wanyu/IteraTeR_v2 huggingface dataset:
Original:  While this condition is generally not directly verifiable, we show that it simplifies to matrix non-degeneracy in a single point when the coefficients are real analytic functions.
Revised:  While this condition is generally not directly verifiable, we show that it simplifies to matrix non-degeneracy in a single point when the pricing functions are real analytic functions.
Edit intent: clarity
Original:  In earlier work (2004) the first author provided a geometric condition under which trading in the underlying and a finite number of vanilla options completes the market.
Revised:  In earlier work (2004) the first author provided a geometric condition under which trading in the nderlying and a finite number of vanilla options completes the market.
Edit intent: fluency
Original:  In earlier work (2004) the first author provided a geometric condition under which trading in the nderlying and a finite number of vanilla options completes the market.
Revised:  In earlier work (2004) the first author provided a geometric condition under which trading in the underlying and a finite number of vanilla options completes the market.
Edit intent: fluency
Original:  Assuming that we restrict the set of phylogenetic networks to some subclass , what is the maximum value of 0 <= p <= 1 such that for every input set T of rooted triplets, there exists some network N(T) from the subclass such that at least p|T| of the triplets are consistent with N(T)?
Revised:  Assuming that we restrict the set of phylogenetic networks , what is the maximum value of 0 <= p <= 1 such that for every input set T of rooted triplets, there exists some network N(T) from the subclass such that at least p|T| of the triplets are consistent with N(T)?
Edit intent: clarity
Original:  Here we prove that the set containing all triplets (the full triplet set) in some sense defines p, and moreover that any network N achieving a ratio p' for the full triplet set can be converted in polynomial time into an isomorphic network N'(T) achieving ratio >= p' for an arbitrary triplet set T.
Revised:  Here we prove that the set containing all triplets (the full triplet set) in some sense defines p, and moreover that any network N achieving fraction p' for the full triplet set can be converted in polynomial time into an isomorphic network N'(T) achieving ratio >= p' for an arbitrary triplet set T.
Edit intent: clarity
Original:  Here we prove that the set containing all triplets (the full triplet set) in some sense defines p, and moreover that any network N achieving a ratio p' for the full triplet set can be converted in polynomial time into an isomorphic network N'(T) achieving ratio >= p' for an arbitrary triplet set T.
Revised:  Here we prove that the set containing all triplets (the full triplet set) in some sense defines p, and moreover that any network N achieving a ratio p' for the full triplet set can be converted in polynomial time into an isomorphic network N'(T) achieving >= p' for an arbitrary triplet set T.
Edit intent: fluency
Original:  We demonstrate the power of this technique by giving worst-case optimal algorithms for the set of level-1 phylogenetic networks  , improving considerably upon the 5/12 ratio obtained recently by Jansson, Nguyen and Sung in the paper "Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network" (SIAM Journal on Computing 2006) .
Revised:  We demonstrate the power of this result for the field of phylogenetics by giving worst-case optimal algorithms for the set of level-1 phylogenetic networks , improving considerably upon the 5/12 ratio obtained recently by Jansson, Nguyen and Sung in the paper "Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network" (SIAM Journal on Computing 2006) .
Edit intent: clarity
Original:  We demonstrate the power of this technique by giving worst-case optimal algorithms for the set of level-1 phylogenetic networks  , improving considerably upon the 5/12 ratio obtained recently by Jansson, Nguyen and Sung in the paper "Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network" (SIAM Journal on Computing 2006) .
Revised:  We demonstrate the power of this technique by giving worst-case optimal algorithms for level-1 phylogenetic networks , improving considerably upon the 5/12 ratio obtained recently by Jansson, Nguyen and Sung in the paper "Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network" (SIAM Journal on Computing 2006) .
Edit intent: clarity
Original:  We demonstrate the power of this technique by giving worst-case optimal algorithms for the set of level-1 phylogenetic networks  , improving considerably upon the 5/12 ratio obtained recently by Jansson, Nguyen and Sung in the paper "Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network" (SIAM Journal on Computing 2006) .
Revised:  We demonstrate the power of this technique by giving worst-case optimal algorithms for the set of level-1 phylogenetic networks , improving considerably upon the 5/12 fraction obtained recently by Jansson, Nguyen and Sung in the paper "Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network" (SIAM Journal on Computing 2006) .
Edit intent: clarity
Original:  We demonstrate the power of this technique by giving worst-case optimal algorithms for the set of level-1 phylogenetic networks  , improving considerably upon the 5/12 ratio obtained recently by Jansson, Nguyen and Sung in the paper "Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network" (SIAM Journal on Computing 2006) .
Revised:  We demonstrate the power of this technique by giving worst-case optimal algorithms for the set of level-1 phylogenetic networks , improving considerably upon the 5/12 ratio obtained recently by Jansson, Nguyen and Sung .
Edit intent: coherence
Original:  Processors are also directly connected to an I/O node attached to the IANUS host, a conventional PC.
Revised:  Processors are also directly connected to an I/O node attached to the JANUS host, a conventional PC.
Edit intent: fluency
Original:  IANUS is tailored for, but not limited to, the requirements of a class of  scientific applications characterized by regular code structure, large ratio of computation over data-base size and heavy use of bit manipulation operations.
Revised:  JANUS is tailored for, but not limited to, the requirements of a class of scientific applications characterized by regular code structure, large ratio of computation over data-base size and heavy use of bit manipulation operations.
Edit intent: fluency
Original:  To clarify this issue, important distinctions between information and signs are introduced here and the concepts of information control and functional equivalence classes in those systems are rigorously defined and used to characterise when top down causation by feedback control happens, in a way that is potentially testable.
Revised:  To clarify this issue, important distinctions between information and signs are introduced here and the concepts of information control and functional equivalence classes in those systems are rigorously defined and used to characterise when top down causation by feedback control happens, in a way that is testable.
Edit intent: clarity
Original:  The method is applied to the folding of a helical peptide in explicit water  .
Revised:  For a helical peptide in explicit water .
Edit intent: clarity
Original:  We use a version of the well--known Fisher--Kolmogorov equation that has been used widely in the field of computational biology .
Revised:  We use a version of the well--known Fisher--Kolmogorov equation , and prescribe a procedure for its parametrization .
Edit intent: clarity
Original: The key to understand a protein's function often lies in its conformational dynamics.
Revised: The key to understanding a protein's function often lies in its conformational dynamics.
Edit intent: fluency
Original:  We found that the N-terminal part in calcium binding loops I and II shows higher flexibility than the C-terminal part which form this EF\beta-scaffold structure.
Revised:  We find that the N-terminal part in calcium binding loops I and II shows higher flexibility than the C-terminal part which form this EF\beta-scaffold structure.
Edit intent: fluency
Original: We present a theoretical investigation of the folding of small proteins assisted by chaperones.
Revised: We present a theoretical study of the folding of small proteins assisted by chaperones.
Edit intent: clarity
Original:  The cage of chaperonins is modeled by an external confining potential which is also able to take into account hydrophobic and hydrophilic effects inside the cavity.
Edit intent: coherence
Original:  We show how the confinement through the chaperon dramatically reduces the phase space available for the protein leading to a much faster folding process.
Revised:  We show that confinement dramatically reduces the phase space available for the protein leading to a much faster folding process.
Edit intent: clarity
Original:  The "Hadwiger number" \eta (G) is the maximum cardinality of a clique minor in G. This paper studies clique minors in the Cartesian product G*H (where G and H are connected graphs, each with at least one edge) .
Revised:  The "Hadwiger number" \eta (G) is the maximum cardinality of a clique minor in G. This paper studies clique minors in the Cartesian product G*H .
Edit intent: clarity
Original:  This implies that the product of two  large graphs has bounded Hadwiger number if and only if it is one of the following graphs: - a planar grid with a vortex of bounded width in the outerface, - a cylindrical grid with vortices of bounded width in each of the two `big' faces, or - a toroidal grid  .
Revised:  This implies that the product of two large graphs has bounded Hadwiger number then it is one of the following graphs: - a planar grid with a vortex of bounded width in the outerface, - a cylindrical grid with vortices of bounded width in each of the two `big' faces, or - a toroidal grid .
Edit intent: clarity
Original:  This implies that the product of two  large graphs has bounded Hadwiger number if and only if it is one of the following graphs: - a planar grid with a vortex of bounded width in the outerface, - a cylindrical grid with vortices of bounded width in each of the two `big' faces, or - a toroidal grid  .
Revised:  This implies that the product of two large graphs has bounded Hadwiger number if and only if it is one of the following graphs: - a planar grid with a vortex of bounded width in the outerface, - a cylindrical grid with a vortex of bounded width in each of the two `big' faces, or - a toroidal grid .
Edit intent: fluency
Original: Proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model.
Revised: The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model.
Edit intent: fluency
Original:  The transport of tumor cells is formulated in terms of the CTRW with an arbitrary waiting time distribution law, while proliferation is modeled by a logistic growth.
Revised:  The transport of tumor cells is formulated in terms of the CTRW with an arbitrary waiting time distribution law, while proliferation is modelled by a logistic growth.
Edit intent: fluency
Original:  When the genome-wide mutation probability U is small, the long time behavior of the model reduces to a point process of fixation events, which can be described as a randomly diluted record process (DRP)  . We develop a systematic analytic approximation scheme for the DRP.
Revised:  When the genome-wide mutation probability U is small, the long time behavior of the model reduces to a point process of fixation events, which is referred to as a diluted record process (DRP) . We develop a systematic analytic approximation scheme for the DRP.
Edit intent: clarity
Original: A convex surface  flat everywhere but on finitely many disjoint smooth curves (or "seams") and points is called a seam form.
Revised: A convex surface that is flat everywhere but on finitely many disjoint smooth curves (or "seams") and points is called a seam form.
Edit intent: clarity
Original: A convex surface  flat everywhere but on finitely many disjoint smooth curves (or "seams") and points is called a seam form.
Revised: A convex surface flat everywhere but on finitely many smooth curves (or "seams") and points is called a seam form.
Edit intent: clarity
Original: A convex surface  flat everywhere but on finitely many disjoint smooth curves (or "seams") and points is called a seam form.
Revised: A convex surface flat everywhere but on finitely many disjoint smooth curves (or "seams") and points is a seam form.
Edit intent: clarity
Original:  We show that the only creases through the flat regions of a seam form are either between vertices or tangent to the seams.
Revised:  We show that the only creases through the flat components of a seam form are either between vertices or tangent to the seams.
Edit intent: clarity
Original:  As corollaries we resolve open problems about certain special seam forms: the flat regions of a D-form have no creases at all, and the flat region of a pita-form has at most one crease  between the seam's endpoints.
Revised:  As corollaries we resolve open problems about certain special seam forms: the flat components of a D-form have no creases at all, and the flat region of a pita-form has at most one crease between the seam's endpoints.
Edit intent: clarity
Original:  As corollaries we resolve open problems about certain special seam forms: the flat regions of a D-form have no creases at all, and the flat region of a pita-form has at most one crease  between the seam's endpoints.
Revised:  As corollaries we resolve open problems about certain special seam forms: the flat regions of a D-form have no creases at all, and the flat component of a pita-form has at most one crease between the seam's endpoints.
Edit intent: clarity
Original:  As corollaries we resolve open problems about certain special seam forms: the flat regions of a D-form have no creases at all, and the flat region of a pita-form has at most one crease  between the seam's endpoints.
Revised:  As corollaries we resolve open problems about certain special seam forms: the flat regions of a D-form have no creases at all, and the flat region of a pita-form has at most one crease , between the seam's endpoints.
Edit intent: fluency
Original:  We solve these equations for different contract specifications in a particular but exemplifying case.
Revised:  We solve these equations for typical contract specifications, in a particular but exemplifying case.
Edit intent: clarity
Original: A recurring theme in the mathematical social sciences is how to select the "most desirable" elements given some binary dominance relation on a set of alternatives.
Revised: A recurring theme in the mathematical social sciences is how to select the "most desirable" elements given a binary dominance relation on a set of alternatives.
Edit intent: fluency
Original:  Schwartz's Tournament Equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context.
Revised:  Schwartz's tournament equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context.
Edit intent: fluency
Original:  We show that the problem of deciding whether a given alternative is contained in the Tournament Equilibrium set is NP-hard.
Revised:  We show that the problem of deciding whether a given alternative is contained in TEQ is NP-hard.
Edit intent: clarity
Original:  They are based on the hypergraph pebble game paradigm, developed by the authors as a generalization of a widely used algorithm for 2-dimensional bar-and-joint frameworks .
Revised:  They are based on the hypergraph pebble game paradigm, developed by the authors .
Edit intent: clarity
Original:  In particular, because many historical records tend to document  the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.
Revised:  In particular, because many historical records tend to document only the temporal distribution of cases or deaths (i.e. epidemic curve), our review focuses on methods to maximize the utility of time-evolution data and to clarify the detailed mechanisms of the spread of influenza.
Edit intent: clarity
Original:  Given that M accepts at least one word in L, we consider how long the shortest word can be.
Revised:  Given that M accepts at least one word in L, we consider how long a shortest word can be.
Edit intent: fluency
Original:  The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), the words matching a general pattern, and the bordered words . Along the way, we improve a bound of Horvath, Karhumaki and Kleijn on the shortest non-palindrome .
Revised:  The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), the words matching a general pattern, the bordered words . Along the way, we improve a bound of Horvath, Karhumaki and Kleijn on the shortest non-palindrome .
Edit intent: fluency
Original:  The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), the words matching a general pattern, and the bordered words . Along the way, we improve a bound of Horvath, Karhumaki and Kleijn on the shortest non-palindrome .
Revised:  The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), the words matching a general pattern, and the bordered words , and the unbordered words .
Edit intent: coherence
Original:  In our network model, nodes are grouped into a number of clusters.
Edit intent: coherence
Original: Emergent pattern formation in systems of self-propelled particles is extensively studied because it addresses a range of swarming phenomena which occur without leadership.
Revised: Emergent pattern formation in self-propelled particles is extensively studied because it addresses a range of swarming phenomena which occur without leadership.
Edit intent: clarity
Original: Emergent pattern formation in systems of self-propelled particles is extensively studied because it addresses a range of swarming phenomena which occur without leadership.
Revised: Emergent pattern formation in systems of self-propelled particle (SPP) systems is extensively studied because it addresses a range of swarming phenomena which occur without leadership.
Edit intent: clarity
Original:  The models produced thus far assume rule sets and parameter settings that are general to many different species, and therefore not sufficient to explain why only certain species engage in super-structural organization such as milling formations in schools of fish and insects.
Edit intent: coherence
Original:  Here we present a dynamic model of self-propelled particles in which a sensory blind zone is introduced into each particle's zone of interaction as a biologically relevant, species-specific trait.
Revised:  Here we present a dynamic SPP model in which a sensory blind zone is introduced into each particle's zone of interaction as a biologically relevant, species-specific trait.
Edit intent: clarity
Original:  Results also show the extreme importance of nearly complete panoramic sensory ability for the emergence of milling behavior , suggesting why some species mill and some do not .
Revised:  Results also show the necessity of nearly complete panoramic sensory ability for the emergence of milling behavior , suggesting why some species mill and some do not .
Edit intent: clarity
Original:  We next describe two versions of a complete set of edge-parameter inequalities for the group-based models;
Revised:  We next describe two complete sets of edge-parameter inequalities for the group-based models;
Edit intent: clarity
Original: Experiments in recent years have vividly demonstrated that gene expression can Hobe highly stochastic.
Revised: Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic.
Edit intent: fluency
Original:  Only when the correlation time of the fluctuations is long compared to the cell cycle time, do they affect the population's growth rate.
Edit intent: coherence
Original:  To overcome this, we consider two modifications to average consensus:%DIFDELCMD < inparaenum[1)] \item %%%   the A-ND algorithm with weights decaying to zero (slowly, satisfying a persistence condition  );
Revised:  To overcome this, we consider two modifications to average consensus:%DIFDELCMD < inparaenum[1)] \item %%% and the A-ND algorithm with weights decaying to zero (slowly, satisfying a persistence condition );
Edit intent: coherence
Original:  To overcome this, we consider two modifications to average consensus:%DIFDELCMD < inparaenum[1)] \item %%%   the A-ND algorithm with weights decaying to zero (slowly, satisfying a persistence condition  );
Revised:  To overcome this, we consider two modifications to average consensus:%DIFDELCMD < inparaenum[1)] \item %%% the A-ND algorithm with weights decaying to zero (slowly, satisfying a persistence condition condition (slowly decaying to zero );
Edit intent: fluency
Original:  and %DIFDELCMD < \item %%% the A-NC algorithm with time invariant weights but that averages successive runs, restarted with the same initial conditions.
Revised:  and %DIFDELCMD < \item %%% the A-NC algorithm 
Edit intent: coherence
Original: Tagging communities are popular instances of a broad class of online communities based on user-generated content.
Revised: Tagging communities represent a subclass of a broader class of user-generated content.
Edit intent: clarity
Original:  Although recent studies advocate and attempt to harness social knowledge generated in this context  , little research has been done to quantify the current level of user collaboration in these communities.
Revised:  Although recent studies advocate and attempt to harness social knowledge in this context , little research has been done to quantify the current level of user collaboration in these communities.
Edit intent: clarity
Original:  Using these two metrics, this paper shows that the current level of collaboration in CiteULike and Connotea is consistently low, which significantly limits the potential of harnessing the social knowledge in collaborative communities.
Revised:  Using these two metrics, this paper shows that the current level of collaboration in CiteULike and Connotea is consistently low, which significantly limits the potential of harnessing the social knowledge in communities.
Edit intent: clarity
Original: A construction method for duplex cage structures with icosahedral symmetry made out of a single-stranded RNA or DNA molecule is presented and applied to an icosidodecahedral cage.
Revised: A construction method for duplex cage structures with icosahedral sym- metry made out of a single-stranded RNA or DNA molecule is presented and applied to an icosidodecahedral cage.
Edit intent: fluency
Original: A construction method for duplex cage structures with icosahedral symmetry made out of a single-stranded RNA or DNA molecule is presented and applied to an icosidodecahedral cage.
Revised: A construction method for duplex cage structures with icosahedral symmetry made out of single-stranded RNA or DNA molecule is presented and applied to an icosidodecahedral cage.
Edit intent: fluency