wanyu/IteraTeR_v2 huggingface dataset:
Original:  We find that, using a combination of projections weights as competition kernel in the Lotka-Volterra equations, the stability of food webs decreases with its complexity (measured as the average degree of the web)
Revised:  We find that, using a combination of projections weights as competition kernel in the Lotka-Volterra equations, the stability of food webs decreases with its ecological complexity.
Edit intent: clarity
Original:  The method is shown to be able to correlate sequences with function in the human proteome database,  and might find other useful applications for structure discovery also in computational linguistics, in the analysis of time series, and in the theory of dynamical systems .
Revised:  The method is shown to be able to correlate sequences with function in the human proteome database, and might find other useful applications to process large amount of data in various fields .
Edit intent: clarity
Original: In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed.
Revised: In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs is constructed.
Edit intent: fluency
Original:  In particular, Ar{\i}kan's polarization technique applied individually to each user polarizes any m-user binary input MAC into a finite collection of extremal MACs.
Revised:  In particular, Ar{\i}kan's polarization technique applied individually to each user transforms independent uses of a m-user binary input MAC into a finite collection of extremal MACs.
Edit intent: clarity
Original:  In particular, Ar{\i}kan's polarization technique applied individually to each user polarizes any m-user binary input MAC into a finite collection of extremal MACs.
Revised:  In particular, Ar{\i}kan's polarization technique applied individually to each user polarizes any m-user binary input MAC into successive uses of extremal MACs.
Edit intent: clarity
Original:  The extremal MACs have a number of desirable properties: (i) the `uniform sum rate' of the original channel is not lost , (ii) the extremal MACs have  rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits;
Revised:  The extremal MACs have a number of desirable properties: (i) the `uniform sum rate' of the original MAC is preserved , (ii) the extremal MACs have rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits;
Edit intent: clarity
Original:  The extremal MACs have a number of desirable properties: (i) the `uniform sum rate' of the original channel is not lost , (ii) the extremal MACs have  rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits;
Revised:  The extremal MACs have a number of desirable properties: (i) the `uniform sum rate' of the original channel is not lost , (ii) the extremal MACs have uniform rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits;
Edit intent: fluency
Original:  An application of this polar code construction to a coding scheme for the AWGN channel is also discussed.
Revised:  An application of this polar code construction to communicating on the AWGN channel is also discussed.
Edit intent: clarity
Original: A graph G is class II  if its chromatic index is at least \Delta+1.
Revised: A graph G is class II , if its chromatic index is at least \Delta+1.
Edit intent: fluency
Original:  Let H be a maximum \Delta -colorable subgraph of G. We prove best possible lower bounds for |E(H)|{|E(G)|}, and structural properties of maximum \Delta -colorable subgraphs.
Revised:  Let H be a maximum \Delta -colorable subgraph of G. The paper proves best possible lower bounds for |E(H)|{|E(G)|}, and structural properties of maximum \Delta -colorable subgraphs.
Edit intent: clarity
Original:  In particular it is shown that every set of vertex disjoint cycles of a class II graph with \Delta\geq3 can be extended to a maximum \Delta -edge colorable subgraph.
Revised:  In particular it is shown that every set of vertex-disjoint cycles of a class II graph with \Delta\geq3 can be extended to a maximum \Delta -edge colorable subgraph.
Edit intent: fluency
Original:  Our proof exploits the second order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts 
Revised:  Our proof exploits the second order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts model.
Edit intent: fluency
Original:  In the majority of cases bistability of the dynamical system is established numerically.
Revised:  In the majority of cases , bistability is established numerically.
Edit intent: clarity
Original:  We derive an upper bound on the satisfiabilit threshold and NAE-satisfiability threshold for regular random k-SAT for any k \geq 3.
Revised:  We derive an upper bound on the satisfiability threshold and NAE-satisfiability threshold for regular random k-SAT for any k \geq 3.
Edit intent: fluency
Original:  We derive lower bound on the threshold by applying the second moment  to the number of satisfying assignments.
Revised:  We derive lower bound on the threshold by applying the second moment method to the number of satisfying assignments.
Edit intent: clarity
Original: Normal dynamics in a one-dimensional channel of length L \to of N hard spheres are analyzed.
Revised: Normal dynamics in a one-dimensional channel of length L (\to of N hard spheres are analyzed.
Edit intent: fluency
Original:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L }  ^(-a), 0 <a<1.
Revised:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W D^(- } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L } ^(-a), 0 <a<1.
Edit intent: clarity
Original:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L }  ^(-a), 0 <a<1.
Revised:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, }), for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L } ^(-a), 0 <a<1.
Edit intent: fluency
Original:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L }  ^(-a), 0 <a<1.
Revised:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density \rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L } ^(-a), 0 <a<1.
Edit intent: fluency
Original:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L }  ^(-a), 0 <a<1.
Revised:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L } l ^(-a), 0 <a<1.
Edit intent: clarity
Original:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L }  ^(-a), 0 <a<1.
Revised:  The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W (D) D^(-g), 0<g<1, } for small D . The initial spheres' density rho is non-uniform and scales with the distance (from the origin) L as, rho(L) L } ^(-a), 0 
Edit intent: fluency
Original:  \leqa\leq1 An approximation for the N-particle PDF for this problem is derived.
Revised:  \leqa\leq1. An approximation for the N-particle PDF for this problem is derived.
Edit intent: fluency
Original:  From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, <r^2> t^[(1-g  )/( 2c-g) } , where c=1/(1+a).
Revised:  From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, <r^2> t^[(1-g )/( 2c- } , where c=1/(1+a).
Edit intent: fluency
Original:  From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, <r^2> t^[(1-g  )/( 2c-g) } , where c=1/(1+a).
Revised:  From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, <r^2> t^[(1-g )/( 2c-g) }) , where c=1/(1+a).
Edit intent: fluency
Original:  We generalize this mechanism in terms of bistability associated to valleys in an epigenetic landscape.
Revised:  We generalize this mechanism in terms of bistability associated with valleys in an epigenetic landscape.
Edit intent: fluency
Original:  Random walks, which normally require fewer resources per sample, can suffer from large estimation errors in the presence of disconnected or quasi-disconnected subgraphs .
Revised:  Random walks, which normally require fewer resources per sample, can suffer from large estimation errors in the presence of disconnected or loosely connected graphs .
Edit intent: clarity
Original:  We prove that the proposed sampling method, which we call Frontier sampling, has all of the nice sampling properties of a regular random walk.
Revised:  We show that the proposed sampling method, which we call Frontier sampling, has all of the nice sampling properties of a regular random walk.
Edit intent: coherence
Original:  We prove that the proposed sampling method, which we call Frontier sampling, has all of the nice sampling properties of a regular random walk.
Revised:  We prove that the proposed sampling method, which we call Frontier sampling, exhibits all of the nice sampling properties of a regular random walk.
Edit intent: clarity
Original:  At the same time, our simulations over large real world graphs show that, in the presence of disconnected or quasi-disconnected subgraphs , Frontier sampling exhibits lower estimation errors than regular random walks.
Revised:  At the same time, our simulations over large real world graphs show that, in the presence of disconnected or loosely connected components , Frontier sampling exhibits lower estimation errors than regular random walks.
Edit intent: clarity
Original:  We also argue that Frontier sampling is more suitable to sample power-law graphs than random vertex sampling  .
Revised:  We also show that Frontier sampling is more suitable to sample power-law graphs than random vertex sampling .
Edit intent: clarity
Original:  We also argue that Frontier sampling is more suitable to sample power-law graphs than random vertex sampling  .
Revised:  We also argue that Frontier sampling is more suitable than random vertex sampling .
Edit intent: clarity
Original:  Special emphasis has been put on a proper treatment of boundary conditions.
Revised:  Special emphasis has been put on a proper treatment of global modes, i.e. the possibility of the chain to perform global movements within the channel.
Edit intent: clarity
Original:  We show that the particular choice of boundary conditions significantly impacts the chain statistics in cases of weak and intermediate confinement.
Revised:  We show that the effect of these global modes significantly impacts the chain statistics in cases of weak and intermediate confinement.
Edit intent: clarity
Original: We study hierachical segmentation in the framework of edge-weighted graphs.
Revised: We study hierarchical segmentation in the framework of edge-weighted graphs.
Edit intent: fluency
Original:  We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical edgesegmentations .
Revised:  We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations .
Edit intent: fluency
Original:  We end this paper by showing how  the proposed framework allows to see constrained connectivityas a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.
Revised:  We end this paper by showing how to use the proposed framework allows to see constrained connectivityas a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.
Edit intent: clarity
Original:  An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination of BIT and TIMESTAMP(0) . This and many other known algorithms, like MTF, are projective in the sense that they can be defined by looking only at any pair of list items at a time.
Revised:  An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination of BIT and TIMESTAMP(0) . This and almost all other list update algorithms, like MTF, are projective in the sense that they can be defined by looking only at any pair of list items at a time.
Edit intent: clarity
Original:  However, removing both the minima and maxima simultaneously is NP-hard, and is even hard to approximate within a factor of O(log log n)  . Moreover, we describe an interesting connection between this problem and a graph problem that is a special case of 2-Disjoint Connected Subgraphs, a problem that has lately received considerable attention from the graph-algorithms community.
Revised:  Interestingly, however, removing both the minima and maxima simultaneously is NP-hard, and is even hard to approximate within a factor of O(log log n) . Moreover, we describe an interesting connection between this problem and a graph problem that is a special case of 2-Disjoint Connected Subgraphs, a problem that has lately received considerable attention from the graph-algorithms community.
Edit intent: coherence
Original: This paper describes a distributed algorithm for rate allocation in wireless networks .
Revised: This paper develops a distributed algorithm for rate allocation in wireless networks .
Edit intent: clarity
Original:  As the main result, the paper establishes that this algorithm is throughput-optimal for very general class of throughput regions.
Revised:  As the main result, the paper establishes that this algorithm is throughput-optimal for general rate regions.
Edit intent: clarity
Original:  In contrast to distributed on-off scheduling algorithms, this algorithm enables optimal utilization of physical layer schemes by scheduling multiple rate levels.
Revised:  In contrast to on-off scheduling algorithms, this algorithm enables optimal utilization of physical layer schemes by scheduling multiple rate levels.
Edit intent: clarity
Original:  In contrast to distributed on-off scheduling algorithms, this algorithm enables optimal utilization of physical layer schemes by scheduling multiple rate levels.
Revised:  In contrast to distributed on-off scheduling , rate allocation enables optimal utilization of physical layer schemes by scheduling multiple rate levels.
Edit intent: clarity
Original:  In contrast to distributed on-off scheduling algorithms, this algorithm enables optimal utilization of physical layer schemes by scheduling multiple rate levels.
Revised:  In contrast to distributed on-off scheduling algorithms, this algorithm enables optimal utilization of physical-layer schemes by scheduling multiple rate levels.
Edit intent: fluency
Original:  Further , the paper describes utilization of existing physical layer control messages for determining rate feasibility.
Revised:  Further , the paper discusses the potential use of existing physical-layer control messages to determine feasibility.
Edit intent: clarity
Original:  This can be considered as an analogous technique to sensing in CSMA (Carrier Sense Multiple Access)  networks.
Revised:  This can be considered as a technique analogous to carrier sensing in CSMA (Carrier Sense Multiple Access) networks.
Edit intent: clarity
Original: PageRank is a web page ranking technique that radically changed the concepts of quality and truth of information found on the Web .
Revised: PageRank is a Web page ranking technique that radically changed the concepts of quality and truth of information found on the Web .
Edit intent: fluency
Original:  The method was developed by Sergey Brin and Larry Page while studying at Stanford University and is currently an important ingredient of Google search engine .
Revised:  The method is still one of the many signals that Google uses to determine which pages are most important .
Edit intent: clarity
Original:  In fact, this thesis in not new, and has been previously successfully exploited in different contexts.
Revised:  In fact, this thesis is not new, and has been previously successfully exploited in different contexts.
Edit intent: fluency
Original:  In this work, we review the PageRank method and link it to some renowned predecessors we have found in the fields of Web information retrieval, bibliometrics, sociology, and economics .
Revised:  We are going to review the PageRank method and link it to some renowned predecessors we have found in the fields of Web information retrieval, bibliometrics, sociology, and economics .
Edit intent: clarity
Original:  In this work, we review the PageRank method and link it to some renowned predecessors we have found in the fields of Web information retrieval, bibliometrics, sociology, and economics .
Revised:  In this work, we review the PageRank method and link it to some renowned previous techniques that we have found in the fields of Web information retrieval, bibliometrics, sociology, and economics .
Edit intent: clarity
Original:  In this work, we review the PageRank method and link it to some renowned predecessors we have found in the fields of Web information retrieval, bibliometrics, sociology, and economics .
Revised:  In this work, we review the PageRank method and link it to some renowned predecessors we have found in the fields of Web information retrieval, bibliometrics, sociometry, and econometrics .
Edit intent: fluency
Original:  The main idea behind PageRank is to determine the importance of a Web page in terms of the very same notion of importance assigned to the pages hyperlinking to it.
Revised:  The main idea behind PageRank is to determine the importance of a Web page in terms of the importance assigned to the pages hyperlinking to it.
Edit intent: clarity
Original:  We are going to review the PageRank method and link it to some renowned previous techniques that we have found in the fields of Web information retrieval, bibliometrics, sociometry, and econometrics.
Revised:  We review the PageRank method and link it to some renowned previous techniques that we have found in the fields of Web information retrieval, bibliometrics, sociometry, and econometrics.
Edit intent: coherence
Original: This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky and Chudnovsky.
Revised: This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be the first general implementation of the fast high-precision numerical evaluation algorithms of Chudnovsky Chudnovsky.
Edit intent: clarity
Original:  In some cases, our descriptions contain small improvements over existing algorithms.
Revised:  In some cases, our descriptions contain improvements over existing algorithms.
Edit intent: clarity
Original: Dynamic Spectrum Access systems exploit temporarily available spectrum (` holes' or ` white spaces') and can spread transmissions over a number of non-contiguous sub-channels.
Revised: Dynamic Spectrum Access systems exploit temporarily available spectrum (` white spaces') and can spread transmissions over a number of non-contiguous sub-channels.
Edit intent: coherence
Original:  Such methods can have significant benefits in terms of spectrum utilization.
Revised:  Such methods are highly beneficial in terms of spectrum utilization.
Edit intent: clarity
Original:  Thus, there is a critical need for an in-depth understanding of these processes so as to determine how best to ensure acceptable levels of fragmentation.
Revised:  Thus, there is a need to study these processes so as to determine how best to ensure acceptable levels of fragmentation.
Edit intent: clarity
Original:  Thus, there is a critical need for an in-depth understanding of these processes so as to determine how best to ensure acceptable levels of fragmentation.
Revised:  Thus, there is a critical need for an in-depth understanding of these processes so as to determine how to ensure acceptable levels of fragmentation.
Edit intent: clarity
Original:  We address this need by presenting experimental and analytical results derived from a mathematical model.
Revised:  Hence, we present experimental and analytical results derived from a mathematical model.
Edit intent: coherence
Original:  In particular, we model a system operating at capacity serving requests for bandwidth by assigning as needed a collection of gaps (sub-channels) with no limitations on  fragment size.
Revised:  We model a system operating at capacity serving requests for bandwidth by assigning as needed a collection of gaps (sub-channels) with no limitations on fragment size.
Edit intent: coherence
Original:  In particular, we model a system operating at capacity serving requests for bandwidth by assigning as needed a collection of gaps (sub-channels) with no limitations on  fragment size.
Revised:  In particular, we model a system operating at capacity serving requests for bandwidth by assigning a collection of gaps (sub-channels) with no limitations on fragment size.
Edit intent: clarity
Original:  In particular, we model a system operating at capacity serving requests for bandwidth by assigning as needed a collection of gaps (sub-channels) with no limitations on  fragment size.
Revised:  In particular, we model a system operating at capacity serving requests for bandwidth by assigning as needed a collection of gaps (sub-channels) with no limitations on the fragment size.
Edit intent: fluency
Original:  Within the very difficult class of dynamic fragmentation models (including notably classical models of computer storage fragmentation), this baseline result appears to be the first of its kind.
Revised:  Within the very difficult class of dynamic fragmentation models (including models of storage fragmentation), this baseline result appears to be the first of its kind.
Edit intent: clarity