wanyu/IteraTeR_full_sent huggingface dataset:
Original:  To implement } Kruskal's MST algorithm on it. To achieve this with limited workspace, we introduce a compact representation of planar graphs , called an s-net which allows us to manipulate its component structure during the execution of the algorithm .
Revised:  To implement } Kruskal's algorithm with O(s) cells of workspace, we introduce a compact representation of planar graphs , called an s-net which allows us to manipulate its component structure during the execution of the algorithm .
Edit intent: meaning-changed
Original:  Currently, there is a notable shift towards machine learning (ML) methodologies to aid this process . Deep learning has recently gained considerable attention as it allows the model to "learn" to extract features that are relevant for the task at hand.
Revised:  Currently, there is a notable shift towards machine learning (ML) methodologies to aid such procedures . Deep learning has recently gained considerable attention as it allows the model to "learn" to extract features that are relevant for the task at hand.
Edit intent: clarity
Original:  We formulate a cache optimization problem to maximize the sum of utilities over all contents under stationary and ergodic request process, which is non-convex in general . We find that the problem can be reformulated as a convex optimization problem when the inter-request  distribution has a non-increasing hazard rate function.
Revised:  We formulate a cache optimization problem to maximize the sum of utilities over all contents under stationary and ergodic request process, which is non-convex in general but we reformulate it as a convex optimization problem when the inter-request distribution has a non-increasing hazard rate function.
Edit intent: coherence
Original:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental  transposition symmetry of tonal music , as reflected by the  circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Revised:  Inspired by seminal work by Guerino Mazzola on the symmetries of tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental transposition symmetry of tonal music , as reflected by the circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Edit intent: clarity
Original:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental  transposition symmetry of tonal music , as reflected by the  circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Revised:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling static and dynamic tonal attraction phenomena in music psychology within the quantum cognition framework . Based on the fundamental transposition symmetry of tonal music , as reflected by the circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Edit intent: meaning-changed
Original:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental  transposition symmetry of tonal music , as reflected by the  circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Revised:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental principles of octave equivalence, fifth similarity and transposition symmetry of tonal music , as reflected by the circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Edit intent: meaning-changed
Original:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental  transposition symmetry of tonal music , as reflected by the  circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Revised:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental transposition symmetry of tonal music that are reflected by the circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Edit intent: clarity
Original:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental  transposition symmetry of tonal music , as reflected by the  circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Revised:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental transposition symmetry of tonal music , as reflected by the structure of the circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Edit intent: clarity
Original:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental  transposition symmetry of tonal music , as reflected by the  circle of fifths, we develop different wave function descriptions over this underlying tonal space , governed by a Schr\"odinger equation containing different interaction energies .
Revised:  Inspired by seminal work by Guerino Mazzola on the connection between musical forces and symmetries in tonal music, our study aims at elucidating and reconciling musical forces in the framework of quantum cognition . Based on the fundamental transposition symmetry of tonal music , as reflected by the circle of fifths, we develop different wave function descriptions over this underlying tonal space .
Edit intent: meaning-changed
Original:  In this paper we investigate the existence of r-rainbow cycles for three different flip graphs on geometric classes of objects: the aforementioned flip graph of triangulations of a convex n-gon, the flip graph of plane trees on an arbitrary set of n points, and the flip graph of non-crossing perfect matchings on a set of n points in convex position.
Revised:  In this paper we investigate the existence of r-rainbow cycles for three different flip graphs on classes of geometric objects: the aforementioned flip graph of triangulations of a convex n-gon, the flip graph of plane trees on an arbitrary set of n points, and the flip graph of non-crossing perfect matchings on a set of n points in convex position.
Edit intent: fluency
Original: This paper derives a generalization of the Granger-Johansen Representation Theorem valid for H-valued autoregressive (AR) processes , where H is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit circle.
Revised: This paper defines the class of \mathcal{H autoregressive (AR) processes , where H is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit circle.
Edit intent: meaning-changed
Original: This paper derives a generalization of the Granger-Johansen Representation Theorem valid for H-valued autoregressive (AR) processes , where H is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit circle.
Revised: This paper derives a generalization of the Granger-Johansen Representation Theorem valid for H-valued autoregressive (AR) processes with a unit root of finite type, where \mathcal{H is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit circle.
Edit intent: meaning-changed
Original: This paper derives a generalization of the Granger-Johansen Representation Theorem valid for H-valued autoregressive (AR) processes , where H is an infinite dimensional separable Hilbert space, under the assumption that 1 is an eigenvalue of finite type of the AR operator function and that no other non-zero eigenvalue lies within or on the unit circle. A necessary and sufficient condition for integration of order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0,%DIFDELCMD < \dots%%% , d, each one associated with components of the process integrated of order h.
Revised: This paper derives a generalization of the Granger-Johansen Representation Theorem valid for H-valued autoregressive (AR) processes , where H is an infinite dimensional separable Hilbert space, and derives a generalization of the Granger-Johansen Representation Theorem valid for any integration order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0,%DIFDELCMD < \dots%%% , d, each one associated with components of the process integrated of order h.
Edit intent: coherence
Original:  A necessary and sufficient condition for integration of order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0,%DIFDELCMD < \dots%%% , d, each one associated with components of the process integrated of order h.
Revised:  A necessary and sufficient condition for integration of order d=1,2,\dots %DIFDELCMD < \dots%%% , d, each one associated with components of the process integrated of order h.
Edit intent: coherence
Original:  A necessary and sufficient condition for integration of order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0,%DIFDELCMD < \dots%%% , d, each one associated with components of the process integrated of order h.
Revised:  A necessary and sufficient condition for integration of order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0,%DIFDELCMD < \dots%%% . An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer d and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and (i) the order of integration, (ii) the structure of the attractor space and the cointegrating space, (iii) the expression of the cointegrating relations, and (iv) the Triangular representation of the process integrated of order h.
Edit intent: meaning-changed
Original:  A necessary and sufficient condition for integration of order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0,%DIFDELCMD < \dots%%% , d, each one associated with components of the process integrated of order h. These results mirror the ones recently obtained in the finite dimensional case, with the only difference that the number of cointegrating relations  of order 0 is infinite  .
Revised:  A necessary and sufficient condition for integration of order d=1,2,\dots is given in terms of the decomposition of the space H into the direct sum of d+1 closed subspaces \tau_h, h=0,%DIFDELCMD < \dots%%% , d, each one associated with components of the process . Except for the fact that the number of cointegrating relations of order 0 is infinite .
Edit intent: coherence
Original:  The focus of the analysis is, apart from the description of the main properties of the graphs, to identify those properties that deviate from the expected values had the networks been build by randomly linking nodes with the same degree distribution.
Revised:  First, we investigate the quality of fits obtained for the nodes degree distributions to power-law functions. This analysis suggests that a power-law distribution poorly describes the data except for the far right tail in the case of PPI networks. Next we obtain descriptive statistics for the main graph parameters and try to identify the analysis is, apart from the description of the main properties of the graphs, to identify those properties that deviate from the expected values had the networks been build by randomly linking nodes with the same degree distribution.
Edit intent: meaning-changed
Original:  The focus of the analysis is, apart from the description of the main properties of the graphs, to identify those properties that deviate from the expected values had the networks been build by randomly linking nodes with the same degree distribution.
Revised:  The focus of the analysis is, apart from the description of the main properties of the graphs, to identify those properties that deviate from the expected values had the networks been built by randomly linking nodes with the same degree distribution.
Edit intent: fluency
Original:  The findings suggest that, while PPI networks have properties that differ from their expected values in their randomized versions with great statistical significance, the differences for metabolic networks have a smaller statistical significance, though it is possible to identify some drift . We also investigate the quality of fits obtained for the nodes degree distributions to power-law functions. The fits for the metabolic networks do describe the distributions if one disregards nodes with degree equal to one, but in the case of PPI networks the power-law distribution poorly describes the data except for the far right tail covering around half or less of the total distribution .
Revised:  The findings suggest that, while PPI networks have properties that differ from their expected values in their randomized versions with great statistical significance, the differences for metabolic networks have a smaller statistical significance, though it is possible to identify some drift .
Edit intent: coherence
Original: In this paper, we investigate a sheaf-theoretic interpretation of stratification learning . Motivated by the work of Alexandroff (1937) and McCord (1978), we aim to redirect efforts in the computational topology of triangulated compact polyhedra to the much more computable realm of sheaves on partially ordered sets .
Revised: In this paper, we investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives .
Edit intent: meaning-changed
Original:  Mild cognitive impairment (MCI) typically precedes Alzheimer's dementia, yet only a fraction (30\%-50\%) of MCI individuals will progress to dementia . Even when a prognosis of dementia is established using machine learning models and biomarkers, the fraction of MCI progressors remain limited (50\%-75\%). Instead of aiming at precise diagnosis in large clinical cohorts known for their heterogeneity, we propose here to identify only a subset of individuals who share a common brain signature highly predictive of oncoming dementia.
Revised:  Mild cognitive impairment (MCI) typically precedes Alzheimer's dementia, yet only a fraction (30\%-50\%) of MCI individuals will progress to dementia , even when screened using biomarkers. We propose here to identify only a subset of individuals who share a common brain signature highly predictive of oncoming dementia.
Edit intent: coherence
Original:  Instead of aiming at precise diagnosis in large clinical cohorts known for their heterogeneity, we propose here to identify only a subset of individuals who share a common brain signature highly predictive of oncoming dementia.
Revised:  Instead of aiming at precise diagnosis in large clinical cohorts known for their heterogeneity, we propose here to identify a subset of individuals who share a common brain signature highly predictive of oncoming dementia.
Edit intent: clarity
Original:  This signature was  discovered using a machine learning model in a reference public sample (ADNI), where the model was trained to identify patterns of brain atrophy and functional dysconnectivity commonly seen in patients suffering from dementia (N = 24), and not seen in cognitively normal individuals (N = 49) .
Revised:  This signature was composed of brain atrophy and functional dysconnectivity and discovered using a machine learning model in a reference public sample (ADNI), where the model was trained to identify patterns of brain atrophy and functional dysconnectivity commonly seen in patients suffering from dementia (N = 24), and not seen in cognitively normal individuals (N = 49) .
Edit intent: meaning-changed
Original:  This signature was  discovered using a machine learning model in a reference public sample (ADNI), where the model was trained to identify patterns of brain atrophy and functional dysconnectivity commonly seen in patients suffering from dementia (N = 24), and not seen in cognitively normal individuals (N = 49) .
Revised:  This signature was discovered using a machine learning model in patients suffering from dementia (N = 24), and not seen in cognitively normal individuals (N = 49) .
Edit intent: clarity
Original:  This signature was  discovered using a machine learning model in a reference public sample (ADNI), where the model was trained to identify patterns of brain atrophy and functional dysconnectivity commonly seen in patients suffering from dementia (N = 24), and not seen in cognitively normal individuals (N = 49) .
Revised:  This signature was discovered using a machine learning model in a reference public sample (ADNI), where the model was trained to identify patterns of brain atrophy and functional dysconnectivity commonly seen in patients suffering from dementia .
Edit intent: coherence
Original:  By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain statistically exhaustive models of the long-timescale behavior of small to intermediate biomolecules and complexes.
Revised:  By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes.
Edit intent: clarity
Original:  To model the interactions of many molecules at large lengthscales, such as in cellular signal transduction, particle-based reaction-diffusion (RD) simulations are more suitable but come at the price of sacrificing molecular detail.
Revised:  To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but come at the price of sacrificing molecular detail.
Edit intent: clarity
Original:  To model the interactions of many molecules at large lengthscales, such as in cellular signal transduction, particle-based reaction-diffusion (RD) simulations are more suitable but come at the price of sacrificing molecular detail.
Revised:  To model the interactions of many molecules at large lengthscales, such as in cellular signal transduction, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail.
Edit intent: clarity
Original:  In this paper, we make a first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation that includes both conformational changes and association/dissociation of proteins with small ligands or substrates . Applications on a toy model and CO diffusion and binding to myoglobin are reported.
Revised:  In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation that includes both conformational changes and association/dissociation of proteins with small ligands or substrates . Applications on a toy model and CO diffusion and binding to myoglobin are reported.
Edit intent: fluency
Original:  In this paper, we make a first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation that includes both conformational changes and association/dissociation of proteins with small ligands or substrates . Applications on a toy model and CO diffusion and binding to myoglobin are reported.
Revised:  In this paper, we make a first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of proteins with small ligands or substrates . Applications on a toy model and CO diffusion and binding to myoglobin are reported.
Edit intent: clarity
Original:  In this paper, we make a first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation that includes both conformational changes and association/dissociation of proteins with small ligands or substrates . Applications on a toy model and CO diffusion and binding to myoglobin are reported.
Revised:  In this paper, we make a first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation that includes both conformational changes and association/dissociation of a protein with a small ligand (A + B <--> C) . Applications on a toy model and CO diffusion and binding to myoglobin are reported.
Edit intent: meaning-changed
Original:  In this paper, we make a first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation that includes both conformational changes and association/dissociation of proteins with small ligands or substrates . Applications on a toy model and CO diffusion and binding to myoglobin are reported.
Revised:  In this paper, we make a first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation that includes both conformational changes and association/dissociation of proteins with small ligands or substrates . Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.
Edit intent: clarity