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The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of $P$. This provides some theoretical justification for the use of such estimators for cluster analysis in case that $P$ has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.

Multi-contrast (MC) Magnetic Resonance Imaging (MRI) reconstruction aims to incorporate a reference image of auxiliary modality to guide the reconstruction process of the target modality. Known MC reconstruction methods perform well with a fully sampled reference image, but usually exhibit inferior performance, compared to single-contrast (SC) methods, when the reference image is missing or of low quality. To address this issue, we propose DuDoUniNeXt, a unified dual-domain MRI reconstruction network that can accommodate to scenarios involving absent, low-quality, and high-quality reference images. DuDoUniNeXt adopts a hybrid backbone that combines CNN and ViT, enabling specific adjustment of image domain and k-space reconstruction. Specifically, an adaptive coarse-to-fine feature fusion module (AdaC2F) is devised to dynamically process the information from reference images of varying qualities. Besides, a partially shared shallow feature extractor (PaSS) is proposed, which uses shared and distinct parameters to handle consistent and discrepancy information among contrasts. Experimental results demonstrate that the proposed model surpasses state-of-the-art SC and MC models significantly. Ablation studies show the effectiveness of the proposed hybrid backbone, AdaC2F, PaSS, and the dual-domain unified learning scheme.

Molecular Communication (MC) has emerged as a promising paradigm employing molecules to transfer information at the nano-scale. Unlike MC channel coding, MC source coding has remained mostly an unexplored area of research. In a recent paper, prefix source coding was introduced into the field, through an MC-adapted version of the Huffman Coding. In the context of MC source coding, this paper proposes the Molecular Arithmetic Coding (MAC) whose algorithmic implementation and code-structure is non-arbitrarily different than that of the widely-known classical arithmetic coding. MAC is designed to mitigate Inter-Symbol Interference (ISI) for alphabets with known symbol probabilities through, in a highly efficient way, avoiding consecutive 1-bits. However, due to bit precision limitations any arithmetic coding method faces, without any assumption made on the structure of the symbol alphabet, unique-decodability of MAC is not guaranteed. Accordingly, a uniquely-decodable new coding scheme named Molecular Arithmetic with Prefix Coding (MAPC) is also introduced. Across multiple alphabets, we show that MAPC provides a better compression performance compared to the optimal MC-adapted prefix coding. Simulation results of an exemplary alphabet demonstrates the superior symbol and word error rate performance of MAPC compared to the optimal MC-adapted prefix coding and to the uncoded BCSK schemes.

Raman spectroscopy is widely used across scientific domains to characterize the chemical composition of samples in a non-destructive, label-free manner. Many applications entail the unmixing of signals from mixtures of molecular species to identify the individual components present and their proportions, yet conventional methods for chemometrics often struggle with complex mixture scenarios encountered in practice. Here, we develop hyperspectral unmixing algorithms based on autoencoder neural networks, and we systematically validate them using both synthetic and experimental benchmark datasets created in-house. Our results demonstrate that unmixing autoencoders provide improved accuracy, robustness and efficiency compared to standard unmixing methods. We also showcase the applicability of autoencoders to complex biological settings by showing improved biochemical characterization of volumetric Raman imaging data from a monocytic cell.

Deep Learning (DL) can predict biomarkers directly from digitized cancer histology in a weakly-supervised setting. Recently, the prediction of continuous biomarkers through regression-based DL has seen an increasing interest. Nonetheless, clinical decision making often requires a categorical outcome. Consequently, we developed a weakly-supervised joint multi-task Transformer architecture which has been trained and evaluated on four public patient cohorts for the prediction of two key predictive biomarkers, microsatellite instability (MSI) and homologous recombination deficiency (HRD), trained with auxiliary regression tasks related to the tumor microenvironment. Moreover, we perform a comprehensive benchmark of 16 approaches of task balancing for weakly-supervised joint multi-task learning in computational pathology. Using our novel approach, we improve over the state-of-the-art area under the receiver operating characteristic by +7.7% and +4.1%, as well as yielding better clustering of latent embeddings by +8% and +5% for the prediction of MSI and HRD in external cohorts, respectively.

Factual recall from a reference source is crucial for evaluating the performance of Retrieval Augmented Generation (RAG) systems, as it directly probes into the quality of both retrieval and generation. However, it still remains a challenge to perform this evaluation reliably and efficiently. Recent work has focused on fact verification via prompting language model (LM) evaluators, however we demonstrate that these methods are unreliable in the presence of incomplete or inaccurate information. We introduce Facts as a Function (FaaF), a new approach to fact verification that utilizes the function calling abilities of LMs and a framework for RAG factual recall evaluation. FaaF substantially improves the ability of LMs to identify unsupported facts in text with incomplete information whilst improving efficiency and lowering cost by several times, compared to prompt-based approaches.

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

Measuring the impact of a publication in a fair way is a significant challenge in bibliometrics, as it must not introduce biases between fields and should enable comparison of the impact of publications from different years. In this paper, we propose a Bayesian approach to tackle this problem, motivated by empirical data demonstrating heterogeneity in citation distributions. The approach uses the a priori distribution of citations in each field to estimate the expected a posteriori distribution in that field. This distribution is then employed to normalize the citations received by a publication in that field. Our main contribution is the Bayesian Impact Score, a measure of the impact of a publication. This score is increasing and concave with the number of citations received and decreasing and convex with the age of the publication. This means that the marginal score of an additional citation decreases as the cumulative number of citations increases and increases as the time since publication of the document grows. Finally, we present an empirical application of our approach in eight subject categories using the Scopus database and a comparison with the normalized impact indicator Field Citation Ratio from the Dimensions AI database.

In a system of many similar self-propelled entities such as flocks of birds, fish school, cells and molecules, the interactions with neighbors can lead to a "coherent state", meaning the formation of visually compelling aggregation patterns due to the local adjustment of speed and direction. In this study, we explore one of the open questions that arise in studying collective patterns. When such entities, considered here as particles, tend to assume a coherent state beginning from an incoherent (random) state, what is the time interval for the transition? Also, how do model parameters affect this transition time interval? Given the observations of particle migration over a given time period as a point cloud data sampled at discrete time points, we use Topological Data Analysis, specifically persistent homology, to infer the transition time interval in which the particles undergo regime change. The topology of the particle configuration at any given time instance is captured by the persistent homology specifically Persistence Landscapes. We localize (in time) when such a transition happens by conducting the statistical significance tests namely functional hypothesis tests on persistent homology outputs corresponding to subsets of the time evolution. This process is validated on a known collective behavior model of the self-propelled particles with the regime transitions triggered by changing the model parameters in time. As an application, the developed technique was ultimately used to describe the transition in cellular movement from a disordered state to collective motion when the environment was altered.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.