Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a novel parameter estimation method utilizing functional approximations with artificial neural networks. Our approach, termed Harmonic Approximation of Discontinuous External Signals using Neural Networks (HADES-NN), operates in two iterated stages. In the first stage, the algorithm employs a neural network to approximate the discontinuous signal with a smooth function. In the second stage, it uses this smooth approximate signal to estimate model parameters. HADES-NN gives highly accurate and precise parameter estimates across various applications, including circadian clock systems regulated by external light inputs measured via wearable devices and the mating response of yeast to external pheromone signals. HADES-NN greatly extends the range of model systems that can be fit to real-world measurements.

$Q$-learning is one of the most fundamental reinforcement learning algorithms. Previously, it is widely believed that $Q$-learning with linear function approximation (i.e., linear $Q$-learning) suffers from possible divergence. This paper instead establishes the first $L^2$ convergence rate of linear $Q$-learning to a bounded set. Notably, we do not make any modification to the original linear $Q$-learning algorithm, do not make any Bellman completeness assumption, and do not make any near-optimality assumption on the behavior policy. All we need is an $\epsilon$-softmax behavior policy with an adaptive temperature. The key to our analysis is the general result of stochastic approximations under Markovian noise with fast-changing transition functions. As a side product, we also use this general result to establish the $L^2$ convergence rate of tabular $Q$-learning with an $\epsilon$-softmax behavior policy, for which we rely on a novel pseudo-contraction property of the weighted Bellman optimality operator.

Low back pain (LBP) is a leading cause of disability globally. Following the onset of LBP and subsequent treatment, adequate patient education is crucial for improving functionality and long-term outcomes. Despite advancements in patient education strategies, significant gaps persist in delivering personalized, evidence-based information to patients with LBP. Recent advancements in large language models (LLMs) and generative artificial intelligence (GenAI) have demonstrated the potential to enhance patient education. However, their application and efficacy in delivering educational content to patients with LBP remain underexplored and warrant further investigation. In this study, we introduce a novel approach utilizing LLMs with Retrieval-Augmented Generation (RAG) and few-shot learning to generate tailored educational materials for patients with LBP. Physical therapists manually evaluated our model responses for redundancy, accuracy, and completeness using a Likert scale. In addition, the readability of the generated education materials is assessed using the Flesch Reading Ease score. The findings demonstrate that RAG-based LLMs outperform traditional LLMs, providing more accurate, complete, and readable patient education materials with less redundancy. Having said that, our analysis reveals that the generated materials are not yet ready for use in clinical practice. This study underscores the potential of AI-driven models utilizing RAG to improve patient education for LBP; however, significant challenges remain in ensuring the clinical relevance and granularity of content generated by these models.

Popular word embedding methods such as GloVe and Word2Vec are related to the factorization of the pointwise mutual information (PMI) matrix. In this paper, we link correspondence analysis (CA) to the factorization of the PMI matrix. CA is a dimensionality reduction method that uses singular value decomposition (SVD), and we show that CA is mathematically close to the weighted factorization of the PMI matrix. In addition, we present variants of CA that turn out to be successful in the factorization of the word-context matrix, i.e. CA applied to a matrix where the entries undergo a square-root transformation (ROOT-CA) and a root-root transformation (ROOTROOT-CA). An empirical comparison among CA- and PMI-based methods shows that overall results of ROOT-CA and ROOTROOT-CA are slightly better than those of the PMI-based methods.

Understanding sleep and activity patterns plays a crucial role in physical and mental health. This study introduces a novel approach for sleep detection using weakly supervised learning for scenarios where reliable ground truth labels are unavailable. The proposed method relies on a set of weak labels, derived from the predictions generated by conventional sleep detection algorithms. Introducing a novel approach, we suggest a novel generalised non-linear statistical model in which the number of weak sleep labels is modelled as outcome of a binomial distribution. The probability of sleep in the binomial distribution is linked to the outcomes of neural networks trained to detect sleep based on actigraphy. We show that maximizing the likelihood function of the model, is equivalent to minimizing the soft cross-entropy loss. Additionally, we explored the use of the Brier score as a loss function for weak labels. The efficacy of the suggested modelling framework was demonstrated using the Multi-Ethnic Study of Atherosclerosis dataset. A \gls{lstm} trained on the soft cross-entropy outperformed conventional sleep detection algorithms, other neural network architectures and loss functions in accuracy and model calibration. This research not only advances sleep detection techniques in scenarios where ground truth data is scarce but also contributes to the broader field of weakly supervised learning by introducing innovative approach in modelling sets of weak labels.

However, the complexity and versatility of modern AI systems calls for a unified framework to assess their trustworthiness, which cannot The probabilistic formal verification (PFV) of be captured by a single evaluation metric or formal property. AI systems is in its infancy. So far, approaches This papers aims to introduce such a framework. We have been limited to ad-hoc algorithms for specific show how by leveraging the Weighted Model Integration classes of models and/or properties. We propose (WMI) [Belle et al., 2015] formalism, it is possible to devise a unifying framework for the PFV of AI systems a unified formulation for the probabilistic verification of based on Weighted Model Integration (WMI), combinatorial AI systems. Broadly speaking, WMI is the which allows to frame the problem in very general task of computing probabilities of arbitrary combinations terms. Crucially, this reduction enables the verification of logical and algebraic constraints given a structured joint of many properties of interest, like fairness, distribution over both continuous and discrete variables.

On a recent evening, my children and I were watching "The Iron Giant," the animated cult classic about a robot from outer space who, in 1957, crash-lands in the woods outside a small town in Maine, befriends a young boy, and wages battle against both a murderously stupid G-man and his own robo-programming as a sentient weapon of war. The boy, named Hogarth, and his mother, Annie, get by on her income as a diner waitress, and, late one night, she comes home from a draining double shift to find her son missing. Frantic with worry, Annie drives around until she locates Hogarth at the edge of the woods--on his own and perfectly fine--where he manically chatters at her about the big metal alien he claims to have spotted nearby. Then she catches herself and, with effort, takes on a low, steadier voice. "I'm not in the mood," she says.

We are in an era of large catalogs and, thus, statistical analysis tools for large data sets, such as machine learning, play a fundamental role. One example of such a survey is the Sloan Moving Object Catalog (MOC), which lists the astrometric and photometric information of all moving objects captured by the Sloan field of view. One great advantage of this telescope is represented by its set of five filters, allowing for taxonomic analysis of asteroids by studying their colors. However, until now, the color variation produced by the change of phase angle of the object has not been taken into account. In this paper, we address this issue by using absolute magnitudes for classification. We aim to produce a new taxonomic classification of asteroids based on their magnitudes that is unaffected by variations caused by the change in phase angle. We selected 9481 asteroids with absolute magnitudes of Hg, Hi and Hz, computed from the Sloan Moving Objects Catalog using the HG12 system. We calculated the absolute colors with them. To perform the taxonomic classification, we applied a unsupervised machine learning algorithm known as fuzzy C-means. This is a useful soft clustering tool for working with {data sets where the different groups are not completely separated and there are regions of overlap between them. We have chosen to work with the four main taxonomic complexes, C, S, X, and V, as they comprise most of the known spectral characteristics. We classified a total of 6329 asteroids with more than 60% probability of belonging to the assigned taxonomic class, with 162 of these objects having been characterized by an ambiguous classification in the past. By analyzing the sample obtained in the plane Semimajor axis versus inclination, we identified 15 new V-type asteroid candidates outside the Vesta family region.

For weeks, Jay Deitcher has been on the hunt for a specific Miles Morales: Spider-Man toy from Spidey and His Amazing Friends. "The thing that makes the toy special is Miles's mask flips up to show his face," Deitcher says. "My son is Black, and it would be great to have a Spider-Man figure that looks like him." But even though the father of two from Albany, New York, started shopping for Hanukkah earlier than usual, he has yet to track down the elusive toy, which is sold out at many retailers. "We were already expecting a shortage, so we got him most of his other presents," he says.

Fluctuations in heart rate are intimately tied to changes in the physiological state of the organism. We examine and exploit this relationship by classifying a human subject's wake/sleep status using his instantaneous heart rate (IHR) series. We use a convolutional neural network (CNN) to build features from the IHR series extracted from a whole-night electrocardiogram (ECG) and predict every 30 seconds whether the subject is awake or asleep. Our training database consists of 56 normal subjects, and we consider three different databases for validation; one is private, and two are public with different races and apnea severities. On our private database of 27 subjects, our accuracy, sensitivity, specificity, and AUC values for predicting the wake stage are 83.1%, 52.4%, 89.4%, and 0.83, respectively. Validation performance is similar on our two public databases. When we use the photoplethysmography instead of the ECG to obtain the IHR series, the performance is also comparable. A robustness check is carried out to confirm the obtained performance statistics. This result advocates for an effective and scalable method for recognizing changes in physiological state using non-invasive heart rate monitoring. The CNN model adaptively quantifies IHR fluctuation as well as its location in time and is suitable for differentiating between the wake and sleep stages.