We present a novel unsupervised machine learning shock capturing algorithm based on Gaussian Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in detecting shocks and is robust across diverse test cases without the need for parameter tuning. We compare the GMM-based sensor with state-of-the-art alternatives. All methods are integrated into a high-order compressible discontinuous Galerkin solver where artificial viscosity can be modulated to capture shocks. Supersonic test cases, including high Reynolds numbers, showcase the sensor's performance, demonstrating the same effectiveness as fine-tuned state-of-the-art sensors. %The nodal DG aproach allows for potential applications in sub-cell flux-differencing formulations, supersonic feature detection, and mesh refinement. The adaptive nature and ability to function without extensive training datasets make this GMM-based sensor suitable for complex geometries and varied flow configurations. Our study reveals the potential of unsupervised machine learning methods, exemplified by the GMM sensor, to improve the robustness and efficiency of advanced CFD codes.
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The Linguistic Matrix Theory programme introduced by Kartsaklis, Ramgoolam and Sadrzadeh is an approach to the statistics of matrices that are generated in type-driven distributional semantics, based on permutation invariant polynomial functions which are regarded as the key observables encoding the significant statistics. In this paper we generalize the previous results on the approximate Gaussianity of matrix distributions arising from compositional distributional semantics. We also introduce a geometry of observable vectors for words, defined by exploiting the graph-theoretic basis for the permutation invariants and the statistical characteristics of the ensemble of matrices associated with the words. We describe successful applications of this unified framework to a number of tasks in computational linguistics, associated with the distinctions between synonyms, antonyms, hypernyms and hyponyms.
Addressing preferred orientation in single-particle cryo-EM through AI-generated auxiliary particles
The single-particle cryo-EM field faces the persistent challenge of preferred orientation, lacking general computational solutions. We introduce cryoPROS, an AI-based approach designed to address the above issue. By generating the auxiliary particles with a conditional deep generative model, cryoPROS addresses the intrinsic bias in orientation estimation for the observed particles. We effectively employed cryoPROS in the cryo-EM single particle analysis of the hemagglutinin trimer, showing the ability to restore the near-atomic resolution structure on non-tilt data. Moreover, the enhanced version named cryoPROS-MP significantly improves the resolution of the membrane protein NaX using the no-tilted data that contains the effects of micelles. Compared to the classical approaches, cryoPROS does not need special experimental or image acquisition techniques, providing a purely computational yet effective solution for the preferred orientation problem. Finally, we conduct extensive experiments that establish the low risk of model bias and the high robustness of cryoPROS.
The emergence of Large Language Models (LLMs) has boosted performance and possibilities in various NLP tasks. While the usage of generative AI models like ChatGPT opens up new opportunities for several business use cases, their current tendency to hallucinate fake content strongly limits their applicability to document analysis, such as information retrieval from documents. In contrast, extractive language models like question answering (QA) or passage retrieval models guarantee query results to be found within the boundaries of an according context document, which makes them candidates for more reliable information extraction in productive environments of companies. In this work we propose an approach that uses and integrates extractive QA models for improved feature extraction of German business documents such as insurance reports or medical leaflets into a document analysis solution. We further show that fine-tuning existing German QA models boosts performance for tailored extraction tasks of complex linguistic features like damage cause explanations or descriptions of medication appearance, even with using only a small set of annotated data. Finally, we discuss the relevance of scoring metrics for evaluating information extraction tasks and deduce a combined metric from Levenshtein distance, F1-Score, Exact Match and ROUGE-L to mimic the assessment criteria from human experts.
Dynamic Ensemble Selection (DES) is a Multiple Classifier Systems (MCS) approach that aims to select an ensemble for each query sample during the selection phase. Even with the proposal of several DES approaches, no particular DES technique is the best choice for different problems. Thus, we hypothesize that selecting the best DES approach per query instance can lead to better accuracy. To evaluate this idea, we introduce the Post-Selection Dynamic Ensemble Selection (PS-DES) approach, a post-selection scheme that evaluates ensembles selected by several DES techniques using different metrics. Experimental results show that using accuracy as a metric to select the ensembles, PS-DES performs better than individual DES techniques. PS-DES source code is available in a GitHub repository
In this paper we present two semi-implicit-type second order Compact Approximate Taylor (CAT2) numerical schemes and blend them with a local a posteriori Multi-dimensional Optimal Order Detection (MOOD) paradigm to solve hyperbolic systems of balance laws with relaxed source term. The resulting scheme presents high accuracy when applied to smooth solutions, essentially non-oscillatory behavior for irregular ones, and offers a nearly fail-safe property in terms of ensuring positivity. The numerical results obtained from a variety of test cases, including smooth and non-smooth well-prepared and unprepared initial condition, assessing the appropriate behavior of the semi-implicit-type second order CATMOOD schemes. These results have been compared in accuracy and efficiency with a second order semi-implicit Runge-Kutta (RK) method.
The main topic of this paper are algorithms for computing Nash equilibria. We cast our particular methods as instances of a general algorithmic abstraction, namely, a method we call {\em algorithmic boosting}, which is also relevant to other fixed-point computation problems. Algorithmic boosting is the principle of computing fixed points by taking (long-run) averages of iterated maps and it is a generalization of exponentiation. We first define our method in the setting of nonlinear maps. Secondly, we restrict attention to convergent linear maps (for computing dominant eigenvectors, for example, in the PageRank algorithm) and show that our algorithmic boosting method can set in motion {\em exponential speedups in the convergence rate}. Thirdly, we show that algorithmic boosting can convert a (weak) non-convergent iterator to a (strong) convergent one. We also consider a {\em variational approach} to algorithmic boosting providing tools to convert a non-convergent continuous flow to a convergent one. Then, by embedding the construction of averages in the design of the iterated map, we constructively prove the existence of Nash equilibria (and, therefore, Brouwer fixed points). We then discuss implementations of averaging and exponentiation, an important matter even for the scalar case. We finally discuss a relationship between dominant (PageRank) eigenvectors and Nash equilibria.
The numerical solution of continuum damage mechanics (CDM) problems suffers from convergence-related challenges during the material softening stage, and consequently existing iterative solvers are subject to a trade-off between computational expense and solution accuracy. In this work, we present a novel unified arc-length (UAL) method, and we derive the formulation of the analytical tangent matrix and governing system of equations for both local and non-local gradient damage problems. Unlike existing versions of arc-length solvers that monolithically scale the external force vector, the proposed method treats the latter as an independent variable and determines the position of the system on the equilibrium path based on all the nodal variations of the external force vector. This approach renders the proposed solver substantially more efficient and robust than existing solvers used in CDM problems. We demonstrate the considerable advantages of the proposed algorithm through several benchmark 1D problems with sharp snap-backs and 2D examples under various boundary conditions and loading scenarios. The proposed UAL approach exhibits a superior ability of overcoming critical increments along the equilibrium path. Moreover, the proposed UAL method is 1-2 orders of magnitude faster than force-controlled arc-length and monolithic Newton-Raphson solvers.
Many classical constructions, such as Plotkin's and Turyn's, were generalized by matrix product (MP) codes. Quasi-twisted (QT) codes, on the other hand, form an algebraically rich structure class that contains many codes with best-known parameters. We significantly extend the definition of MP codes to establish a broader class of generalized matrix product (GMP) codes that contains QT codes as well. We propose a generator matrix formula for any linear GMP code and provide a condition for determining the code size. We prove that any QT code has a GMP structure. Then we show how to build a generator polynomial matrix for a QT code from its GMP structure, and vice versa. Despite that the class of QT codes contains many codes with best-known parameters, we present different examples of GMP codes with best-known parameters that are neither MP nor QT. Two different lower bounds on the minimum distance of GMP codes are presented; they generalize their counterparts in the MP codes literature. The second proposed lower bound replaces the non-singular by columns matrix with a less restrictive condition. Some examples are provided for comparing the two proposed bounds, as well as showing that these bounds are tight.
This paper details our speaker diarization system designed for multi-domain, multi-microphone casual conversations. The proposed diarization pipeline uses weighted prediction error (WPE)-based dereverberation as a front end, then applies end-to-end neural diarization with vector clustering (EEND-VC) to each channel separately. It integrates the diarization result obtained from each channel using diarization output voting error reduction plus overlap (DOVER-LAP). To harness the knowledge from the target domain and results integrated across all channels, we apply self-supervised adaptation for each session by retraining the EEND-VC with pseudo-labels derived from DOVER-LAP. The proposed system was incorporated into NTT's submission for the distant automatic speech recognition task in the CHiME-7 challenge. Our system achieved 65 % and 62 % relative improvements on development and eval sets compared to the organizer-provided VC-based baseline diarization system, securing third place in diarization performance.
This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the procedures via theoretical analyses and numerical studies to highlight how the best choice of algorithm depends on spectral properties of the matrix and the computational resources available. Despite superior performance for many problems, randomized block Krylov iteration has not been widely adopted in computational science. The paper strengthens the case for this method in three ways. First, it presents new pseudocode that can significantly reduce computational costs. Second, it provides a new analysis that yields simple, precise, and informative error bounds. Last, it showcases applications to challenging scientific problems, including principal component analysis for genetic data and spectral clustering for molecular dynamics data.
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