetuated by altered tooth movement. Data highlight the “resilience” of DAJ function through the predominance of nonlinear growth response of cementum, changes in PDL-space, and bone architecture. Despite the significant differences in bone and cementum architectures, data provided insights into the reactionary effects of cementum as a built-in compensatory mechanism to reestablish functional competence of the DAJ. The spatial shifts in architectures of alveolar bone and cementum, and consequently ligament space, highlight adaptations farther away from the site of insult, which also is another novel insight from this study. These adaptations when correlated within the context of joint function (biomechanics) illustrate that they are indeed necessary to sustain DAJ function albeit being pathological.

60 APPLIED LIFE SCIENCES↗

Toward a coordinated understanding of hydro‐biogeochemical root functions in tropical forests for application in vegetation models

Summary Tropical forest root characteristics and resource acquisition strategies are underrepresented in vegetation and global models, hampering the prediction of forest–climate feedbacks for these carbon‐rich ecosystems. Lowland tropical forests often have globally unique combinations of high taxonomic and functional biodiversity, rainfall seasonality, and strongly weathered infertile soils, giving rise to distinct patterns in root traits and functions compared with higher latitude ecosystems. We provide a roadmap for integrating recent advances in our understanding of tropical forest belowground function into vegetation models, focusing on water and nutrient acquisition. We offer comparisons of recent advances in empirical and model understanding of root characteristics that represent important functional processes in tropical forests. We focus on: (1) fine‐root strategies for soil resource exploration, (2) coupling and trade‐offs in fine‐root water vs nutrient acquisition, and (3) aboveground–belowground linkages in plant resource acquisition and use. We suggest avenues for representing these extremely diverse plant communities in computationally manageable and ecologically meaningful groups in models for linked aboveground–belowground hydro‐nutrient functions. Tropical forests are undergoing warming, shifting rainfall regimes, and exacerbation of soil nutrient scarcity caused by elevated atmospheric CO 2 . The accurate model representation of tropical forest functions is crucial for understanding the interactions of this biome with the climate.

Plant Sciences↗

Atmospheric pressure plasma functionalization of polystyrene

Atmospheric pressure plasma jets (APPJs) are used to improve the adhesive and hydrophilic properties of commodity hydrocarbon polymers such as polypropylene, polyethylene, and polystyrene (PS). These improvements largely result from adding oxygen functional groups to the surface. PS functionalization is of interest to produce high value biocompatible well-plates and dishes, which require precise control over surface properties. In this paper, we discuss results from a computational investigation of APPJ functionalization of PS surfaces using He/O 2 /H 2 O gas mixtures. A newly developed surface reaction mechanism for functionalization of PS upon exposure to these plasmas is discussed. A global plasma model operated in plug-flow mode was used to predict plasma-produced species fluxes onto the PS surface. A surface site balance model was used to predict oxygen-functionalization of the PS following exposure to the plasma and ambient air. We found that O-occupancy on the surface strongly correlates with the O-atom flux to the PS, with alcohol groups and cross-linked products making the largest contributors to total oxygen fraction. Free radical sites, such as alkoxy and peroxy, are quickly consumed in the post-plasma exposure to air through passivation and cross-linking. O-atom fluences approaching 10 17 cm -2 saturate the O-occupancy on the PS surface, creating functionality that is not particularly sensitive to moderate changes in operating conditions.

36 MATERIALS SCIENCE↗

Practical considerations in using a binary pseudorandom array for instrument transfer function calibration

Binary pseudo-random array (BPRA) artifacts are useful devices for calibrating the instrument transfer function (ITF) of interferometric microscopes and other optical and non-optical surface and wavefront measurement instruments. The intrinsic white noise character of the power spectral density function of the artifact simplifies the deconvolution of the ITF from the measured power spectral density (PSD). However, resampling of the BPRA intrinsic artifact features with the measurement tool's specific sampling pattern modifies the white noise character of the intrinsic spectrum and needs to be accounted for in the ITF-based data deconvolution process. We have developed an analytic solution to the spectrum of a resampled one- and two- dimensional BPRA. The resultant nominal PSD function is a simple twoparameter cosine function with a period equal to the resampled pixel width. A transfer function model for interferometric microscopes that incorporates this function, along with an ITF that includes aliasing effects and variable numerical aperture (NA), wavelength, and obscuration factor, is used to fit to the BPRA PSDs measured by an interference microscope for a range of objective and zoom lens magnification combinations.

Takacs, PZ↗

Sphingomonas clade and functional distribution with simulated climate change

Microbes are essential for the functioning of all ecosystems, and as global warming and anthropogenic pollution threaten ecosystems, it is critical to understand how microbes respond to these changes. We investigated the climate response of Sphingomonas, a widespread gram-negative bacterial genus, during an 18-month microbial community reciprocal transplant experiment across a Southern California climate gradient. We hypothesized that after 18 months, the transplanted Sphingomonas clade and functional composition would correspond with site conditions and reflect the Sphingomonas composition of native communities. We extracted Sphingomonas sequences from metagenomic data across the gradient and assessed their clade and functional composition. Representatives of at least 12 major Sphingomonas clades were found at varying relative abundances along the climate gradient, and transplanted Sphingomonas clade composition shifted after 18 months. Site had a significant effect (PERMANOVA; P < 0.001) on the distribution of both Sphingomonas functional (R 2 = 0.465) and clade composition (R 2 = 0.400), suggesting that Sphingomonas composition depends on climate parameters. Additionally, for both Sphingomonas clade and functional composition, ordinations revealed that the transplanted communities shifted closer to the native Sphingomonas composition of the grassland site compared with the site they were transplanted into. Overall, our results indicate that climate and substrate collectively determine Sphingomonas clade and functional composition.

59 BASIC BIOLOGICAL SCIENCES↗

Identification and characterization of proteins of unknown function (PUFs) in Clostridium thermocellum DSM 1313 strains as potential genetic engineering targets

Abstract Background Mass spectrometry-based proteomics can identify and quantify thousands of proteins from individual microbial species, but a significant percentage of these proteins are unannotated and hence classified as proteins of unknown function (PUFs). Due to the difficulty in extracting meaningful metabolic information, PUFs are often overlooked or discarded during data analysis, even though they might be critically important in functional activities, in particular for metabolic engineering research. Results We optimized and employed a pipeline integrating various “guilt-by-association” (GBA) metrics, including differential expression and co-expression analyses of high-throughput mass spectrometry proteome data and phylogenetic coevolution analysis, and sequence homology-based approaches to determine putative functions for PUFs in Clostridium thermocellum . Our various analyses provided putative functional information for over 95% of the PUFs detected by mass spectrometry in a wild-type and/or an engineered strain of C. thermocellum . In particular, we validated a predicted acyltransferase PUF (WP_003519433.1) with functional activity towards 2-phenylethyl alcohol, consistent with our GBA and sequence homology-based predictions. Conclusions This work demonstrates the value of leveraging sequence homology-based annotations with empirical evidence based on the concept of GBA to broadly predict putative functions for PUFs, opening avenues to further interrogation via targeted experiments.

09 BIOMASS FUELS↗

The impact of kidney function on Alzheimer’s disease blood biomarkers: implications for predicting amyloid-β positivity

Impaired kidney function has a potential confounding effect on blood biomarker levels, including biomarkers for Alzheimer’s disease (AD). Given the imminent use of certain blood biomarkers in the routine diagnostic work-up of patients with suspected AD, knowledge on the potential impact of comorbidities on the utility of blood biomarkers is important. We aimed to evaluate the association between kidney function, assessed through estimated glomerular filtration rate (eGFR) calculated from plasma creatinine and AD blood biomarkers, as well as their influence over predicting Aβ-positivity. We included 242 participants from the Translational Biomarkers in Aging and Dementia (TRIAD) cohort, comprising cognitively unimpaired individuals (CU; n = 124), mild cognitive impairment (MCI; n = 58), AD dementia (n = 34), and non-AD dementia (n = 26) patients all characterized by [ 18 F] AZD-4694. Plasma samples were analyzed for Aβ42, Aβ40, glial fibrillary acidic protein (GFAP), neurofilament light chain (NfL), tau phosphorylated at threonine 181 (p-tau181), 217 (p-tau217), 231 (p-tau231) and N-terminal containing tau fragments (NTA-tau) using Simoa technology. Kidney function was assessed by eGFR in mL/min/1.73 m 2 , based on plasma creatinine levels, age, and sex. Participants were also stratified according to their eGFR-indexed stages of chronic kidney disease (CKD). We evaluated the association between eGFR and blood biomarker levels with linear models and assessed whether eGFR provided added predictive value to determine Aβ-positivity with logistic regression models. Biomarker concentrations were highest in individuals with CKD stage 3, followed by stages 2 and 1, but differences were only significant for NfL, Aβ42, and Aβ40 (not Aβ42/Aβ40). All investigated biomarkers showed significant associations with eGFR except plasma NTA-tau, with stronger relationships observed for Aβ40 and NfL. However, after adjusting for either age, sex or Aβ-PET SUVr, the association with eGFR was no longer significant for all biomarkers except Aβ40, Aβ42, NfL, and GFAP. When evaluating whether accounting for kidney function could lead to improved prediction of Aβ-positivity, we observed no improvements in model fit (Akaike Information Criterion, AIC) or in discriminative performance (AUC) by adding eGFR to a base model including each plasma biomarker, age, and sex. While covariates like age and sex improved model fit, eGFR contributed minimally, and there were no significant differences in clinical discrimination based on AUC values. We found that kidney function seems to be associated with AD blood biomarker concentrations. However, these associations did not remain significant after adjusting for age and sex, except for Aβ40, Aβ42, NfL, and GFAP. While covariates such as age and sex improved prediction of Aβ-positivity, including eGFR in the models did not lead to improved prediction for any biomarker. Our findings indicate that renal function, within the normal to mild impairment range, does not seem to have a clinically relevant impact when using highly accurate blood biomarkers, such as p-tau217, in a biomarker-supported diagnosis.

60 APPLIED LIFE SCIENCES↗

The Cross-sectional and Longitudinal Association Between Thyroid Function and Depression: A Population-Based Study

Abstract Context An association of thyroid function with mood disorders has been widely suggested, but very few studies have examined this association longitudinally. Objective We assessed the cross-sectional and longitudinal association between thyroid function and depression in a population-based cohort. Methods A total of 9471 individuals were included in cross-sectional analyses, of whom 8366 had longitudinal data. At baseline, we assessed thyroid function using serum samples (thyrotropin [TSH], free thyroxine (FT4), and thyroid peroxidase antibodies) and depressive symptoms using the Centre for Epidemiologic Studies Depression (CES-D) scale. Incident depressive events (n = 1366) were continuously followed up with the CES-D and clinical interviews. We analyzed the cross-sectional association of thyroid function and thyroid disease with depressive symptoms using linear and logistic regression, and the longitudinal association with Cox proportional hazard models for depressive events. Results Lower TSH levels and lower and higher FT4 levels were cross-sectionally associated with more depressive symptoms with a B value of −0.07 per 1 unit increase of natural log-transformed TSH (95% CI −0.11; −0.04). Furthermore, hypothyroidism was cross-sectionally associated with less depressive symptoms and hyperthyroidism with more depressive symptoms. Longitudinally, there was a U-shaped association between FT4 and incident depressive events but only in euthyroid participants. Conclusion We show a cross-sectional association between thyroid (dys)function with depressive symptoms, and a U-shaped association between FT4 and incident depressive events in euthyroid individuals. Our findings suggest an association of thyroid function with the risk of developing depression, albeit small. Reverse causation and additional underlying factors may also contribute to the association.

Roa Dueñas, Oscar Hernando (ORCID:0000000207522261↗

Dataset for manuscript "Rotational Memory Function of SPC/E water"

Memory effect are essential for dynamics of condensed materials and are responsible for non-exponential relaxation of correlation functions of dynamic variables through the memory function entering the memory equation. Memory functions of dipole rotations for polar liquids have never been calculated. We present here calculations of memory functions and single-dipole rotations and of the overall system dipole moment for SPC/E water measured by dielectric spectroscopy. The memory functions for single-particle and collective dynamics turn out to be nearly identical. This result validates theories of dielectric spectroscopy in terms of single-particle time correlation function and the connection between the collective and single-particle relaxation times in terms of the Kirkwood factor. The dataset includes single particle and system dipole moments, including their time-dependence.

74 ATOMIC AND MOLECULAR PHYSICS↗

Multi-domain automated patterning of DNA-functionalized hydrogels

DNA-functionalized hydrogels are capable of sensing oligonucleotides, proteins, and small molecules, and specific DNA sequences sensed in the hydrogels’ environment can induce changes in these hydrogels’ shape and fluorescence. Fabricating DNA-functionalized hydrogel architectures with multiple domains could make it possible to sense multiple molecules and undergo more complicated macroscopic changes, such as changing fluorescence or changing the shapes of regions of the hydrogel architecture. However, automatically fabricating multi-domain DNA-functionalized hydrogel architectures, capable of enabling the construction of hydrogel architectures with tens to hundreds of different domains, presents a significant challenge. We describe a platform for fabricating multi-domain DNA-functionalized hydrogels automatically at the micron scale, where reaction and diffusion processes can be coupled to program material behavior. Using this platform, the hydrogels’ material properties, such as shape and fluorescence, can be programmed, and the fabricated hydrogels can sense their environment. DNA-functionalized hydrogel architectures with domain sizes as small as 10 microns and with up to 4 different types of domains can be automatically fabricated using ink volumes as low as 50 μL. We also demonstrate that hydrogels fabricated using this platform exhibit responses similar to those of DNA-functionalized hydrogels fabricated using other methods by demonstrating that DNA sequences can hybridize within them and that they can undergo DNA sequence-induced shape change.

Rubanov, Moshe (ORCID:0000000180507407)↗

The Effects of Atmospheric Models on the Estimation of Infrasonic Source Functions at the Source Physics Experiment

We invert infrasound signals for an equivalent seismoacoustic source function using different atmospheric models to produce the necessary Green’s functions. The infrasound signals were produced by a series of underground chemical explosions as part of the Source Physics Experiment (SPE). In a previous study, we inverted the infrasound data using so-called predictive atmospheric models, which were based on historic, regional-scaled, publicly available weather observations interpolated onto a 3D grid. For the work presented here, we invert the same infrasound data, but using atmospheric models based on weather data collected in a time window that includes the approximate time of the explosion experiments, which we term postdictive models. We build two versions of the postdictive models for each SPE event: one that is based solely on the regional scaled observations, and one that is based on both regional scaled observations combined with on-site observations obtained by a weather sonde released at the time of the SPE. We then invert the observed data set three times, once for each atmospheric model type. We find that the estimated seismoacoustic source functions are relatively similar in waveform shape regardless of which atmospheric model that we used to construct the Green’s functions. However, we find that the amplitude of the estimated source functions is systematically dependent on the atmospheric model type: using the predictive atmospheric models to invert the data generally yields estimated source functions that are larger in amplitude than those estimated using the postdictive models.

54 ENVIRONMENTAL SCIENCES↗

Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation

The accuracy of the forward scattering approximation for two-point Green's functions of the Anderson localization model on the Cayley tree is studied. A relationship between the moments of the Green's function and the largest eigenvalue of the linearized transfer-matrix equation is proved in the framework of the supersymmetric functional-integral method. The new large-disorder approximation for this eigenvalue is derived and its accuracy is established. Using this approximation the probability distribution of the two-point Green's function is found and compared with that in the forward scattering approximation (FSA). It is shown that FSA overestimates the role of resonances and thus the probability for the Green's function to be significantly larger than its typical value. The error of FSA increases with increasing the distance between points in a two-point Green's function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Approximating and incorporating model uncertainty in an inversion for seismic source functions: Preliminary results

We present preliminary work on propagating model uncertainty into the estimation of the time domain source time functions of the seismic source. Our method is based on an estimated model covariance function, which we estimate from the data. The model covariance function is then used to construct a suite of surrogate Greens functions which we use in a Monte Carlo type inversion scheme. The result is a probability density function of the six independent source time functions, each of which corresponds to an individual component of the seismic moment tensor. We compare the results of our method with those obtained using a computationally expensive finite difference Monte Carlo method and find that our new method produces results that are deficient in low frequencies. The advantage of our new method, which we term the Karhunen-Loeve Monte Carlo (KLMC) method, is that is several orders of magnitude faster than our current method, which uses a finite difference scheme to produce the suite of forward models.

42 ENGINEERING↗

GaAs Neutron Response Functions and Radiation Damage Metrics

The radiation effects community needs clear, well-documented, neutron energy-dependent responses that can be used in assessing radiation-induced material damage to GaAs semiconductors and for correlating observed radiation-induced changes in the GaAs electronic properties with computed damage metrics. In support of the objective, this document provides: a) a clearly defined set of relevant neutron response functions for use in dosimetry applications; b) clear mathematical expressions for the defined response functions; and c) updated quantitative values for the energy- dependent response functions that reflect the best current nuclear data and modelling. This document recaps the legacy response functions. It then surveys the latest nuclear data and updates the recommended response function to support current GaAs damage studies. A detailed tabulation for six of the energy-dependent response functions is provided in an Appendix.

36 MATERIALS SCIENCE↗

Open library of g-functions for 34,321 configurations

Thermal response functions, known as g-functions, are commonly used in ground heat exchanger design tools and whole building energy simulation programs to simulate the ground heat exchanger performance. Calculation of g-functions can be quite computationally time-consuming, particularly as the number of boreholes gets large. However, once the g-function is computed, the actual simulation time can be quite short, particularly if a hybrid time-step (Cullin and Spitler 2011) approach is used. Because of this, pre-computed g-function libraries are commonly used in design tools and building simulation tools. This paper describes development of a new, publicly available library containing g-functions for 34,321 borehole field configurations; for each configuration, gfunctions are provided for 5 depths to allow interpolation between different borehole-to-height ratios. The available configurations include configurations in standard shapes: lines, rectangles, open rectangles, L-shapes, and U-shapes. It also includes new configurations: C-shapes, lopsided-U-shapes, and zoned rectangles, which are rectangular configurations with different interior and perimeter spacing of the boreholes.

Spitler, Jeffery↗