wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper, we present a hierarchical recurrent neural network for melody generation, which consists of three Long-Short-Term-Memory (LSTM) subnetworks working in a coarse-to-fine manner  . Specifically, the three subnetworks generate bar profiles, beat profiles and notes in turn, and the output of the high-level subnetworks are fed into the low-level subnetworks, serving as guidance for generating the finer time-scale melody components  .
Revised:  In this paper, we present a hierarchical recurrent neural network for melody generation, which consists of three Long-Short-Term-Memory (LSTM) subnetworks working in a coarse-to-fine manner . Specifically, the three subnetworks generate bar profiles, beat profiles and notes in turn, and the output of the high-level subnetworks are fed into the low-level subnetworks, serving as guidance for generating the finer time-scale melody components in low-level subnetworks .
Edit intent: clarity
Original:  The pervasiveness of criticality suggests that there may be general principles inducing this behaviour, yet there is no well-founded theory for understanding how criticality is found at a wide range of levels and contexts.
Revised:  The pervasiveness of criticality suggests that there may be general principles inducing this behaviour, yet there is no well-founded theory for understanding how criticality is found at a wide span of levels and contexts.
Edit intent: clarity
Original:  In both cases the neural controller reaches a point of criticality, which coincides with a transition point between two regimes of the agent's behaviour.
Revised:  In both cases the neural controller appears to reach a point of criticality, which coincides with a transition point between two regimes of the agent's behaviour.
Edit intent: clarity
Original:  The pervasiveness of criticality suggests that there may be general principles inducing this behaviour, yet there is no well-founded theory for understanding how criticality is found at a wide span of levels and contexts.
Revised:  The pervasiveness of criticality suggests that there may be general principles inducing this behaviour, yet there is no well-founded theory for understanding how criticality is generated at a wide span of levels and contexts.
Edit intent: clarity
Original: Emerging 5G systems will need to efficiently support both  broadband traffic (eMBB) and ultra-low-latency  (URLLC) traffic.
Revised: Emerging 5G systems will need to efficiently support both broadband traffic (eMBB) and ultra-low-latency communications (URLLC) traffic.
Edit intent: clarity
Original:  We study joint eMBB and URLLC schedulers for such systems, with the dual objectives of maximizing utility for eMBB traffic while satisfying instantaneous URLLC demands.
Revised:  We study joint eMBB and URLLC schedulers for such systems, with the dual objectives of maximizing utility for eMBB traffic while immediately satisfying URLLC demands.
Edit intent: clarity
Original:  Somewhat counter-intuitively, our results show that our dual objectives can be met by an iterative gradient scheduler for eMBB traffic that anticipates the expected loss from URLLC traffic, along with an URLLC demand scheduler that is oblivious to eMBB channel states, utility functions and allocations decisions of the eMBB scheduler.
Revised:  Somewhat counter-intuitively, our results show that our dual objectives can be met by an iterative gradient scheduler for eMBB traffic that anticipates the expected loss from URLLC traffic, along with an URLLC demand scheduler that is oblivious to eMBB channel states, utility functions and allocation decisions of the eMBB scheduler.
Edit intent: fluency
Original: We propose a fragment of many-sorted second order logic ESMT and show that checking satisfiability of sentences in this fragment is decidable.
Revised: We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable.
Edit intent: clarity
Original:  Our decision procedure reduces the satisfiability of ESMT formulae to satisfiability queries of the background theories , allowing us to use existing efficient SMT solvers  for these theories;
Revised:  Our decision procedure reduces the satisfiability of EQSMT formulae to satisfiability queries of the background theories , allowing us to use existing efficient SMT solvers for these theories;
Edit intent: fluency
Original: Graphs are commonly used to encode relationships among entities, yet , their abstractness makes them incredibly difficult to analyze.
Revised: Graphs are commonly used to encode relationships among entities, yet their abstractness makes them incredibly difficult to analyze.
Edit intent: fluency
Original:  Node-link diagrams are a popular method for drawing graphs . Classical techniques for the node-link diagrams include various layout methods that rely on derived information to position points, which often lack interactive exploration functionalities;
Revised:  Node-link diagrams are a popular method for drawing graphs ,
Edit intent: coherence
Original:  and force-directed layouts , which ignore global structures of the graph.
Revised:  and force-directed layouts provide a flexible method for node layouts that use local relationships in an attempt to reveal the global shape of the graph.
Edit intent: clarity
Original:  We then introduce an interactive persistence barcodes to study the substructures of a force-directed graph layout ;
Revised:  We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout ;
Edit intent: clarity
Original:  in particular, we add contracting and repulsing forces guided by the 0-dimensional persistent homology features  .
Revised:  in particular, we add contracting and repulsing forces generated by the persistent homology features .
Edit intent: clarity
Original:  Finally, we demonstrate the utility of our approach across three datasets.
Revised:  Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets.
Edit intent: clarity
Original: Graphs are commonly used to encode relationships among entities, yet their abstractness makes them incredibly difficult to analyze.
Revised: Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze.
Edit intent: clarity
Original:  Node-link diagrams are a popular method for drawing graphs, and force-directed layouts provide a flexible method for node layouts that use local relationships in an attempt to reveal the global shape of the graph.
Revised:  Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node layouts that use local relationships in an attempt to reveal the global shape of the graph.
Edit intent: fluency
Original:  Node-link diagrams are a popular method for drawing graphs, and force-directed layouts provide a flexible method for node layouts that use local relationships in an attempt to reveal the global shape of the graph.
Revised:  Node-link diagrams are a popular method for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph.
Edit intent: clarity
Original:  However, clutter and overlap of unrelated structure can lead to confusing graph visualizations.
Revised:  However, clutter and overlap of unrelated structures can lead to confusing graph visualizations.
Edit intent: fluency
Original:  This paper addresses the problem by leveraging the persistent homology features of an undirected graph as derived information for interactively manipulating force-directed layouts.
Revised:  This paper leverages the persistent homology features of an undirected graph as derived information for interactively manipulating force-directed layouts.
Edit intent: clarity
Original:  This paper addresses the problem by leveraging the persistent homology features of an undirected graph as derived information for interactively manipulating force-directed layouts.
Revised:  This paper addresses the problem by leveraging the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts.
Edit intent: fluency
Original:  To account for the amplitudes of the many biomolecular species that may be part of the oscillation circuit, we use a power norm-based amplitude metric, finding an increase of instances where an increase in period correlates with an increase in this amplitude metric .
Revised:  To account for the amplitudes of the many biomolecular species that may be part of the oscillations, finding largely similar trends .
Edit intent: clarity
Original:  Finally, we calculate "scaling laws" of period-amplitude co-variation for a subset of these benchmark oscillators , finding that as period increases the amplitude increases or remains constant .
Revised:  Finally, we calculate "scaling laws" of period-amplitude co-variation for a subset of these benchmark oscillators finding that as period increases the amplitude increases or remains constant .
Edit intent: fluency
Original: Under the action of the general linear group  , the ranks of matrices A and B forming a m \times n pencil A + \lambda B can change, but in a restricted manner.
Revised: Under the action of the general linear group , the ranks of matrices A and B forming an m \times n pencil A + \lambda B can change, but in a restricted manner.
Edit intent: fluency
Original:  Specifically, to every pencil one can associate a pair of minimal ranks, which is unique up to a permutation.
Revised:  Specifically, with every pencil one can associate a pair of minimal ranks, which is unique up to a permutation.
Edit intent: clarity
Original:  The natural hierarchy it induces in a pencil space is discussed .
Revised:  The natural hierarchy it induces in a pencil space .
Edit intent: clarity
Original:  Then, a characterization of the minimal ranks of a pencil in terms of its Kronecker canonical form is provided.
Revised:  Then, we show how the minimal ranks of a pencil in terms of its Kronecker canonical form is provided.
Edit intent: clarity
Original:  Then, a characterization of the minimal ranks of a pencil in terms of its Kronecker canonical form is provided.
Revised:  Then, a characterization of the minimal ranks of a pencil can be determined from its Kronecker canonical form is provided.
Edit intent: clarity
Original:  We classify the orbits according to their minimal ranks - under the action of the general linear group - in the case of real pencils with m, n \le 4.
Revised:  We classify the orbits according to their minimal ranks ( under the action of the general linear group - in the case of real pencils with m, n \le 4.
Edit intent: fluency
Original:  We classify the orbits according to their minimal ranks - under the action of the general linear group - in the case of real pencils with m, n \le 4.
Revised:  We classify the orbits according to their minimal ranks - under the action of the general linear group ) in the case of real pencils with m, n \le 4.
Edit intent: fluency
Original:  By relying on this classification , we show that no real regular 4 \times 4 pencil having only complex-valued eigenvalues admits a best approximation (in the norm topology) on the set of real pencils whose minimal ranks are bounded by 3.
Revised:  Subsequently , we show that no real regular 4 \times 4 pencil having only complex-valued eigenvalues admits a best approximation (in the norm topology) on the set of real pencils whose minimal ranks are bounded by 3.
Edit intent: coherence
Original:  Our results can be interpreted from a tensor viewpoint, where the minimal ranks of a degree-(d-1) matrix polynomial characterize the minimal ranks of matrices constituting a block-term decomposition of a m \times n \times d tensor into a sum of matrix-vector tensor products.
Revised:  Our results can be interpreted from a tensor viewpoint, where the minimal ranks of a degree-(d-1) matrix polynomial characterize the minimal ranks of matrices constituting a block-term decomposition of an m \times n \times d tensor into a sum of matrix-vector tensor products.
Edit intent: fluency
Original:  This theorem  has consequences for the A-Hierarchy as well , namely that unless W[P] is a subset of some class A[t], there are structural differences between the A-Hierarchy and the Polynomial Hierarchy.
Revised:  This theorem also has consequences for the A-Hierarchy as well , namely that unless W[P] is a subset of some class A[t], there are structural differences between the A-Hierarchy and the Polynomial Hierarchy.
Edit intent: coherence
Original: Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioral rules that sheep follow at the individual scale in order to sustain collective motion.
Revised: Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion.
Edit intent: fluency
Original:  Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronizing when they decide to switch between the two modes.
Revised:  Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronising when they decide to switch between the two modes.
Edit intent: fluency
Original:  Numerical solving these equations display a solitary wave propagating at constant speed . Coupling individual and collective levels, groups motion can then be seen as a wave propagating at some fraction of the individual walking speed even though each individual is at any moment either stopped or walking.
Revised:  Numerical solving these equations display a traveling pulse propagating at constant speed . Coupling individual and collective levels, groups motion can then be seen as a wave propagating at some fraction of the individual walking speed even though each individual is at any moment either stopped or walking.
Edit intent: clarity
Original:  Numerical solving these equations display a solitary wave propagating at constant speed . Coupling individual and collective levels, groups motion can then be seen as a wave propagating at some fraction of the individual walking speed even though each individual is at any moment either stopped or walking.
Revised:  Numerical solving these equations display a solitary wave propagating at constant speed even though each individual is at any moment either stopped or walking.
Edit intent: clarity
Original:  The convergence to only one solitary wave from any initial condition, and which can recover from perturbation, gives a high robustness to this biological system .
Revised:  The convergence to only one solitary wave from any initial condition, and to recover the pulse after perturbation. This gives a high robustness to this biological system .
Edit intent: clarity
Original:  The convergence to only one solitary wave from any initial condition, and which can recover from perturbation, gives a high robustness to this biological system .
Revised:  The convergence to only one solitary wave from any initial condition, and which can recover from perturbation, gives a high robustness to this coordination mechanism .
Edit intent: clarity
Original:  Emergy,  defined as the amount of (solar) energy used to make a product or a service, is becoming an important ecological indicator.
Revised:  Emergy, defined as the amount of (solar) energy used to make a product or service, is becoming an important ecological indicator.
Edit intent: fluency
Original:  To explain observed self-organization of systems by emergy the Maximum Empower Principle (MEP) was proposed initially without a mathematical formulation.
Revised:  The Maximum Empower Principle (MEP) was proposed initially without a mathematical formulation.
Edit intent: coherence
Original: In this paper we fix attention on a recently developed tensor decomposition scheme named tensor SVD (t-SVD) . the t-SVD not only provides similar properties as the matrix case, but also convert the tensor tubal-rank minimization into matrix rank minimization in the Fourier domain.
Revised: A recently developed novel tensor decomposition scheme named tensor SVD (t-SVD) . the t-SVD not only provides similar properties as the matrix case, but also convert the tensor tubal-rank minimization into matrix rank minimization in the Fourier domain.
Edit intent: clarity
Original:  Generally, minimizing the tensor nuclear norm (TNN)  may cause some bias .
Revised:  Generally, minimizing the tensor nuclear norm (TNN) may cause some biases .
Edit intent: fluency
Original:  In this paper, to alleviate these bias phenomenon , we consider to minimize the proposed partial sum of the tensor nuclear norm (PSTNN) in place of the tensor nuclear norm .
Revised:  In this paper, to alleviate these bias phenomenons , we consider to minimize the proposed partial sum of the tensor nuclear norm (PSTNN) in place of the tensor nuclear norm .
Edit intent: clarity
Original:  In this paper, to alleviate these bias phenomenon , we consider to minimize the proposed partial sum of the tensor nuclear norm (PSTNN) in place of the tensor nuclear norm .
Revised:  In this paper, to alleviate these bias phenomenon , we consider to minimize the proposed partial sum of the tensor nuclear norm (PSTNN) in place of the TNN .
Edit intent: clarity
Original:  The novel PSTNN is used for the problems of tensor completion (TC) and tensor principal component analysis (TRPCA).
Revised:  The novel PSTNN is applied to the tasks of tensor completion (TC) and tensor principal component analysis (TRPCA).
Edit intent: clarity
Original:  The novel PSTNN is used for the problems of tensor completion (TC) and tensor principal component analysis (TRPCA).
Revised:  The novel PSTNN is used for the problems of tensor completion and tensor principal component analysis (TRPCA).
Edit intent: clarity
Original:  The effectiveness of the proposed methods are conducted on the synthetic data and real world data, and experimental results reveal that the algorithm outperforms TNN based methods.
Revised:  The effectiveness of the proposed methods are conducted on the synthetic data and real-world data, and experimental results reveal that the algorithm outperforms TNN based methods.
Edit intent: fluency
Original:  The effectiveness of the proposed methods are conducted on the synthetic data and real world data, and experimental results reveal that the algorithm outperforms TNN based methods.
Revised:  The effectiveness of the proposed methods are conducted on the synthetic data and real world data, and experimental results reveal the effectiveness of the proposed methods.
Edit intent: clarity
Original:  The novel PSTNN is applied to the tasks of tensor completion and tensor principal component analysis.
Revised:  The novel PSTNN is applied to the tasks of tensor principal component analysis.
Edit intent: clarity
Original:  Numerical experiments are conducted on the synthetic data and real-world data , and experimental results reveal the effectiveness of the proposed methods .
Revised:  Numerical experiments are conducted on the synthetic data and real-world data reveal the superior of the proposed methods .
Edit intent: clarity
Original:  In particular, they imply computable error bounds for norms associated with stabilised space--time IgA approximations .
Revised:  In particular, they provide computable error bounds for norms associated with stabilised space--time IgA approximations .
Edit intent: clarity
Original: Experimental studies of microbial communities routinely reveal several stable states.
Revised: Experimental studies of microbial communities routinely reveal that they have multiple stable states.
Edit intent: clarity
Original:  While each of these states is generally resilient, exposure to antibiotics, probiotics , or different diets often trigger transitions to other states.
Revised:  While each of these states is generally resilient, certain perturbations such as antibiotics, probiotics , or different diets often trigger transitions to other states.
Edit intent: clarity
Original:  While each of these states is generally resilient, exposure to antibiotics, probiotics , or different diets often trigger transitions to other states.
Revised:  While each of these states is generally resilient, exposure to antibiotics, probiotics and diet shifts, result in transitions to other states.
Edit intent: clarity
Original:  Can we predict which specific perturbations will cause such transitions ?
Revised:  Can we reliably both predict such stable states as well as direct and control transitions between them ?
Edit intent: clarity
Original:  Here we present a new conceptual model - inspired by the stable marriage problem - which both exhibits these emergent phenomena and makes such predictions .
Revised:  Here we present a new conceptual model inspired by the stable marriage problem - which both exhibits these emergent phenomena and makes such predictions .
Edit intent: fluency
Original:  Our model's core ingredient is that microbes utilize nutrients one at a time , while competing with each other.
Revised:  Our model's core ingredient is that microbes utilize nutrients one at a time while competing with each other.
Edit intent: fluency
Original:  Using only two ranked tables  with microbes' nutrient preferences and  competitive abilities, we can determine all the stable states as well as the specific perturbations driving a community from one state to another.
Revised:  Using only two ranked tables with microbes' nutrient preferences and competitive abilities, we can determine all possible stable states as well as the specific perturbations driving a community from one state to another.
Edit intent: clarity
Original:  Supply-demand at  nodes is monotonically nonincreasing under admissible control.
Revised:  Supply-demand at the nodes is monotonically nonincreasing under admissible control.
Edit intent: fluency
Original:  Supply-demand at  nodes is monotonically nonincreasing under admissible control.
Revised:  Supply-demand at nodes is monotonically non-increasing under admissible control.
Edit intent: fluency
Original:  Under the failure rule, a link is removed permanently if its flow exceeds its capacities .
Revised:  Under the failure rule, a link is removed permanently if its flow exceeds capacity constraints .
Edit intent: clarity
Original:  We propose two approaches for computing optimal control , and provide time complexity analysis for these approaches .
Revised:  We propose two approaches for computing optimal control .
Edit intent: clarity
Original:  An algorithmic procedure to construct this representation is provided by leveraging and extending tools for arrangement of hyperplanes and convex polytopes.
Revised:  An algorithmic procedure to construct this representation is provided by leveraging and extending tools for arrangement of hyperplanes and polytopes.
Edit intent: clarity
Original:  In just the last year , researchers have obtained many interesting results concerning Boolean dimension and local dimension, contrasting these parameters with the classic Dushnik-Miller concept of dimension, and establishing links between both parameters and structural graph theory, path-width, and tree-width in particular.
Revised:  Since that time , researchers have obtained many interesting results concerning Boolean dimension and local dimension, contrasting these parameters with the classic Dushnik-Miller concept of dimension, and establishing links between both parameters and structural graph theory, path-width, and tree-width in particular.
Edit intent: clarity