wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this work we relate conservation, essentiality and functional repertoire of a gene to the connectivity k of the corresponding protein in the PPI networks. Focusing on a set of 42 bacterial species with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivity values changes between PPI subnetworks of essential and nonessential genes;
Revised:  In this work we relate conservation, essentiality and functional repertoire of a gene to the connectivity k of the corresponding protein in the PPI network. On a set of 42 bacterial species with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivity values changes between PPI subnetworks of essential and nonessential genes;
Edit intent: coherence
Original:  Focusing on a set of 42 bacterial species with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivity values changes between PPI subnetworks of essential and nonessential genes;
Revised:  Focusing on a set of 42 bacterial genomes of different sizes, and with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivity values changes between PPI subnetworks of essential and nonessential genes;
Edit intent: meaning-changed
Original:  Focusing on a set of 42 bacterial species with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivity values changes between PPI subnetworks of essential and nonessential genes;
Revised:  Focusing on a set of 42 bacterial species with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivities changes between PPI subnetworks of essential and nonessential genes;
Edit intent: clarity
Original:  Noteworthy, a structural transition in the network is observed such that, for connectivities k\ge40 , bacterial PPI networks are mostly populated by genesthat are conserved, essential and which , in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.
Revised:  In particular, we isolate a core of highly connected proteins (with connectivities k\ge40 , bacterial PPI networks are mostly populated by genesthat are conserved, essential and which , in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.
Edit intent: meaning-changed
Original:  Noteworthy, a structural transition in the network is observed such that, for connectivities k\ge40 , bacterial PPI networks are mostly populated by genesthat are conserved, essential and which , in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.
Revised:  Noteworthy, a structural transition in the network is observed such that, for connectivities k\ge40 ), which is ubiquitous among the species considered here -- though mostly visible in the degree distributions of bacteria with small genomes (less than 1000 genes). The genes that belong to this highly connected core are conserved, essential and which , in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.
Edit intent: meaning-changed
Original:  Noteworthy, a structural transition in the network is observed such that, for connectivities k\ge40 , bacterial PPI networks are mostly populated by genesthat are conserved, essential and which , in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.
Revised:  Noteworthy, a structural transition in the network is observed such that, for connectivities k\ge40 , bacterial PPI networks are mostly populated by genesthat are conserved, essential and , in most cases, belong to the COG cluster J, related to ribosomal functions and to the processing of genetic information.
Edit intent: fluency
Original:  This identification yields a variety of theoretical tools for efficiently computing boundary-aligned quad meshes, with provable guarantees on the resulting mesh, for example, the number of mesh defects and bounds on the defect locations.
Revised:  This yields a variety of theoretical tools for efficiently computing boundary-aligned quad meshes, with provable guarantees on the resulting mesh, for example, the number of mesh defects and bounds on the defect locations.
Edit intent: clarity
Original:  This identification yields a variety of theoretical tools for efficiently computing boundary-aligned quad meshes, with provable guarantees on the resulting mesh, for example, the number of mesh defects and bounds on the defect locations.
Revised:  This identification yields a variety of theoretical tools for efficiently computing boundary-aligned quad meshes, with provable guarantees on the resulting mesh, such as the number of mesh defects and bounds on the defect locations.
Edit intent: coherence
Original:  The procedure for generating the quad mesh is to (i) find a complex-valued "representation" field that minimizes the Dirichlet energy subject to a boundary constraint, (ii) convert the representation field into a boundary-aligned, smooth cross field, (iii) use separatrices of the cross field to partition the domain into four sided regions, and (iv) mesh each of these four-sided regions using standard techniques.
Revised:  The procedure for generating the quad mesh is to (i) find a complex-valued "representation" field that minimizes the Ginzburg-Landau energy subject to a boundary constraint, (ii) convert the representation field into a boundary-aligned, smooth cross field, (iii) use separatrices of the cross field to partition the domain into four sided regions, and (iv) mesh each of these four-sided regions using standard techniques.
Edit intent: meaning-changed
Original:  To solve the energy minimization problem for the representation field, we use an extension of the Merriman-Bence-Osher (MBO) threshold dynamics method, originally conceived as an algorithm to simulate motion by mean curvature , to minimize the Ginzburg-Landau energy for the optimal representation field .
Revised:  To minimize the Ginzburg-Landau energy for the representation field, we use an extension of the Merriman-Bence-Osher (MBO) threshold dynamics method, originally conceived as an algorithm to simulate motion by mean curvature , to minimize the Ginzburg-Landau energy for the optimal representation field .
Edit intent: clarity
Original:  To solve the energy minimization problem for the representation field, we use an extension of the Merriman-Bence-Osher (MBO) threshold dynamics method, originally conceived as an algorithm to simulate motion by mean curvature , to minimize the Ginzburg-Landau energy for the optimal representation field .
Revised:  To solve the energy minimization problem for the representation field, we use an extension of the Merriman-Bence-Osher (MBO) threshold dynamics method, originally conceived as an algorithm to simulate mean curvature flow .
Edit intent: clarity
Original: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one,  partition the points into  clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Revised: We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one, partition the points into clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Edit intent: meaning-changed
Original: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one,  partition the points into  clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Revised: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in a metric space , that arrive one by one, partition the points into clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Edit intent: meaning-changed
Original: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one,  partition the points into  clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Revised: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one, Unit Clustering asks to partition the points into clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Edit intent: meaning-changed
Original: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one,  partition the points into  clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Revised: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one, partition the points into the minimum number of clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Edit intent: meaning-changed
Original: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one,  partition the points into  clusters (subsets) of diameter at most one , so as to minimize the number of clusters used .
Revised: We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in \mathbb{R , that arrive one by one, partition the points into clusters (subsets) of diameter at most one ; while Unit Covering asks to cover all points by the minimum number of balls of unit radius .
Edit intent: meaning-changed
Original:  We also give a randomized online algorithm with competitive ratio O(d^2) for Unit Clustering of integer points (i.e., points in Z^d, d\in N, under L_{\infty} norm)  .
Revised:  We also give a randomized online algorithm with competitive ratio O(d^2) for Unit Clustering of integer points (i.e., points in Z^d, d\in N, under L_{\infty} norm) . We show that the competitive ratio of any deterministic online algorithm for Unit Covering is at least 2^d. This ratio is the best possible, as it can be attained by a simple deterministic algorithm that assigns points to a predefined set of unit cubes .
Edit intent: meaning-changed
Original:  We obtain an essentially complete answer to these questions for convex functions. Our approach is based on the observation that, due to the convexity of the ReLU activation, ReLU nets are particularly well-suited for representing convex functions.
Revised:  Our approach to this paper is based on the observation that, due to the convexity of the ReLU activation, ReLU nets are particularly well-suited for representing convex functions.
Edit intent: clarity
Original:  In particular, we prove that ReLU nets with width d+1 can approximate any continuous convex function of d variables arbitrarily well . Moreover, when approximating convex, piecewise affine functions by such nets, we obtain matching upper and lower bounds on the required depth, proving that our construction is essentially optimal .
Revised:  In particular, we prove that ReLU nets with width d+1 can approximate any continuous convex function of d variables arbitrarily well .
Edit intent: clarity
Original:  Our statistics are based on a well-known property of the \%%DIFDELCMD < \left( %%% r +1%DIFDELCMD < \right) %%% -th eigenvalue of the sample covariance matrix of the data (having defined r as the number of common factors ): whilst under the null the \left( r+1\right) -
Revised:  Our statistics are based on a well-known property of the \%%DIFDELCMD < \left( %%% r +1%DIFDELCMD < \right) %%% Letting r be the number of common factors ): whilst under the null the \left( r+1\right) -
Edit intent: clarity
Original: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked  . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Revised: th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Edit intent: clarity
Original: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked  . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Revised: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked under changes . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Edit intent: clarity
Original: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked  . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Revised: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked . Given that sample eigenvalues cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Edit intent: fluency
Original: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked  . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Revised: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked . Given that the sample eigenvalue cannot be estimated consistently under the null, we randomise the test statistic , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Edit intent: clarity
Original: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked  . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Revised: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Edit intent: fluency
Original: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked  . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
Revised: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . statistics, which are used for the monitoring scheme.
Edit intent: clarity
Original:  We provide a rigorous formulation of this result in a fully general setting, only allowing for buy-and-hold positions and without imposing any semimartingale restriction . We show that asset prices do not exhibit predictable jumps if and only if there is no possibility of obtaining sure profits via high-frequency limits of buy-and-hold trading strategies.
Revised:  We provide a rigorous formulation of this result in a fully general setting, only allowing for buy-and-hold positions and without imposing any semimartingale restriction and only allowing for buy-and-hold positions. We prove that asset prices do not exhibit predictable jumps if and only if there is no possibility of obtaining sure profits via high-frequency limits of buy-and-hold trading strategies.
Edit intent: coherence
Original:  Our results imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Revised:  We furthermore show that right-continuity is an indispensable requirement for any price process that does not admit sure profits. Our results are robust with respect to transaction costs or model mis-specifications and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Edit intent: meaning-changed
Original: In an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable magnitude at predictable times. We provide a rigorous formulation of this result in a fully general setting, without imposing any semimartingale restriction and only allowing for buy-and-hold positions.
Revised: We introduce and study the notion of sure profit via flash strategy, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction and only allowing for buy-and-hold positions.
Edit intent: meaning-changed
Original:  We provide a rigorous formulation of this result in a fully general setting, without imposing any semimartingale restriction and only allowing for buy-and-hold positions. We prove that asset prices do not exhibit predictable jumps if and only if there is no possibility of obtaining sure profits via high-frequency limits of buy-and-hold trading strategies .
Revised:  We provide a rigorous formulation of this result in a fully general setting, without imposing any semimartingale restriction , we prove that there are no sure profits via flash strategies if and only if asset prices do not exhibit predictable jumps if and only if there is no possibility of obtaining sure profits via high-frequency limits of buy-and-hold trading strategies .
Edit intent: clarity
Original:  We prove that asset prices do not exhibit predictable jumps if and only if there is no possibility of obtaining sure profits via high-frequency limits of buy-and-hold trading strategies .
Revised:  We prove that asset prices do not exhibit predictable jumps . This result relies on the general theory of processes and provides the most general formulation of the well-known fact that, in an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable direction or magnitude at predictable times .
Edit intent: meaning-changed
Original:  Our results are robust with respect to  transaction costs or model mis-specifications and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Revised:  Our results are robust with respect to small transaction costs or model mis-specifications and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.
Edit intent: meaning-changed
Original:  We performed simulations of tumor invasion using a minimal three dimensional model, accounting for cell elasticity and adhesive cell-cell interactions  to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches.
Revised:  We performed simulations of tumor invasion using a minimal three dimensional model, accounting for cell elasticity and adhesive cell-cell interactions as well as cell birth and death to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches.
Edit intent: meaning-changed
Original:  The mean square displacement, \Delta(t), of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, \Delta (t) \approx t^{\alpha}  , at longer times.
Revised:  The mean square displacement, \Delta(t), of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, \Delta (t) \approx t^{\alpha} (\alpha > 1) , at longer times.
Edit intent: meaning-changed
Original:  We present a computationally efficient, information-theoretic approach to predicting the locations of wavebreaks that initiate fibrillation in a cardiac system where the order-disorder behavior is controlled by one single driving component, mimicking electrical misfirings from the pulmonary veins or the Purkinje fibers.
Revised:  We present a computationally efficient, information-theoretic approach to predicting the locations of wavebreaks that initiate fibrillation in a cardiac system where the order-disorder behavior is controlled by a single driving component, mimicking electrical misfirings from the pulmonary veins or the Purkinje fibers.
Edit intent: fluency
Original:  We present a computationally efficient, information-theoretic approach to predicting the locations of wavebreaks that initiate fibrillation in a cardiac system where the order-disorder behavior is controlled by one single driving component, mimicking electrical misfirings from the pulmonary veins or the Purkinje fibers.
Revised:  We present a computationally efficient, information-theoretic approach to predicting the locations of wavebreaks that initiate fibrillation in a cardiac system where the order-disorder behavior is controlled by one single driving component, mimicking electrical misfiring from the pulmonary veins or the Purkinje fibers.
Edit intent: fluency