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A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of Euler for the rotation of a rigid body about a fixed point. The formulation turns initial-(boundary) value problems into degenerate elliptic boundary value problems in (space)-time domains representing the Euler-Lagrange equations of suitably designed dual functionals in each of the above problems. We demonstrate reasonable success in approximating solutions of this range of parabolic, hyperbolic, and ODE primal problems, which includes energy dissipation as well as conservation, by a unified dual strategy lending itself to a variational formulation. The scheme naturally associates a family of dual solutions to a unique primal solution; such `gauge invariance' is demonstrated in our computed solutions of the heat and transport equations, including the case of a transient dual solution corresponding to a steady primal solution of the heat equation. Primal evolution problems with causality are shown to be correctly approximated by non-causal dual problems.

The detection of Alzheimer's disease (AD) from spontaneous speech has attracted increasing attention while the sparsity of training data remains an important issue. This paper handles the issue by knowledge transfer, specifically from both speech-generic and depression-specific knowledge. The paper first studies sequential knowledge transfer from generic foundation models pretrained on large amounts of speech and text data. A block-wise analysis is performed for AD diagnosis based on the representations extracted from different intermediate blocks of different foundation models. Apart from the knowledge from speech-generic representations, this paper also proposes to simultaneously transfer the knowledge from a speech depression detection task based on the high comorbidity rates of depression and AD. A parallel knowledge transfer framework is studied that jointly learns the information shared between these two tasks. Experimental results show that the proposed method improves AD and depression detection, and produces a state-of-the-art F1 score of 0.928 for AD diagnosis on the commonly used ADReSSo dataset.

We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are: nonsmooth initial data and time-dependent diffusion coefficient. We prove the stability and convergence of the method under weak assumptions concerning regularity of the diffusivity. We find optimal pointwise in space and global in time errors, which are verified with several numerical experiments.

Research in high energy physics (HEP) requires huge amounts of computing and storage, putting strong constraints on the code speed and resource usage. To meet these requirements, a compiled high-performance language is typically used; while for physicists, who focus on the application when developing the code, better research productivity pleads for a high-level programming language. A popular approach consists of combining Python, used for the high-level interface, and C++, used for the computing intensive part of the code. A more convenient and efficient approach would be to use a language that provides both high-level programming and high-performance. The Julia programming language, developed at MIT especially to allow the use of a single language in research activities, has followed this path. In this paper the applicability of using the Julia language for HEP research is explored, covering the different aspects that are important for HEP code development: runtime performance, handling of large projects, interface with legacy code, distributed computing, training, and ease of programming. The study shows that the HEP community would benefit from a large scale adoption of this programming language. The HEP-specific foundation libraries that would need to be consolidated are identified

We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint. We establish (weak) convergence of discrete solutions as well as a priori error estimates for the velocity vector field and the scalar kinematic pressure. Numerical experiments complement the theoretical findings.

Acceleration of gradient-based optimization methods is an issue of significant practical and theoretical interest, particularly in machine learning applications. Most research has focused on optimization over Euclidean spaces, but given the need to optimize over spaces of probability measures in many machine learning problems, it is of interest to investigate accelerated gradient methods in this context too. To this end, we introduce a Hamiltonian-flow approach that is analogous to moment-based approaches in Euclidean space. We demonstrate that algorithms based on this approach can achieve convergence rates of arbitrarily high order. Numerical examples illustrate our claim.

To understand the biological characteristics of neurological disorders with functional connectivity (FC), recent studies have widely utilized deep learning-based models to identify the disease and conducted post-hoc analyses via explainable models to discover disease-related biomarkers. Most existing frameworks consist of three stages, namely, feature selection, feature extraction for classification, and analysis, where each stage is implemented separately. However, if the results at each stage lack reliability, it can cause misdiagnosis and incorrect analysis in afterward stages. In this study, we propose a novel unified framework that systemically integrates diagnoses (i.e., feature selection and feature extraction) and explanations. Notably, we devised an adaptive attention network as a feature selection approach to identify individual-specific disease-related connections. We also propose a functional network relational encoder that summarizes the global topological properties of FC by learning the inter-network relations without pre-defined edges between functional networks. Last but not least, our framework provides a novel explanatory power for neuroscientific interpretation, also termed counter-condition analysis. We simulated the FC that reverses the diagnostic information (i.e., counter-condition FC): converting a normal brain to be abnormal and vice versa. We validated the effectiveness of our framework by using two large resting-state functional magnetic resonance imaging (fMRI) datasets, Autism Brain Imaging Data Exchange (ABIDE) and REST-meta-MDD, and demonstrated that our framework outperforms other competing methods for disease identification. Furthermore, we analyzed the disease-related neurological patterns based on counter-condition analysis.

Peptides are formed by the dehydration condensation of multiple amino acids. The primary structure of a peptide can be represented either as an amino acid sequence or as a molecular graph consisting of atoms and chemical bonds. Previous studies have indicated that deep learning routes specific to sequential and graphical peptide forms exhibit comparable performance on downstream tasks. Despite the fact that these models learn representations of the same modality of peptides, we find that they explain their predictions differently. Considering sequential and graphical models as two experts making inferences from different perspectives, we work on fusing expert knowledge to enrich the learned representations for improving the discriminative performance. To achieve this, we propose a peptide co-modeling method, RepCon, which employs a contrastive learning-based framework to enhance the mutual information of representations from decoupled sequential and graphical end-to-end models. It considers representations from the sequential encoder and the graphical encoder for the same peptide sample as a positive pair and learns to enhance the consistency of representations between positive sample pairs and to repel representations between negative pairs. Empirical studies of RepCon and other co-modeling methods are conducted on open-source discriminative datasets, including aggregation propensity, retention time, antimicrobial peptide prediction, and family classification from Peptide Database. Our results demonstrate the superiority of the co-modeling approach over independent modeling, as well as the superiority of RepCon over other methods under the co-modeling framework. In addition, the attribution on RepCon further corroborates the validity of the approach at the level of model explanation.

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.