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We propose a novel neural network architecture based on conformer transducer that adds contextual information flow to the ASR systems. Our method improves the accuracy of recognizing uncommon words while not harming the word error rate of regular words. We explore the uncommon words accuracy improvement when we use the new model and/or shallow fusion with context language model. We found that combination of both provides cumulative gain in uncommon words recognition accuracy.

Background and Objective: Vital sign monitoring in the Intensive Care Unit (ICU) is crucial for enabling prompt interventions for patients. This underscores the need for an accurate predictive system. Therefore, this study proposes a novel deep learning approach for forecasting Heart Rate (HR), Systolic Blood Pressure (SBP), and Diastolic Blood Pressure (DBP) in the ICU. Methods: We extracted $24,886$ ICU stays from the MIMIC-III database which contains data from over $46$ thousand patients, to train and test the model. The model proposed in this study, Transformer-based Diffusion Probabilistic Model for Sparse Time Series Forecasting (TDSTF), merges Transformer and diffusion models to forecast vital signs. The TDSTF model showed state-of-the-art performance in predicting vital signs in the ICU, outperforming other models' ability to predict distributions of vital signs and being more computationally efficient. The code is available at //github.com/PingChang818/TDSTF. Results: The results of the study showed that TDSTF achieved a Standardized Average Continuous Ranked Probability Score (SACRPS) of $0.4438$ and a Mean Squared Error (MSE) of $0.4168$, an improvement of $18.9\%$ and $34.3\%$ over the best baseline model, respectively. The inference speed of TDSTF is more than $17$ times faster than the best baseline model. Conclusion: TDSTF is an effective and efficient solution for forecasting vital signs in the ICU, and it shows a significant improvement compared to other models in the field.

Multi-product formulas (MPF) are linear combinations of Trotter circuits offering high-quality simulation of Hamiltonian time evolution with fewer Trotter steps. Here we report two contributions aimed at making multi-product formulas more viable for near-term quantum simulations. First, we extend the theory of Trotter error with commutator scaling developed by Childs, Su, Tran et al. to multi-product formulas. Our result implies that multi-product formulas can achieve a quadratic reduction of Trotter error in 1-norm (nuclear norm) on arbitrary time intervals compared with the regular product formulas without increasing the required circuit depth or qubit connectivity. The number of circuit repetitions grows only by a constant factor. Second, we introduce dynamic multi-product formulas with time-dependent coefficients chosen to minimize a certain efficiently computable proxy for the Trotter error. We use a minimax estimation method to make dynamic multi-product formulas robust to uncertainty from algorithmic errors, sampling and hardware noise. We call this method Minimax MPF and we provide a rigorous bound on its error.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

The Discrete Event System Specification formalism (DEVS), which supports hierarchical and modular model composition, has been widely used to understand, analyze and develop a variety of systems. DEVS has been implemented in various languages and platforms over the years. The DEVStone benchmark was conceived to generate a set of models with varied structure and behavior, and to automate the evaluation of the performance of DEVS-based simulators. However, DEVStone is still in a preliminar phase and more model analysis is required. In this paper, we revisit DEVStone introducing new equations to compute the number of events triggered. We also introduce a new benchmark, called HOmem, designed as an alternative version of HOmod, with similar CPU and memory requirements, but with an easier implementation and analytically more manageable. Finally, we compare both the performance and memory footprint of five different DEVS simulators in two different hardware platforms.

On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of real-life problems. This work is set on the existence of one (or multiple) soft information sources, independent of the network considered, assuming this extra knowledge is modeled by a vector of fuzzy sets (or a family of vectors). This information may represent, for example, how much some people agree with a specific law, or their position against several politicians. We emphasize the importance of being able to manage the vagueness which usually appears in real life because of the common use of linguistic terms. Then, we propose a constructive method to build fuzzy measures from fuzzy sets. These measures are the basis of a new representation model which combines the information of a network with that of fuzzy sets, specifically when it comes to linguistic terms. We propose a specific application of that model in terms of finding communities in a network with additional soft information. To do so, we propose an efficient algorithm and measure its performance by means of a benchmarking process, obtaining high-quality results.

In this paper, we propose the Continuous Time Fractional Topic Model (cFTM), a new method for dynamic topic modeling. This approach incorporates fractional Brownian motion~(fBm) to effectively identify positive or negative correlations in topic and word distribution over time, revealing long-term dependency or roughness. Our theoretical analysis shows that the cFTM can capture these long-term dependency or roughness in both topic and word distributions, mirroring the main characteristics of fBm. Moreover, we prove that the parameter estimation process for the cFTM is on par with that of LDA, traditional topic models. To demonstrate the cFTM's property, we conduct empirical study using economic news articles. The results from these tests support the model's ability to identify and track long-term dependency or roughness in topics over time.

We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which is applied to Gaussian priors. The resulting posteriors, as well as their posterior means, are shown to converge to the ground truth at the minimax optimal rate over H\"older smoothness classes in any dimension. Of independent interest and as part of our proofs, we show that certain frequentist penalized least squares estimators are also minimax optimal.

Researchers would often like to leverage data from a collection of sources (e.g., primary studies in a meta-analysis) to estimate causal effects in a target population of interest. However, traditional meta-analytic methods do not produce causally interpretable estimates for a well-defined target population. In this paper, we present the CausalMetaR R package, which implements efficient and robust methods to estimate causal effects in a given internal or external target population using multi-source data. The package includes estimators of average and subgroup treatment effects for the entire target population. To produce efficient and robust estimates of causal effects, the package implements doubly robust and non-parametric efficient estimators and supports using flexible data-adaptive (e.g., machine learning techniques) methods and cross-fitting techniques to estimate the nuisance models (e.g., the treatment model, the outcome model). We describe the key features of the package and demonstrate how to use the package through an example.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.