wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our main contribution is to prove that the following problem is 2-ExpTime -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her adversary .
Revised:  Our main contribution is to prove that the following problem is 2-ExpTime -complete : decide whether the first player has a strategy that ensures her to almost-surely win against any possible strategy of her oponent .
Edit intent: clarity
Original:  We also precisely characterise those strategies needed by the first player to almost-surely win.
Revised:  We also characterise those strategies needed by the first player to almost-surely win.
Edit intent: clarity
Original: Changes in the extent of local concavity and surface roughness of binding sites of proteins have long been considered as useful markers to study functional sites of proteins.
Revised: Changes in the extent of local concavity along with changes in surface roughness of binding sites of proteins have long been considered as useful markers to study functional sites of proteins.
Edit intent: clarity
Original: Changes in the extent of local concavity and surface roughness of binding sites of proteins have long been considered as useful markers to study functional sites of proteins.
Revised: Changes in the extent of local concavity and surface roughness of binding sites of proteins have long been considered as useful markers to identify functional sites of proteins.
Edit intent: clarity
Original:  However, an objective algorithm that describes the connection between the simultaneous changes of these important parameters , eludes the students of structural biology.
Revised:  However, an algorithm that describes the connection between the simultaneous changes of these important parameters , eludes the students of structural biology.
Edit intent: clarity
Original:  However, an objective algorithm that describes the connection between the simultaneous changes of these important parameters , eludes the students of structural biology.
Revised:  However, an objective algorithm that describes the connection between the simultaneous changes of these important parameters - eludes the students of structural biology.
Edit intent: fluency
Original:  Here we propose a simple yet rigorous algorithm that attempts to achieve the same.
Revised:  Here a simple yet rigorous algorithm that attempts to achieve the same.
Edit intent: clarity
Original:  Here we propose a simple yet rigorous algorithm that attempts to achieve the same.
Revised:  Here we propose a simple yet general mathematical scheme is proposed that attempts to achieve the same.
Edit intent: clarity
Original: A dichotomy theorem for counting problems due to Creignou and Hermann states that or any finite set S of logical relations, the counting problem #SAT(S) is either in FP, or #P-complete.
Revised: A dichotomy theorem for counting problems due to Creignou and Hermann states that or any nite set S of logical relations, the counting problem #SAT(S) is either in FP, or #P-complete.
Edit intent: fluency
Original:  We show that the "hard" cases in the Creignou-Hermann theorem give rise to VNP-complete families of polynomials , and we give partial results for the "easy" case of this dichotomy theorem .
Revised:  We show that the "hard" cases in the Creignou-Hermann theorem give rise to VNP-complete families of polynomials , and we give partial results for the "easy" and "hard" polynomials .
Edit intent: clarity
Original:  One open question they asked was how the model would change if it permitted multiple nucleation, i.e., independent groups of tiles growing before attaching to the original seed assembly.
Revised:  One open question they asked was how much computational power would be added if the model permitted multiple nucleation, i.e., independent groups of tiles growing before attaching to the original seed assembly.
Edit intent: clarity
Original:  This paper provides a partial answer, by proving that no tile assembly model can use multiple nucleation to achieve speedup from polynomial time to constant time without sacrificing computational power: if a tile assembly system T uses multiple nucleation to tile a surface in constant time (  independent of the size of the surface) , then T is unable to solve computational problems that have low complexity in the (single-seeded) Winfree-Rothemund Tile Assembly Model .
Revised:  This paper provides a partial answer, by proving that if a tile assembly system T uses multiple nucleation to tile a surface in constant time ( independent of the size of the surface) , then T is unable to solve computational problems that have low complexity in the (single-seeded) Winfree-Rothemund Tile Assembly Model .
Edit intent: coherence
Original:  This paper provides a partial answer, by proving that no tile assembly model can use multiple nucleation to achieve speedup from polynomial time to constant time without sacrificing computational power: if a tile assembly system T uses multiple nucleation to tile a surface in constant time (  independent of the size of the surface) , then T is unable to solve computational problems that have low complexity in the (single-seeded) Winfree-Rothemund Tile Assembly Model .
Revised:  This paper provides a partial answer, by proving that no tile assembly model can use multiple nucleation to achieve speedup from polynomial time to constant time without sacrificing computational power: if a tile assembly system T uses multiple nucleation to tile a surface in constant time ( independent of the size of the surface) .
Edit intent: coherence
Original:  The proof technique defines a new model of distributed computing that simulates tile (and robotic) self-assembly , so a tile assembly model can be described as a distributed computing model . Keywords: self-assembly, multiple nucleation, locally checkable labeling.
Revised:  The proof technique defines a new model of distributed computing that simulates tile (and robotic) self-assembly . Keywords: self-assembly, multiple nucleation, locally checkable labeling.
Edit intent: coherence
Original:  This paper confirms the intuition that the non-degenerate diffusion component dictates the regularity of the value function in the optimal stopping problem for jump processes.
Edit intent: coherence
Original:  A function that generates such pseudorandom strings from shorter but truly random seeds is known as a pseudorandom generator.
Revised:  A function that generates pseudorandom strings from shorter but truly random seeds is known as a pseudorandom generator.
Edit intent: clarity
Original:  Our generators are designed to fool languages, rather than probabilistic algorithms .
Revised:  Our generators are designed to "fool" Boolean-valued functions (or equivalently, languages) .
Edit intent: clarity
Original:  In particular, our generators take context-free languages with advice as their adversaries.
Revised:  In particular, our generator fools advised context-free languages with advice as their adversaries.
Edit intent: clarity
Original:  We present an explicit example of such a pseudorandom generator, which can be also computed by a single-tape deterministic Turing machine running in time O(n^2) .
Revised:  We present an explicit example of such a pseudorandom generator, which is computed by a single-tape deterministic Turing machine running in time O(n^2) .
Edit intent: clarity
Original:  We present an explicit example of such a pseudorandom generator, which can be also computed by a single-tape deterministic Turing machine running in time O(n^2) .
Revised:  We present an explicit example of such a pseudorandom generator, which can be also computed by a deterministic Turing machine running in time O(n^2) .
Edit intent: clarity
Original:  In contrast, we show that there is no almost 1-1 pseudorandom generator against even context-free languages (without advice) if we demand  it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Revised:  In contrast, we show that there is no almost 1-1 pseudorandom generator against context-free languages (without advice) if we demand it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Edit intent: clarity
Original:  In contrast, we show that there is no almost 1-1 pseudorandom generator against even context-free languages (without advice) if we demand  it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Revised:  In contrast, we show that there is no almost 1-1 pseudorandom generator against even context-free languages if we demand it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Edit intent: clarity
Original:  In contrast, we show that there is no almost 1-1 pseudorandom generator against even context-free languages (without advice) if we demand  it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Revised:  In contrast, we show that there is no almost 1-1 pseudorandom generator against even context-free languages (without advice) if we demand that it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Edit intent: fluency
Original:  Our proofs are all elementary, requiring no complicated proof techniques as in a polynomial-time setting, and utilize a specific feature of nondeterministic pushdown automata,  which is interesting on its own light.
Revised:  Our proofs are all elementary, requiring no complicated proof techniques as in a polynomial-time setting, and utilize a specific feature of nondeterministic pushdown automata, which is interesting in its own light.
Edit intent: fluency
Original:  We explicitly construct such a pseudorandom generator, which is computed by a deterministic Turing machine using logarithmic space and also belongs to a functional extension of the 2-conjunctive closure of CFL with a help of appropriate advice.
Revised:  We explicitly construct such a pseudorandom generator, which is computed by a deterministic Turing machine using logarithmic space and also belongs to a functional extension of the 2-conjunctive closure of CFL with the help of appropriate advice.
Edit intent: fluency
Original:  Our generators are designed to "fool " Boolean-valued functions (or equivalently, languages ).
Revised:  Our generators are designed to "fool " Boolean-valued functions (or equivalently, Boolean-valued functions ).
Edit intent: clarity
Original:  We explicitly construct such a pseudorandom generator, which is computed by a deterministic Turing machine using logarithmic space and also belongs to a functional extension of the 2-conjunctive closure of CFL with the help of appropriate  advice.
Revised:  We explicitly construct such a pseudorandom generator, which is computed by a deterministic Turing machine using logarithmic space and also belongs to a functional extension of the 2-conjunctive closure of CFL with the help of appropriate deterministic advice.
Edit intent: clarity
Original:  In contrast, we show that there is no almost 1-1 pseudorandom generator against context-free languages if we demand that it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Revised:  In contrast, we show that there is no almost one-to-one pseudorandom generator against context-free languages if we demand that it should be computed by a nondeterministic pushdown automaton equipped with a write-only output tape.
Edit intent: clarity
Original:  Our proofs are all elementary, built on an early work in the literature regarding the pseudorandomness against advised regular languages  , and in particular, one  proof utilizes a special feature of the behaviors of nondeterministic pushdown automata, called a swapping property, which is interesting in its own light .
Revised:  Our proofs are all elementary, built on an early work in the literature regarding the pseudorandomness against advised regular languages , and in particular, one part of the proof utilizes a special feature of the behaviors of nondeterministic pushdown automata, called a swapping property, which is interesting in its own light .
Edit intent: clarity
Original: Leader election and arbitrary pattern formation are fundammental tasks for a set of autonomous mobile robots.
Revised: Leader election and arbitrary pattern formation are fundammental tasks for a set of au- tonomous mobile robots.
Edit intent: fluency
Original:  The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such that an identity) allowing to differentiate any of them.
Revised:  The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such that an identity) allowing to di?erentiate any of them.
Edit intent: fluency
Original:  In such a system, we show that both problems are equivalent, that is ]  it is possible to solve the pattern formation problem for n not equal to 2 if and only if the leader election is solvable too .
Revised:  In such a system, we show that both problems are equivalent, that is ] that it is possible to solve the pattern formation problem for n not equal to 2 if and only if the leader election is solvable too .
Edit intent: fluency
Original:  In such a system, we show that both problems are equivalent, that is ]  it is possible to solve the pattern formation problem for n not equal to 2 if and only if the leader election is solvable too .
Revised:  In such a system, we show that both problems are equivalent, that is ] it is possible to solve the leader election problem for n not equal to 2 if and only if the leader election is solvable too .
Edit intent: clarity
Original: Leader election and arbitrary pattern formation are fundammental tasks for a set of au- tonomous mobile robots.
Revised: Leader election and arbitrary pattern formation are funda- mental tasks for a set of au- tonomous mobile robots.
Edit intent: fluency
Original: Leader election and arbitrary pattern formation are fundammental tasks for a set of au- tonomous mobile robots.
Revised: Leader election and arbitrary pattern formation are fundammental tasks for a set of autonomous mobile robots.
Edit intent: fluency
Original:  The solvability of both these tasks turns out to be necessary in order to achieve more complex tasks.
Revised:  The solv- ability of both these tasks turns out to be necessary in order to achieve more complex tasks.
Edit intent: clarity
Original:  The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such that an identity) allowing to di?erentiate any of them.
Revised:  The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such as an identity) allowing to di?erentiate any of them.
Edit intent: fluency
Original:  The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such that an identity) allowing to di?erentiate any of them.
Revised:  The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such that an identity) allowing to differentiate any of them.
Edit intent: fluency
Original:  Moreover,  none of them share any kind of common coordinate mechanism or common sense of direction , except that they agree on a common handedness (  chirality).
Revised:  Moreover, we assume that none of them share any kind of common coordinate mechanism or common sense of direction , except that they agree on a common handedness ( chirality).
Edit intent: clarity
Original:  Moreover,  none of them share any kind of common coordinate mechanism or common sense of direction , except that they agree on a common handedness (  chirality).
Revised:  Moreover, none of them share any kind of common coordinate mechanism or common sense of direction , except that they agree on a common handedness ( i.e., chirality).
Edit intent: coherence
Original:  In such a system, Flochini et al. proved in [ 9 ] that it is possible to solve the leader election problem for n ? 3 robots if the arbitrary pattern formation is solvable for n ? 3. In this paper, we show that the converse is true for n ? 4 and thus , we deduce that  both problems are equivalent for n ? 4 in CORDA provided the robots share the same chirality.
Revised:  In such a system, Flochini et al. proved in [ 9 ] that it is possible to elect a leader for n \geq 3 robots if the arbitrary pattern formation is solvable for n ? 3. In this paper, we show that the converse is true for n ? 4 and thus , we deduce that both problems are equivalent for n ? 4 in CORDA provided the robots share the same chirality.
Edit intent: clarity
Original:  In such a system, Flochini et al. proved in [ 9 ] that it is possible to solve the leader election problem for n ? 3 robots if the arbitrary pattern formation is solvable for n ? 3. In this paper, we show that the converse is true for n ? 4 and thus , we deduce that  both problems are equivalent for n ? 4 in CORDA provided the robots share the same chirality.
Revised:  In such a system, Flochini et al. proved in [ 9 ] that it is possible to solve the leader election problem for n ? 3 robots if it is possible to form any pattern for n \geq 3. In this paper, we show that the converse is true for n ? 4 and thus , we deduce that both problems are equivalent for n ? 4 in CORDA provided the robots share the same chirality.
Edit intent: clarity
Original: In this paper we embedd the Riordan group into a semi-direct product "algebra" of  formal power series .
Revised: In this paper we embedd the Riordan group into a semi-direct product "algebra" of the formal power series .
Edit intent: fluency
Original: In this paper the Riordan skew algebra is defined as the semi-direct product "algebra" of the formal power series and the principal ideal generated by the variable x.
Revised: The Riordan group is the semi-direct product "algebra" of the formal power series and the principal ideal generated by the variable x.
Edit intent: clarity
Original:  The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation.
Revised:  The underlying algorithm is the next subvolume method , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation.
Edit intent: clarity
Original:  The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation.
Revised:  The underlying algorithm is the next subvolume method (NSM) , extended to unstructured meshes by obtaining jump coefficients from a finite element formulation of the corresponding macroscopic equation.
Edit intent: fluency
Original:  URDME 1.3 includes support for Comsol Multiphysics 5.x and PDE Toolbox version 1.5 and above .
Revised:  Refer to www.urdme.org for the latest updates .
Edit intent: clarity
Original: Molecular motors are biogenic force generators acting in the nanometer range .
Revised: Molecular motors are single macromolecules that generate forces at the piconewton range and nanometer scale .
Edit intent: clarity
Original:  They convert chemical energy into mechanical work and move along filamentous structures.
Revised:  They convert chemical energy into mechanical work by moving along filamentous structures.
Edit intent: coherence
Original:  In this research, we will discuss the velocity of molecular motors, in framework of a mechanochemical network theory.
Revised:  In this paper, we study the velocity of molecular motors, in framework of a mechanochemical network theory.
Edit intent: clarity
Original:  Relying on this mechanism, we have calculated the change in the elastic free energy of the membrane caused by nascent LDs.
Revised:  Relying on this mechanism, we have calculated the change in elastic free energy of the membrane caused by nascent LDs.
Edit intent: fluency
Original:  We found a gradual de-mixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation.
Revised:  We found a gradual demixing of lipids in the membrane leaflet that goes along with an increase in surface curvature at the site of LD formation.
Edit intent: clarity
Original:  As a result of de-mixing , the phospholipid monolayer was able to gain energy during LD growth .
Revised:  During demixing , the phospholipid monolayer was able to gain energy during LD growth .
Edit intent: clarity
Original:  In the case of Saccharomyces cerevisiae LDs eventually detached from the ER at a critical diameter of about 30-50 nm.
Revised:  In the case of Saccharomyces cerevisiae our model predicts a LD bud-off diameter of about 30-50 nm.
Edit intent: clarity
Original:  The final part of the paper casts relational lattice perspective onto database dependency theory  .
Revised:  The final parts of the paper casts relational lattice perspective onto database dependency theory .
Edit intent: fluency
Original:  We prove the fixed-parameter tractability of the s-t Cut, Multicut, and Bipartization problems (parameterized by the maximal number k of vertices being removed) with various additional restrictions (e.g., the vertices being removed from the graph form an independent set).
Revised:  We prove the fixed-parameter tractability of a number of well-known separation and bipartization problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set).
Edit intent: clarity
Original:  Mexico,%DIFDELCMD < {\bf %%% 16 , 205 (1946)%DIFDELCMD < ]%%% . We demonstrate that topological charge is not conserved when the core of the vortex is large compared to the pinning center, allowing removal of such vortices.
Revised:  Mexico,%DIFDELCMD < {\bf %%% , 205 (1946)%DIFDELCMD < ]%%% . We demonstrate that topological charge is not conserved when the core of the vortex is large compared to the pinning center, allowing removal of such vortices.
Edit intent: coherence
Original:  Mexico,%DIFDELCMD < {\bf %%% 16 , 205 (1946)%DIFDELCMD < ]%%% . We demonstrate that topological charge is not conserved when the core of the vortex is large compared to the pinning center, allowing removal of such vortices.
Revised:  Mexico,%DIFDELCMD < {\bf %%% 16 %DIFDELCMD < ]%%% . We demonstrate that topological charge is not conserved when the core of the vortex is large compared to the pinning center, allowing removal of such vortices.
Edit intent: coherence
Original:  Our results suggest that decreasing excitability facilitates removal of vortices in cardiac tissue.
Revised:  Our results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.
Edit intent: clarity
Original: e introduce a microscopic model for the dynamics of the order book which permits to study how finite liquidity (liquidity crisis) and the associated granularity influence price fluctuations.
Revised: We introduce a microscopic model for the dynamics of the order book which permits to study how finite liquidity (liquidity crisis) and the associated granularity influence price fluctuations.
Edit intent: fluency
Original: e introduce a microscopic model for the dynamics of the order book which permits to study how finite liquidity (liquidity crisis) and the associated granularity influence price fluctuations.
Revised: e introduce a microscopic model for the dynamics of the order book to study how finite liquidity (liquidity crisis) and the associated granularity influence price fluctuations.
Edit intent: coherence
Original: e introduce a microscopic model for the dynamics of the order book which permits to study how finite liquidity (liquidity crisis) and the associated granularity influence price fluctuations.
Revised: e introduce a microscopic model for the dynamics of the order book which permits to study how the lack of liquidity influences price fluctuations.
Edit intent: clarity