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In recently years, a significant amount of research has been conducted on applying deep learning methods for glaucoma classification and detection. However, the explainability of those established machine learning models remains a big concern. In this research, in contrast, we learn from cognitive science concept and study how ophthalmologists judge glaucoma detection. Simulating experts' efforts, we propose a hierarchical decision making system, centered around a holistic set of carefully designed biomarker-oriented machine learning models. While biomarkers represent the key indicators of how ophthalmologists identify glaucoma, they usually exhibit latent inter-relations. We thus construct a time series model, named TRI-LSTM, capable of calculating and uncovering potential and latent relationships among various biomarkers of glaucoma. Our model is among the first efforts to explore the intrinsic connections among glaucoma biomarkers. We monitor temporal relationships in patients' disease states over time and to capture and retain the progression of disease-relevant clinical information from prior visits, thereby enriching biomarker's potential relationships. Extensive experiments over real-world dataset have demonstrated the effectiveness of the proposed model., Comment: 9 pages, 4 images

Due to the rapid growth of scientific publications, identifying all related reference articles in the literature has become increasingly challenging yet highly demanding. Existing methods primarily assess candidate publications from a static perspective, focusing on the content of articles and their structural information, such as citation relationships. There is a lack of research regarding how to account for the evolving impact among papers on their embeddings. Toward this goal, this paper introduces a temporal dimension to paper recommendation strategies. The core idea is to continuously update a paper's embedding when new citation relationships appear, enhancing its relevance for future recommendations. Whenever a citation relationship is added to the literature upon the publication of a paper, the embeddings of the two related papers are updated through a Temporal Graph Neural Network (TGN). A learnable memory update module based on a Recurrent Neural Network (RNN) is utilized to study the evolution of the embedding of a paper in order to predict its reference impact in a future timestamp. Such a TGN-based model learns a pattern of how people's views of the paper may evolve, aiming to guide paper recommendations more precisely. Extensive experiments on an open citation network dataset, including 313,278 articles from https://paperswithcode.com/about PaperWithCode, have demonstrated the effectiveness of the proposed approach., Comment: 10 pages, 4 figures, accepted by SDU@AAAI-2024. The AAAI Workshop on Scientific Document Understanding (2024)

Cognitive diagnosis aims to gauge students' mastery levels based on their response logs. Serving as a pivotal module in web-based online intelligent education systems (WOIESs), it plays an upstream and fundamental role in downstream tasks like learning item recommendation and computerized adaptive testing. WOIESs are open learning environment where numerous new students constantly register and complete exercises. In WOIESs, efficient cognitive diagnosis is crucial to fast feedback and accelerating student learning. However, the existing cognitive diagnosis methods always employ intrinsically transductive student-specific embeddings, which become slow and costly due to retraining when dealing with new students who are unseen during training. To this end, this paper proposes an inductive cognitive diagnosis model (ICDM) for fast new students' mastery levels inference in WOIESs. Specifically, in ICDM, we propose a novel student-centered graph (SCG). Rather than inferring mastery levels through updating student-specific embedding, we derive the inductive mastery levels as the aggregated outcomes of students' neighbors in SCG. Namely, SCG enables to shift the task from finding the most suitable student-specific embedding that fits the response logs to finding the most suitable representations for different node types in SCG, and the latter is more efficient since it no longer requires retraining. To obtain this representation, ICDM consists of a construction-aggregation-generation-transformation process to learn the final representation of students, exercises and concepts. Extensive experiments across real-world datasets show that, compared with the existing cognitive diagnosis methods that are always transductive, ICDM is much more faster while maintains the competitive inference performance for new students., Comment: WWW 2024

This paper investigates Voiculescu's theorem on approximate equivalence in separable properly infinite factors. We establish the norm-denseness of the set of all reducible operators and prove Voiculescu's bicommutant theorem. Additionally, we extend these results to the multiplier algebras within separable type $\mathrm{III}$ factors.

Recent advancements have seen Large Language Models (LLMs) and Large Multimodal Models (LMMs) surpassing general human capabilities in various tasks, approaching the proficiency level of human experts across multiple domains. With traditional benchmarks becoming less challenging for these models, new rigorous challenges are essential to gauge their advanced abilities. In this work, we present OlympiadBench, an Olympiad-level bilingual multimodal scientific benchmark, featuring 8,476 problems from Olympiad-level mathematics and physics competitions, including the Chinese college entrance exam. Each problem is detailed with expert-level annotations for step-by-step reasoning. Evaluating top-tier models on OlympiadBench, we implement a comprehensive assessment methodology to accurately evaluate model responses. Notably, the best-performing model, GPT-4V, attains an average score of 17.97% on OlympiadBench, with a mere 10.74% in physics, highlighting the benchmark rigor and the intricacy of physical reasoning. Our analysis orienting GPT-4V points out prevalent issues with hallucinations, knowledge omissions, and logical fallacies. We hope that our challenging benchmark can serve as a valuable resource for helping future AGI research endeavors. The data and evaluation code are available at \url{https://github.com/OpenBMB/OlympiadBench}, Comment: Accepted by ACL 2024 (main), update

Cognitive diagnosis assessment is a fundamental and crucial task for student learning. It models the student-exercise interaction, and discovers the students' proficiency levels on each knowledge attribute. In real-world intelligent education systems, generalization and interpretability of cognitive diagnosis methods are of equal importance. However, most existing methods can hardly make the best of both worlds due to the complicated student-exercise interaction. To this end, this paper proposes a symbolic cognitive diagnosis~(SCD) framework to simultaneously enhance generalization and interpretability. The SCD framework incorporates the symbolic tree to explicably represent the complicated student-exercise interaction function, and utilizes gradient-based optimization methods to effectively learn the student and exercise parameters. Meanwhile, the accompanying challenge is that we need to tunnel the discrete symbolic representation and continuous parameter optimization. To address this challenge, we propose to hybridly optimize the representation and parameters in an alternating manner. To fulfill SCD, it alternately learns the symbolic tree by derivative-free genetic programming and learns the student and exercise parameters via gradient-based Adam. The extensive experimental results on various real-world datasets show the superiority of SCD on both generalization and interpretability. The ablation study verifies the efficacy of each ingredient in SCD, and the case study explicitly showcases how the interpretable ability of SCD works.

In order to increase the prediction accuracy of the online vehicle velocity prediction (VVP) strategy, a self-adaptive velocity prediction algorithm fused with traffic information was presented for the multiple scenarios. Initially, traffic scenarios were established inside the co-simulation environment. In addition, the algorithm of a general regressive neural network (GRNN) paired with datasets of the ego-vehicle, the front vehicle, and traffic lights was used in traffic scenarios, which increasingly improved the prediction accuracy. To ameliorate the robustness of the algorithm, then the strategy was optimized by particle swarm optimization (PSO) and k-fold cross-validation to find the optimal parameters of the neural network in real-time, which constructed a self-adaptive online PSO-GRNN VVP strategy with multi-information fusion to adapt with different operating situations. The self-adaptive online PSO-GRNN VVP strategy was then deployed to a variety of simulated scenarios to test its efficacy under various operating situations. Finally, the simulation results reveal that in urban and highway scenarios, the prediction accuracy is separately increased by 27.8% and 54.5% when compared to the traditional GRNN VVP strategy with fixed parameters utilizing only the historical ego-vehicle velocity dataset., Comment: 9 pages, 7 figures

Based on the characterization of surjective $L^p$-isometries of unitary groups in finite factors, we describe all surjective $L^p$-isometries between Grassmann spaces of projections with the same trace value in semifinite factors., Comment: 14 pages

A famous question of Halmos asks whether every operator on a separable infinite dimensional Hilbert space is a norm limit of reducible operators. In [30] , Voiculescu gave this problem an affirmative answer by his remarkable non-commutative Weyl-von Neumann theorem. We investigate the existence or non-existence of an analogue of Voiculescu's result in factors of type ${\rm II}_1$. In the paper we prove that, in the operator norm topology, the set of reducible operators is ${\it nowhere}$ dense in a non-$\Gamma$ factor $\mathcal M$ of type ${\rm II}_1$, where separable and non-separable cases of $\mathcal M$ are both considered. Main tools developed in the paper are a new characterization of Murray and von Neumann's Property $\Gamma$ for a factor of type ${\rm II}_1$ and a spectral gap property for a single operator in a non-$\Gamma$ factor of type ${\rm II}_1$., Comment: 32 pages

We give two characterizations of tracially nuclear C*-algebras. The first is that the finite summand of the second dual is hyperfinite. The second is in terms of a variant of the weak* uniqueness property. The necessary condition holds for all tracially nuclear C*-algebras. When the algebra is separable, we prove the sufficiency.

In this paper, we prove a non-commutative version of the Weyl-von Neumann theorem for representations of unital, separable AH algebras into countably decomposable, semifinite, properly infinite, von Neumann factors, where an AH algebra means an approximately homogeneous ${\rm C}^{\ast}$-algebra. We also prove a result for approximate summands of representations of unital, separable AH algebras into finite von Neumann factors., Comment: 26 pages

In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$ and let $\tau$ be a faithful normal semifinite tracial weight of $\mathcal M$. Suppose that $H$ and $H_1$ are self-adjoint operators affiliated with $\mathcal{M}$. We show that if $H-H_1$ is in $\mathcal{M}\cap L^{1}\left(\mathcal{M},\tau\right)$, then the ${norm}$ absolutely continuous parts of $H$ and $H_1$ are unitarily equivalent. This implies that the real part of a non-normal hyponormal operator in $\mathcal M$ is not a perturbation by $\mathcal{M}\cap L^{1}\left(\mathcal{M},\tau\right)$ of a diagonal operator. Meanwhile, for $n\ge 2$ and $1\leq p

In this paper, we provide a generalized version of the Voiculescu theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful normal semifinite tracial weight $\tau$, a normal operator is an arbitrarily small $(\max\{\|\cdot\|, \Vert\cdot\Vert_{2}\})$-norm perturbation of a diagonal operator. Furthermore, in a countably decomposable, properly infinite von Neumann algebra with a faithful normal semifinite tracial weight, we prove that each self-adjoint operator can be diagonalized modulo norm ideals satisfying a natural condition., Comment: 46

This paper is a continuation of our work on D. Voiculescu's topological free entropy dimension in unital C*-algebras. In this paper we first prove the topological free entropy dimension of a MF-nuclear and inner QD algebra is irrelevant to its generating family. Then we give the relation between the topological orbit dimension $K_{top}^2$ and the modified free orbit dimension$ K_2^2$ by using MF-traces. We also introduce a new invariant $K_{top}^3$ which is a modification of the topological orbit dimension $K_{top}^2$ when$ K_{top}^2$ is defined. As the applications of $K_{top}^3$, We prove that$ K_{top}^3(A)=0$ if A has property $ c^*-{\Gamma}$ and has no finite-dimensional representations. We also give the definition of property MF-c^*-{\Gamma}. We then conclude that, for the unital MF $ C^*$-algebra with no finite-dimensional representations, if A has property MF-c*-{\Gamma}, then $K_{top}^3(A)=0$.

In 1967, Arveson invented a non-commutative generalization of classical $H^{\infty},$ known as finite maximal subdiagonal subalgebras, for a finite von Neumann algebra $\mathcal M$ with a faithful normal tracial state $\tau$. In 2008, Blecher and Labuschagne proved a version of Beurling's theorem on $H^\infty$-right invariant subspaces in a non-commutative $L^{p}(\mathcal M,\tau)$ space for $1\le p\le \infty$. In the present paper, we define and study a class of norms ${\mathcal{N}}_{c}(\mathcal M, \tau)$ on $\mathcal{M},$ called normalized, unitarily invariant, $\Vert \cdot \Vert_{1}$-dominating, continuous norms, which properly contains the class $\{ \Vert \cdot \Vert_{p}:1\leq p< \infty \}.$ For $\alpha \in \mathcal{N}_{c}(\mathcal M, \tau),$ we define a non-commutative $L^{\alpha }({\mathcal{M}},\tau)$ space and a non-commutative $H^{\alpha}$ space. Then we obtain a version of the Blecher-Labuschagne-Beurling invariant subspace theorem on $H^\infty$-right invariant subspaces in a non-commutative $L^{\alpha }({\mathcal{M}},\tau)$ space. Key ingredients in the proof of our main result include a characterization theorem of $H^\alpha$ and a density theorem for $L^\alpha(\mathcal M,\tau)$., Comment: 25 pages

In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite dimensional C*- algebra is quasidiagonal. Applying this result, we conclude that a unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree.

In this paper, we discuss some equivalent definitions of Property $\Gamma$ for a type II$_1$ von Neumann algebra. Using these equivalent definitions, we prove that the Pisier's similarity degree of a type II$_1$ von Neumann algebra with Property $\Gamma$ is equal to $3$.

Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\mathcal M$ has Property $\Gamma$, then the similarity degree of $\mathcal M$ is less than or equal to $5$. If $\mathcal A$ has Property c$^*$-$\Gamma$, then the similarity degree of $\mathcal A$ is equal to $3$. In particular, the similarity degree of a $\mathcal Z$-stable, separable, non-nuclear, unital C$^*$-algebra is equal to $3$., Comment: arXiv admin note: text overlap with arXiv:1407.0664

In this paper, Property $\Gamma$ for a type II$_{1}$ von Neumann algebra is introduced as a generalization of Murray and von Neumann's Property $\Gamma$ for a type II$_{1}$ factor. The main result of this paper is that if a type II$_{1}$ von Neumann algebra $\mathcal{M}$ with separable predual has Property $\Gamma$, then the continuous Hochschild cohomology group $H^{k}(\mathcal{M}, \mathcal{M})$ vanishes for every $k \geq 2$. This gives a generalization of an earlier result due to E. Christensen, F. Pop, A.M. Sinclair and R.R. Smith.