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The locations of different mRNA molecules can be revealed by multiplexed in situ RNA detection. By assigning detected mRNA molecules to individual cells, it is possible to identify many different cell types in parallel. This in turn enables investigation of the spatial cellular architecture in tissue, which is crucial for furthering our understanding of biological processes and diseases. However, cell typing typically depends on the segmentation of cell nuclei, which is often done based on images of a DNA stain, such as DAPI. Limiting cell definition to a nuclear stain makes it fundamentally difficult to determine accurate cell borders, and thereby also difficult to assign mRNA molecules to the correct cell. As such, we have developed a computational tool that segments cells solely based on the local composition of mRNA molecules. First, a small neural network is trained to compute attractive and repulsive edges between pairs of mRNA molecules. The signed graph is then partitioned by a mutex watershed into components corresponding to different cells. We evaluated our method on two publicly available datasets and compared it against the current state-of-the-art and older baselines. We conclude that combining neural networks with combinatorial optimization is a promising approach for cell segmentation of in situ transcriptomics data.

We present a rigorous and precise analysis of the maximum degree and the average degree in a dynamic duplication-divergence graph model introduced by Sol\'e, Pastor-Satorras et al. in which the graph grows according to a duplication-divergence mechanism, i.e. by iteratively creating a copy of some node and then randomly alternating the neighborhood of a new node with probability $p$. This model captures the growth of some real-world processes e.g. biological or social networks. In this paper, we prove that for some $0 < p < 1$ the maximum degree and the average degree of a duplication-divergence graph on $t$ vertices are asymptotically concentrated with high probability around $t^p$ and $\max\{t^{2 p - 1}, 1\}$, respectively, i.e. they are within at most a polylogarithmic factor from these values with probability at least $1 - t^{-A}$ for any constant $A > 0$.

While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization with internal linear layers and $L_2$ regularization (weight decay) to automatically estimate the underlying dimensionality of a data set, produce an orthogonal manifold coordinate system, and provide the mapping functions between the ambient space and manifold space, allowing for out-of-sample projections. We validate our framework's ability to estimate the manifold dimension for a series of datasets from dynamical systems of varying complexities and compare to other state-of-the-art estimators. We analyze the training dynamics of the network to glean insight into the mechanism of low-rank learning and find that collectively each of the implicit regularizing layers compound the low-rank representation and even self-correct during training. Analysis of gradient descent dynamics for this architecture in the linear case reveals the role of the internal linear layers in leading to faster decay of a "collective weight variable" incorporating all layers, and the role of weight decay in breaking degeneracies and thus driving convergence along directions in which no decay would occur in its absence. We show that this framework can be naturally extended for applications of state-space modeling and forecasting by generating a data-driven dynamic model of a spatiotemporally chaotic partial differential equation using only the manifold coordinates. Finally, we demonstrate that our framework is robust to hyperparameter choices.

Alzheimer's disease has an increasing prevalence in the population world-wide, yet current diagnostic methods based on recommended biomarkers are only available in specialized clinics. Due to these circumstances, Alzheimer's disease is usually diagnosed late, which contrasts with the currently available treatment options that are only effective for patients at an early stage. Blood-based biomarkers could fill in the gap of easily accessible and low-cost methods for early diagnosis of the disease. In particular, immune-based blood-biomarkers might be a promising option, given the recently discovered cross-talk of immune cells of the central nervous system with those in the peripheral immune system. With the help of machine learning algorithms and mechanistic modeling approaches, such as agent-based modeling, an in-depth analysis of the simulation of cell dynamics is possible as well as of high-dimensional omics resources indicative of pathway signaling changes. Here, we give a background on advances in research on brain-immune system cross-talk in Alzheimer's disease and review recent machine learning and mechanistic modeling approaches which leverage modern omics technologies for blood-based immune system-related biomarker discovery.

Hesitant fuzzy sets are widely used in the instances of uncertainty and hesitation. The inclusion relationship is an important and foundational definition for sets. Hesitant fuzzy set, as a kind of set, needs explicit definition of inclusion relationship. Base on the hesitant fuzzy membership degree of discrete form, several kinds of inclusion relationships for hesitant fuzzy sets are proposed. And then some foundational propositions of hesitant fuzzy sets and the families of hesitant fuzzy sets are presented. Finally, some foundational propositions of hesitant fuzzy information systems with respect to parameter reductions are put forward, and an example and an algorithm are given to illustrate the processes of parameter reductions.

The identification of essential proteins in protein-protein interaction networks (PINs) can help to discover drug targets and prevent disease. In order to improve the accuracy of the identification of essential proteins, researchers attempted to obtain a refined PIN by combining multiple biological information to filter out some unreliable interactions in the PIN. Unfortunately, such approaches drastically reduce the number of nodes in the PIN after multiple refinements and result in a sparser PIN. It makes a considerable portion of essential proteins unidentifiable. In this paper, we propose a multi-layer refined network (MR-PIN) that addresses this problem. Firstly, four refined networks are constructed by respectively integrating different biological information into the static PIN to form a multi-layer heterogeneous network. Then scores of proteins in each network layer are calculated by the existing node ranking method, and the importance score of a protein in the MR-PIN is evaluated in terms of the geometric mean of its scores in all layers. Finally, all nodes are sorted by their importance scores to determine their essentiality. To evaluate the effectiveness of the multi-layer refined network model, we apply 16 node ranking methods on the MR-PIN, and compare the results with those on the SPIN, DPIN and RDPIN. Then the predictive performances of these ranking methods are validated in terms of the identification number of essential protein at top100 - top600, sensitivity, specificity, positive predictive value, negative predictive value, F-measure, accuracy, Jackknife, ROCAUC and PRAUC. The experimental results show that the MR-PIN is superior to the existing refined PINs in the identification accuracy of essential proteins.

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently large. We find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are H\"older continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the $\ell_2$-Expected Calibration Error (ECE). We further propose Adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which -- combined with classical tests for discrete-valued predictors -- can be used to test the calibration of virtually any probabilistic classification method.

Modelling human cognition can provide key insights into behavioral dynamics under changing conditions. This enables synthetic data generation and guides adaptive interventions for cognitive regulation. Challenges arise when environments are highly dynamic, obscuring stimulus-behavior relationships. We propose a cognitive agent integrating drift-diffusion with deep reinforcement learning to simulate granular stress effects on logical reasoning process. Leveraging a large dataset of 21,157 logical responses, we investigate performance impacts of dynamic stress. This prior knowledge informed model design and evaluation. Quantitatively, the framework improves cognition modelling by capturing both subject-specific and stimuli-specific behavioural differences. Qualitatively, it captures general trends in human logical reasoning under stress. Our approach is extensible to examining diverse environmental influences on cognition and behavior. Overall, this work demonstrates a powerful, data-driven methodology to simulate and understand the vagaries of human logical reasoning process in dynamic contexts.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.