Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far little-understood. Here, we present a first numerical method to simulate the continuum dynamics of droplets interacting with deformable membranes via wetting. The method combines the advantages of the phase field method for multi-phase flow simulation and the arbitrary Lagrangian-Eulerian (ALE) method for an explicit description of the elastic surface. The model is thermodynamically consistent, coupling bulk hydrodynamics with capillary forces, as well as bending, tension, and stretching of a thin membrane. The method is validated by comparing simulations for single droplets to theoretical results of shape equations, and its capabilities are illustrated in 2D and 3D axisymmetric scenarios.
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The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.
Skew normal model suffers from inferential drawbacks, namely singular Fisher information in the vicinity of symmetry and diverging of maximum likelihood estimation. To address the above drawbacks, Azzalini and Arellano-Valle (2013) introduced maximum penalised likelihood estimation (MPLE) by subtracting a penalty function from the log-likelihood function with a pre-specified penalty coefficient. Here, we propose a cross-validated MPLE to improve its performance when the underlying model is close to symmetry. We develop a theory for MPLE, where an asymptotic rate for the cross-validated penalty coefficient is derived. We further show that the proposed cross-validated MPLE is asymptotically efficient under certain conditions. In simulation studies and a real data application, we demonstrate that the proposed estimator can outperform the conventional MPLE when the model is close to symmetry.
The classification of different grapevine varieties is a relevant phenotyping task in Precision Viticulture since it enables estimating the growth of vineyard rows dedicated to different varieties, among other applications concerning the wine industry. This task can be performed with destructive methods that require time-consuming tasks, including data collection and analysis in the laboratory. However, Unmanned Aerial Vehicles (UAV) provide a more efficient and less prohibitive approach to collecting hyperspectral data, despite acquiring noisier data. Therefore, the first task is the processing of these data to correct and downsample large amounts of data. In addition, the hyperspectral signatures of grape varieties are very similar. In this work, a Convolutional Neural Network (CNN) is proposed for classifying seventeen varieties of red and white grape variants. Rather than classifying single samples, these are processed together with their neighbourhood. Hence, the extraction of spatial and spectral features is addressed with 1) a spatial attention layer and 2) Inception blocks. The pipeline goes from processing to dataset elaboration, finishing with the training phase. The fitted model is evaluated in terms of response time, accuracy and data separability, and compared with other state-of-the-art CNNs for classifying hyperspectral data. Our network was proven to be much more lightweight with a reduced number of input bands, a lower number of trainable weights and therefore, reduced training time. Despite this, the evaluated metrics showed much better results for our network (~99% overall accuracy), in comparison with previous works barely achieving 81% OA.
Non-significant randomized control trials can hide subgroups of good responders to experimental drugs, thus hindering subsequent development. Identifying such heterogeneous treatment effects is key for precision medicine and many post-hoc analysis methods have been developed for that purpose. While several benchmarks have been carried out to identify the strengths and weaknesses of these methods, notably for binary and continuous endpoints, similar systematic empirical evaluation of subgroup analysis for time-to-event endpoints are lacking. This work aims to fill this gap by evaluating several subgroup analysis algorithms in the context of time-to-event outcomes, by means of three different research questions: Is there heterogeneity? What are the biomarkers responsible for such heterogeneity? Who are the good responders to treatment? In this context, we propose a new synthetic and semi-synthetic data generation process that allows one to explore a wide range of heterogeneity scenarios with precise control on the level of heterogeneity. We provide an open source Python package, available on Github, containing our generation process and our comprehensive benchmark framework. We hope this package will be useful to the research community for future investigations of heterogeneity of treatment effects and subgroup analysis methods benchmarking.
On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes
For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-$p$ setting, and answer a question of Talagrand on the analogous result for general positive empirical processes.
Anemia is a prevalent medical condition that typically requires invasive blood tests for diagnosis and monitoring. Electronic health records (EHRs) have emerged as valuable data sources for numerous medical studies. EHR-based hemoglobin level/anemia degree prediction is non-invasive and rapid but still faces some challenges due to the fact that EHR data is typically an irregular multivariate time series containing a significant number of missing values and irregular time intervals. To address these issues, we introduce HgbNet, a machine learning-based prediction model that emulates clinicians' decision-making processes for hemoglobin level/anemia degree prediction. The model incorporates a NanDense layer with a missing indicator to handle missing values and employs attention mechanisms to account for both local irregularity and global irregularity. We evaluate the proposed method using two real-world datasets across two use cases. In our first use case, we predict hemoglobin level/anemia degree at moment T+1 by utilizing records from moments prior to T+1. In our second use case, we integrate all historical records with additional selected test results at moment T+1 to predict hemoglobin level/anemia degree at the same moment, T+1. HgbNet outperforms the best baseline results across all datasets and use cases. These findings demonstrate the feasibility of estimating hemoglobin levels and anemia degree from EHR data, positioning HgbNet as an effective non-invasive anemia diagnosis solution that could potentially enhance the quality of life for millions of affected individuals worldwide. To our knowledge, HgbNet is the first machine learning model leveraging EHR data for hemoglobin level/anemia degree prediction.
We consider Maxwell eigenvalue problems on uncertain shapes with perfectly conducting TESLA cavities being the driving example. Due to the shape uncertainty, the resulting eigenvalues and eigenmodes are also uncertain and it is well known that the eigenvalues may exhibit crossings or bifurcations under perturbation. We discuss how the shape uncertainties can be modelled using the domain mapping approach and how the deformation mapping can be expressed as coefficients in Maxwell's equations. Using derivatives of these coefficients and derivatives of the eigenpairs, we follow a perturbation approach to compute approximations of mean and covariance of the eigenpairs. For small perturbations, these approximations are faster and more accurate than Monte Carlo or similar sampling-based strategies. Numerical experiments for a three-dimensional 9-cell TESLA cavity are presented.
We study the complexity (that is, the weight of the multiplication table) of the elliptic normal bases introduced by Couveignes and Lercier. We give an upper bound on the complexity of these elliptic normal bases, and we analyze the weight of some special vectors related to the multiplication table of those bases. This analysis leads us to some perspectives on the search for low complexity normal bases from elliptic periods.
Recently, a family of unconventional integrators for ODEs with polynomial vector fields was proposed, based on the polarization of vector fields. The simplest instance is the by now famous Kahan discretization for quadratic vector fields. All these integrators seem to possess remarkable conservation properties. In particular, it has been proved that, when the underlying ODE is Hamiltonian, its polarization discretization possesses an integral of motion and an invariant volume form. In this note, we propose a new algebraic approach to derivation of the integrals of motion for polarization discretizations.
Human cognition operates on a "Global-first" cognitive mechanism, prioritizing information processing based on coarse-grained details. This mechanism inherently possesses an adaptive multi-granularity description capacity, resulting in computational traits such as efficiency, robustness, and interpretability. The analysis pattern reliance on the finest granularity and single-granularity makes most existing computational methods less efficient, robust, and interpretable, which is an important reason for the current lack of interpretability in neural networks. Multi-granularity granular-ball computing employs granular-balls of varying sizes to daptively represent and envelop the sample space, facilitating learning based on these granular-balls. Given that the number of coarse-grained "granular-balls" is fewer than sample points, granular-ball computing proves more efficient. Moreover, the inherent coarse-grained nature of granular-balls reduces susceptibility to fine-grained sample disturbances, enhancing robustness. The multi-granularity construct of granular-balls generates topological structures and coarse-grained descriptions, naturally augmenting interpretability. Granular-ball computing has successfully ventured into diverse AI domains, fostering the development of innovative theoretical methods, including granular-ball classifiers, clustering techniques, neural networks, rough sets, and evolutionary computing. This has notably ameliorated the efficiency, noise robustness, and interpretability of traditional methods. Overall, granular-ball computing is a rare and innovative theoretical approach in AI that can adaptively and simultaneously enhance efficiency, robustness, and interpretability. This article delves into the main application landscapes for granular-ball computing, aiming to equip future researchers with references and insights to refine and expand this promising theory.
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