wanyu/IteraTeR_v2 huggingface dataset:
Original:  Learning and innovation help to preserve cooperation during network re-organization  , and may be key mechanisms promoting the evolution of self-organizing, complex systems.
Revised:  Learning and innovation help to preserve cooperation during network re-organization , and may play a prominent role in the evolution of self-organizing, complex systems.
Edit intent: clarity
Original: The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed .
Revised: In an equilibrium chemical reaction mixture are Poisson distributed .
Edit intent: clarity
Original: The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed .
Revised: The numbers of each sort of molecule present in an equilibrium chemical reaction mixture , the number of molecules present obeys a Poisson distribution .
Edit intent: clarity
Original:  Such driven systems also obey an analog of the fluctuation-dissipation theorem and can equilibrate when in contact with each other .
Revised:  Such driven systems also obey an analog of the fluctuation-dissipation theorem .
Edit intent: clarity
Original:  Our results may be relevant to biological systems and to the larger question of how equilibrium ideas might extend to nonequilibrium systems.
Revised:  Our results may be relevant to biological systems and to the larger question of how equilibrium concepts might apply to nonequilibrium systems.
Edit intent: clarity
Original:  We show that this problem is equivalent to sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems.
Revised:  We show that it can be formulated as a sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems.
Edit intent: clarity
Original: The trade size \omega has direct impact on the price of stock traded.
Revised: The trade size \omega has direct impact on the price formation of the stock traded.
Edit intent: clarity
Original:  Econophysical analyses of transaction data in the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization  is included as an argument in the scaling relation.
Revised:  Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization is included as an argument in the scaling relation.
Edit intent: clarity
Original:   Using order book data from the Chinese market, we show that trades from filled and unfilled limit orders have very different price impact.
Revised:  Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impact.
Edit intent: clarity
Original:  The price impact of trades from unfilled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r\sim \omega^\alpha with an exponent of \alpha=2\approx2 /3.
Revised:  The price impact of trades from unfilled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r\sim \omega^\alpha with \alpha\approx2 /3.
Edit intent: clarity
Original:  This issue has also been addressed from a dynamical systems perspective, with especial emphasis on the concept of the "Balanced Scorecard" .
Revised:  This issue has also been addressed from a dynamical systems perspective, with especial emphasis on the concept of the Balanced Scorecard .
Edit intent: fluency
Original:  We have mathematically demonstrated the likely occurrence of this feature under various possible situations , including the "Red Ocean " and the "Blue Ocean" . Finally and most importantly, our arguments and their associated mathematical modelling have received remarkable support from the growth pattern indicated by empirical data gathered from a well-recognized global company like IBM.
Revised:  We have mathematically demonstrated the likely occurrence of this feature under various possible circumstances , including the "Red Ocean " and the "Blue Ocean" . Finally and most importantly, our arguments and their associated mathematical modelling have received remarkable support from the growth pattern indicated by empirical data gathered from a well-recognized global company like IBM.
Edit intent: fluency
Original:  We have mathematically demonstrated the likely occurrence of this feature under various possible situations , including the "Red Ocean " and the "Blue Ocean" . Finally and most importantly, our arguments and their associated mathematical modelling have received remarkable support from the growth pattern indicated by empirical data gathered from a well-recognized global company like IBM.
Revised:  We have mathematically demonstrated the likely occurrence of this feature under various possible situations , including the Red Ocean and the Blue Ocean . Finally and most importantly, our arguments and their associated mathematical modelling have received remarkable support from the growth pattern indicated by empirical data gathered from a well-recognized global company like IBM.
Edit intent: fluency
Original:  \] This is a common generalization of previous results known before on bounding the Betti numbers of closed semi-algebraic sets defined by polynomials of degree d and 2, respectively.
Revised:  \] This is a common generalization of previous results on bounding the Betti numbers of closed semi-algebraic sets defined by polynomials of degree d and 2, respectively.
Edit intent: clarity
Original:  We also describe algorithms for computing the Euler-Poincar\'e characteristic , as well as all the Betti numbers of such sets  .
Revised:  We also describe an algorithm for computing the Euler-Poincar\'e characteristic , as well as all the Betti numbers of such sets .
Edit intent: fluency
Original:  We also describe algorithms for computing the Euler-Poincar\'e characteristic , as well as all the Betti numbers of such sets  .
Revised:  We also describe algorithms for computing the Euler-Poincar\'e characteristic of such sets .
Edit intent: clarity
Original:  The complexity of the first algorithm is bounded by (\ell s m d)^{O(m(m+k))} , while that of the second is bounded by (\ell s m d)^{2^{O(m+k) .
Revised:  The complexity of the algorithm is bounded by (\ell s m d)^{O(m(m+k))} , while that of the second is bounded by (\ell s m d)^{2^{O(m+k) .
Edit intent: fluency
Original:  We allowing various interactions between chemically unbonded residues in a given sequence \chi and the solvent (water), and exactly enumerate the number of conformations W(E) as a function of the energy E on an infinite lattice under two different conditions: (i) we allow conformations that are restricted to be compact (known as Hamilton walk conformations), and (ii) we allow unrestricted conformations that can also be non-compact.
Revised:  We allow various interactions between chemically unbonded residues in a given sequence \chi and the solvent (water), and exactly enumerate the number of conformations W(E) as a function of the energy E on an infinite lattice under two different conditions: (i) we allow conformations that are restricted to be compact (known as Hamilton walk conformations), and (ii) we allow unrestricted conformations that can also be non-compact.
Edit intent: fluency
Original:  We allowing various interactions between chemically unbonded residues in a given sequence \chi and the solvent (water), and exactly enumerate the number of conformations W(E) as a function of the energy E on an infinite lattice under two different conditions: (i) we allow conformations that are restricted to be compact (known as Hamilton walk conformations), and (ii) we allow unrestricted conformations that can also be non-compact.
Revised:  We allowing various interactions between chemically unbonded residues in a given sequence and the solvent (water), and exactly enumerate the number of conformations W(E) as a function of the energy E on an infinite lattice under two different conditions: (i) we allow conformations that are restricted to be compact (known as Hamilton walk conformations), and (ii) we allow unrestricted conformations that can also be non-compact.
Edit intent: clarity
Original: A set of many identical agents are supposed to interact among them verifying a global additive constraint  .
Revised: A set of many identical interacting agents obeying a global additive constraint .
Edit intent: clarity
Original:   (3 ) that the rank-2 version always has an affirmative answer;
Revised:  and (3 ) that the rank-2 version always has an affirmative answer;
Edit intent: fluency
Original:  Furthermore, these codes can also be applied as Differential Space-Time codes for noncoherent communication in classical point to point multiple antenna systems.
Revised:  Furthermore, these codes can also be applied as Differential Space-Time codes for non-coherent communication in classical point to point multiple antenna systems.
Edit intent: fluency
Original:  Pach and Tardos have posed a related problem: can any straight-line drawing of any planar graph with n vertices be made plane by vertex moves while keeping \Omega(n ^\epsilon ) vertices fixed for some absolute constant \epsilon >0?
Revised:  Pach and Tardos have posed a related problem: can any straight-line drawing of any planar graph with n vertices be made plane by vertex moves while keeping \Omega(n ^\epsilon ) vertices fixed for some absolute constant \gamma >0?
Edit intent: clarity
Original:  It is known that three vertices can always be kept (if n \ge 3).
Revised:  It was known that three vertices can always be kept (if n \ge 3).
Edit intent: fluency
Original: In John Tantalo's on-line gamePlanarity the player is given a non-plane straight-line drawing  of a planar graph .
Revised: Planarity the player is given a non-plane straight-line drawing of a planar graph .
Edit intent: clarity
Original: In John Tantalo's on-line gamePlanarity the player is given a non-plane straight-line drawing  of a planar graph .
Revised: In John Tantalo's on-line game the player is given a non-plane straight-line drawing of a planar graph .
Edit intent: clarity
Original: In John Tantalo's on-line gamePlanarity the player is given a non-plane straight-line drawing  of a planar graph .
Revised: In John Tantalo's on-line gamePlanarity A straight-line drawing of a planar graph .
Edit intent: clarity
Original:  On the other hand we construct, for arbitrarily large n, an n-vertex planar graph G and a drawing \delta_G of G with } fix(G,\delta ) over all drawings \delta of G. We show that fix(H) \in \Theta(n) for any\le  n-vertex outerplanar graph H and fix(G) \in \Omega(\log n/\log \log n) \cap O(n) for any general planar graph G with n vertices\le  .
Revised:  On the other hand we construct, for arbitrarily large n, an n-vertex planar graph G and a drawing \delta_G of G with } fix(G,\delta _G)\le n-vertex outerplanar graph H and fix(G) \in \Omega(\log n/\log \log n) \cap O(n) for any general planar graph G with n vertices\le .
Edit intent: coherence
Original:  When each node has full knowledge of the global network connectivity, finding efficient communication paths is merely a matter of distributed computation.
Revised:  When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation.
Edit intent: clarity
Original:  Here we show that the peculiar structural characteristics of observable complex networks are exactly the characteristics needed to maximize their communication efficiency without global knowledge.
Revised:  Here we show that the peculiar structural characteristics of many complex networks support efficient communication without global knowledge.
Edit intent: clarity
Original:  Their discovery would have enormous practical applications ranging from routing in the Internet and searching social networks, to studying information flows in neural, gene regulatory networks, or signaling pathways.
Revised:  Their discovery would have practical applications ranging from routing in the Internet and searching social networks, to studying information flows in neural, gene regulatory networks, or signaling pathways.
Edit intent: clarity
Original: We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of pairwise sequence-dependent  contact energies.
Revised: We analytically derive the lower bound of the total conformational energy of a protein structure by assuming that the total conformational energy is well approximated by the sum of sequence-dependent contact energies.
Edit intent: clarity
Original:  Subsequently, the condition for the native structure achieving the lower bound of the energy to be the unique global minimum energy conformation is determined.
Revised:  The condition for the native structure achieving the lower bound of the energy to be the unique global minimum energy conformation is determined.
Edit intent: coherence
Original:  This condition reads that the native structure is the most compact structure among those containing all the native contacts, and that the contact energy matrix  is a scalar multiple of the native contact matrix, i.e., the so-called G\=o potential.
Revised:  This condition reads that the native structure is the most compact structure among those containing all the native contacts, and that the contact energy matrix that is a scalar multiple of the native contact matrix, i.e., the so-called G\=o potential.
Edit intent: fluency
Original:  Based on these results, it is concluded that protein structure prediction is almost trivial once a function is identified to construct the optimum contact potential from a given amino acid sequence, or the contact potential representation alone is inappropriate for structure prediction .
Revised:  Implications for protein structure prediction is almost trivial once a function is identified to construct the optimum contact potential from a given amino acid sequence, or the contact potential representation alone is inappropriate for structure prediction .
Edit intent: clarity
Original:  Based on these results, it is concluded that protein structure prediction is almost trivial once a function is identified to construct the optimum contact potential from a given amino acid sequence, or the contact potential representation alone is inappropriate for structure prediction .
Revised:  Based on these results, it is concluded that protein structure prediction are discussed .
Edit intent: clarity
Original:  This is the first proof of identifiability of a phylogenetic model with a continuous distribution of rate classes .
Revised:  This is the first proof of identifiability of a phylogenetic model with a continuous distribution of rates .
Edit intent: clarity
Original:  Overall, we demonstrate to biologists the great potential that leaping methods hold for real-world biological research while highlighting to algorithmists areas still in need of improvement .
Revised:  Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while also elucidating the obstacles that one can expect to encounter .
Edit intent: clarity
Original:  We also illustrate prime bottlenecks that can hinder the approach and  discuss possible strategies for overcoming them.
Revised:  We also illustrate bottlenecks that can hinder the approach and discuss possible strategies for overcoming them.
Edit intent: clarity
Original:  We also illustrate prime bottlenecks that can hinder the approach and  discuss possible strategies for overcoming them.
Revised:  We also illustrate prime bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them.
Edit intent: clarity
Original:  Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while also elucidating the obstacles that one can expect to encounter .
Revised:  Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice .
Edit intent: clarity
Original: Each node in a wireless multihop network can adjust the power  at which it makes its transmissions and thus change the topology of the network  by choosing the neighbors with which it directly communicates.
Revised: Each node in a wireless multi-hop network can adjust the power at which it makes its transmissions and thus change the topology of the network by choosing the neighbors with which it directly communicates.
Edit intent: fluency
Original: Each node in a wireless multihop network can adjust the power  at which it makes its transmissions and thus change the topology of the network  by choosing the neighbors with which it directly communicates.
Revised: Each node in a wireless multihop network can adjust the power level at which it makes its transmissions and thus change the topology of the network by choosing the neighbors with which it directly communicates.
Edit intent: clarity
Original: Each node in a wireless multihop network can adjust the power  at which it makes its transmissions and thus change the topology of the network  by choosing the neighbors with which it directly communicates.
Revised: Each node in a wireless multihop network can adjust the power at which it transmits and thus change the topology of the network by choosing the neighbors with which it directly communicates.
Edit intent: clarity
Original:  Many previous algorithms for distributed topology control have assumed an ability at each node to deduce some spatial information such as the direction and the distance of its neighbor nodes with respect to itself.
Revised:  Many previous algorithms for distributed topology control have assumed an ability at each node to deduce some location-based information such as the direction and the distance of its neighbor nodes with respect to itself.
Edit intent: clarity
Original:  However, such a deduction of spatial information cannot be relied upon in a multipath environment where different paths of a signal may have different loss characteristics  and none of the paths may be line-of-sight  .
Revised:  Such a deduction of spatial information cannot be relied upon in a multipath environment where different paths of a signal may have different loss characteristics and none of the paths may be line-of-sight .
Edit intent: coherence
Original:  However, such a deduction of spatial information cannot be relied upon in a multipath environment where different paths of a signal may have different loss characteristics  and none of the paths may be line-of-sight  .
Revised:  However, such a deduction of spatial information cannot be relied upon in a multipath environment where different loss characteristics and none of the paths may be line-of-sight .
Edit intent: clarity
Original:  However, such a deduction of spatial information cannot be relied upon in a multipath environment where different paths of a signal may have different loss characteristics  and none of the paths may be line-of-sight  .
Revised:  However, such a deduction of spatial information cannot be relied upon in a multipath environment where different paths of a signal may have different loss characteristics , and none of the paths may be line-of-sight .
Edit intent: fluency
Original:  However, such a deduction of spatial information cannot be relied upon in a multipath environment where different paths of a signal may have different loss characteristics  and none of the paths may be line-of-sight  .
Revised:  However, such a deduction of spatial information cannot be relied upon in a multipath environment where different paths of a signal may have different loss characteristics and none of these paths may be line-of-sight .
Edit intent: fluency
Original:  In this report , we present Step Topology Control (STC), a simple distributed topology control algorithm which reduces power consumption while preserving the connectivity of a heterogeneous sensor network in a multipath environment.
Revised:  In this paper , we present Step Topology Control (STC), a simple distributed topology control algorithm which reduces power consumption while preserving the connectivity of a heterogeneous sensor network in a multipath environment.
Edit intent: fluency
Original:  We show that the STC algorithm achieves the same or better order of communication and computational complexity in comparison to other known algorithms that also preserve connectivity and can be similarly adapted to a multipath environment .
Revised:  We show that the STC algorithm achieves the same or better order of communication and computational complexity when compared to other known algorithms that also preserve connectivity and can be similarly adapted to a multipath environment .
Edit intent: clarity
Original:  The results show that  the STC algorithm performs better than other algorithms in uniform wireless environments and especially better in the presence of radio irregularities and multipath propagation .
Revised:  The results show that the STC algorithm performs better than other algorithms in uniform wireless environments and especially better when path loss characteristics are non-uniform .
Edit intent: clarity
Original: The search for more realistic modeling of financial time series reviews several stylized facts of real markets.
Revised: The search for more realistic modeling of financial time series reveals several stylized facts of real markets.
Edit intent: clarity
Original:  As a main application, we show that Martin-Lof dependent type theory extended with a program for Spector double negation shift.
Revised:  As a main application, we show that Martin-L\"{o dependent type theory extended with a program for Spector double negation shift.
Edit intent: fluency
Original:  Specifically, we show that for every m:=3k+1, the Graver complexity of the vertex-edge incidence matrix of the complete bipartite graph K_{3,m} satisfies g(m) \geq 2 \SUPERSCRIPT k+ 2   } -3.
Revised:  Specifically, we show that the Graver complexity of the vertex-edge incidence matrix of the complete bipartite graph K_{3,m} satisfies g(m) \geq 2 \SUPERSCRIPT k+ 2 } -3.
Edit intent: clarity
Original:  Specifically, we show that for every m:=3k+1, the Graver complexity of the vertex-edge incidence matrix of the complete bipartite graph K_{3,m} satisfies g(m) \geq 2 \SUPERSCRIPT k+ 2   } -3.
Revised:  Specifically, we show that for every m:=3k+1, the Graver complexity of the incidence matrix of the complete bipartite graph K_{3,m} satisfies g(m) \geq 2 \SUPERSCRIPT k+ 2 } -3.
Edit intent: clarity
Original:  Specifically, we show that for every m:=3k+1, the Graver complexity of the vertex-edge incidence matrix of the complete bipartite graph K_{3,m} satisfies g(m) \geq 2 \SUPERSCRIPT k+ 2   } -3.
Revised:  Specifically, we show that for every m:=3k+1, the Graver complexity of the vertex-edge incidence matrix of the complete bipartite graph K_{3,m} satisfies g(m) \geq 2 \SUPERSCRIPT k+ 2 \SUPERSCRIPT } -3.
Edit intent: fluency