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Weakly hard real-time systems can, to some degree, tolerate deadline misses, but their schedulability still needs to be analyzed to ensure their quality of service. Such analysis usually occurs at early design stages to provide implementation guidelines to engineers so that they can make better design decisions. Estimating worst-case execution times (WCET) is a key input to schedulability analysis. However, early on during system design, estimating WCET values is challenging and engineers usually determine them as plausible ranges based on their domain knowledge. Our approach aims at finding restricted, safe WCET sub-ranges given a set of ranges initially estimated by experts in the context of weakly hard real-time systems. To this end, we leverage (1) multi-objective search aiming at maximizing the violation of weakly hard constraints in order to find worst-case scheduling scenarios and (2) polynomial logistic regression to infer safe WCET ranges with a probabilistic interpretation. We evaluated our approach by applying it to an industrial system in the satellite domain and several realistic synthetic systems. The results indicate that our approach significantly outperforms a baseline relying on random search without learning, and estimates safe WCET ranges with a high degree of confidence in practical time (< 23h).

Individuals or companies in a large social or financial network often display rather heterogeneous behaviors for various reasons. In this work, we propose a network vector autoregressive model with a latent group structure to model heterogeneous dynamic patterns observed from network nodes, for which group-wise network effects and timeinvariant fixed-effects can be naturally incorporated. In our framework, the model parameters and network node memberships can be simultaneously estimated by minimizing a least-squares type objective function. In particular, our theoretical investigation allows the number of latent groups G to be over-specified when achieving the estimation consistency of the model parameters and group memberships, which significantly improves the robustness of the proposed approach. When G is correctly specified, valid statistical inference can be made for model parameters based on the asymptotic normality of the estimators. A data-driven criterion is developed to consistently identify the true group number for practical use. Extensive simulation studies and two real data examples are used to demonstrate the effectiveness of the proposed methodology.

This paper introduces a novel It\^{o} diffusion process for both factor and idiosyncratic volatilities whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR-It\^{o} (FIVAR-It\^o) model. The FIVAR-It\^o model considers dynamics of the factor and idiosyncratic volatilities and involve many parameters. In addition, the empirical studies have shown that the financial returns often exhibit heavy tails. To address these two issues simultaneously, we propose a penalized optimization procedure with a truncation scheme for a parameter estimation. We apply the proposed parameter estimation procedure to predicting large volatility matrices and investigate its asymptotic properties. Using high-frequency trading data, the proposed method is applied to large volatility matrix prediction and minimum variance portfolio allocation.

Large skew-t factor copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a conditionally Gaussian generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A fast stochastic gradient ascent algorithm is used to solve the variational optimization. The new methodology is used to estimate copula models for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. We show that intraday predictive densities from the skew-t copula are more accurate than from some other copula models, while portfolio selection strategies based on the estimated pairwise tail dependencies improve performance relative to the benchmark index.

This paper considers the problem of symbol detection in massive multiple-input multiple-output (MIMO) wireless communication systems. We consider hard-thresholding preceeded by two variants of the regularized least squares (RLS) decoder; namely the unconstrained RLS and the RLS with box constraint. For all schemes, we focus on the evaluation of the mean squared error (MSE) and the symbol error probability (SEP) for M-ary pulse amplitude modulation (M-PAM) symbols transmitted over a massive MIMO system when the channel is estimated using linear minimum mean squared error (LMMSE) estimator. Under such circumstances, the channel estimation error is Gaussian which allows for the use of the convex Gaussian min-max theorem (CGMT) to derive asymptotic approximations for the MSE and SER when the system dimensions and the coherence duration grow large with the same pace. The obtained expressions are then leveraged to derive the optimal power distribution between pilot and data under a total transmit energy constraint. In addition, we derive an asymptotic approximation of the goodput for all schemes which is then used to jointly optimize the number of training symbols and their associated power. Numerical results are presented to support the accuracy of the theoretical results.

Passive acoustic monitoring offers a scalable, non-invasive method for tracking global biodiversity and anthropogenic impacts on species. Although deep learning has become a vital tool for processing this data, current models are inflexible, typically cover only a handful of species, and are limited by data scarcity. In this work, we propose BioLingual, a new model for bioacoustics based on contrastive language-audio pretraining. We first aggregate bioacoustic archives into a language-audio dataset, called AnimalSpeak, with over a million audio-caption pairs holding information on species, vocalization context, and animal behavior. After training on this dataset to connect language and audio representations, our model can identify over a thousand species' calls across taxa, complete bioacoustic tasks zero-shot, and retrieve animal vocalization recordings from natural text queries. When fine-tuned, BioLingual sets a new state-of-the-art on nine tasks in the Benchmark of Animal Sounds. Given its broad taxa coverage and ability to be flexibly queried in human language, we believe this model opens new paradigms in ecological monitoring and research, including free-text search on the world's acoustic monitoring archives. We open-source our models, dataset, and code.

This paper introduces a new method of discretization that collocates both endpoints of the domain and enables the complete convergence of the costate variables associated with the Hamilton boundary-value problem. This is achieved through the inclusion of an \emph{exceptional sample} to the roots of the Legendre-Lobatto polynomial, thus promoting the associated differentiation matrix to be full-rank. We study the location of the new sample such that the differentiation matrix is the most robust to perturbations and we prove that this location is also the choice that mitigates the Runge phenomenon associated with polynomial interpolation. Two benchmark problems are successfully implemented in support of our theoretical findings. The new method is observed to converge exponentially with the number of discretization points used.

Balance assessment during physical rehabilitation often relies on rubric-oriented battery tests to score a patient's physical capabilities, leading to subjectivity. While some objective balance assessments exist, they are often limited to tracking the center of pressure (COP), which does not fully capture the whole-body postural stability. This study explores the use of the center of mass (COM) state space and presents a promising avenue for monitoring the balance capabilities in humans. We employ a musculoskeletal model integrated with a balance controller, trained through reinforcement learning (RL), to investigate balancing capabilities. The RL framework consists of two interconnected neural networks governing balance recovery and muscle coordination respectively, trained using Proximal Policy Optimization (PPO) with reference state initialization, early termination, and multiple training strategies. By exploring recovery from random initial COM states (position and velocity) space for a trained controller, we obtain the final BR enclosing successful balance recovery trajectories. Comparing the BRs with analytical postural stability limits from a linear inverted pendulum model, we observe a similar trend in successful COM states but more limited ranges in the recoverable areas. We further investigate the effect of muscle weakness and neural excitation delay on the BRs, revealing reduced balancing capability in different regions. Overall, our approach of learning muscular balance controllers presents a promising new method for establishing balance recovery limits and objectively assessing balance capability in bipedal systems, particularly in humans.

Image-level weakly supervised semantic segmentation (WSSS) is a fundamental yet challenging computer vision task facilitating scene understanding and automatic driving. Most existing methods resort to classification-based Class Activation Maps (CAMs) to play as the initial pseudo labels, which tend to focus on the discriminative image regions and lack customized characteristics for the segmentation task. To alleviate this issue, we propose a novel activation modulation and recalibration (AMR) scheme, which leverages a spotlight branch and a compensation branch to obtain weighted CAMs that can provide recalibration supervision and task-specific concepts. Specifically, an attention modulation module (AMM) is employed to rearrange the distribution of feature importance from the channel-spatial sequential perspective, which helps to explicitly model channel-wise interdependencies and spatial encodings to adaptively modulate segmentation-oriented activation responses. Furthermore, we introduce a cross pseudo supervision for dual branches, which can be regarded as a semantic similar regularization to mutually refine two branches. Extensive experiments show that AMR establishes a new state-of-the-art performance on the PASCAL VOC 2012 dataset, surpassing not only current methods trained with the image-level of supervision but also some methods relying on stronger supervision, such as saliency label. Experiments also reveal that our scheme is plug-and-play and can be incorporated with other approaches to boost their performance.

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.