Статті в журналах з теми "Robust hierarchical ensemble"

Summary This paper presents the hierarchical ensemble Kalman filter (HEnKF) as a robust extension of the ensemble Kalman filter (EnKF). The HEnKF is developed to be robust against features like estimation uncertainty and rank deficiency related to covariance estimation in EnKF. The HEnKF imposes a hierarchical model on the state variables and uses prior distributions from the Gauss conjugate family of distributions to obtain more-robust estimates. An empirical study demonstrates that the HEnKF provides more-reliable results than the traditional EnKF approach. Better predictions and more-realistic prediction intervals are provided. The latter is caused by model-parameter uncertainty being an integral part of the HEnKF approach, while this effect is ignored in traditional EnKF. The two versions of the ensemble Kalman filter are also compared on a synthetic-reservoir study. The HEnKF appears as significantly better.

As a research hotspot in ensemble learning, clustering ensemble obtains robust and highly accurate algorithms by integrating multiple basic clustering algorithms. Most of the existing clustering ensemble algorithms take the linear clustering algorithms as the base clusterings. As a typical unsupervised learning technique, clustering algorithms have difficulties properly defining the accuracy of the findings, making it difficult to significantly enhance the performance of the final algorithm. AGglomerative NESting method is used to build base clusters in this article, and an integration strategy for integrating multiple AGglomerative NESting clusterings is proposed. The algorithm has three main steps: evaluating the credibility of labels, producing multiple base clusters, and constructing the relation among clusters. The proposed algorithm builds on the original advantages of AGglomerative NESting and further compensates for the inability to identify arbitrarily shaped clusters. It can establish the proposed algorithm’s superiority in terms of clustering performance by comparing the proposed algorithm’s clustering performance to that of existing clustering algorithms on different datasets.

A unique three dimensional (3D) hierarchical microcapsule structure (NiS_x@NCV) has been put forward, which is realized by the ensemble of N-doped carbon vesicles encapsulating dual-NiS_x (α-NiS/NiS₂) nanoparticles via an in situ nanospace-confined pyrolysis strategy.

One of the main problems in the analysis of real data is often related to the presence of anomalies. Namely, anomalous cases can both spoil the resulting analysis and contain valuable information at the same time. In both cases, the ability to detect these occurrences is very important. In the biomedical field, a correct identification of outliers could allow the development of new biological hypotheses that are not considered when looking at experimental biological data. In this work, we address the problem of detecting outliers in gene expression data, focusing on microarray analysis. We propose an ensemble approach for detecting anomalies in gene expression matrices based on the use of Hierarchical Clustering and Robust Principal Component Analysis, which allows us to derive a novel pseudo-mathematical classification of anomalies.

Rule-based reservoir modeling methods integrate geological depositional process concepts to generate reservoir models that capture realistic geologic features for improved subsurface predictions and uncertainty models to support development decision making. However, the robust and direct conditioning of these models to subsurface data, such as well logs, core descriptions, and seismic inversions and interpretations, remains as an obstacle for the broad application as a standard subsurface modeling technology. We implement a machine learning-based method for fast and flexible data conditioning of rule-based models. This study builds on a rule-based modeling method for deep-water lobe reservoirs. The model has three geological inputs: (1) the depositional element geometry, (2) the compositional exponent for element stacking pattern, and (3) the distribution of petrophysical properties with hierarchical trends conformable to the surfaces. A deep learning-based workflow is proposed for robust and non-iterative data conditioning. First, a generative adversarial network learns salient geometric features from the ensemble of the training rule-based models. Then, a new rule-based model is generated and a mask is applied to remove the model near local data along the well trajectories. Last, semantic image inpainting restores the mask with the optimum generative adversarial network realization that is consistent with both local data and the surrounding model. For the deep-water lobe example, the generative adversarial network learns the primary geological spatial features to generate reservoir realizations that reproduce hierarchical trend as well as the surface geometries and stacking pattern. Moreover, the trained generative adversarial network explores the latent reservoir manifold and identifies the ensemble of models to represent an uncertainty model. Semantic image inpainting determines the optimum replacement for the near-data mask that is consistent with the local data and the rest of the model. This work results in subsurface models that accurately reproduce reservoir heterogeneity, continuity, and spatial distribution of petrophysical parameters while honoring the local well data constraints.

Performing clustering analysis on a large amount of historical trajectory data can obtain information such as frequent flight patterns of aircraft and air traffic flow distribution, which can provide a reference for the revision of standard flight procedures and the optimization of the division of airspace sectors. At present, most trajectory clustering uses a single clustering algorithm. When other processing remains unchanged, it is difficult to improve the clustering effect by using a single clustering method. Therefore, this paper proposes a trajectory clustering ensemble method based on a similarity matrix. Firstly, a stacked autoencoder is used to learn a small number of features that are sufficiently representative of the trajectory and used as the input to the subsequent clustering algorithm. Secondly, each basis cluster is used to cluster the data set, and then a consistent similarity matrix is obtained by using the clustering results of each basis cluster. On this basis, using the deformation of the matrix as the distance matrix between trajectories, the agglomerative hierarchical clustering algorithm is used to ensemble the results of each basis cluster. Taking the Nanjing Lukou Airport terminal area as an example, the experimental results show that integrating multiple basis clusters eliminates the inherent randomness of a single clustering algorithm, and the trajectory clustering results are more robust.

Summary Model-based economic optimization of oil production has a significant scope to increase financial life-cycle performance. The net-present-value (NPV) objective in this optimization, because of its nature, focuses on long-term gains, whereas short-term production is not explicitly addressed. At the same time, the achievable NPV is highly uncertain because of strongly varying economic conditions and limited knowledge of the reservoir-model parameters. The prime focus of this work is to develop optimization strategies that balance both long-term and short-term economic objectives and also offer robustness to the long-term NPV. An earlier robust hierarchical optimization method honoring geological uncertainty with robust long-term and short-term NPV objectives serves as a starting base of this work. We address the issue of extending this approach to include economic uncertainty and aim to analyze how the optimal solution reduces the uncertainty in the achieved average NPV. An ensemble of varying oil prices is used to model economic uncertainty with average NPVs as robust objectives in the hierarchical approach. A weighted-sum approach is used with the same objectives to quantify the effect of uncertainty. To reduce uncertainty, a mean-variance-optimization (MVO) objective is then considered to maximize the mean and also minimize the variance. A reduced effect of uncertainty on the long-term NPV is obtained compared with the uncertainty in the mean-optimization (MO) objectives. Last, it is investigated whether, because of the better handling of uncertainty in MVO, a balance between short-term and long-term gains can be naturally obtained by solving a single-objective MVO. Simulation examples show that a faster NPV buildup is naturally achieved by choosing appropriate weighting of the variance term in the MVO objective.

Abstract. For much of the last century, forecasting centers around the world have offered seasonal streamflow predictions to support water management. Recent work suggests that the two major avenues to advance seasonal predictability are improvements in the estimation of initial hydrologic conditions (IHCs) and the incorporation of climate information. This study investigates the marginal benefits of a variety of methods using IHCs and/or climate information, focusing on seasonal water supply forecasts (WSFs) in five case study watersheds located in the US Pacific Northwest region. We specify two benchmark methods that mimic standard operational approaches – statistical regression against IHCs and model-based ensemble streamflow prediction (ESP) – and then systematically intercompare WSFs across a range of lead times. Additional methods include (i) statistical techniques using climate information either from standard indices or from climate reanalysis variables and (ii) several hybrid/hierarchical approaches harnessing both land surface and climate predictability. In basins where atmospheric teleconnection signals are strong, and when watershed predictability is low, climate information alone provides considerable improvements. For those basins showing weak teleconnections, custom predictors from reanalysis fields were more effective in forecast skill than standard climate indices. ESP predictions tended to have high correlation skill but greater bias compared to other methods, and climate predictors failed to substantially improve these deficiencies within a trace weighting framework. Lower complexity techniques were competitive with more complex methods, and the hierarchical expert regression approach introduced here (hierarchical ensemble streamflow prediction – HESP) provided a robust alternative for skillful and reliable water supply forecasts at all initialization times. Three key findings from this effort are (1) objective approaches supporting methodologically consistent hindcasts open the door to a broad range of beneficial forecasting strategies; (2) the use of climate predictors can add to the seasonal forecast skill available from IHCs; and (3) sample size limitations must be handled rigorously to avoid over-trained forecast solutions. Overall, the results suggest that despite a rich, long heritage of operational use, there remain a number of compelling opportunities to improve the skill and value of seasonal streamflow predictions.

Abstract Hierarchical analysis of binary black hole (BBH) detections by the Advanced LIGO and Virgo detectors has offered an increasingly clear picture of their mass, spin, and redshift distributions. Fully understanding the formation and evolution of BBH mergers will require not just the characterization of these marginal distributions, but the discovery of any correlations that exist between the properties of BBHs. Here, we hierarchically analyze the ensemble of BBHs discovered by LIGO and Virgo with a model that allows for intrinsic correlations between their mass ratios q and effective inspiral spins χ eff. At 98.7% credibility, we find that the mean of the χ eff distribution varies as a function of q, such that more unequal-mass BBHs exhibit systematically larger χ eff. We find a Bayesian odds ratio of 10.5 in favor of a model that allows for such a correlation over one that does not. Finally, we use simulated signals to verify that our results are robust against degeneracies in the measurements of q and χ eff for individual events. While many proposed astrophysical formation channels predict some degree correlation between spins and mass ratio, these predicted correlations typically act in an opposite sense to the trend we observationally identify in the data.

Circular RNAs (circRNAs) are non-coding RNAs with a special circular structure produced formed by the reverse splicing mechanism. Increasing evidence shows that circular RNAs can directly bind to RNA-binding proteins (RBP) and play an important role in a variety of biological activities. The interactions between circRNAs and RBPs are key to comprehending the mechanism of posttranscriptional regulation. Accurately identifying binding sites is very useful for analyzing interactions. In past research, some predictors on the basis of machine learning (ML) have been presented, but prediction accuracy still needs to be ameliorated. Therefore, we present a novel calculation model, CRBPDL, which uses an Adaboost integrated deep hierarchical network to identify the binding sites of circular RNA-RBP. CRBPDL combines five different feature encoding schemes to encode the original RNA sequence, uses deep multiscale residual networks (MSRN) and bidirectional gating recurrent units (BiGRUs) to effectively learn high-level feature representations, it is sufficient to extract local and global context information at the same time. Additionally, a self-attention mechanism is employed to train the robustness of the CRBPDL. Ultimately, the Adaboost algorithm is applied to integrate deep learning (DL) model to improve prediction performance and reliability of the model. To verify the usefulness of CRBPDL, we compared the efficiency with state-of-the-art methods on 37 circular RNA data sets and 31 linear RNA data sets. Moreover, results display that CRBPDL is capable of performing universal, reliable, and robust. The code and data sets are obtainable at https://github.com/nmt315320/CRBPDL.git.

Abstract. The ability to monitor, understand, and predict the dynamics of the terrestrial carbon cycle requires the capacity to robustly and coherently synthesize multiple streams of information that each provide partial information about different pools and fluxes. In this study, we introduce a new terrestrial carbon cycle data assimilation system, built on the PEcAn model–data eco-informatics system, and its application for the development of a proof-of-concept carbon “reanalysis” product that harmonizes carbon pools (leaf, wood, soil) and fluxes (GPP, Ra, Rh, NEE) across the contiguous United States from 1986–2019. We first calibrated this system against plant trait and flux tower net ecosystem exchange (NEE) using a novel emulated hierarchical Bayesian approach. Next, we extended the Tobit–Wishart ensemble filter (TWEnF) state data assimilation (SDA) framework, a generalization of the common ensemble Kalman filter which accounts for censored data and provides a fully Bayesian estimate of model process error, to a regional-scale system with a calibrated localization. Combined with additional workflows for propagating parameter, initial condition, and driver uncertainty, this represents the most complete and robust uncertainty accounting available for terrestrial carbon models. Our initial reanalysis was run on an irregular grid of ∼ 500 points selected using a stratified sampling method to efficiently capture environmental heterogeneity. Remotely sensed observations of aboveground biomass (Landsat LandTrendr) and leaf area index (LAI) (MODIS MOD15) were sequentially assimilated into the SIPNET model. Reanalysis soil carbon, which was indirectly constrained based on modeled covariances, showed general agreement with SoilGrids, an independent soil carbon data product. Reanalysis NEE, which was constrained based on posterior ensemble weights, also showed good agreement with eddy flux tower NEE and reduced root mean square error (RMSE) compared to the calibrated forecast. Ultimately, PEcAn's new open-source regional data assimilation framework provides a scalable workflow for harmonizing multiple data constraints and providing a uniform synthetic platform for carbon monitoring, reporting, and verification (MRV) as well as accelerating terrestrial carbon cycle research.

Purpose – The purpose of this paper is to posit a hierarchical classification of enactments, practices and virtues that comprise an emerging adaptive leadership response to the prevailing volatile, uncertain, complex and ambiguous (VUCA) conditions. Design/methodology/approach – Reports and discusses the findings of two neo-classical grounded theory research studies to theorise augmented leadership repertoires for VUCA worlds. The first study was conducted with eight large regional and multinational organisations in Australia. The second is an on going, longitudinal study undertaken with 18 regional, national and multinational organisations in New Zealand. Findings – The first neo-classical grounded theory study in Australia identifies a set of emerging leadership practices labelled, “Zeitgeist – Integrating Cognition, Conscience and Collective Spirit”, as part of such a repertoire. The preliminary results of the second neo-classical grounded theory research extension in New Zealand, results in the further grounded theorising of the ensemble leadership repertoire (ELR), which is an emerging and hierarchical classification of leadership enactments, practices and virtues for prevailing times. The classification is robust because of its methodological similarities and conceptual congruence with other emerging and well-accepted classifications like, for example, character strengths in positive psychology. Originality/value – The grounded theorising provides a core category of the ELR which has its origins in substantive context. It lists 93 enactments inducted from leaders’ key phrases. These enactments in turn aggregate in relational sets through the process of constant comparison to describe 14 practices, which in sets of dyads and triads describe the five zeitgeist leadership virtues of being present, being good, being in touch, being creative and being global.

With the new coronavirus raging around the world, home isolation has become an effective way to interrupt the spread of the virus. Effective monitoring of people in home isolation has also become a pressing issue. However, the large number of isolated people and the privatized isolated spaces pose challenges for traditional sensing techniques. Ubiquitous Wi-Fi offers new ideas for sensing people indoors. Advantages such as low cost, wide deployment, and high privacy make indoor human activity sensing technology based on Wi-Fi signals increasingly used. Therefore, this paper proposes a contactless indoor person continuous activity sensing method based on Wi-Fi signal Wi-CAS. The method allows for the sensing of continuous movements of home isolated persons. Wi-CAS designs an ensemble classification method based on Hierarchical Clustering (HEC) for the classification of different actions, which effectively improves the action classification accuracy while reducing the processing time. We have conducted extensive experimental evaluations in real home environments. By recording the activities of different people throughout the day, Wi-CAS is very sensitive to unusual activities of people and also has a combined activity recognition rate of 94.3%. The experimental results show that our proposed method provides a low-cost and highly robust solution for supervising the activities of home isolates.

Chromosomes are giant chain molecules organized into an ensemble of three-dimensional structures characterized with its genomic state and the corresponding biological functions. Despite the strong cell-to-cell heterogeneity, the cell-type specific pattern demonstrated in high-throughput chromosome conformation capture (Hi-C) data hints at a valuable link between structure and function, which makes inference of chromatin domains (CDs) from the pattern of Hi-C a central problem in genome research. Here we present a unified method for analyzing Hi-C data to determine spatial organization of CDs over multiple genomic scales. By applying statistical physics-based clustering analysis to a polymer physics model of the chromosome, our method identifies the CDs that best represent the global pattern of correlation manifested in Hi-C. The multi-scale intra-chromosomal structures compared across different cell types uncover the principles underlying the multi-scale organization of chromatin chain: (i) Sub-TADs, TADs, and meta-TADs constitute a robust hierarchical structure. (ii) The assemblies of compartments and TAD-based domains are governed by different organizational principles. (iii) Sub-TADs are the common building blocks of chromosome architecture. Our physically principled interpretation and analysis of Hi-C not only offer an accurate and quantitative view of multi-scale chromatin organization but also help decipher its connections with genome function.

Abstract. Hierarchical agglomerative cluster analysis was performed on single-particle multi-spatial datasets comprising optical diameter, asymmetry and three different fluorescence measurements, gathered using two dual Waveband Integrated Bioaerosol Sensor (WIBS). The technique is demonstrated on measurements of various fluorescent and non-fluorescent polystyrene latex spheres (PSL) before being applied to two separate contemporaneous ambient WIBS datasets recorded in a forest site in Colorado, USA as part of the BEACHON-RoMBAS project. Cluster analysis results between both datasets are consistent. Clusters are tentatively interpreted by comparison of concentration time series and cluster average measurement values to the published literature (of which there is a paucity) to represent: non-fluorescent accumulation mode aerosol; bacterial agglomerates; and fungal spores. To our knowledge, this is the first time cluster analysis has been applied to long term online PBAP measurements. The novel application of this clustering technique provides a means for routinely reducing WIBS data to discrete concentration time series which are more easily interpretable, without the need for any a priori assumptions concerning the expected aerosol types. It can reduce the level of subjectivity compared to the more standard analysis approaches, which are typically performed by simple inspection of various ensemble data products. It also has the advantage of potentially resolving less populous or subtly different particle types. This technique is likely to become more robust in the future as fluorescence-based aerosol instrumentation measurement precision, dynamic range and the number of available metrics is improved.

Machine learning techniques can be useful in applications such as credit approval and college admission. However, to be classified more favorably in such contexts, an agent may decide to strategically withhold some of her features, such as bad test scores. This is a missing data problem with a twist: which data is missing depends on the chosen classifier, because the specific classifier is what may create the incentive to withhold certain feature values. We address the problem of training classifiers that are robust to this behavior. We design three classification methods: MINCUT, Hill-Climbing (HC) and Incentive-Compatible Logistic Regression (IC-LR). We show that MINCUT is optimal when the true distribution of data is fully known. However, it can produce complex decision boundaries, and hence be prone to overfitting in some cases. Based on a characterization of truthful classifiers (i.e., those that give no incentive to strategically hide features), we devise a simpler alternative called HC which consists of a hierarchical ensemble of out-of-the-box classifiers, trained using a specialized hill-climbing procedure which we show to be convergent. For several reasons, MINCUT and HC are not effective in utilizing a large number of complementarily informative features. To this end, we present IC-LR, a modification of Logistic Regression that removes the incentive to strategically drop features. We also show that our algorithms perform well in experiments on real-world data sets, and present insights into their relative performance in different settings.

Customer Choice Modeling aims to model the decision-making process of customers, or segments of customers, through their choices and preferences identified by the analysis of their behaviors in one or more specific contexts. Clustering techniques are used in this context to identify patterns in their choices and preferences, to define segments of customers with similar behaviors, and to model how customers of different segments respond to competing products and offers. However, data clustering is an unsupervised learning task by nature, that is the grouping of customers with similar behaviors in clusters must be performed without prior knowledge about the nature and the number of intrinsic groups of data instances, i.e., customers, in the data space. Thus, the choice of both the clustering algorithm used and its parameterization, and of the evaluation method used to assess the relevance of the resulting clusters are central issues. Consensus clustering, or ensemble clustering, aims to solve these issues by combining the results of different clustering algorithms and parameterizations to generate a more robust and relevant final clustering result. We present a Multi-level Consensus Clustering approach combining the results of several clustering algorithmic configurations to generate a hierarchy of consensus clusters in which each cluster represents an agreement between different clustering results. A closed sets based approach is used to identified relevant agreements, and a graphical hierarchical representation of the consensus cluster construction process and their inclusion relationships is provided to the end-user. This approach was developed and experimented in travel industry context with Amadeus SAS. Experiments show how it can provide a better segmentation, and refine the customer segments by identifying relevant sub-segments represented as sub-clusters in the hierarchical representation, for Customer Choice Modeling. The clustering of travelers was able to distinguish relevant segments of customers with similar needs and desires (i.e., customers purchasing tickets according to different criteria, like price, duration of flight, lay-over time, etc.) and at different levels of precision, which is a major issue for improving the personalization of recommendations in flight search queries.

Abstract. Hierarchical agglomerative cluster analysis was performed on single-particle multi-spatial data sets comprising optical diameter, asymmetry and three different fluorescence measurements, gathered using two dual Wideband Integrated Bioaerosol Sensors (WIBSs). The technique is demonstrated on measurements of various fluorescent and non-fluorescent polystyrene latex spheres (PSL) before being applied to two separate contemporaneous ambient WIBS data sets recorded in a forest site in Colorado, USA, as part of the BEACHON-RoMBAS project. Cluster analysis results between both data sets are consistent. Clusters are tentatively interpreted by comparison of concentration time series and cluster average measurement values to the published literature (of which there is a paucity) to represent the following: non-fluorescent accumulation mode aerosol; bacterial agglomerates; and fungal spores. To our knowledge, this is the first time cluster analysis has been applied to long-term online primary biological aerosol particle (PBAP) measurements. The novel application of this clustering technique provides a means for routinely reducing WIBS data to discrete concentration time series which are more easily interpretable, without the need for any a priori assumptions concerning the expected aerosol types. It can reduce the level of subjectivity compared to the more standard analysis approaches, which are typically performed by simple inspection of various ensemble data products. It also has the advantage of potentially resolving less populous or subtly different particle types. This technique is likely to become more robust in the future as fluorescence-based aerosol instrumentation measurement precision, dynamic range and the number of available metrics are improved.

The tremendous boost in next generation sequencing and in the “omics” technologies makes it possible to characterize the human gut microbiome—the collective genomes of the microbial community that reside in our gastrointestinal tract. Although some of these microorganisms are considered to be essential regulators of our immune system, the alteration of the complexity and eubiotic state of microbiota might promote autoimmune and inflammatory disorders such as diabetes, rheumatoid arthritis, Inflammatory bowel diseases (IBD), obesity, and carcinogenesis. IBD, comprising Crohn’s disease and ulcerative colitis, is a gut-related, multifactorial disease with an unknown etiology. IBD presents defects in the detection and control of the gut microbiota, associated with unbalanced immune reactions, genetic mutations that confer susceptibility to the disease, and complex environmental conditions such as westernized lifestyle. Although some existing studies attempt to unveil the composition and functional capacity of the gut microbiome in relation to IBD diseases, a comprehensive picture of the gut microbiome in IBD patients is far from being complete. Due to the complexity of metagenomic studies, the applications of the state-of-the-art machine learning techniques became popular to address a wide range of questions in the field of metagenomic data analysis. In this regard, using IBD associated metagenomics dataset, this study utilizes both supervised and unsupervised machine learning algorithms, (i) to generate a classification model that aids IBD diagnosis, (ii) to discover IBD-associated biomarkers, (iii) to discover subgroups of IBD patients using k-means and hierarchical clustering approaches. To deal with the high dimensionality of features, we applied robust feature selection algorithms such as Conditional Mutual Information Maximization (CMIM), Fast Correlation Based Filter (FCBF), min redundancy max relevance (mRMR), Select K Best (SKB), Information Gain (IG) and Extreme Gradient Boosting (XGBoost). In our experiments with 100-fold Monte Carlo cross-validation (MCCV), XGBoost, IG, and SKB methods showed a considerable effect in terms of minimizing the microbiota used for the diagnosis of IBD and thus reducing the cost and time. We observed that compared to Decision Tree, Support Vector Machine, Logitboost, Adaboost, and stacking ensemble classifiers, our Random Forest classifier resulted in better performance measures for the classification of IBD. Our findings revealed potential microbiome-mediated mechanisms of IBD and these findings might be useful for the development of microbiome-based diagnostics.

AbstractThe choice of a prior model can have a large impact on the ability to assimilate data. In standard applications of ensemble-based data assimilation, all realizations in the initial ensemble are generated from the same covariance matrix with the implicit assumption that this covariance is appropriate for the problem. In a hierarchical approach, the parameters of the covariance function, for example, the variance, the orientation of the anisotropy and the ranges in two principal directions, may all be uncertain. Thus, the hierarchical approach is much more robust against model misspecification. In this paper, three approaches to sampling from the posterior for hierarchical parameterizations are discussed: an optimization-based sampling approach (randomized maximum likelihood, RML), an iterative ensemble smoother (IES), and a novel hybrid of the previous two approaches (hybrid IES). The three approximate sampling methods are applied to a linear-Gaussian inverse problem for which it is possible to compare results with an exact “marginal-then-conditional” approach. Additionally, the IES and the hybrid IES methods are tested on a two-dimensional flow problem with uncertain anisotropy in the prior covariance. The standard IES method is shown to perform poorly in the flow examples because of the poor representation of the local sensitivity matrix by the ensemble-based method. The hybrid method, however, samples well even with a relatively small ensemble size.

This paper describes a design that can be used for Explainable AI. The lower level is a nested ensemble of patterns created by self-organisation. The upper level is a hierarchical tree, where nodes are linked through individual concepts, so there is a transition from mixed ensemble masses to specific categories. Lower-level pattern ensembles are learned in an unsupervised manner and then split into branches when it is clear that the category has changed. Links between the two levels define that the concepts are learned and missing links define that they are guessed only. This paper proposes some new clustering algorithms for producing the pattern ensembles, that are themselves an ensemble which converges through aggregations. Multiple solutions are also combined, to make the final result more robust. One measure of success is how coherent these ensembles are, which means that every data row in the cluster belongs to the same category. The total number of clusters is also important and the teaching phase can correct the ensemble estimates with respect to both of these. A teaching phase would then help the classifier to learn the true category for each input row. During this phase, any classifier can learn or infer correct classifications from some other classifier's knowledge, thereby reducing the required number of presentations. As the information is added, cross-referencing between the two structures allows it to be used more widely, where a unique structure can build up that would not be possible by either method separately.

AbstractCritical services depend on infrastructure networks for their operation and any disruption to these networks can have significant impacts on society, the economy, and quality of life. Such networks can be characterised as graphs which can be used to understand their structural properties, and the effect on their behaviour and robustness to hazards. Using a suite of graphs and critical infrastructure networks, this study aims to show that networks which exhibit a hierarchical structure are more likely to be less robust comparatively to non-hierarchical networks when exposed to failures, including those which supply critical services. This study investigates the properties of a hierarchical structure through identifying a set of key characteristics from an ensemble of graph models which are then used in a comparative analysis against a suite of spatial critical infrastructure networks. A failure model is implemented and applied to understand the implications of hierarchical structures in real world networks for their robustness to perturbations. The study concludes that a set of three graph metrics, cycle basis, maximum betweenness centrality and assortativity coefficient, can be used to identify the extent of a hierarchy in graphs, where a lack of robustness is linked to the hierarchical structure, a feature exhibited in both graph models and infrastructure networks.

Abstract Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore, researchers often seek simpler descriptions that describe complex phenomena without numerically resolving all the interacting components. Stochastic differential equations (SDEs) arise naturally as models in this context. The growth in data acquisition, both through experiment and through simulations, provides an opportunity for the systematic derivation of SDE models in many disciplines. However, inconsistencies between SDEs and real data at short time scales often cause problems, when standard statistical methodology is applied to parameter estimation. The incompatibility between SDEs and real data can be addressed by deriving sufficient statistics from the time-series data and learning parameters of SDEs based on these. Here, we study sufficient statistics computed from time averages, an approach that we demonstrate to lead to sufficient statistics on a variety of problems and that has the secondary benefit of obviating the need to match trajectories. Following this approach, we formulate the fitting of SDEs to sufficient statistics from real data as an inverse problem and demonstrate that this inverse problem can be solved by using ensemble Kalman inversion. Furthermore, we create a framework for non-parametric learning of drift and diffusion terms by introducing hierarchical, refinable parameterizations of unknown functions, using Gaussian process regression. We demonstrate the proposed methodology for the fitting of SDE models, first in a simulation study with a noisy Lorenz ’63 model, and then in other applications, including dimension reduction in deterministic chaotic systems arising in the atmospheric sciences, large-scale pattern modeling in climate dynamics and simplified models for key observables arising in molecular dynamics. The results confirm that the proposed methodology provides a robust and systematic approach to fitting SDE models to real data.

AbstractAn ‘emergent constraint’ (EC) is a statistical relationship, across a model ensemble, between a measurable aspect of the present day climate (the predictor) and an aspect of future projected climate change (the predictand). If such a relationship is robust and understood, it may provide constrained projections for the real world. Here, Coupled Model Intercomparison Project 6 (CMIP6) models are used to revisit several ECs that were proposed in prior model intercomparisons with two aims: (1) to assess whether these ECs survive the partial out-of-sample test of CMIP6 and (2) to more rigorously quantify the constrained projected change than previous studies. To achieve the latter, methods are proposed whereby uncertainties can be appropriately accounted for, including the influence of internal variability, uncertainty on the linear relationship, and the uncertainty associated with model structural differences, aside from those described by the EC. Both least squares regression and a Bayesian Hierarchical Model are used. Three ECs are assessed: (a) the relationship between Southern Hemisphere jet latitude and projected jet shift, which is found to be a robust and quantitatively useful constraint on future projections; (b) the relationship between stationary wave amplitude in the Pacific-North American sector and meridional wind changes over North America (with extensions to hydroclimate), which is found to be robust but improvements in the predictor in CMIP6 result in it no longer substantially constrains projected change in either circulation or hydroclimate; and (c) the relationship between ENSO teleconnections to California and California precipitation change, which does not appear to be robust when using historical ENSO teleconnections as the predictor.

Abstract Legume plants such as soybean produce two major types of root lateral organs, lateral roots and root nodules. A robust computational framework was developed to predict potential gene regulatory networks (GRNs) associated with root lateral organ development in soybean. A genome-scale expression data set was obtained from soybean root nodules and lateral roots and subjected to biclustering using QUBIC (QUalitative BIClustering algorithm). Biclusters and transcription factor (TF) genes with enriched expression in lateral root tissues were converged using different network inference algorithms to predict high-confidence regulatory modules that were repeatedly retrieved in different methods. The ranked combination of results from all different network inference algorithms into one ensemble solution identified 21 GRN modules of 182 co-regulated genes networks, potentially involved in root lateral organ development stages in soybean. The workflow correctly predicted previously known nodule- and lateral root-associated TFs including the expected hierarchical relationships. The results revealed distinct high-confidence GRN modules associated with early nodule development involving AP2, GRF5 and C3H family TFs, and those associated with nodule maturation involving GRAS, LBD41 and ARR18 family TFs. Knowledge from this work supported by experimental validation in the future is expected to help determine key gene targets for biotechnological strategies to optimize nodule formation and enhance nitrogen fixation.

AbstractThe cingulate cortex is known to be a complex structure, involved in several cognitive and emotional functions, as well as being altered by a variety of brain disorders. This heterogeneity is reflected in the multiple parceling models proposed in the literature. At the present, sub-regions of the cingulate cortex had been identified taking into account functional and structural connectivity, as well as cytological and electrochemical properties. In the present work, we propose an innovative node-wise parceling approach based on meta-analytic Bayesian co-alteration. To this aim, 193 case–control voxel-based morphometry experiments were analyzed, and the Patel’s κ index was used to assess probability of morphometric co-alteration between nodes placed in the cingulate cortex and in the rest of the brain. Hierarchical clustering was then applied to identify nodes in the cingulate cortex exhibiting a similar pattern of whole-brain co-alteration. The obtained dendrogram highlighted a robust fronto-parietal cluster compatible with the default mode network, and being supported by the interplay between the retrosplenial cortex and the anterior and posterior cingulate cortex, rarely described in the literature. This ensemble was further confirmed by the analysis of functional patterns. Leveraging on co-alteration to investigate cortical organization could, therefore, allow to combine multimodal information, resolving conflicting results sometimes coming from the separate use of singular modalities. Crucially, this provides a valuable way to understand the pathological brain using data driven, whole-brain informed and context-specific evidence in a way not yet explored in the field.

Abstract Motivation Single-cell RNA-sequencing (scRNA-seq) is fast and becoming a powerful technique for studying dynamic gene regulation at unprecedented resolution. However, scRNA-seq data suffer from problems of extremely high dropout rate and cell-to-cell variability, demanding new methods to recover gene expression loss. Despite the availability of various dropout imputation approaches for scRNA-seq, most studies focus on data with a medium or large number of cells, while few studies have explicitly investigated the differential performance across different sample sizes or the applicability of the approach on small or imbalanced data. It is imperative to develop new imputation approaches with higher generalizability for data with various sample sizes. Results We proposed a method called scHinter for imputing dropout events for scRNA-seq with special emphasis on data with limited sample size. scHinter incorporates a voting-based ensemble distance and leverages the synthetic minority oversampling technique for random interpolation. A hierarchical framework is also embedded in scHinter to increase the reliability of the imputation for small samples. We demonstrated the ability of scHinter to recover gene expression measurements across a wide spectrum of scRNA-seq datasets with varied sample sizes. We comprehensively examined the impact of sample size and cluster number on imputation. Comprehensive evaluation of scHinter across diverse scRNA-seq datasets with imbalanced or limited sample size showed that scHinter achieved higher and more robust performance than competing approaches, including MAGIC, scImpute, SAVER and netSmooth. Availability and implementation Freely available for download at https://github.com/BMILAB/scHinter. Supplementary information Supplementary data are available at Bioinformatics online.

Abstract Background Bronchoscopy for suspected lung cancer has low diagnostic sensitivity, rendering many inconclusive results. The Bronchial Genomic Classifier (BGC) was developed to help with patient management by identifying those with low risk of lung cancer when bronchoscopy is inconclusive. The BGC was trained and validated on patients in the Airway Epithelial Gene Expression in the Diagnosis of Lung Cancer (AEGIS) trials. A modern patient cohort, the BGC Registry, showed differences in key clinical factors from the AEGIS cohorts, with less smoking history, smaller nodules and older age. Additionally, we discovered interfering factors (inhaled medication and sample collection timing) that impacted gene expressions and potentially disguised genomic cancer signals. Methods In this study, we leveraged multiple cohorts and next generation sequencing technology to develop a robust Genomic Sequencing Classifier (GSC). To address demographic composition shift and interfering factors, we synergized three algorithmic strategies: 1) ensemble of clinical dominant and genomic dominant models; 2) development of hierarchical regression models where the main effects from clinical variables were regressed out prior to the genomic impact being fitted in the model; and 3) targeted placement of genomic and clinical interaction terms to stabilize the effect of interfering factors. The final GSC model uses 1232 genes and four clinical covariates – age, pack-years, inhaled medication use, and specimen collection timing. Results In the validation set (N = 412), the GSC down-classified low and intermediate pre-test risk subjects to very low and low post-test risk with a specificity of 45% (95% CI 37–53%) and a sensitivity of 91% (95%CI 81–97%), resulting in a negative predictive value of 95% (95% CI 89–98%). Twelve percent of intermediate pre-test risk subjects were up-classified to high post-test risk with a positive predictive value of 65% (95%CI 44–82%), and 27% of high pre-test risk subjects were up-classified to very high post-test risk with a positive predictive value of 91% (95% CI 78–97%). Conclusions The GSC overcame the impact of interfering factors and achieved consistent performance across multiple cohorts. It demonstrated diagnostic accuracy in both down- and up-classification of cancer risk, providing physicians actionable information for many patients with inconclusive bronchoscopy.

Abstract We consider a black hole with a stretched horizon as a toy model for a fuzzball microstate. The stretched horizon provides a cut-off, and therefore one can determine the normal (as opposed to quasi-normal) modes of a probe scalar in this geometry. For the BTZ black hole, we compute these as a function of the level n and the angular quantum number J. Conventional level repulsion is absent in this system, and yet we find that the Spectral Form Factor (SFF) shows clear evidence for a dip-ramp-plateau structure with a linear ramp of slope ~ 1 on a log-log plot, with or without ensemble averaging. We show that this is a robust feature of stretched horizons by repeating our calculations on the Rindler wedge (times a compact space). We also observe that this is not a generic feature of integrable systems, as illustrated by standard examples like integrable billiards and random 2-site coupled SYK model, among others. The origins of the ramp can be traced to the hierarchically weaker dependence of the normal mode spectrum on the quantum numbers of the compact directions, and the resulting quasi-degeneracy. We conclude by noting an analogy between the 4-site coupled SYK model and the quartic coupling responsible for the non-linear instability of capped geometries. Based on this, we speculate that incorporating probe self-interactions will lead to stronger connections to random matrix behavior.

IntroductionInteractive improvisational musical spaces (which is to say, nearly all musical spaces) involve affective relations among bodies: between the bodies of human performers, between performers and active listeners, between the sonic "bodies" that comprise the multiple overlapping events that constitute a musical performance’s unfolding. Music scholarship tends to focus on either music’s sonic materialities (the sensible; what can be heard) or the cultural resonances that locate in and through music (the political or hermeneutic; how meaning is inscribed in and for a listening subject).An embodied turn, however, has recently been manifesting, bringing music scholarship into communication with feminist theory, queer theory, and approaches that foreground subjectivity and embodiment. Exemplary in this area are works by Naomi Cumming (who asks a critical question, “does the self form the sound, or the sound the self?;” Cumming 7), Suzanne Cusick, Marion Guck, Fred Maus, and Susan McClary. All of these scholars, in various ways, thematise the performative—what it feels like to make or experience music, and what effect that making or experiencing has on subject-formation.All of these authors strive to foreground the role of the performer and performativity in the context of the extended Western art music tradition. While each makes persuasive, significant points, my contention in this paper is that improvised music is a more fruitful starting place for thinking about embodiment and the co-constitutive relationship between performer and sound. That is, while (nearly) all music is improvised to a greater or lesser degree, the more radical contexts, in which paths are being selected and large-scale shapes drawn in the “heat of the moment,” can bring these issues into stark relief and serve as more productive entry points for thinking through crucial questions of embodiment, perspective, identity, and emergent meaning.Music-Improvisational ContextsA musical improvisational space is a “context,” in Lawrence Grossberg’s sense of the term (26), where acts of territorialisation unfold an ongoing process of meaning-constitution. Territorialisation refers to an always-ongoing process of mapping out a space within which subjects and objects are constituted (Deleuze and Guattari 314). I posit that musical acts of territorialising are performed by two kinds of bodies in mutually constitutive relationships: interacting corporeal performing bodies, with individual pasts, tendencies, wills, and affective attunements (Massumi, Semblance), and what I term musical-objects-as-bodies. This second category represents a way of considering music’s sonic materiality from an affective perspective—relational, internally differentiating, temporal. On the one hand musical-objects-as-bodies refer to the materiality of the now-ongoing music itself: from the speeds and slownesses of air molecules that are received by the ear and interpreted as sound in the brain, to notes and rhythms and musical gestures; to the various ways in which abstract forms are actively shaped by performers and interpreted by listeners, with their own individuated constellations of histories, tendencies, wants, attunements, and corporeal perspectives. On the other hand, musical-objects-as-bodies can refer to the histories, genres, dislocations, and nomadic movements that partially condition how sonic materialities are produced and perceived. These last two concepts should be read both in terms of how histories and genres become dislocated from themselves through the actions of practitioners, and as a priori principles—that is, not as aberrations that disrupt a norm, but as norms themselves.This involves two levels of abstraction: ascribing body-status to sound-complexes, and then doing the same for historical trajectories, cultural conditionings, and dislocations. Elizabeth Grosz asks us to theorise the body as “the threshold or borderline concept that hovers perilously and undecidably at the pivotal joint of binary pairs” (Grosz, Volatile 23); one such binary that is problematised is that of production and perception, which within the context of an improvising music ensemble are really two perspectives on the same phenomenon. The producers are also the perceivers, in other words. This is true of listeners too: acts of perception are themselves productive in the sense that they create contexts in which meanings emerge.In Gilles Deleuze and Félix Guattari’s language (46–54), an emerging context represents a plurality of milieux that are brought together in acts of territorialisation (and deterritorialisation; see below). The term “milieu” refers to the notion that acts of territorialisation always take place in the middle—they are always already bound up in ongoing processes of context-building. Nothing ever emerges from whole cloth; everything modifies by differential degree the contexts upon which it draws. In musical contexts, we might consider four types of milieux. External milieux are articulated by such factors as syntactic norms (what makes a piece of music sound like it belongs within a genre) and cultural conditionings. Internal milieux refer to what gives the elements of a piece of music a sense of belonging together, including formal designs, motivic structures, and melodic or harmonic singularities. An intermediary milieu involves the way gestures acquire sign-status in a context, thereby becoming meaningful. Annexed milieux are locations where new materials are absorbed and incorporated from without.Bodies ImprovisingA small example should put these points into focus. Four jazz musicians are on stage, performing a version of the well-known (in that community) song “Stella by Starlight.” External milieux here include the conventions of the genre: syntactic expectations, prescribed roles for different instruments, certain perspectives on historical performance practices. Internal milieux include the defining features of this song: its melody, harmonic progression, formal design. The performers’ affective attunements to the history of the song’s complex life so far form an intermediary milieu; note that that history is in a process of modification by the very act of the now-ongoing performance. Annexed milieux might include flights into the unexpected, fracturings of stylistic norms, or incorporations of other contexts into this one. The act of territorialisation is how these (and more) milieux are drawn together as forces in this performance, this time. Each performer is an agent, articulating sounds that represent the now-emerging object, this “Stella by Starlight.” Those articulated sounds, as musical-objects-as-bodies, conjoin with each other, and with performers, in ongoing processes of subject-formation.A double movement is at play in this characterisation. The first is strategic: thinking of musical forces as bodies in order to consider how relationships unfold between them in embodied terms—in terms of affect. But simultaneous with this is a reverse move that begins with affective forces and from there constructs those very bodies—human performing bodies as well as musical-objects-as-bodies. In other words, in order to draw lines between bodies that suggest contextual co-determinations where each exists in a continual process of engendering the other, we can turn to a consideration of the encounters between, and impingements of, affective forces through which bodies are constructed and actions are mobilised. This double movement is a paradox that requires three presuppositions. First, that bodies are indeed constituted through encounters of affective forces—this is Deleuze’s Spinozist claim (Deleuze, Spinoza 49–50). Second, that identity is performative within the context of a discourse. This is Judith Butler’s position, which I modify slightly to consider the potential of non- (or pre-) linguistic discourse, such as what can stem from drastic (active, experiential) music-syntactic spaces (Abbate). And third, that concepts like agency and passivity involve force-relations between human actors (with embodied perspectives, agencies, histories, tendencies, and diverse ranges of affective attunements), and the musical utterances expressed by and between them. Therefore, there is value in considering both actor and utterance as unfolding along the same plane, each participating in the other’s constitution.What is at stake when we conceive of sonic materiality in bodily terms in this way? The sounds produced in interactive music-improvisational settings are products of human agency. But there is a passive element to human musical-sound production. There is a degree of passivity that owes to learned behaviors, habits, and the singularities of one’s own history—this is the passive nature of Deleuze’s first synthesis of time (Deleuze, Difference 71–79), where past experiences and activities are drawn into a now-present action, partially conditioning it. Even overtly active selection in the living present is founded on this passivity, since one can only draw upon one’s own history and experience, which provides a limiting force on technique, which in turn directs expressive possibilities. In music-improvisation pedagogy, this might be phrased as “you can only play what you can hear.” Another way to say this is that passive synthesis conditions active selection.One way to overcome the foreclosure of possibility that necessarily falls out of passive synthesis is through interaction and engagement with the affective forces at play in interactive encounters. Through encounters, conditions for new possibilities emerge. The limiting concept “you can only play what you hear” is mitigated by an encounter with newly received stimuli: a heard gesture that invites further excavation of a motivic idea or that sparks a “line of flight” into a thus-far unthought-of next action. The way a newly received stimulus inspires new action is an affective encounter, and it re-conditions—it deterritorialises—the ongoing process of subject-formation. The encounter is a direct line drawn between the two types of bodies—that is, between the situated body of a producing and perceiving subject and the sonic materiality of a musical-object-as-body. While there are other kinds of encounters that unfold in the course of interactive musical performance (visual cues, for example, or tactile nearnesses), the events of heard sounds are the primary locations where bodies are constituted or subjects are formed. This is made transparent in a recent study by Schober and Spiro, where jazz musicians improvised together with no visual or tactile connection, relying solely on sound for their points of interactive contact. This suggested that jazz musicians are able to communicate effectively with only sonic data exchanged. That many improvisers play with their eyes closed, or with their backs to one another, only reinforces this.There are three aspects of sound that I wish to offer as support for a reading of musical objects as bodies. First is that sounds are temporally articulated and perceived. The materiality of sound is bound up with its temporality in ways that are more directly perceivable than many other worldly materialities. The obviousness of its temporally bound nature is one reason that music is used so often as an entry point for thinking through the ontological nature of time and process; viz. Husserl’s utilisation of musical melodies to explicate his phenomenology of internal time-consciousness, and Deleuze and Guattari’s location of acts of territorialisation in the (musical) refrain. Of course the distinction between sonic and other materialities is only a matter of degree: all matter, including bodies, is “continually subjected to transformation, to becoming, to unfolding over time” (Grosz, Time 79), but music foregrounds temporality in ways that many philosophers have found vivid and constructive.Second, musical sounds acquire meaning through their relationships with other sounds in contexts, both in the immediate context of the now-ongoing performance and in extended contexts of genre, syntax, and so on. Those relationships are with histories of past sounds, now-ongoing sounds, and future sounds expressed as results of accumulations of meaning-complexes. A gesture is played, and it acquires meaning through the ways it is “picked up” by differently attuned performers and listeners.In this sense, third, the line is blurred between action and agent; the distinction between the gesture and the execution of the gesture is effectively erased. From the performer’s perspective, how a gesture is “picked up” is made somewhat evident by the sonic materiality of the next gesture. This next gesture is a sign that represents the singularity of the performer’s affective attunement, or an expression of a stage (or, better, some now-ongoing aspect) of what Whitehead would call her “eventful” subjectivity (166–167). What is expressed is the way the performer is (actively or passively) attuning to the constellations of meanings that resonate in the event of the encounter with the musical-object-as-body, as that musical-object-as-body in turn expresses the history of past encounters that (actively or passively) engendered it. The present action as most-contracted expression of the past is Deleuze’s second synthesis of time, while the eventful way an action cuts into the future marks the time of his third synthesis (Deleuze, Difference 80–91).What is at stake in a turn to corporeality in music analysis? Nietzsche admonishes us to turn from the “facts” that the senses take in, process, and evaluate and re-begin our inquiry by questioning the body (272). This means, for music analysis, turning away from certain quantifiable aspects of sonic materiality (pitches, chords, rhythms, formal designs), towards the ways in which sounds are articulated by bodies in interactive contexts. This has been attempted from various perspectives in recent music scholarship, but again the reading of musical bodies I am pursuing foregrounds affective forces, eventful subject-formation, and performativity as identity, on the ground of improvised interaction. Improvising bodies engage in spaces where “all kinds of affects play their game” (Nietzsche 264), and they exist in constant states of change as they are impinged on by events (and as they impinge on events), those events also forming conduits to other bodies. Subjects are not just impinged on by events; they are events, processes, accumulations, and distributions of affective forces. As Grosz puts it, “the body codes the meanings projected onto it” (Volatile 18). In musical improvisation, performers are always in the process of becoming a subject, conditioned by the ways in which they are impinged upon by affective forces and the creative ways those impingements are taken up.Musical-objects-as-bodies, likewise, unfold as ongoing processes, their identity emerging through accumulations and distributions of relationships with other musical-objects-as-bodies. A musical gesture acquires meaning through the emerging context in which it participates, just as a performer acquires a sense of identity through acts of production and perception in, and that help create, a context. Moreover, an affective consideration of performer (as corporeal body) and musical gesture (as sonic utterance) involves “the torsion of one into the other, the passage, vector, or uncontrollable drift of the inside into the outside and the outside into the inside” (Grosz, Volatile xii). Grosz is describing the essential irreducibility of body and mind, but her language is compelling for thinking through the relationships between bodies and musical-objects-as-bodies as an ongoing co-constitutive, boundary-dissolving process.Bodies and/as AffectAffect begins in the in-between, in the productive space of the event in which bodies encounter one another. This is not, however, a pure in-between. Bodies are constructed by the ways in which affective forces impinge on them, but affective forces also stem from bodies. Bodies affect and are affected by one another, as Deleuze is fond of repeating (Spinoza 49). No affect, no bodies, but also no bodies, no affect. What does this mean? The in-between does not subvert corporeality, perspective, intention, or subjectivity, nor is there a hierarchical relation between them (that is, bodies do not emerge because of affective relations, nor the reverse). If we think of bodies as emergent subjectivities—as processes of subject-formation irreducibly connected to the ecological conditions in which they are acting—then the ways in which their identities come to be constructed are intricately connected to the performative utterances they are making and the variable ways they are taking up those utterances and folding them into their emergent processes of becoming. Here, the utterer–utterance distinction begins to break down. Judith Butler (24-25) argues that the ways in which bodies are defined emerge from performative acts, and that every such act constitutes a political action that contributes to the constitution of identity. As Butler writes, “that the gendered body is performative suggests that it has no ontological status apart from the various acts which constitute its reality” (136). Gender is a status that emerges through one’s actions in contexts—we perform gender, and by performing it we undergo a process of inscribing it on ourselves. This is one of many key points where music scholarship can learn from feminist theory. Like gender, musical identity is performed—we inscribe upon ourselves an emergent musical subjectivity through acts of performance and perception (which is itself a performance too, as an interaction with a musical-object-as-body).Performative acts, therefore, are not simply enacted by bodies; if identity is performed, then the acts themselves are what define the very bodies performing them. Again, the hierarchy breaks down: rather than beginning with a body (a subject) that acts, actions comprise what a body is, as an emergent subject, as the product of its actions. For Deleuze and Guattari, performed acts involve masks; masks do not disguise expression or identity but rather are expressions through which identity is drawn. “The mask does not hide the face, it is the face” (115); “the mask assures the […] construction of the face, the facialization of the head and the body: the mask is now the face itself, the abstraction or operation of the face. […] Never does the face assume a prior signifier or subject” (Deleuze and Guattari 181). In Butler’s terms, the performance does not presuppose the performer; the performer is the performance.Affect corresponds, then, not only to the pre-linguistic (Deleuze’s “dark precursor;” Difference 119–121) but also to the super-discursive: to the multiple embedded meaning-trajectories implicit in any discursive utterance; to the creative ways in which those meaning-trajectories can be taken up variably within the performance space; to the micro-political implications of both utterance and taking-up. Bergson writes: “[m]y body is […] in the aggregate of the material world […] receiving and giving back movement, with, perhaps, this difference only, that my body appears to choose, within certain limits, the manner in which it shall restore what it receives” (Bergson 4–5; also cited in Grosz, The Nick 165). This is exactly Grossberg’s “context,” by the way. The “manner in which it shall restore what it receives” refers, in the case of musically performing (corporeal) bodies, to how a gesture is taken up in a next performed action. In the case of musical-objects-as-bodies, conversely, it refers to how a next gesture contributes to the ongoing sense of meaning-accumulation in response to the ongoing flux of musical-objects-as-bodies within which it locates.In music-improvisational spaces, not only does the utterer–utterance, agent–action, or performer–­performed gesture distinction break down, but the distinction between performed and received gesture likewise blurs, in two senses: because of the nature of eventful subject-formation (whereby a musical gesture’s meaning is being drawn within its emergent context), and because the events of individual musical gestures are subsumed into larger composite events. This problematises the utterer-utterance breakdown by blurring the threshold between individual performed events, inviting a consideration of a paradoxical, but productive, excluded middle where musical-objects-as-bodies are both expressions of corporeal performative acts (engendering contextual subject-formations) and constituent elements of an emergent musical subjectivity (“the performance.” See Massumi (Parables) for more on productive engagements with the excluded middle). While beyond the scope of this paper, we might consider the radical co-constitution of different kinds of bodies in this way as a system, following Gregory Seigworth’s description: “the transitive effect undergone by a body (human or otherwise) in a system—a mobile and open system—composed of the various, innumerable forces of existing and the relations between those forces” (161).Performing Bodies and the Emergent WorkThis, ultimately, is my thesis: how to think about musical performance beginning with performing bodies rather than with a reified notion of musical materiality. Performing bodies are situated within the emerging context of improvised, interactive music-making. Musical utterances are enacted by those bodies, which are also taking up the utterances made by other bodies—as musical-objects-as-bodies. The context that is being built through this process of affective exchange is the performance (the this performance, this time of the jazz example above). Christopher Hasty writes,to perform, from per-formare is to really, actually (fully) form or shape. The ‘-ance’ of performance connotes action and process. The thing performed apart from or outside the forming is problematic. Is it a fixed, ideal form above or beyond (transcending), or beneath or behind (founding) the actual doing, a thing that can be known quite apart from the situated knowing itself? (200)The work–performance dichotomy that animates Hasty’s question (as well as those of Abbate, Goehr, and others) is not my question, since I suggest that using improvised music as an entry point into musical inquiry makes a turn to performance axiomatic. The improvised work is necessarily an active, emergent process, its particularities, boundaries, and meanings being drawn through its performed actions. Perhaps the question that underlies my query is, instead, how do we think about the processes of subject-formation that unfold through interactive music-making; how are performing and performed bodies being inscribed through what kinds of relationships with musical materialities?Is there, in the end, simply a musical body that subsumes both utterer and utterance, both subjectively-forming body and material sonic gesture? I do not wish to go quite that far, but I do wish to continue to problematise where one body stops and the next begins. To paraphrase one of themes of this special issue, where do the boundaries, thresholds, and intersections of musical bodies lie? Deleuze, following Spinoza, tells us frequently that we do not yet know what a body is capable of. This must be at least in part because we know not what a body is at any given point—the body, like the subject which we might now think of as no more than a sign, is in a process of becoming; there is no is (ontology), there is only and (conjunction). And there is no body, there are only bodies, for a body only exists in a complex and emergent ecological relationship with other bodies (see Grosz, Volatile 19). To conceive of porous thresholds between performing bodies and musical-objects-as-bodies is to foreground the performative aspects of improvised music-making and to break down the hierarchy, and possibly even the distinction, between agent, action, and the content of that action. Bodies of all types inscribe one another in ongoing acts of meaning-constitution: this is the properly drastic starting place for inquiry into the nature of musical process.ReferencesAbbate, Carolyn. “Music—Drastic or Gnostic?” Critical Inquiry 30.3 (2004): 505–536.Bergson, Henri. Matter and Memory. 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