wanyu/IteraTeR_v2 huggingface dataset:
Original:  We can therefore exactly account for the interactions with the radii along the chain which in the proteomics are classified as medium- and moderately long-range interactions .
Revised:  We can therefore exactly account for the interactions which in proteomics are classified as medium- and moderately long-range interactions .
Edit intent: clarity
Original:  We can therefore exactly account for the interactions with the radii along the chain which in the proteomics are classified as medium- and moderately long-range interactions .
Revised:  We can therefore exactly account for the interactions with the radii along the chain which in the proteomics are classified as medium- and moderately long-range ones .
Edit intent: clarity
Original:  Few attention, however, has been spent on the efficient construction of minimal DFAs.
Revised:  Little attention, however, has been spent on the efficient construction of minimal DFAs.
Edit intent: fluency
Original:  Few attention, however, has been spent on the efficient construction of minimal DFAs.
Revised:  Few attention, however, has been given to the efficient construction of minimal DFAs.
Edit intent: clarity
Original:  In this article, we define simple non-deterministic finite automata (NFAs) and prove that  NFAs of this special type are always transformed into minimal DFAs by the standard subset construction .
Revised:  In this article, we define simple non-deterministic finite automata (NFAs) and prove that NFAs of this type into minimal DFAs by the standard subset construction .
Edit intent: clarity
Original:  In this article, we define simple non-deterministic finite automata (NFAs) and prove that  NFAs of this special type are always transformed into minimal DFAs by the standard subset construction .
Revised:  In this article, we define simple non-deterministic finite automata (NFAs) and prove that NFAs of this special type are always transformed into minimal DFAs .
Edit intent: clarity
Original: In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.  it is not exactly reproducible by any algorithm.
Revised: In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e. \ it is not exactly reproducible by any algorithm.
Edit intent: fluency
Original:  We provide  evidence of incomputability - an asymptotic property - of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
Revised:  We provide experimental evidence of incomputability - an asymptotic property - of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
Edit intent: clarity
Original:  We provide  evidence of incomputability - an asymptotic property - of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
Revised:  We provide evidence of incomputability --- an asymptotic property - of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
Edit intent: fluency
Original:  We provide  evidence of incomputability - an asymptotic property - of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
Revised:  We provide evidence of incomputability - an asymptotic property --- of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.
Edit intent: fluency
Original:  These mechanisms aim to correct for the field and the year in which a publication was published.
Revised:  These mechanisms aim to normalize citation counts for the field and the year in which a publication was published.
Edit intent: clarity
Original:  One mechanism is applied in the current  crown indicator of our institute.
Revised:  One mechanism is applied in the current so-called crown indicator of our institute.
Edit intent: clarity
Original:  We find that at high aggregation levels, such as at the level of large institutes or at the level of countries, the differences between the two mechanisms are very small.
Revised:  We find that at high aggregation levels, such as at the level of large research institutions or at the level of countries, the differences between the two mechanisms are very small.
Edit intent: clarity
Original: We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects  . Depending on the contribution of the involved agents a project will flourish or drown, and to measure the success we use a reward function for each project .
Revised: We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects or relationships . Depending on the contribution of the involved agents a project will flourish or drown, and to measure the success we use a reward function for each project .
Edit intent: clarity
Original: We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects  . Depending on the contribution of the involved agents a project will flourish or drown, and to measure the success we use a reward function for each project .
Revised: We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects . Depending on the contribution of the involved agents a relationship will flourish or drown, and to measure the success we use a reward function for each project .
Edit intent: clarity
Original: We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects  . Depending on the contribution of the involved agents a project will flourish or drown, and to measure the success we use a reward function for each project .
Revised: We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects . Depending on the contribution of the involved agents a project will flourish or drown, and to measure the success we use a reward function for each relationship .
Edit intent: clarity
Original:  Every agent is trying to maximize the reward from all projects that it is involved in.
Revised:  Every agent is trying to maximize the reward from all relationships that it is involved in.
Edit intent: clarity
Original:  For example, when all reward functions are concave, we prove that a pairwise equilibrium always exists, and the price of anarchy is at most 2.
Revised:  For example, when all reward functions are concave, we prove that the price of anarchy is at most 2.
Edit intent: clarity
Original:  A special focus of the paper are minimum effort games, where the success of a project depends only on the minimum effort of any of the participants.
Revised:  A special focus of the paper are minimum effort games, where the reward of a relationship depends only on the minimum effort of any of the participants.
Edit intent: clarity
Original: This paper's focus is the following family of problems, denoted k-ECSS, where k denotes a positive integer: given a graph (V, E) and costs for each edge,  find a minimum-cost subset F of E such that (V, F) is k-edge-connected.
Revised: This paper's focus is the following family of problems, denoted k-ECSS, where k denotes a positive integer: given a graph (V, E) and costs for each edge, and want to find a minimum-cost subset F of E such that (V, F) is k-edge-connected.
Edit intent: coherence
Original:  Thus we establish a gap between the unit-cost and general-cost versions , for large enough k . Next, we consider the multi-subgraph cousin of k-ECSS, in which we are allowed to buy arbitrarily many copies of any edges (i.e., F is now a multi-subset  of E, with parallel copies having the same cost as the original edge ).
Revised:  Thus we establish a gap between the unit-cost and general-cost versions . Next, we consider the multi-subgraph cousin of k-ECSS, in which we are allowed to buy arbitrarily many copies of any edges (i.e., F is now a multi-subset of E, with parallel copies having the same cost as the original edge ).
Edit intent: clarity
Original:  Thus we establish a gap between the unit-cost and general-cost versions , for large enough k . Next, we consider the multi-subgraph cousin of k-ECSS, in which we are allowed to buy arbitrarily many copies of any edges (i.e., F is now a multi-subset  of E, with parallel copies having the same cost as the original edge ).
Revised:  Thus we establish a gap between the unit-cost and general-cost versions , for large enough k . Next, we consider the multi-subgraph cousin of k-ECSS, in which we purchase a multi-subset of E, with parallel copies having the same cost as the original edge ).
Edit intent: coherence
Original:  Thus we establish a gap between the unit-cost and general-cost versions , for large enough k . Next, we consider the multi-subgraph cousin of k-ECSS, in which we are allowed to buy arbitrarily many copies of any edges (i.e., F is now a multi-subset  of E, with parallel copies having the same cost as the original edge ).
Revised:  Thus we establish a gap between the unit-cost and general-cost versions , for large enough k . Next, we consider the multi-subgraph cousin of k-ECSS, in which we are allowed to buy arbitrarily many copies of any edges (i.e., F is now a multi-subset F of E, with parallel copies having the same cost as the original edge ).
Edit intent: fluency
Original:  Thus we establish a gap between the unit-cost and general-cost versions , for large enough k . Next, we consider the multi-subgraph cousin of k-ECSS, in which we are allowed to buy arbitrarily many copies of any edges (i.e., F is now a multi-subset  of E, with parallel copies having the same cost as the original edge ).
Revised:  Thus we establish a gap between the unit-cost and general-cost versions , for large enough k . Next, we consider the multi-subgraph cousin of k-ECSS, in which we are allowed to buy arbitrarily many copies of any edges (i.e., F is now a multi-subset of E, with unlimited parallel copies available at the same cost as the original edge ).
Edit intent: clarity
Original:  Not so much is known about this natural variant, but we conjecture that a (1 + Theta(1/k))-approximation algorithm exists, and we describe an approach based on its naive linear programming relaxation (LP) and graph decompositions .
Revised:  Not so much is known about this natural variant, but we conjecture that a (1 + Theta(1/k))-approximation algorithm exists, and we describe an approach based on its naive linear programming relaxation (LP) relaxation .
Edit intent: coherence
Original:  The LP is well-known --- it is essentially the same as the Held-Karp  TSP and the undirected LP for Steiner tree --- and in order to further our understanding, we give a family of extreme points for this LP with exponentially bad fractionality .
Revised:  The LP is essentially equivalent to the Held-Karp TSP and the undirected LP for Steiner tree --- and in order to further our understanding, we give a family of extreme points for this LP with exponentially bad fractionality .
Edit intent: clarity
Original:  The LP is well-known --- it is essentially the same as the Held-Karp  TSP and the undirected LP for Steiner tree --- and in order to further our understanding, we give a family of extreme points for this LP with exponentially bad fractionality .
Revised:  The LP is well-known --- it is essentially the same as the Held-Karp LP for TSP and the undirected LP for Steiner tree --- and in order to further our understanding, we give a family of extreme points for this LP with exponentially bad fractionality .
Edit intent: fluency
Original:  The LP is well-known --- it is essentially the same as the Held-Karp  TSP and the undirected LP for Steiner tree --- and in order to further our understanding, we give a family of extreme points for this LP with exponentially bad fractionality .
Revised:  The LP is well-known --- it is essentially the same as the Held-Karp TSP and the undirected LP for Steiner tree . We give a family of extreme points for this LP with exponentially bad fractionality .
Edit intent: clarity
Original: We propose algorithms for Tucker approximation of  3-tensor, that use it only through tensor-by-vector-by-vector multiplication subroutine.
Revised: New algorithms are proposed for the Tucker approximation of 3-tensor, that use it only through tensor-by-vector-by-vector multiplication subroutine.
Edit intent: clarity
Original: We propose algorithms for Tucker approximation of  3-tensor, that use it only through tensor-by-vector-by-vector multiplication subroutine.
Revised: We propose algorithms for Tucker approximation of a 3-tensor, that use it only through tensor-by-vector-by-vector multiplication subroutine.
Edit intent: fluency
Original: We propose algorithms for Tucker approximation of  3-tensor, that use it only through tensor-by-vector-by-vector multiplication subroutine.
Revised: We propose algorithms for Tucker approximation of 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine.
Edit intent: clarity
Original:  In  matrix case, Krylov methods are methods of choice to approximate  dominant column and row subspace of sparse or structured matrix given through  matrix-by-vector subroutine.
Revised:  In the matrix case, Krylov methods are methods of choice to approximate dominant column and row subspace of sparse or structured matrix given through matrix-by-vector subroutine.
Edit intent: fluency
Original:  In  matrix case, Krylov methods are methods of choice to approximate  dominant column and row subspace of sparse or structured matrix given through  matrix-by-vector subroutine.
Revised:  In matrix case, Krylov methods are methods of choice to approximate the dominant column and row subspace of sparse or structured matrix given through matrix-by-vector subroutine.
Edit intent: fluency
Original:  In  matrix case, Krylov methods are methods of choice to approximate  dominant column and row subspace of sparse or structured matrix given through  matrix-by-vector subroutine.
Revised:  In matrix case, Krylov methods are methods of choice to approximate dominant column and row subspaces of a sparse or structured matrix given through matrix-by-vector subroutine.
Edit intent: fluency
Original:  In  matrix case, Krylov methods are methods of choice to approximate  dominant column and row subspace of sparse or structured matrix given through  matrix-by-vector subroutine.
Revised:  In matrix case, Krylov methods are methods of choice to approximate dominant column and row subspace of sparse or structured matrix given through the matrix-by-vector subroutine.
Edit intent: fluency
Original:  Using Wedderburn rank reduction formula, we propose  algorithm of matrix approximation that computes Krylov subspaces and allows generalization to  tensor case.
Revised:  Using Wedderburn rank reduction formula, we propose an algorithm of matrix approximation that computes Krylov subspaces and allows generalization to tensor case.
Edit intent: fluency
Original:  Using Wedderburn rank reduction formula, we propose  algorithm of matrix approximation that computes Krylov subspaces and allows generalization to  tensor case.
Revised:  Using Wedderburn rank reduction formula, we propose algorithm of matrix approximation that computes Krylov subspaces and allows generalization to the tensor case.
Edit intent: fluency
Original:  By convincing numerical experiments we show that  proposed methods are faster and more accurate than  minimal Krylov recursion  .
Revised:  By convincing numerical experiments we show that the proposed methods are faster and more accurate than minimal Krylov recursion .
Edit intent: fluency
Original:  By convincing numerical experiments we show that  proposed methods are faster and more accurate than  minimal Krylov recursion  .
Revised:  By convincing numerical experiments we show that proposed methods are faster and more accurate than the minimal Krylov recursion .
Edit intent: fluency
Original:  We find that if stochastic strategies for the iterated Prisoner's Dilemma (IPD)  are encoded as genes  , the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory .
Revised:  Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) are encoded as genes , the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory .
Edit intent: coherence
Original:  These results imply that previous identifications of mechanisms that promote cooperation can be understood within a broader framework where increased predictability is sufficient for the evolution of cooperation
Edit intent: coherence
Original:  Is is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of universal covers of compact manifolds .
Revised:  It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of universal covers of compact manifolds .
Edit intent: fluency
Original:  Also an explicit example is constructed which leads to a compact manifold whose fundamental group is a threefold direct product of the lamplighter group Z/ 2Z wr Z, and whose universal cover has a transcendental l^2-Betti number .
Revised:  Also an explicit example is constructed which leads to a compact manifold whose fundamental group is a threefold direct product of the lamplighter group Z/ 2 wr Z .
Edit intent: coherence
Original:  In 2008, Eickmeyer et. al. showed that the BME method is equivalent to optimizing a linear function, the dissimilarity map, over the BME polytope which is defined as the convex hull of  vectors obtained from Pauplin's formula applied to all binary trees.
Revised:  In 2008, Eickmeyer et. al. showed that the BME method is equivalent to optimizing a linear function, the dissimilarity map, over the BME polytope , the convex hull of vectors obtained from Pauplin's formula applied to all binary trees.
Edit intent: coherence
Original:  Gascuel and Steel showed that the Neighbor Joining (NJ) algorithm is a greedy optimization of the BME principle.
Revised:  The BME method is related to the Neighbor Joining (NJ) algorithm is a greedy optimization of the BME principle.
Edit intent: clarity
Original:  Eickmeyer et. al. also studied how often the NJ algorithm returns a BME tree for small number of taxa.
Revised:  Further, the NJ and BME algorithms have been studied previously to understand when the NJ Algorithm returns a BME tree for small number of taxa.
Edit intent: coherence
Original:  Eickmeyer et. al. also studied how often the NJ algorithm returns a BME tree for small number of taxa.
Revised:  Eickmeyer et. al. also studied how often the NJ algorithm returns a BME tree for small numbers of taxa.
Edit intent: fluency
Original:  Moreover, we describe an entire family of faces parametrized by disjoint clades , which we call clades-faces .
Revised:  Moreover, we describe an entire family of faces parametrized by disjoint clades .
Edit intent: coherence
Original:  We show that these clades-faces {\em  are smaller dimensional BME polytopes themselves.
Revised:  We show that these {\em are smaller dimensional BME polytopes themselves.
Edit intent: clarity
Original:  Then we show that for any choice of picking neighbors (cherries) , there exists a distance matrix such that the NJ algorithm returns the BME tree  .
Revised:  Finally, we show that for any choice of picking neighbors (cherries) , there exists a distance matrix such that the NJ algorithm returns the BME tree .
Edit intent: fluency
Original:  We show that fixed points of our dynamics correspond to Nash bargaining solutions when such solutions exist, and that%DIFDELCMD < \eps%%% -approximate fixed points correspond to approximate Nash bargaining solutions for small enough%DIFDELCMD < \eps%%% . Crucially, we also prove that our dynamics converges to an%DIFDELCMD < \eps%%% -approximate fixed point in time O(%DIFDELCMD < \eps%%% ^{-2) independent of the network size when the potential earnings (weights) are uniformly bounded.
Revised:  We show that fixed points of our dynamics correspond to Nash bargaining solutions when such solutions exist, and that%DIFDELCMD < \eps%%% %DIFDELCMD < \eps%%% . Crucially, we also prove that our dynamics converges to an%DIFDELCMD < \eps%%% -approximate fixed point in time O(%DIFDELCMD < \eps%%% ^{-2) independent of the network size when the potential earnings (weights) are uniformly bounded.
Edit intent: clarity
Original: " Disorder-induced volatility" (DIV) describes the enhanced fluctuations of collective behaviors exhibited by bistable systems in the presence of a rapidly fluctuating external signal.
Revised: " Disorder-induced volatility" refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly fluctuating external signal.
Edit intent: clarity
Original:  At the DIV resonance, a defining characteristics is that the response of the system becomes uncorrelated with the external driving noise, making DIV resonance different from stochastic resonance.
Revised:  At the DIV resonance, a defining characteristics is that the response of the system becomes uncorrelated with the external driving force, making it different from stochastic resonance.
Edit intent: clarity
Original:  Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of DIV , which is proposed as a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of out-of-equilibrium systems and of strong selective responses of immune systems of complex biological organisms  .
Revised:  Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of this phenomenon , which is proposed as a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of out-of-equilibrium systems and of strong selective responses of immune systems of complex biological organisms .
Edit intent: clarity
Original:  Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of DIV , which is proposed as a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of out-of-equilibrium systems and of strong selective responses of immune systems of complex biological organisms  .
Revised:  Numerical simulations and an analytical theory of a stochastic dynamical version of the Ising model on regular and random networks demonstrate the ubiquity and robustness of DIV , which is argued to be a possible cause of excess volatility in financial markets, of enhanced effective temperatures in a variety of out-of-equilibrium systems and of strong selective responses of immune systems of complex biological organisms .
Edit intent: clarity
Original:  We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analogue of Frege proofs, different from that given in [BIKPRS96,GH03].
Revised:  We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a Cook-Reckhow (i.e., polynomially verifiable) algebraic analog of Frege proofs, different from that given in [BIKPRS96,GH03].
Edit intent: fluency