wanyu/IteraTeR_v2 huggingface dataset:
Original:  Here, I point out that it is the elongated shapes of these cells that allows for this behavior.
Revised:  Here, I point out that it is the elongated profiles of such cells that allows for this behavior.
Edit intent: clarity
Original:  Fits of experimental growth curves to these forms would return cellular metabolic rate estimates .
Revised:  Fits of experimental growth curves to such bounds can be used to estimate various quantities of interest, including generalized metabolic rates .
Edit intent: clarity
Original: Non-linear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks.
Revised: Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks.
Edit intent: fluency
Original:  Such multilingual users may serve an important function in diffusing information across different language editions of the project , and prior work has suggested this could reduce the level of self-focus bias in each edition.
Revised:  Such multilingual users may serve an important function in diffusing information across different language editions of the encyclopedia , and prior work has suggested this could reduce the level of self-focus bias in each edition.
Edit intent: clarity
Original:  Second, we derive and evaluate TRAIL, a generic scheme for topology authentication in RPL. TRAIL solely relies on the basic assumptions of RPL that (1) the root node serves as a trust anchor and (2) each node interconnects to the root in a straight hierarchy.
Revised:  Second, we derive and evaluate TRAIL, a generic scheme for topology authentication in RPL. TRAIL solely relies on the basic assumptions of RPL that (1) the root node serves as a trust anchor and (2) each node interconnects to the root as part of a hierarchy.
Edit intent: clarity
Original: The macroscopic properties, the properties of individual components , and how those components arrange themselves are three important aspects of a complex structure.
Revised: The macroscopic properties, the properties of individual components and how those components arrange themselves are three important aspects of a complex structure.
Edit intent: fluency
Original: The macroscopic properties, the properties of individual components , and how those components arrange themselves are three important aspects of a complex structure.
Revised: The macroscopic properties, the properties of individual components , and how those components interact with each other are three important aspects of a complex structure.
Edit intent: clarity
Original:  Here we perform a theoretical study of a composited system that is slender and can be coarse-grained as a simple smooth 3-dimensional curve.
Revised:  Here we perform a theoretical study of slender structures that can be coarse-grained as a simple smooth 3-dimensional curve.
Edit intent: clarity
Original: Given a finite set of points in \mathbb R^n and a positive radius , we consider the Cech, Delaunay-Cech, alpha, and wrap complexes as examples of a generalized discrete Morse theory.
Revised: Given a finite set of points in \mathbb R^n and a radius parameter, we study the Cech, Delaunay-Cech, alpha, and wrap complexes as examples of a generalized discrete Morse theory.
Edit intent: clarity
Original: Given a finite set of points in \mathbb R^n and a radius parameter, we study the Cech, Delaunay-Cech, Delaunay (or alpha ), and Wrap complexes in the light of generalized discrete Morse theory.
Revised: Given a finite set of points in \mathbb R^n and a radius parameter, we study the Cech, Delaunay-Cech, Delaunay (or Alpha ), and Wrap complexes in the light of generalized discrete Morse theory.
Edit intent: fluency
Original: }[  T. W. Burkhardt, Y. Yang, G. Gompper, Phys.
Revised: }[ Y. Yang, T. W. Burkhardt, Y. Yang, G. Gompper, Phys.
Edit intent: fluency
Original: The epidermis renewal and homeostasis is maintained by a multistage process including cell proliferation, differentiation, migration, apoptosis and desquamation.
Edit intent: coherence
Original:  The bimodal psoriasis is established by the interaction between psoriatic stem cells and the immune system  .
Revised:  The interconversion between the two modes is established by the interaction between psoriatic stem cells and the immune system .
Edit intent: clarity
Original: We present a computational model of the spatial-temporal dynamics of the epidermis homeostasis  .
Revised: We present a computational model to study the spatiotemporal dynamics of the epidermis homeostasis .
Edit intent: clarity
Original:  The model recapitulates observed  cell density distribution and the epidermal turnover time .
Revised:  The model recapitulates observed cell density distribution , the epidermal turnover time .
Edit intent: fluency
Original:  The interconversion between the two modes is established by the interaction between psoriatic stem cells and the immune system and by the normal and psoriatic stem cells competing for  niches.
Revised:  Interconversion between the two modes is established by the interaction between psoriatic stem cells and the immune system and by the normal and psoriatic stem cells competing for niches.
Edit intent: coherence
Original:  The interconversion between the two modes is established by the interaction between psoriatic stem cells and the immune system and by the normal and psoriatic stem cells competing for  niches.
Revised:  The interconversion between the two modes can be controlled by interactions between psoriatic stem cells and the immune system and by the normal and psoriatic stem cells competing for niches.
Edit intent: clarity
Original:  The interconversion between the two modes is established by the interaction between psoriatic stem cells and the immune system and by the normal and psoriatic stem cells competing for  niches.
Revised:  The interconversion between the two modes is established by the interaction between psoriatic stem cells and the immune system and by the normal and psoriatic stem cells competing for growth niches.
Edit intent: clarity
Original:  The restriction of this function to bit strings of any given length can be computed according to the Karatsuba multiplication algorithm by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction.
Revised:  The restriction of this function to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction.
Edit intent: clarity
Original:  We describe instruction sequences of this kind that compute the function on bit strings that models multiplication on natural numbers  with respect to their representations in the binary number system, restricted to bit strings of  a fixed but arbitrary length , according to the long multiplication algorithm and the Karatsuba multiplication algorithm.
Revised:  We describe instruction sequences of this kind that compute the function on bit strings that models multiplication on natural numbers with respect to their binary representation by bit strings of a fixed but arbitrary length , according to the long multiplication algorithm and the Karatsuba multiplication algorithm.
Edit intent: clarity
Original:  It is also designed to target a range of hardware platforms via use of a custom domain specific language  .
Revised:  It is also designed to target a range of hardware platforms via use of an in-built domain specific language .
Edit intent: clarity
Original:  We give a bound on the number of polynomials of degree d in a Gr\"obner basis computed by Faug\`ere's F5 algorithm (Fau02) in this generic case for the grevlex ordering (which is also a bound on the number of polynomials for a reduced Gr\"obner basis ), and use it to bound the exponent of the complexity of the F5 algorithm .
Revised:  We give a bound on the number of polynomials of degree d in a Gr\"obner basis computed by Faug\`ere's F5 algorithm (Fau02) in this generic case for the grevlex ordering (which is also a bound on the number of polynomials for a reduced Gr\"obner basis ), and use it to bound the complexity of the F5 algorithm .
Edit intent: clarity
Original: In this paper, we present a reduction algorithm for abstract simpli- cial complexe that we apply to Vietoris-Rips complexes based on random point processes.
Revised: In this paper, we present a reduction algorithm for abstract simplicial complexes that we apply to Vietoris-Rips complexes based on random point processes.
Edit intent: fluency
Original:  The vertices are removed in a optimal order for the ab- stract simplicial complex implementation complexity.
Revised:  The vertices are removed in an optimal order for the ab- stract simplicial complex implementation complexity.
Edit intent: fluency
Original:  The vertices are removed in a optimal order for the ab- stract simplicial complex implementation complexity.
Revised:  The vertices are removed in a optimal order for the abstract simplicial complex implementation complexity.
Edit intent: fluency
Original:  Our algorithm aims at reducing the number of simplices of an abstract simplicial complex without modifying its topology, i.e. its Betti numbers.
Revised:  Our algorithm aims at reducing the number of points of an abstract simplicial complex without modifying its topology, i.e. its Betti numbers.
Edit intent: clarity
Original:  First, we propose a frequency auto-planning algorithm for the self-configuration of future cellular networks.
Revised:  The first one is a frequency auto-planning algorithm for the self-configuration of future cellular networks.
Edit intent: coherence
Original:  Then, we present an energy conservation algorithm for the self- optimization of future cellular networks  during off-peak hours .
Revised:  Then, our energy conservation algorithm for the self- optimization of future cellular networks during off-peak hours .
Edit intent: clarity
Original:  Then, we present an energy conservation algorithm for the self- optimization of future cellular networks  during off-peak hours .
Revised:  Then, we present an energy conservation algorithm falls into the self-optimization feature of future cellular networks during off-peak hours .
Edit intent: clarity
Original: Simplicial homology is a tool that provides a mathematical way to compute the connectivity and the coverage of a cellular network without any node location information.
Revised: Simplicial homology is a tool that provides a math- ematical way to compute the connectivity and the coverage of a cellular network without any node location information.
Edit intent: fluency
Original:  The first one is a frequency auto-planning algorithm for the self-configuration of future cellular networks.
Revised:  The first one is a frequency auto-planning algorithm for the self- configuration of future cellular networks.
Edit intent: fluency
Original: Simplicial homology is a tool that provides a math- ematical way to compute the connectivity and the coverage of a cellular network without any node location information.
Revised: Simplicial homology is a tool that provides a mathematical way to compute the connectivity and the coverage of a cellular network without any node location information.
Edit intent: fluency
Original:  The first one is a frequency auto-planning algorithm for the self- configuration of future cellular networks.
Revised:  The first one is a frequency auto-planning algorithm for the self-configuration of future cellular networks.
Edit intent: fluency
Original:  In this paper we make a strawman proposal for how OpenFlow should evolve in the future , starting with the definition of an abstract forwarding model for switches .
Revised:  In this paper we make a strawman proposal for how OpenFlow should evolve in the future .
Edit intent: clarity
Original:  ( 2 ) Target independence: Programmers should describe how switches are to process packets in a way that can be compiled down to any target switch that fits our abstract forwarding model.
Revised:  ( 3 ) Target independence: Programmers should describe how switches are to process packets in a way that can be compiled down to any target switch that fits our abstract forwarding model.
Edit intent: fluency
Original:  We describe  how to write programs using our abstract forwarding model and our P4 programming language in order to configure switches and populate their forwarding tables .
Revised:  We describe how to use P4 programming language in order to configure switches and populate their forwarding tables .
Edit intent: clarity
Original:  We develop a new phenotypic variation method that tests our understanding of the landscape.
Revised:  We develop a phenotypic variation method that tests our understanding of the landscape.
Edit intent: clarity
Original:  We develop a new phenotypic variation method that tests our understanding of the landscape.
Revised:  We develop a new phenotypic variation method that tests the new understanding of the landscape.
Edit intent: clarity
Original:  We also develop a modified function set that tests our understanding of synchronization constraintswe identify .
Revised:  We also develop a modified function set that tests newly identified synchronization constraints .
Edit intent: clarity
Original:  Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics is still to be understood .
Revised:  Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear .
Edit intent: clarity
Original:  As an important application of this analytical model, an intensity planning scenario is investigated, in which we aim to maximize the total income of the network operator with respect to the intensities of tier-2 cells, under constraints on the outage probabilities of tier-1  users.
Revised:  As an important application of this analytical model, an intensity planning scenario is investigated, in which we aim to maximize the total income of the network operator with respect to the intensities of tier-2 cells, under constraints on the outage probabilities of tier-1 and tier-2 users.
Edit intent: clarity
Original:  We strengthen this result by showing that it is still \Sigma_2^P-complete for \%a proper subclass of perfect graphs, namely weakly chordal graphs.
Revised:  We strengthen this result by showing that it is still \Sigma_2^P-complete for weakly chordal graphs.
Edit intent: clarity
Original:  We also present a practical application of our model to assess public health guidelines about emergency preparedness and response in the event of a smallpox bioterrorist attack  .
Revised:  We also present two practical applications of our model to assess public health guidelines about emergency preparedness and response in the event of a smallpox bioterrorist attack .
Edit intent: clarity
Original: We consider two basic problems arising in the theory of synchronizing automata: deciding, whether or not a given n-state automaton is synchronizing and the problem of approximating the reset threshold for a given synchronizing automata .
Revised: We consider two basic problems arising in the theory of synchronizing automata: deciding, whether or not a given n-state automaton is synchronizing and the problem of approximating the reset threshold for a given synchronizing automaton .
Edit intent: fluency
Original:  For the first problem of deciding whether or not a given n-state automaton is synchronizing we present an algorithm based on  RandSynch with linear in n expected time, while the best known algorithm is quadratic for all automata .
Revised:  For the first problem of deciding whether or not a given n-state automaton is synchronizing we present an algorithm based on ~ RandSynch with linear in n expected time, while the best known algorithm is quadratic for all automata .
Edit intent: fluency
Original:  For the first problem of deciding whether or not a given n-state automaton is synchronizing we present an algorithm based on  RandSynch with linear in n expected time, while the best known algorithm is quadratic for all automata .
Revised:  For the first problem of deciding whether or not a given n-state automaton is synchronizing we present an algorithm based on RandSynch with linear in n expected time, while the best known algorithm is quadratic on each instance .
Edit intent: clarity
Original:  For the second problem, we prove that unless P = NP, no polynomial-time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from \mbox{ AMS6 improves the previous result of the author  MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from  \cite{Gerb1}.
Revised:  For the second problem, we prove that unless P = NP, no polynomial time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from \mbox{ AMS6 improves the previous result of the author MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from \cite{Gerb1}.
Edit intent: fluency
Original:  For the second problem, we prove that unless P = NP, no polynomial-time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from \mbox{ AMS6 improves the previous result of the author  MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from  \cite{Gerb1}.
Revised:  For the second problem, we prove that unless P = NP, no polynomial-time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from ~\mbox{ AMS6 improves the previous result of the author MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from \cite{Gerb1}.
Edit intent: clarity
Original:  For the second problem, we prove that unless P = NP, no polynomial-time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from \mbox{ AMS6 improves the previous result of the author  MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from  \cite{Gerb1}.
Revised:  For the second problem, we prove that unless P = NP, no polynomial-time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from \mbox{ AMS6 improves the previous result of the author ~ MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from \cite{Gerb1}.
Edit intent: fluency
Original:  For the second problem, we prove that unless P = NP, no polynomial-time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from \mbox{ AMS6 improves the previous result of the author  MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from  \cite{Gerb1}.
Revised:  For the second problem, we prove that unless P = NP, no polynomial-time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from \mbox{ AMS6 improves the previous result of the author MyTOCS2013 about non-approximability within any constant factor and also gives the positive answer to the corresponding conjecture from ~ \cite{Gerb1}.
Edit intent: fluency
Original:  For the first problem of deciding whether or not a given n-state automaton is synchronizing we present an algorithm based on~\mbox{ RandSynch problem  , we prove that unless P = NP, no polynomial time algorithm approximates the reset threshold for a given n-state 2-letter  automata within performance ratio less than 0.5 c (n) where c is a specific constant from~AMS6.
Revised:  For the first problem of deciding whether or not a given n-state automaton is synchronizing we present an algorithm based on~\mbox{ RandSynch problem NP , we prove that unless P = NP, no polynomial time algorithm approximates the reset threshold for a given n-state 2-letter automata within performance ratio less than 0.5 c (n) where c is a specific constant from~AMS6.
Edit intent: clarity
Original:  First, we prove that the problem of testing a given reachable partial automaton for synchronization isNP -complete while the corresponding problem for complete automata is polynomial.
Revised:  First, we prove that the problem of testing a given reachable partial automaton NP -complete while the corresponding problem for complete automata is polynomial.
Edit intent: clarity
Original:  First, we prove that the problem of testing a given reachable partial automaton for synchronization isNP -complete while the corresponding problem for complete automata is polynomial.
Revised:  First, we prove that the problem of testing a given reachable partial automaton for synchronization is -complete while the corresponding problem for complete automata is polynomial.
Edit intent: clarity
Original:  At the second part, we prove that unlessP =NP , no polynomial time algorithm approximates the reset threshold for a given n-state 2-letter complete automata within performance ratio less than 0.5 c (n) where c is a specific constant from~\mbox{ AMS60pt .
Revised:  At the second part, we prove that unlessP NP , no polynomial time algorithm approximates the reset threshold for a given n-state 2-letter complete automata within performance ratio less than 0.5 c (n) where c is a specific constant from~\mbox{ AMS60pt .
Edit intent: clarity
Original:  At the second part, we prove that unlessP =NP , no polynomial time algorithm approximates the reset threshold for a given n-state 2-letter complete automata within performance ratio less than 0.5 c (n) where c is a specific constant from~\mbox{ AMS60pt .
Revised:  At the second part, we prove that unlessP = , no polynomial time algorithm approximates the reset threshold for a given n-state 2-letter complete automata within performance ratio less than 0.5 c (n) where c is a specific constant from~\mbox{ AMS60pt .
Edit intent: clarity
Original:  Platelets aggregate at the injury site through tethering and rolling on the injured endothelium layer expressing surface-bound von Willebrand factor (vWF) during the initial stage of the blood clot formation.
Revised:  Platelets aggregate at the injury site through tethering and rolling on the injured endothelium is a critical initial step in blood clot formation.
Edit intent: clarity
Original:  A  three-dimensional multiscale model is introduced  to simulate receptor-mediated platelet adhesion to substrate exposed with vWF under different shear rates of blood flow.
Revised:  A novel three-dimensional multiscale model is introduced to simulate receptor-mediated platelet adhesion to substrate exposed with vWF under different shear rates of blood flow.
Edit intent: clarity
Original:  A  three-dimensional multiscale model is introduced  to simulate receptor-mediated platelet adhesion to substrate exposed with vWF under different shear rates of blood flow.
Revised:  A three-dimensional multiscale model is introduced to simulate receptor-mediated adhesion of deformable platelets at the site of vascular injury under different shear rates of blood flow.
Edit intent: clarity