wanyu/IteraTeR_v2 huggingface dataset:
Original: For linear square matrix eigenproblems, eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors .
Revised: Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors .
Edit intent: clarity
Original:  The extended method involves complex moments given by  contour integrals of generalized resolvents associated with nonsquare matrices.
Revised:  The extended method involves complex moments given by the contour integrals of generalized resolvents associated with nonsquare matrices.
Edit intent: fluency
Original:  We give conditions such that the method gives all finite eigenvalues in a prescribed region in the complex plane.
Revised:  We establish conditions such that the method gives all finite eigenvalues in a prescribed region in the complex plane.
Edit intent: clarity
Original:  The primary cost is in the solutions of linear least squares problems that arise from quadrature points, and they can be readily parallelized in practice.
Revised:  The primary cost lies in the solutions of linear least squares problems that arise from quadrature points, and they can be readily parallelized in practice.
Edit intent: clarity
Original:  As compared to previous methods, the new method is found to be more robust and efficient and is conjectured by experiment results to be more efficient in parallelized settings.
Revised:  As compared to previous methods, the new method is more robust and efficient and is conjectured by experiment results to be more efficient in parallelized settings.
Edit intent: clarity
Original:  Notably, the proposed method does not fail in cases involving pairs of extremely close eigenvalues ;
Revised:  Notably, the proposed method does not fail in cases involving pairs of extremely close eigenvalues , and
Edit intent: fluency
Original: Deep neural network classifiers have been used frequently and are efficient.
Edit intent: coherence
Original:   In the proposed approach, a single (one-versus-all) deep network binary classifier is dedicated to each category classification .
Revised:  In the proposed approach, a single (one-versus-all) deep network binary classifier is dedicated to each category .
Edit intent: fluency
Original:  For classification of the test sample, the sample is presented to each network in the ensemble.
Revised:  For classification of a test sample, the sample is presented to each network in the ensemble.
Edit intent: fluency
Original:  After softmax-layer score voting, the network with the largest score is assumed to have classified the sample.
Revised:  After prediction score voting, the network with the largest score is assumed to have classified the sample.
Edit intent: clarity
Original:  Here, we propose to combine an organ-scale biophysical mathematical model and longitudinal PET to extract characteristic growth patterns and spreading of tau.
Revised:  Here, we propose to calibrate an organ-scale biophysical mathematical model and longitudinal PET to extract characteristic growth patterns and spreading of tau.
Edit intent: clarity
Original:  Here, we propose to combine an organ-scale biophysical mathematical model and longitudinal PET to extract characteristic growth patterns and spreading of tau.
Revised:  Here, we propose to combine an organ-scale biophysical mathematical model using longitudinal PET scans to extract characteristic growth patterns and spreading of tau.
Edit intent: clarity
Original:  We describe the method, present a numerical scheme for the calibration of the growth and spreading parameters, perform a sensitivity study using synthetic data, and apply it to clinical scans from the ADNI dataset.
Revised:  We describe the method, present a numerical scheme for the calibration of the growth and spreading parameters, perform a sensitivity study using synthetic data, and we perform a preliminary evaluation on clinical scans from the ADNI dataset.
Edit intent: clarity
Original: The adaptive immune system in vertebrates consists of highly diverse immune receptors to mount specific responses against a multitude of pathogens.
Revised: The adaptive immune system provides a diverse set of molecules that can mount specific responses against a multitude of pathogens.
Edit intent: clarity
Original:  A central feature of the adaptive immune system is the ability to form a memory to act more efficiently in future encounters with similar pathogens .
Revised:  Memory is a key feature of adaptive immunity, which allows organisms to respond more readily upon re-infections .
Edit intent: clarity
Original:  However, memory formation especially in B-cells is one of the least understood cell fate decisions in the immune system .
Revised:  However, differentiation of memory cells is still one of the least understood cell fate decisions in the immune system .
Edit intent: clarity
Original:  However, memory formation especially in B-cells is one of the least understood cell fate decisions in the immune system .
Revised:  However, memory formation especially in B-cells is one of the least understood cell fate decisions .
Edit intent: clarity
Original:  Here, we present a framework to characterize optimal strategies to store memory in order to maximize the utility of immune response to counter evolving pathogens throughout an organism's lifetime.
Revised:  Here, we introduce a mathematical framework to characterize optimal strategies to store memory in order to maximize the utility of immune response to counter evolving pathogens throughout an organism's lifetime.
Edit intent: clarity
Original:  Here, we present a framework to characterize optimal strategies to store memory in order to maximize the utility of immune response to counter evolving pathogens throughout an organism's lifetime.
Revised:  Here, we present a framework to characterize optimal strategies to store memory to maximize the utility of immune response to counter evolving pathogens throughout an organism's lifetime.
Edit intent: coherence
Original:  Here, we present a framework to characterize optimal strategies to store memory in order to maximize the utility of immune response to counter evolving pathogens throughout an organism's lifetime.
Revised:  Here, we present a framework to characterize optimal strategies to store memory in order to maximize the utility of immune response over an organism's lifetime.
Edit intent: clarity
Original: - a recipe that is consistent with recent experimental findings 1,2 . Moreover, we show that the specificity of memory should depend on the organism's lifespan, and shorter-lived organisms with fewer pathogenic encounters throughout their lifetime should store more cross-reactive memory.
Revised: - a recipe that is consistent with recent experimental findings 1,2 . Moreover, we predict that specificity of memory should depend on the organism's lifespan, and shorter-lived organisms with fewer pathogenic encounters throughout their lifetime should store more cross-reactive memory.
Edit intent: clarity
Original: - a recipe that is consistent with recent experimental findings 1,2 . Moreover, we show that the specificity of memory should depend on the organism's lifespan, and shorter-lived organisms with fewer pathogenic encounters throughout their lifetime should store more cross-reactive memory.
Revised: - a recipe that is consistent with recent experimental findings 1,2 . Moreover, we show that the specificity of memory should depend on the organism's lifespan, and shorter-lived organisms with fewer pathogenic encounters should store more cross-reactive memory.
Edit intent: clarity
Original:  Overall, our framework provides a baseline to gauge the efficacy of immune memory formation in light of an organism's coevolutionary history with pathogens.
Revised:  Our framework provides a baseline to gauge the efficacy of immune memory formation in light of an organism's coevolutionary history with pathogens.
Edit intent: coherence
Original:  Overall, our framework provides a baseline to gauge the efficacy of immune memory formation in light of an organism's coevolutionary history with pathogens.
Revised:  Overall, our framework provides a baseline to gauge the efficacy of immune memory in light of an organism's coevolutionary history with pathogens.
Edit intent: clarity
Original:  Using a test design where each individual is assigned to a fixed number of tests, we derive explicit algorithmic bounds for two commonly considered inference algorithms and thereby improve on results by Scarlett \& Cevher (SODA 2016) and Scarlett \& Johnson (2020) and providing the strongest performance guarantees currently proved for  these noisy group testing models.
Revised:  Using a test design where each individual is assigned to a fixed number of tests, we derive explicit algorithmic bounds for two commonly considered inference algorithms and thereby improve on results by Scarlett \& Cevher (SODA 2016) and Scarlett \& Johnson (2020) and providing the strongest performance guarantees currently proved for efficient algorithms in these noisy group testing models.
Edit intent: clarity
Original:  In addition, we show that any positive homogeneous monetary risk measure can be represented through Minkowski gauges.
Edit intent: coherence
Original:  We show that  given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework.
Revised:  We show that , given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework.
Edit intent: fluency
Original:  In particular, the Minkowski gauge of a set which is convex, stable under scalar addition, and radially bounded at non-constants, is a generalized deviation measure.
Revised:  In particular, the Minkowski Deviation of a set which is convex, stable under scalar addition, and radially bounded at non-constants, is a generalized deviation measure.
Edit intent: clarity
Original: Most algorithms used in neural networks (NN)-based leaning tasks are strongly affected by the choices of initialization  . Good initialization can avoid sub-optimal solutions and alleviate saturation during training.
Revised: Neural networks (NN)-based leaning tasks are strongly affected by the choices of initialization . Good initialization can avoid sub-optimal solutions and alleviate saturation during training.
Edit intent: clarity
Original: Most algorithms used in neural networks (NN)-based leaning tasks are strongly affected by the choices of initialization  . Good initialization can avoid sub-optimal solutions and alleviate saturation during training.
Revised: Most algorithms used in neural networks (NN)-based learning algorithms are strongly affected by the choices of initialization . Good initialization can avoid sub-optimal solutions and alleviate saturation during training.
Edit intent: clarity
Original: Most algorithms used in neural networks (NN)-based leaning tasks are strongly affected by the choices of initialization  . Good initialization can avoid sub-optimal solutions and alleviate saturation during training.
Revised: Most algorithms used in neural networks (NN)-based leaning tasks are strongly affected by the choices of initialization . 
Edit intent: coherence
Original:  However, designing improved initialization strategies is a difficult task and our understanding of good initialization is still very primitive .
Revised:  However, designing improved optimization strategies is a difficult task and our understanding of good initialization is still very primitive .
Edit intent: coherence
Original:  Here, we propose persistent neurons, a  strategy that optimizes the learning trajectory using information from previous converged solutions.
Revised:  Here, we propose persistent neurons, a strategy that optimizes the learning task using information from previous converged solutions.
Edit intent: clarity
Original:  Moreover, we evaluate full and partial persistent model and show it can be used to boost the performance on a range of NN structures, such as AlexNet and residual neural network . Saturation of activation functions during persistent training is also studied .
Revised:  We evaluate the full and partial persistent model and show it can be used to boost the performance on a range of NN structures, such as AlexNet and residual neural network . Saturation of activation functions during persistent training is also studied .
Edit intent: coherence
Original:  To assess this concern, we use in silico datasets with known binding rules to develop a general framework for evaluating model attribution.
Revised:  To assess this concern, we use in silico datasets with known binding rules to develop a general framework for evaluating model attribution.
Edit intent: fluency
Original:  Our result immediately implies a strongly polynomial algorithm for the Submodular Function Minimization problem that makes at most O(n^3) calls to an evaluation oracle .
Revised:  Our result immediately implies a strongly polynomial algorithm that makes at most O(n^3) calls to an evaluation oracle .
Edit intent: coherence
Original:  Our result is achieved by an application of the LLL algorithm Lenstra, Lenstra and Lov\'asz, Math.
Revised:  Our result is achieved Lenstra, Lenstra and Lov\'asz, Math.
Edit intent: clarity
Original:  Ann. 1982%DIFDELCMD < ] %%% for the shortest lattice vector problem.
Revised:  Ann. 1982%DIFDELCMD < ] %%% via a reduction to the Shortest Vector Problem in lattices.
Edit intent: clarity
Original:  To achieve the O(n^2) term in the oracle complexity, technical ingredients from convex geometry are applied .
Revised:  To achieve the O(n^2) term in the oracle complexity, technical ingredients from convex geometry .
Edit intent: clarity
Original: We extend the concept of using an active user' s emotion embeddings and movies' emotion embeddings to evaluate a Recommender top-N recommendation list as illustrated in a previous paper to encompass the emotional features of a film as a component of building Emotion Aware Recommender Systems.
Revised: We apply the concept of using an active user' s emotion embeddings and movies' emotion embeddings to evaluate a Recommender top-N recommendation list as illustrated in a previous paper to encompass the emotional features of a film as a component of building Emotion Aware Recommender Systems.
Edit intent: clarity
Original: We extend the concept of using an active user' s emotion embeddings and movies' emotion embeddings to evaluate a Recommender top-N recommendation list as illustrated in a previous paper to encompass the emotional features of a film as a component of building Emotion Aware Recommender Systems.
Revised: We extend the concept of using an active user' s emotion embeddings and movies' emotion vectors (MVECs) as building components of Emotion Aware Recommender Systems.
Edit intent: clarity
Original:  We then apply the movie emotion embeddings obtained from classifying the emotional features of movie overviews by the Tweets Emotion Classifier, which we have developed to add an emotional dimension of embeddings for the Recommender.
Revised:  We employed a Tweets Affective Classifier to classify movies' emotion profiles through movie overviews. We construct MVECs from the Tweets Emotion Classifier, which we have developed to add an emotional dimension of embeddings for the Recommender.
Edit intent: clarity
Original:  We reckon that the Emotion Aware Recommender top-N list, which matches the active user's emotional profile, is useful for providing serendipity recommendationsand remedying the cold start problem commonly present in Recommender .
Revised:  We reckon that the Emotion Aware Recommender showed serendipity recommendations .
Edit intent: clarity
Original: In this paper, we investigate the effect ] of the prolonged service time at the non-dedicated servers in a pooling systemon the system performance.
Revised: The prolonged service time at non-dedicated servers has been observed in ] of the prolonged service time at the non-dedicated servers in a pooling systemon the system performance.
Edit intent: coherence
Original: In this paper, we investigate the effect ] of the prolonged service time at the non-dedicated servers in a pooling systemon the system performance.
Revised: In this paper, we investigate the effect ] of the prolonged service time at non-dedicated servers in a pooling systemon the system performance.
Edit intent: fluency
Original: Finding latent structures in data is drawing increasing attention in broad and diverse fields such as fluid dynamics, signal processing, and machine learning.
Revised: Finding latent structures in data is drawing increasing attention in diverse fields such as fluid dynamics, signal processing, and machine learning.
Edit intent: clarity
Original:  In this work, we formulate for two types of dynamical system.
Revised:  for two types of dynamical system.
Edit intent: clarity
Original:  Regarding to the first type, dynamical systems, derived by \gamma-homogeneous operators \gamma\in 0, 1), reach the steady state in finite time.
Revised:  Regarding to the first type, dynamical systems, derived by \gamma-homogeneous operators 0, 1), reach the steady state in finite time.
Edit intent: clarity
Original:  This inherently contradicts the Dynamic Mode Decomposition (DMD) model, which can be seen as an exponential data fitting algorithm.
Revised:  DMD, on the other hand, can be viewed as an exponential data fitting algorithm.
Edit intent: clarity
Original:  Therefore, the induced operator leads to artifacts in the decomposition.
Revised:  operator leads to artifacts in the decomposition.
Edit intent: coherence
Original:  This requirement is embeded in a variant of the DMD algorithm, termed as Symmetric DMD (SDMD) . With these adaptations, we formulate a closed form solution of DMD for dynamics u_t = P(u) , u(t=0)=u_0, where P is a nonlinear \gamma-homogeneous operator, when the initial condition u_0 admits the nonlinear eigenvalue problem P(u_0)=\lambda u_0 (u_0 is a nonlinear eigenfunction, with respect to the operator P).
Revised:  This requirement is embeded in a variant of the DMD algorithm, termed as Symmetric DMD (SDMD) . With these adaptations, we provide a closed form solution of DMD for dynamics u_t = P(u) , u(t=0)=u_0, where P is a nonlinear \gamma-homogeneous operator, when the initial condition u_0 admits the nonlinear eigenvalue problem P(u_0)=\lambda u_0 (u_0 is a nonlinear eigenfunction, with respect to the operator P).
Edit intent: clarity
Original:  This requirement is embeded in a variant of the DMD algorithm, termed as Symmetric DMD (SDMD) . With these adaptations, we formulate a closed form solution of DMD for dynamics u_t = P(u) , u(t=0)=u_0, where P is a nonlinear \gamma-homogeneous operator, when the initial condition u_0 admits the nonlinear eigenvalue problem P(u_0)=\lambda u_0 (u_0 is a nonlinear eigenfunction, with respect to the operator P).
Revised:  This requirement is embeded in a variant of the DMD algorithm, termed as Symmetric DMD (SDMD) . With these adaptations, we formulate a closed form solution of DMD for dynamics u_t = P(u) , u(t=0)=u_0, where P is a nonlinear \gamma-homogeneous operator, when u_0 admits the nonlinear eigenvalue problem P(u_0)=\lambda u_0 (u_0 is a nonlinear eigenfunction, with respect to the operator P).
Edit intent: clarity
Original:  This requirement is embeded in a variant of the DMD algorithm, termed as Symmetric DMD (SDMD) . With these adaptations, we formulate a closed form solution of DMD for dynamics u_t = P(u) , u(t=0)=u_0, where P is a nonlinear \gamma-homogeneous operator, when the initial condition u_0 admits the nonlinear eigenvalue problem P(u_0)=\lambda u_0 (u_0 is a nonlinear eigenfunction, with respect to the operator P).
Revised:  This requirement is embeded in a variant of the DMD algorithm, termed as Symmetric DMD (SDMD) . With these adaptations, we formulate a closed form solution of DMD for dynamics u_t = P(u) , u(t=0)=u_0, where P is a nonlinear \gamma-homogeneous operator, when the initial condition u_0 admits P(u_0)=\lambda u_0 (u_0 is a nonlinear eigenfunction, with respect to the operator P).
Edit intent: clarity
Original:  Finally, we formulate a discrete decomposition, related to nonlinear eigenfunctions of \gamma-homogeneous operator .
Revised:  Finally, we formulate a discrete decomposition, related to nonlinear eigenfunctions of \gamma-homogeneous operators .
Edit intent: fluency
Original:  Third, we formulate a new dynamic mode decomposition that constrains the matrix of the dynamics to be symmetric, termed SDMD. With these adaptations, we provide a closed form solution of DMD for dynamics u_t = P(u) , u(t = 0)=u_0, where P is a nonlinear \gamma-homogeneous operator, when u_0 admits P(u_0) =%DIFDELCMD < \lambdau%%% _0 . Then, we prove the validity of the blind homogeneity normalization.
Revised:  Third, we formulate a new dynamic mode decomposition that constrains the matrix of the dynamics to be symmetric, termed SDMD. With these adaptations, we provide a closed form solution of DMD for dynamics u_t = P(u) , u(t = %DIFDELCMD < \lambdau%%% _0 . Then, we prove the validity of the blind homogeneity normalization.
Edit intent: coherence
Original:  In this work,  we propose a conceptual framework and taxonomy for assisted reinforcement learning, aimed at fostering such collaboration by classifying and comparing various methods that use external information in the learning process.
Revised:  In this work, we propose a conceptual framework and taxonomy for assisted reinforcement learning, aimed at fostering collaboration by classifying and comparing various methods that use external information in the learning process.
Edit intent: clarity
Original:  The proposed algorithm represents a novel machine-learning-based approach to noise-robust adaptation control for challenging online supervised acoustic system identification applications characterized by high-level and non-stationary interfering noise signals  .
Revised:  The proposed algorithm represents a novel machine-learning based approach to noise-robust adaptation control for challenging online supervised acoustic system identification applications characterized by high-level and non-stationary interfering noise signals .
Edit intent: fluency
Original: The guarded fragment of FO fails to have the Craig Interpolation Property (CIP) and the Projective Beth Definability Property (PBDP) .
Revised: In logics with the Craig interpolation property (CIP) and the Projective Beth Definability Property (PBDP) .
Edit intent: clarity
Original:  In this article, we show that nevertheless  the existence of guarded interpolants and explicit definitions is decidable.
Revised:  In this article, we show that nevertheless the existence of interpolants and explicit definitions is decidable.
Edit intent: clarity
Original:  Deciding the existence of guarded interpolants and explicit definitions is thus by one exponential harder than validity in the guarded fragment .
Revised:  Deciding the existence of guarded interpolants and explicit definitions are decidable but harder than validity in the guarded fragment .
Edit intent: clarity
Original:  We also consider settings where agents must pay a search cost to discover their own types.
Revised:  We also consider a setting where agents must pay a search cost to discover their own types.
Edit intent: fluency
Original:  A solution to the problem was obtained by Thistle in 1995 which uses complex manipulations of automata.
Revised:  A solution to this problem was obtained by Thistle in 1995 which uses complex manipulations of automata.
Edit intent: clarity
Original:  This algorithm is notoriously hard to understand and, to the best of our knowledge, has never been implemented.
Edit intent: coherence
Original:  This establishes a new connection between the research areas of (I) supervisory control theory in the field of control engineering and (II) reactive synthesis in the field of computer science.
Edit intent: coherence