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The development of cubical type theory inspired the idea of "extension types" which has been found to have applications in other type theories that are unrelated to homotopy type theory or cubical type theory. This article describes these applications, including on records, metaprogramming, controlling unfolding, and some more exotic ones.

We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed for solving the Cahn-Hilliard-Navier-Stokes phase field model with variable density and viscosity. We have successfully applied this method to simulate droplet formation in scenarios where a Newtonian fluid is injected through a vertical tube into another immiscible Newtonian fluid. To tackle the challenges posed by nonhomogeneous Dirichlet boundary conditions at the tube entrance, we have introduced additional nonlocal auxiliary variables and associated ordinary differential equations. These additions effectively eliminate the influence of boundary terms. Moreover, we have incorporated stabilization terms into the scheme to enhance its numerical effectiveness. Notably, our resulting scheme is fully decoupled, requiring the solution of only linear systems at each time step. We have also demonstrated the energy decaying property of the scheme, with suitable modifications. To assess the accuracy and stability of our algorithm, we have conducted extensive numerical simulations. Additionally, we have examined the dynamics of droplet formation and explored the impact of dimensionless parameters on the process. Overall, our work presents a refined method for simulating droplet formation dynamics, offering improved efficiency, energy stability, and accuracy.

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational model admits a low-dimensional representation. This assumption can be met by numerous uncertainty quantification applications with physics-based computational models. The proposed approach differs from a sequential application of dimensionality reduction followed by surrogate modeling, as we "extract" a surrogate model from the results of dimensionality reduction in the input-output space. This feature becomes desirable when the input space is genuinely high-dimensional. The proposed method also diverges from the Probabilistic Learning on Manifold, as a reconstruction mapping from the feature space to the input-output space is circumvented. The final product of the proposed method is a stochastic simulator that propagates a deterministic input into a stochastic output, preserving the convenience of a sequential "dimensionality reduction + Gaussian process regression" approach while overcoming some of its limitations. The proposed method is demonstrated through two uncertainty quantification problems characterized by high-dimensional input uncertainties.

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.

We propose a novel class of temporal high-order parametric finite element methods for solving a wide range of geometric flows of curves and surfaces. By incorporating the backward differentiation formulae (BDF) for time discretization into the BGN formulation, originally proposed by Barrett, Garcke, and N\"urnberg (J. Comput. Phys., 222 (2007), pp.~441--467), we successfully develop high-order BGN/BDF$k$ schemes. The proposed BGN/BDF$k$ schemes not only retain almost all the advantages of the classical first-order BGN scheme such as computational efficiency and good mesh quality, but also exhibit the desired $k$th-order temporal accuracy in terms of shape metrics, ranging from second-order to fourth-order accuracy. Furthermore, we validate the performance of our proposed BGN/BDF$k$ schemes through extensive numerical examples, demonstrating their high-order temporal accuracy for various types of geometric flows while maintaining good mesh quality throughout the evolution.

Using dominating sets to separate vertices of graphs is a well-studied problem in the larger domain of identification problems. In such problems, the objective is typically to separate any two vertices of a graph by their unique neighbourhoods in a suitably chosen dominating set of the graph. Such a dominating and separating set is often referred to as a \emph{code} in the literature. Depending on the types of dominating and separating sets used, various problems arise under various names in the literature. In this paper, we introduce a new problem in the same realm of identification problems whereby the code, called the \emph{open-separating dominating code}, or the \emph{OSD-code} for short, is a dominating set and uses open neighbourhoods for separating vertices. The paper studies the fundamental properties concerning the existence, hardness and minimality of OSD-codes. Due to the emergence of a close and yet difficult to establish relation of the OSD-codes with another well-studied code in the literature called the open locating dominating codes, or OLD-codes for short, we compare the two on various graph classes. Finally, we also provide an equivalent reformulation of the problem of finding OSD-codes of a graph as a covering problem in a suitable hypergraph and discuss the polyhedra associated with OSD-codes, again in relation to OLD-codes of some graph classes already studied in this context.

We present a label-free method for detecting anomalies during thermographic inspection of building envelopes. It is based on the AI-driven prediction of thermal distributions from color images. Effectively the method performs as a one-class classifier of the thermal image regions with high mismatch between the predicted and actual thermal distributions. The algorithm can learn to identify certain features as normal or anomalous by selecting the target sample used for training. We demonstrated this principle by training the algorithm with data collected at different outdoors temperature, which lead to the detection of thermal bridges. The method can be implemented to assist human professionals during routine building inspections or combined with mobile platforms for automating examination of large areas.

We propose a new class of finite element approximations to ideal compressible magnetohydrody- namic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built via a discrete variational principle mimicking the continuous Euler-Poincare principle, and to further exploit the geometrical structure of the prob- lem, vector fields are represented by their action as Lie derivatives on differential forms of any degree. The resulting semi-discrete approximations are shown to conserve the total mass, entropy and energy of the solutions for a wide class of finite element approximations. In addition, the divergence-free nature of the magnetic field is preserved in a pointwise sense and a time discretiza- tion is proposed, preserving those invariants and giving a reversible scheme at the fully discrete level. Numerical simulations are conducted to verify the accuracy of our approach and its ability to preserve the invariants for several test problems.

This study focuses on how different modalities of human communication can be used to distinguish between healthy controls and subjects with schizophrenia who exhibit strong positive symptoms. We developed a multi-modal schizophrenia classification system using audio, video, and text. Facial action units and vocal tract variables were extracted as low-level features from video and audio respectively, which were then used to compute high-level coordination features that served as the inputs to the audio and video modalities. Context-independent text embeddings extracted from transcriptions of speech were used as the input for the text modality. The multi-modal system is developed by fusing a segment-to-session-level classifier for video and audio modalities with a text model based on a Hierarchical Attention Network (HAN) with cross-modal attention. The proposed multi-modal system outperforms the previous state-of-the-art multi-modal system by 8.53% in the weighted average F1 score.

The matched case-control design, up until recently mostly pertinent to epidemiological studies, is becoming customary in biomedical applications as well. For instance, in omics studies, it is quite common to compare cancer and healthy tissue from the same patient. Furthermore, researchers today routinely collect data from various and variable sources that they wish to relate to the case-control status. This highlights the need to develop and implement statistical methods that can take these tendencies into account. We present an R package penalizedclr, that provides an implementation of the penalized conditional logistic regression model for analyzing matched case-control studies. It allows for different penalties for different blocks of covariates, and it is therefore particularly useful in the presence of multi-source omics data. Both L1 and L2 penalties are implemented. Additionally, the package implements stability selection for variable selection in the considered regression model. The proposed method fills a gap in the available software for fitting high-dimensional conditional logistic regression model accounting for the matched design and block structure of predictors/features. The output consists of a set of selected variables that are significantly associated with case-control status. These features can then be investigated in terms of functional interpretation or validation in further, more targeted studies.