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We explore the Ziv-Lempel and Crochemore factorizations of some classical automatic sequences making an extensive use of the theorem prover Walnut.

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

In this paper, we aim to improve the percentage of packets meeting their deadline in discrete-time M/M/1 queues with infrequent monitoring. More specifically, we look into policies that only monitor the system (and subsequently take actions) after a packet arrival. We model the system as an MDP and provide the optimal policy for some special cases. Furthermore, we introduce a heuristic algorithm called "AB-n" for general deadlines. Finally, we provide numerical results demonstrating the desirable performance of "AB-n" policies.

We develop a new coarse-scale approximation strategy for the nonlinear single-continuum Richards equation as an unsaturated flow over heterogeneous non-periodic media, using the online generalized multiscale finite element method (online GMsFEM) together with deep learning. A novelty of this approach is that local online multiscale basis functions are computed rapidly and frequently by utilizing deep neural networks (DNNs). More precisely, we employ the training set of stochastic permeability realizations and the computed relating online multiscale basis functions to train neural networks. The nonlinear map between such permeability fields and online multiscale basis functions is developed by our proposed deep learning algorithm. That is, in a new way, the predicted online multiscale basis functions incorporate the nonlinearity treatment of the Richards equation and refect any time-dependent changes in the problem's properties. Multiple numerical experiments in two-dimensional model problems show the good performance of this technique, in terms of predictions of the online multiscale basis functions and thus finding solutions.

On the Boolean domain, there is a class of symmetric signatures called ``Fibonacci gates" for which a beautiful P-time combinatorial algorithm has been designed for the corresponding $\operatorname{Holant}^*$ problems. In this work, we give a combinatorial view for $\operatorname{Holant}^*(\mathcal{F})$ problems on a domain of size 3 where $\mathcal{F}$ is a set of arity 3 functions with inputs taking values on the domain of size 3 and the functions share some common properties. The combinatorial view can also be extended to the domain of size 4. Specifically, we extend the definition of "Fibonacci gates" to the domain of size 3 and the domain of size 4. Moreover, we give the corresponding combinatorial algorithms.

In this paper we study predictive mean matching mass imputation estimators to integrate data from probability and non-probability samples. We consider two approaches: matching predicted to observed ($\hat{y}-y$ matching) or predicted to predicted ($\hat{y}-\hat{y}$ matching) values. We prove the consistency of two semi-parametric mass imputation estimators based on these approaches and derive their variance and estimators of variance. Our approach can be employed with non-parametric regression techniques, such as kernel regression, and the analytical expression for variance can also be applied in nearest neighbour matching for non-probability samples. We conduct extensive simulation studies in order to compare the properties of this estimator with existing approaches, discuss the selection of $k$-nearest neighbours, and study the effects of model mis-specification. The paper finishes with empirical study in integration of job vacancy survey and vacancies submitted to public employment offices (admin and online data). Open source software is available for the proposed approaches.

We present a specific-purpose globalized and preconditioned Newton-CG solver to minimize a metric-aware curved high-order mesh distortion. The solver is specially devised to optimize curved high-order meshes for high polynomial degrees with a target metric featuring non-uniform sizing, high stretching ratios, and curved alignment -- exactly the features that stiffen the optimization problem. To this end, we consider two ingredients: a specific-purpose globalization and a specific-purpose Jacobi-$\text{iLDL}^{\text{T}}(0)$ preconditioning with varying accuracy and curvature tolerances (dynamic forcing terms) for the CG method. These improvements are critical in stiff problems because, without them, the large number of non-linear and linear iterations makes curved optimization impractical. Finally, to analyze the performance of our method, the results compare the specific-purpose solver with standard optimization methods. For this, we measure the matrix-vector products indicating the solver computational cost and the line-search iterations indicating the total amount of objective function evaluations. When we combine the globalization and the linear solver ingredients, we conclude that the specific-purpose Newton-CG solver reduces the total number of matrix-vector products by one order of magnitude. Moreover, the number of non-linear and line-search iterations is mainly smaller but of similar magnitude.

Emotion Recognition in Conversation (ERC) has attracted growing attention in recent years as a result of the advancement and implementation of human-computer interface technologies. In this paper, we propose an emotional inertia and contagion-driven dependency modeling approach (EmotionIC) for ERC task. Our EmotionIC consists of three main components, i.e., Identity Masked Multi-Head Attention (IMMHA), Dialogue-based Gated Recurrent Unit (DiaGRU), and Skip-chain Conditional Random Field (SkipCRF). Compared to previous ERC models, EmotionIC can model a conversation more thoroughly at both the feature-extraction and classification levels. The proposed model attempts to integrate the advantages of attention- and recurrence-based methods at the feature-extraction level. Specifically, IMMHA is applied to capture identity-based global contextual dependencies, while DiaGRU is utilized to extract speaker- and temporal-aware local contextual information. At the classification level, SkipCRF can explicitly mine complex emotional flows from higher-order neighboring utterances in the conversation. Experimental results show that our method can significantly outperform the state-of-the-art models on four benchmark datasets. The ablation studies confirm that our modules can effectively model emotional inertia and contagion.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

Widely present in the primary circuit of Nuclear Power Plants (NPP), Dissimilar Metal Welds (DMW) are inspected using Ultrasonic nondestructive Testing (UT) techniques to ensure the integrity of the structure and detect defects such as Stress Corrosion Cracking (SCC).In a previous collaborative research, CRIEPI and CEA have worked on the understanding of the propagation of ultrasonic waves in complex materials. Indeed, the ultrasonic propagation can be disturbed due to the anisotropic and inhomogeneous properties of the medium and the interpretation of inspection results can then be difficult. An analytical model, based on a dynamic ray theory, developed by CEA-LIST and implemented in the CIVA software had been used to predict the ultrasonic propagation in a DMW. The model evaluates the ray trajectories, the travel-time and the computation of the amplitude along the ray tube in a medium described thanks to a continuously varying description of its physical properties. In this study, the weld had been described by an analytical law of the crystallographic orientation. The simulated results of the detection of calibrated notches located in the buttering and the weld had been compared with experimental data and had shown a good agreement.The new collaborative program presented in this paper aims at detecting a real SCC defect located close to the root of the DMW. Thus, simulations have been performed for a DMW described with an analytical law and a smooth cartography of the crystallographic orientation. Furthermore, advanced ultrasonic testing methods have been used to inspect the specimen and detect the real SCC defect. Experimental and simulated results of the mock-up inspection have been compared.