High-dimensional Models Research Articles

Uncertainty quantification in high-dimensional linear models incorporating graphical structures with applications to gene set analysis.

The functions of genes in networks are typically correlated due to their functional connectivity. Variable selection methods have been developed to select important genes associated with a trait while incorporating network graphical information. However, no method has been proposed to quantify the uncertainty of individual genes under such settings. In this paper, we construct confidence intervals (CIs) and provide P-values for parameters of a high-dimensional linear model incorporating graphical structures where the number of variables p diverges with the number of observations. For combining the graphical information, we propose a graph-constrained desparsified LASSO (least absolute shrinkage and selection operator) (GCDL) estimator, which reduces dramatically the influence of high correlation of predictors and enjoys the advantage of faster computation and higher accuracy compared with the desparsified LASSO. Theoretical results show that the GCDL estimator achieves asymptotic normality. The asymptotic property of the uniform convergence is established, with which an explicit expression of the uniform CI can be derived. Extensive numerical results indicate that the GCDL estimator and its (uniform) CI perform well even when predictors are highly correlated. An R package implementing the proposed method is available at https://github.com/XiaoZhangryy/gcdl.

Seismic traveltime tomography based on ensemble Kalman inversion

SUMMARY In this paper, we present a new seismic traveltime tomography approach that combines ensemble Kalman inversion (EKI) with neural networks (NNs) to facilitate the inference of complex underground velocity fields. Our methodology tackles the challenges of high-dimensional velocity models through an efficient NN parametrization, enabling efficient training on coarse grids and accurate output on finer grids. This unique strategy, combined with a reduced-resolution forward solver, significantly enhances computational efficiency. Leveraging the robust capabilities of EKI, our method not only achieves rapid computations but also delivers informative uncertainty quantification for the estimated results. Through extensive numerical experiments, we demonstrate the exceptional accuracy and uncertainty quantification capabilities of our EKI-NNs approach. Even in the face of challenging geological scenarios, our method consistently generates valuable initial models for full wave inversion (FWI).

Calibrating high-dimensional rock creep constitutive models for geological disaster prevention: An application of data assimilation methods

The study of rock creep phenomena is of paramount importance due to its potential to trigger geological disasters, such as landslides. To predict and prevent such disasters, creep constitutive models are widely employed to comprehend the time-dependent deformation of rocks. These models encompass various mechanical parameters that describe the intricate stress-strain behaviors. Nevertheless, significant challenges persist in achieving accurate and consistent parameter estimation and state prediction. In this study, we introduce three advanced data assimilation (DA) methods, including one Markov chain Monte Carlo method, DREAM(KZS), and two ensemble smoother methods, ESMDA and ILUES. This marks the first application of such methods for calibrating rock creep models in the scenario of geological disaster prevention. We conducted numerical simulations under both low- and high-dimensional conditions to assess the performance of these DA methods. For the single partition model, all three DA methods demonstrated promising results. In the high-dimensional case, DREAM(KZS) displayed inefficiency, while both ESMDA and ILUES proved to be still effective. ESMDA offered improved data matching but tended to underestimate parameter uncertainties, whereas ILUES excelled in addressing the issue of equifinality. In a real-world case focusing on characterizing creep deformation at the Mogu tilting deformation body near the Lianghekou Dam, China, we employed all three DA methods, and they collectively demonstrated satisfactory performance. Particularly noteworthy is the enhanced performance of the DREAM(KZS) method during the accelerated creep phase, even in the presence of limited data. The findings of this research bear significant importance in reducing uncertainties associated with model parameters in the realm of rock mechanics, thereby advancing our capabilities in predicting and preventing disasters.

Uncertainty quantification in epigenetic clocks via conformalized quantile regression.

DNA methylation (DNAm) is a chemical modification of DNA that can be influenced by various factors, including age, environment, and lifestyle. An epigenetic clock is a predictive tool that measures biological age based on DNAm levels. It can provide insights into an individual's biological age, which may differ from their chronological age. This difference, known as the epigenetic age acceleration, may indicate the state of one's health and risk for age-related diseases. Moreover, epigenetic clocks are used in studies of aging to assess the effectiveness of anti-aging interventions and to understand the underlying mechanisms of aging and disease. Various epigenetic clocks have been developed using samples from different populations, tissues, and cell types, typically by training high-dimensional linear regression models with an elastic net penalty. While these models can predict mean biological age with high precision, there is a lack of uncertainty quantification which is important for interpreting the precision of age estimations and for clinical decision-making. To understand the distribution of a biological age clock beyond its mean, we propose a general pipeline for training epigenetic clocks, based on an integration of high-dimensional quantile regression and conformal prediction, to effectively reveal population heterogeneity and construct prediction intervals. Our approach produces adaptive prediction intervals not only achieving nominal coverage but also accounting for the inherent variability across individuals. By using the data collected from 728 blood samples in 11 DNAm datasets from children, we find that our quantile regression-based prediction intervals are narrower than those derived from conventional mean regression-based epigenetic clocks. This observation demonstrates an improved statistical efficiency over the existing pipeline for training epigenetic clocks. In addition, the resulting intervals have a synchronized varying pattern to age acceleration, effectively revealing cellular evolutionary heterogeneity in age patterns in different developmental stages during individual childhoods and adolescent cohort. Our findings suggest that conformalized high-dimensional quantile regression can produce valid prediction intervals and uncover underlying population heterogeneity. Although our methodology focuses on the distribution of aging in children, it is applicable to a broader range of populations to improve understanding of epigenetic age beyond the mean. This inference-based toolbox could provide valuable insights for future applications of epigenetic interventions for age-related diseases.

The future of cosmological likelihood-based inference: accelerated high-dimensional parameter estimation and model comparison

We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we combine (i) emulation, where a machine learning model is trained to mimic cosmological observables, e.g. CosmoPower-JAX; (ii) differentiable and probabilistic programming, e.g. JAX and NumPyro, respectively; (iii) scalable Markov chain Monte Carlo (MCMC) sampling techniques that exploit gradients, e.g. Hamiltonian Monte Carlo; and (iv) decoupled and scalable Bayesian model selection techniques that compute the Bayesian evidence purely from posterior samples, e.g. the learned harmonic mean implemented in harmonic. This paradigm allows us to carry out a complete Bayesian analysis, including both parameter estimation and model selection, in a fraction of the time of traditional approaches. First, we demonstrate the application of this paradigm on a simulated cosmic shear analysis for a Stage IV survey in 37- and 39-dimensional parameter spaces, comparing ΛCDM and a dynamical dark energy model ( w0waCDM). We recover posterior contours and evidence estimates that are in excellent agreement with those computed by the traditional nested sampling approach while reducing the computational cost from 8 months on 48 CPU cores to 2 days on 12 GPUs. Second, we consider a joint analysis between three simulated next-generation surveys, each performing a 3x2pt analysis, resulting in 157- and 159-dimensional parameter spaces. Standard nested sampling techniques are simply unlikely to be feasible in this high-dimensional setting, requiring a projected 12 years of compute time on 48 CPU cores; on the other hand, the proposed approach only requires 8 days of compute time on 24 GPUs. All packages used in our analyses are publicly available.

Machine Learning for Continuous-Time Finance

Abstract We develop an algorithm for solving a large class of nonlinear high-dimensional continuous-time models in finance. We approximate value and policy functions using deep learning and show that a combination of automatic differentiation and Ito’s lemma allows for the computation of exact expectations, resulting in a negligible computational cost that is independent of the number of state variables. We illustrate the applicability of our method to problems in asset pricing, corporate finance, and portfolio choice and show that the ability to solve high-dimensional problems allows us to derive new economic insights.

Exploring Siamese network to estimate sea state bias of synthetic aperture radar altimeter

Sea state bias (SSB) is a crucial error of satellite radar altimetry over the ocean surface. For operational nonparametric SSB (NPSSB) models, such as two-dimensional (2D) or three-dimensional (3D) NPSSB, the solution process becomes increasingly complex and the construction of their regression functions pose challenges as the dimensionality of relevant variables increases. And most current SSB correction models for altimeters still follow those of traditional nadir radar altimeters, which limits their applicability to Synthetic Aperture Radar altimeters. Therefore, to improve this situation, this study has explored the influence of multi-dimensional SSB models on Synthetic Aperture Radar altimeters. This paper proposes a deep learning-based SSB estimation model called SNSSB, which employs a Siamese network framework, takes various multi-dimensional variables related to sea state as inputs, and uses the difference in sea surface height (SSH) at self-crossover points as the label. Experiments were conducted using Sentinel-6 self-crossover data from 2021 to 2023, and the model is evaluated using three main metrics: the variance of the SSH difference, the explained variance, and the SSH difference variance index (SVDI). The experimental results demonstrate that the proposed SNSSB model can further improve the accuracy of SSB estimation. On a global scale, compared to the traditional NPSSB, the multi-dimensional SNSSB not only decreases the variance of the SSH difference by over 11%, but also improves the explained variance by 5-10 cm2 in mid- and low-latitude regions. And the regional SNSSB also performs well, reducing the variance of the SSH difference by over 10% compared to the NPSSB. Additionally, the SNSSB model improves the computational efficiency by approximately 100 times. The favorable results highlight the potential of the multi-dimensional SNSSB in constructing SSB models, particularly the five-dimensional (5D) SNSSB, representing a breakthrough in overcoming the limitations of traditional NPSSB for constructing high-dimensional models. This study provides a novel approach to exploring the multiple influencing factors of SSB.

Algorithm for globally identifiable reparametrizations of ODEs

Structural global parameter identifiability indicates whether one can determine a parameter's value in an ODE model from given inputs and outputs. If a given model has parameters for which there is exactly one value, such parameters are called globally identifiable. Given an ODE model involving not globally identifiable parameters, first we transform the system into one with locally identifiable parameters. As a main contribution of this paper, then we present a procedure for replacing, if possible, the ODE model with an equivalent one that has globally identifiable parameters. We first derive this as an algorithm for one-dimensional ODE models and then reuse this approach for higher-dimensional models.

Enhancing Temporal Knowledge Graph Representation with Curriculum Learning

Temporal knowledge graph representation approaches encounter significant challenges in handling the complex dynamic relations among entities, relations, and time. These challenges include the high difficulty of training and poor generalization performance, particularly with large datasets. To address these issues, this paper introduces curriculum learning strategies from machine learning, aiming to improve learning efficiency through effective curriculum planning. The proposed framework constructs a high-dimensional filtering model based on graph-based high-order receptive fields and employs a scoring model that uses a curriculum temperature strategy to evaluate the difficulty of temporal knowledge graph data quadruples at each stage. By progressively expanding the receptive field and dynamically adjusting the difficulty of learning samples, the model can better understand and capture multi-level information within the graph structure, thereby improving its generalization capabilities. Additionally, a temperature factor is introduced during model training to optimize parameter gradients, alongside a gradually increasing training strategy to reduce training difficulty. Experiments on the benchmark datasets ICEWS14 and ICEWS05-15 demonstrate that this framework not only significantly enhances model performance on these datasets but also substantially reduces training convergence time.

Theory-guided neural network for studying the ground state of 2D spin-orbit coupled Bose–Einstein condensates

Machine learning has been a powerful tool to study various models in many fields, which requires plenty of data to ensure accuracy. It is a challenge to reduce the dependence on the amount of data and ensure that the predictions are both accurate and physical. We develop a theory-guided neural network (TgNN) to explore the ground states of two-component spin–orbit coupled Bose–Einstein condensation in two-dimension. Only randomly selected few data from the twelve ground states as training data, TgNN performs higher accuracy, broader generalization ability and stronger robustness than deep neural network (DNN). Moreover, in the neighborhood of the phase transition where the predictions of DNN have obvious deviations, while TgNN still keeps relative accuracy. TgNN is less dependent on data and exhibits potential for high-dimensional and complicated models.

The principal components of meaning, revisited.

Osgood, Suci, and Tannebaum were the first to attempt to identify the principal components of semantics using dimensional reduction of a high-dimensional model of semantics constructed from human judgments of word relatedness. Modern word-embedding models analyze patterns of words to construct higher dimensional models of semantics that can be similarly subjected to dimensional reduction. Hollis and Westbury characterized the first eight principal components (PCs) of a word-embedding model by correlating them with several well-known lexical measures, such as logged word frequency, age of acquisition, valence, arousal, dominance, and concreteness. The results show some clear differentiation of interpretation between the PCs. Here, we extend this work by analyzing a larger word-embedding matrix using semantic measures initially derived from subjective inspection of the PCs. We then use quantitative analysis to confirm the utility of these subjective measures for predicting PC values and cross-validate them on two word-embedding matrices developed on distinct corpora. Several semantic and word class measures are strongly predictive of early PC values, including first-person and second-person verbs, personal relevance of abstract and concrete words, affect terms, and names of places and people. The predictors of the lowest magnitude PCs generalized well to word-embedding matrices constructed from separate corpora, including matrices constructed using different word-embedding methods. The predictive categories we describe are consistent with Wittgenstein's argument that an autonomous level of social interaction grounds linguistic meaning.

Strange star model in higher dimensions (D ≥ 4) with density-dependent B in pseudo-spheroidal geometry

In this paper, we have developed a class of new solutions for relativistic compact stars in higher-dimensional [Formula: see text] space-time assuming pseudo-spheroidal geometry of the [Formula: see text] metric component. To study the physical properties, we consider equation of state of interior strange matter [Formula: see text], as proposed in MIT bag model in the presence of a density-dependent [Formula: see text] parameter. The interior matter of a quark star may consist of three flavor quarks. We observe some interesting results. The parameter [Formula: see text] depends on the anisotropy [Formula: see text] in the interior, and at the stellar surface, [Formula: see text] attains a constant value independent of [Formula: see text]. At the interior, [Formula: see text] increases with the increase of [Formula: see text]. We also note that the value of B approaches a constant value with increasing spheroidal parameter [Formula: see text]. [Formula: see text] also depends on space-time dimensions and it is interesting to note that [Formula: see text] picks up negative values near core region which limits the number of space-time dimensions available for a stellar model. All the stability criterion and energy conditions hold good for a physically realistic stellar configuration. It is observed that strange quark matter may be stable or metastable or unstable depending upon the value of energy per baryon [Formula: see text]. Strange quark matter will be stable if energy per baryon [Formula: see text]. It is noted that the maximum mass obtainable in this model is [Formula: see text] considering stable strange quark matter when dimension [Formula: see text]. In addition, we observe that the dimensions have some effect on the gross properties of strange stars (SS).

MPeat2D – a fully coupled mechanical–ecohydrological model of peatland development in two dimensions

Abstract. Higher-dimensional models of peatland development are required to analyse the influence of spatial heterogeneity and complex feedback mechanisms on peatland behaviour. However, the current models exclude the mechanical process that leads to uncertainties in simulating the spatial variability in the water table position, vegetation composition, and peat physical properties. Here, we propose MPeat2D, a peatland development model in two dimensions, which considers mechanical, ecological, and hydrological processes together with the essential feedback from spatial interactions. MPeat2D employs poroelasticity theory that couples fluid flow and solid deformation to model the influence of peat volume changes on peatland ecology and hydrology. To validate the poroelasticity formulation, the comparisons between numerical and analytical solutions of Mandel's problems for two-dimensional test cases are conducted. The application of MPeat2D is illustrated by simulating peatland growth over 5000 years above a flat and impermeable substrate with free-draining boundaries at the edges, using constant and variable climate. In both climatic scenarios, MPeat2D produces lateral variability in the water table depth, which results in the variation in the vegetation composition. Furthermore, the drop in the water table at the margin increases the compaction effect, leading to a higher value of bulk density and a lower value of active porosity and hydraulic conductivity. These spatial variations obtained from MPeat2D are consistent with the field observations, suggesting plausible outputs from the proposed model. By comparing the results of MPeat2D to a one-dimensional model and a two-dimensional model without the mechanical process, we argue that mechanical–ecohydrological feedbacks are important for analysing spatial heterogeneity, shape, carbon accumulation, and resilience of peatlands.

Structural integrity assessment of CANDU pressure tubes using Sobol indices for global sensitivity analysis

CANDU11CANDU is a registered trademark of Atomic Energy of Canada Limited. reactors are a channel-type design where up to 480 zirconium alloy pressure tubes (PTs) act as the reactor pressure boundary. Fitness-for-service standards such as CSA N285.8 (CSA Group, 2015) have been established to prescribe the requirements of pressure tube evaluations to maintain their integrity throughout their lifetime. Probabilistic leak-before-break (LBB) assessments can be used in evaluations to demonstrate that the likelihood of a flaw growing past the stability point while undetected (or before a safe shutdown can be achieved) is below regulatory limits. The assessments typically require a ranking of model parameters based on their influence. The ranking process traditionally uses expert judgment and local sensitivity analysis methods. There has been recent interest in implementing global methods for LBB assessments as they can manage large numbers of variables and extensive sampling spaces. However, their adoption is hindered by the computational cost of the models involved.The current study proposes a method for performing global sensitivity parameter rankings during probabilistic LBB assessments. The study is the continuation of the CANDU nuclear power plant (NPP) pressure tube (PT) case study in El Bouzidi et al., (2024) where a probabilistic approach was implemented in RAVEN (Rabiti and Alfonsi, 2019) to estimate whether the probability of unstable crack growth in PTs is within acceptable limits. This follow-up work proposes surrogate modeling using a high-dimensional model representation to derive Sobol indices and establish a parameter influence ranking. The methodology is demonstrated in a Monte Carlo simulation campaign of a pressure tube inlet rolled joint. The implemented approach successfully identified and quantified critical parameters of the model while efficiently ranking and quantifying the interactions between input variables.

Exploring the response and prediction of phytoplankton to environmental factors in eutrophic marine areas using interpretable machine learning methods

Coastal marine areas are frequently affected by human activities and face ecological and environmental threats, such as algal blooms and climate change. The community structure of phytoplankton—primary producers in marine ecosystems—is highly sensitive to environmental factors, such as temperature, salinity, and nutrients. However, traditional methods for exploring the relationship between phytoplankton communities and environmental factors in eutrophic marine areas are limited by various factors. Therefore, this study employed interpretable machine learning models, integrating high-dimensional data analysis and complex system modeling, to quantitatively and thoroughly analyze the dynamic relationship between phytoplankton communities and environmental variables in high-frequency samples collected over 53 weeks from eutrophic marine areas. The cell abundance of phytoplankton exhibited a distinct “two-peak pattern” variation. Interpretable machine learning model analysis revealed the dynamic contributions of different environmental factors during changes in the phytoplankton community structure. The results showed that temperature was a key environmental factor that affected phytoplankton growth during peak periods. In addition, the contribution of salinity increased during the second peak in phytoplankton abundance, highlighting its central role in the ecological dynamics of this phase. During green tide outbreaks, particularly in Area 01, the contributions of factors such as temperature and salinity increased, whereas those of phosphates and silicates decreased, indicating that green tide outbreaks substantially altered the nutritional dynamics of the ecosystem. Furthermore, different phytoplankton species, such as Skeletonema costatum, Thalassiosira spp., and Nitzschia spp., exhibit varying responses to environmental factors. Hence, the predictions made using random forest and generalized additive models for phytoplankton cell abundance in two marine areas revealed complex nonlinear relationships between environmental factors, such as temperature, salinity, and phytoplankton abundance.

A pointwise weighting prediction variance–high-dimensional model representation model-based global optimization approach for ship hull parametric design

Ship hull optimization techniques based on computer-aided design/computational fluid dynamics can effectively enhance the efficiency and stability of ship designs, with significant application prospects. To enhance the potential of ship hull optimization, increasing design variable dimensionality is essential, but can cause a significant increase in hydrodynamic simulations. To reduce simulations required for high-dimensional ship hull optimization, a new surrogate method, pointwise weighting prediction variance–high-dimensional model representation (PWPV-HDMR), which uses pointwise weighting prediction variance (PWPV) to aggregate different a priori assumptions, is developed. Moreover, a differential evolution algorithm is used to identify promising hull design parameters, using the PWPV-HDMR model instead of costly simulation as the fitness function. The proposed approach is tested on the hydrostatic resistance optimization of KRISO Container Ship. The results show that PWPV-HDMR outperforms kriging-HDMR, with a better resistance optimization effect, illustrating the effectiveness of the PWPV-HDMR-based global optimization approach in discovering promising ship hull parameters.

Examining the influence of 2.5-D ultra-low velocity zone morphology on ScP waveforms and estimated elastic parameters

Summary Ultra-low velocity zones (ULVZs) have been identified as regions of extremely low velocity anomalies in the Earth's lowermost mantle using seismic observations from reflected, refracted, and diffracted arrivals along the mantle side of the core-mantle boundary (CMB). Estimation of ULVZ geometrical (i.e., shape and size) and elastic (i.e., velocity and density) parameters with uncertainties is crucial in understanding the role of ULVZs in the ongoing dynamic processes within the Earth's mantle; however, these parameters are still poorly known due to uncertainties and tradeoffs of the seismically resolved ULVZ geometries and elastic parameters. Computation of synthetic waveforms for 2-D and 3-D ULVZs shapes is currently computationally feasible, but past studies utilize higher dimensional waveform modeling of mostly only low-frequency diffracted waves. Most studies focusing on high-frequency core-reflected waveforms (e.g., ScP) still use 1-D modeling approaches to determine ULVZ properties. This approach might lead to wrong results if the imaged structures have inherently 3-D geometries. This study investigates high-frequency synthetic ScP waveforms for various 2.5-D ULVZ geometries showing that additional seismic arrivals are generated even when the ScP geometrical ray path does not directly strike the location of the ULVZ. The largest amplitude additional phases in the 2.5-D models are post-cursor arrivals that are generated at the edges of the finite-length ULVZs. These newly identified ScP post-cursors can arrive within the ScsP post-cursor time window traditionally analyzed in 1-D ULVZ studies. These post-cursors might then be misidentified or constructively/destructively interfere with the ScsP postcursor, leading to incorrect estimation of ULVZ parameters. In this study we investigate the bias introduced by the 2.5-D morphologies on the 1D estimated ULVZ elastic properties in a Bayesian waveform inversion scheme. We further expand the Bayesian method by including the data noise covariance matrix in the inversion and compare it to an autoregressive noise model that was utilized in previous studies. From the application to the observed ScP data, we find that the new approach converges faster, particularly for the inversion of data from multiple events, and the new algorithm retrieves ULVZ parameters with more realistic uncertainties. The inversion of 2.5-D synthetic ScP waveforms suggests that the retrieved ULVZ parameters can be misleading with unrealistically high confidence if we do not consider the data noise covariance matrix in the inversion. Our new approach can also retrieve the shape of a multi-dimensional Gaussian ULVZ if its length is 12o or longer in the great circle arc direction. However, 2.5-D synthetic waveforms show additional waveform complexity which can constructively interfere with the ScP wavefield. Hence, in many cases the estimation of ULVZ properties using 1-D forward modeling can provide incorrect ULVZ parameters. Hence previous ULVZ modeling efforts using 1-D parameter estimation methods may be incorrect.

Institutional structure and governance capability in universities: an empirical study from the perspectives of time, space, and quantity dimensions

Institutions are pivotal in university governance, symbolizing stable organizational power reflective of governance capacity. The strategic organization of a university’s internal structures aims to align with its developmental goals. The effectiveness of these arrangements is evaluated by their congruence with the university’s characteristics and norms, aiming to enhance governance for growth and sustainability. Thus, the primary aim of this study is to determine whether this layout can strengthen the university’s governance ability, enhancing its prospects for survival and development. This study introduces a novel theoretical framework across the dimensions of time, space, and quantity, utilizing governance elements to assess the impact of institutional layouts on governance capabilities. Data were gathered through a self-developed survey questionnaire, with a total of 742 valid responses collected, and by employing a high-dimensional fixed-effects model, we found that the three-dimensional institutional layouts significantly impact governance capabilities, with effects varying by the institution’s affiliation. Furthermore, the mechanism analysis shows that university governance capabilities are also manifested through different configurations of governance elements under institutional layout, and are influenced by the responsiveness, collaboration, and expansion of the entire institutional system. Moreover, our analysis indicates a threshold effect in the tenure of institutional members, where both excessive and insufficient enthusiasm impact governance capabilities differently. This suggests the importance of a strategic institutional layout that aligns with the governance elements’ dynamics of timeliness, flexibility, distribution, and scarcity across time, space, and quantity. Achieving an optimal arrangement enhances the university’s governance efficiency significantly. In light of these findings, policy implications were proposed.

The Spatial Structure of the Tumor Immune Microenvironment Can Explain and Predict Patient Response in High-Grade Serous Carcinoma.

Ovarian cancer is the deadliest gynecologic malignancy, and therapeutic options and mortality rates over the last three decades have largely not changed. Recent studies indicate that the composition of the tumor immune microenvironment (TIME) influences patient outcomes. To improve spatial understanding of the TIME, we performed multiplexed ion beam imaging on 83 human high-grade serous carcinoma tumor samples, identifying approximately 160,000 cells across 23 cell types. From the 77 of these samples that met inclusion criteria, we generated composition features based on cell type proportions, spatial features based on the distances between cell types, and spatial network features representing cell interactions and cell clustering patterns, which we linked to traditional clinical and IHC variables and patient overall survival (OS) and progression-free survival (PFS) outcomes. Among these features, we found several significant univariate correlations, including B-cell contact with M1 macrophages (OS HR = 0.696; P = 0.011; PFS HR = 0.734; P = 0.039). We then used high-dimensional random forest models to evaluate out-of-sample predictive performance for OS and PFS outcomes and to derive relative feature importance scores for each feature. The top model for predicting low or high PFS used TIME composition and spatial features and achieved an average AUC score of 0.71. The results demonstrate the importance of spatial structure in understanding how the TIME contributes to treatment outcomes. Furthermore, the present study provides a generalizable roadmap for spatial analyses of the TIME in ovarian cancer research.

A computationally efficient [formula omitted]-spectral form for partial dispersion analyses within the wave finite element framework

This paper addresses the computation of frequency-dependent dispersion curves (i.e., k(ω)) and wave modes within the framework of the Wave Finite Element Method (WFEM) and in the context of high-dimensional periodic unit cell models. Numerous applications, ranging from phononics to vibroacoustics, now rely on dispersion analyses or wave expansion over a subset of eigensolutions – complex wavenumbers and Bloch waves – resulting from the resolution of an eigenvalue problem with a T-palindromic quadratic structure (T-PQEP). To exploit the structure of finite element models, various structure-preserving linearizations such as the Zhong-Williams and the (S+S−1)-transform have already been developed to achieve partial wave resolution of large T-PQEP, primarily targeting the dominating (least decaying) waves. In this paper we derive an alternative linearization of the T-PQEP for the k(ω) problem, which leads to enhanced targeting of the eigenvalues around the unit circle and reduces the inaccuracies induced by root multiplicity. A specific form of the problem is then proposed as an optimal compromise between ease of implementation, numerical stability, convergence and accuracy enhancement. The performance of our proposed linearization is compared against existing ones across various iterative eigensolvers, since the generalized eigenvalue problems involve complex non-hermitian matrices, which are not extensively included in eigensolvers. Results indicate that the proposed linearization should be favored for the WFEM, as it provides numerical enhancements in dispersion and wave vectors computation for large eigenvalue problems, as well as for further wave expansion applications.