wanyu/IteraTeR_v2 huggingface dataset:
Original: In the literature, there are several hybrid models of quantum finite automata (QFA) which are distinguished from other QFA models by consisting of two interactive components: a quantum component and a classical one, accompanied with possible communication between them.
Revised: In the literature, there exist several quantum finite automata (QFA) which are distinguished from other QFA models by consisting of two interactive components: a quantum component and a classical one, accompanied with possible communication between them.
Edit intent: clarity
Original:  Specifically, we show that the existing hybrid models of QFA can be simulated exactly by QFA with quantum operations, which in turn has  close relationship with two early proposed models: {\it anciall QFA} and {\it quantum sequential machines 
Revised:  In particular, it is shown that hybrid QFA can be simulated exactly by QFA with quantum operations, which in turn has close relationship with two early proposed models: {\it anciall QFA} and {\it quantum sequential machines 
Edit intent: clarity
Original:  Specifically, we show that the existing hybrid models of QFA can be simulated exactly by QFA with quantum operations, which in turn has  close relationship with two early proposed models: {\it anciall QFA} and {\it quantum sequential machines 
Revised:  Specifically, we show that the existing hybrid models of QFA can be simulated exactly by QFA with quantum operations, which in turn has a close relationship with two early proposed models: {\it anciall QFA} and {\it quantum sequential machines 
Edit intent: fluency
Original:  Specifically, we show that the existing hybrid models of QFA can be simulated exactly by QFA with quantum operations, which in turn has  close relationship with two early proposed models: {\it anciall QFA} and {\it quantum sequential machines 
Revised:  Specifically, we show that the existing hybrid models of QFA can be simulated exactly by QFA with quantum operations, which in turn has close relationship with two early proposed models: {\it ancialla QFA} and {\it quantum sequential machines 
Edit intent: fluency
Original:  Specifically, we show that the existing hybrid models of QFA can be simulated exactly by QFA with quantum operations, which in turn has  close relationship with two early proposed models: {\it anciall QFA} and {\it quantum sequential machines 
Revised:  Specifically, we show that the existing hybrid models of QFA can be simulated exactly by QFA with quantum operations, which in turn has close relationship with two early proposed models: {\it anciall QFA} and {\it quantum sequential machines .
Edit intent: fluency
Original:  Cables and rings spontaneously emerge as steady state configurations of active filaments on the cylinder, and can be stationary or moving, helical or segments moving along helical trajectories.
Revised:  Cables and rings spontaneously emerge as steady state configurations on the cylinder, and can be stationary or moving, helical or segments moving along helical trajectories.
Edit intent: clarity
Original:  Our results are relevant in a variety of cellular contexts involving the dynamics and patterning  of active biopolymers in cylindrical cells.
Revised:  Our results are relevant to the dynamics and patterning of active biopolymers in cylindrical cells.
Edit intent: clarity
Original:  Our results are relevant in a variety of cellular contexts involving the dynamics and patterning  of active biopolymers in cylindrical cells.
Revised:  Our results are relevant in a variety of cellular contexts involving the dynamics and patterning of a variety of active biopolymers in cylindrical cells.
Edit intent: fluency
Original:  and cyclicity, modelling the property that v can point to a cyclic data structure.
Revised:  and cyclicity, modeling the property that v can point to a cyclic data structure.
Edit intent: fluency
Original:  The analysis is proven to be sound , and to be optimal with respect to the chosen abstraction.
Revised:  The analysis is proven to be sound and optimal with respect to the chosen abstraction.
Edit intent: coherence
Original:  In particular we  extend the PCP[ nloglog(n ), nloglog(n ) ] result of Feige et al. to W 1 , and discuss some corollaries.
Revised:  In particular we extend the PCP[ nloglog(n ), nloglog(n ) ] result of Feige et al. to 1 , and discuss some corollaries.
Edit intent: clarity
Original:  Motivated by the idea of self-managed networks, in the developed framework the decision-making entities are associated with individual transmission links, deciding on the way they split capacity among concurrent flows.
Revised:  Motivated by the idea of self-managed networks, in the developed framework decision-making entities are associated with individual transmission links, deciding on the way they split capacity among concurrent flows.
Edit intent: fluency
Original:  An efficient  algorithm is given for computing a strongly Pareto-optimal strategy , constituting a pure Nash equilibrium.
Revised:  An efficient algorithm is given for computing strongly Pareto-optimal strategy , constituting a pure Nash equilibrium.
Edit intent: fluency
Original:  An efficient  algorithm is given for computing a strongly Pareto-optimal strategy , constituting a pure Nash equilibrium.
Revised:  An efficient algorithm is given for computing a strongly Pareto-optimal strategies , constituting a pure Nash equilibrium.
Edit intent: fluency
Original: Recently, several works have analyzed the efficiency of photosynthetic complexes in a transient scenario and how such an efficiency is affected by environmental noise.
Revised: Recently, several works have analysed the efficiency of photosynthetic complexes in a transient scenario and how such an efficiency is affected by environmental noise.
Edit intent: fluency
Original: Recently, several works have analyzed the efficiency of photosynthetic complexes in a transient scenario and how such an efficiency is affected by environmental noise.
Revised: Recently, several works have analyzed the efficiency of photosynthetic complexes in a transient scenario and how that efficiency is affected by environmental noise.
Edit intent: clarity
Original:  The analysis is carried out for the steady state of the system where  excitation energy is constantly "flowing" through the system.
Revised:  The analysis is carried out for the steady state of the system where the excitation energy is constantly "flowing" through the system.
Edit intent: clarity
Original:  By adding dephasing to the system, we analyze the possibility of noise-enhancement of the quantum transport.
Revised:  By adding dephasing to the system, we analyse the possibility of noise-enhancement of the quantum transport.
Edit intent: fluency
Original: It has been shown recently that the use of two pairs of resistors with enhanced Johnson-noise and a Kirchhoff-loop-i.e., a Kirchhoff-Law-Johnson-like-Noise (KLJN) protocol-for secure key distribution leads to information theoretic security levels superior to those of a quantum key distribution, including a natural immunity against a man-in-the-middle attack.
Revised: It has been shown recently that the use of two pairs of resistors with enhanced Johnson-noise and a Kirchhoff-loop-i.e., a Kirchhoff-Law-Johnson-Noise (KLJN) protocol-for secure key distribution leads to information theoretic security levels superior to those of a quantum key distribution, including a natural immunity against a man-in-the-middle attack.
Edit intent: fluency
Original:  In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the system  behaviour.
Revised:  In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the system 's behaviour.
Edit intent: clarity
Original: In the present paper, we introduce a numerical scheme for the price of a barrier option when the  underlying follows a diffusion process.
Revised: In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process.
Edit intent: clarity
Original:  We here show that this diversity of decision systems corresponds to a single and optimal rule of decision-making in collectives.
Revised:  We here show that this diversity of decision systems corresponds to a single rule of decision-making in collectives.
Edit intent: clarity
Original:  Further, these results show that the different counting systems used by animals, including humans, can emerge from the common principle of optimally using social information to make good decisions.
Revised:  Further, these results show that the different counting systems used by animals, including humans, can emerge from the common principle of using social information to make good decisions.
Edit intent: clarity
Original:  We show that, given a point set S in the Euclidean plane and two triangulations T_1 and T_2 of S, it is an NP-complete problem to find the smallest number of edge flips to transform T_1 to T_2 . We note that Lubiw and Pathak (ArXiv e-prints, arXiv:1205.2425, 2012) simultaneously and independently obtained the same result, using a different reduction .
Revised:  We show that, given a point set S in the Euclidean plane and two triangulations T_1 and T_2 of S, it is an APX-hard problem to minimize the number of edge flips to transform T_1 to T_2 . We note that Lubiw and Pathak (ArXiv e-prints, arXiv:1205.2425, 2012) simultaneously and independently obtained the same result, using a different reduction .
Edit intent: clarity
Original: Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and bubbles in asset prices.
Revised: Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and "bubbles" in asset prices.
Edit intent: fluency
Original:  The proof of the Soundness Theorem is formalized in Coq, leading to certified upper bounds on the cost of any expression in the target language.
Revised:  The proof of the Soundness Theorem is formalized in Coq, providing certified upper bounds on the cost of any expression in the target language.
Edit intent: clarity
Original: The broadcasting models on a d-ary tree T arise in many contexts such as biology, information theory, statistical physics , and computer science.
Revised: The broadcasting models on a d-ary tree T arise in many contexts such as biology, statistical physics and computer science.
Edit intent: clarity
Original:  In this paper we consider the k-colouring model.
Revised:  Here we consider the k-colouring model.
Edit intent: clarity
Original:  A basic question here is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Revised:  A basic question is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Edit intent: coherence
Original:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows  . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  It is well known that d/\ln d poses a threshold, in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: clarity
Original:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows  . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  It is well known that d/\ln d is a threshold in the sense that 1) if k> d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: clarity
Original:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows  . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root vanishes as the height of the tree grows . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: clarity
Original:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows  . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: coherence
Original:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows  . 2) if k< (1-\epsilon) d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  It is well known that d/\ln d is a threshold in the sense that 1) if k> (1+\epsilon) d/\ln d, then the information of the colouring of the root at the leaves vanishes as the height of the tree grows . 2) if k< d/\ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: fluency
Original:  The above implies that for k> (1+\epsilon) d/\ln d and two broadcasting processes that assign the root different colours there is a coupling such that the probability of having vertices which take different colour assignments in the two processes reduces as we move away from the root.
Revised:  The above implies that for k> (1+\epsilon) d/\ln d and two broadcasting processes that assign the root different colours the following holds: There is a coupling such that the probability of having vertices which take different colour assignments in the two processes reduces as we move away from the root.
Edit intent: clarity
Original:  The description of such a coupling , especially a combinatorial one, is a stronger statement than the reconstruction/non-reconstruction threshold.
Revised:  The description of such a coupling is a stronger statement than the reconstruction/non-reconstruction threshold.
Edit intent: clarity
Original:  It would cast a light on the actual nature of this, very impressing , phenomenon.
Revised:  It would cast a light on the actual nature of this, very impressive , phenomenon.
Edit intent: fluency
Original:  In this work we provide a coupling which has the aforementioned property for any k>2d/\ln d . It is of combinatorial nature and the decisions it makes are based on simple local rules.
Revised:  In this work we provide a coupling which has the aforementioned properties for k>2d/\ln d . It is of combinatorial nature and the decisions it makes are based on simple local rules.
Edit intent: clarity
Original:  Here we consider the k-colouring model . A basic question  is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Revised:  We consider the k-colouring model . A basic question is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Edit intent: coherence
Original:  Here we consider the k-colouring model . A basic question  is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Revised:  Here we consider the k-colouring model . A basic question here is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Edit intent: clarity
Original:  Here we consider the k-colouring model . A basic question  is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Revised:  Here we consider the k-colouring model . A basic question is whether the information of the assignment at the root affects the distribution of the colourings of the leaves.
Edit intent: clarity
Original:  Here we consider the k-colouring model . A basic question  is whether the information of the assignment of the root affects the distribution of the colourings of the leaves.
Revised:  Here we consider the k-colouring model . A basic question is whether the information of the assignment of the root affects the distribution of the colourings at the leaves.
Edit intent: fluency
Original:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps d/ \ln d, then the information of the colouring of the root vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves.
Revised:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps) d/ \ln d, then the information of the colouring of the root vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves.
Edit intent: fluency
Original:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps d/ \ln d, then the information of the colouring of the root vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves.
Revised:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps d/ ln d, then the information of the colouring of the root vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves.
Edit intent: fluency
Original:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps d/ \ln d, then the information of the colouring of the root vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves.
Revised:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps d/ \ln d, then the colouring of the root vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves.
Edit intent: clarity
Original:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps d/ \ln d, then the information of the colouring of the root vanishes as the height of the tree grows and it does not affect the distribution of the colourings of the leaves.
Revised:  It is well known that d/ \ln d poses a threshold , in the sense that 1 ) if k >\eps d/ \ln d, then the information of the colouring of the root has a vanishing effect on the distribution of the colourings of the leaves.
Edit intent: clarity
Original:  2) if k<\eps d/ \ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  2) if k<\eps) d/ \ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: fluency
Original:  2) if k<\eps d/ \ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  2) if k<\eps d/ ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: fluency
Original:  2) if k<\eps d/ \ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  2) if k<\eps d/ \ln d, then the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: clarity
Original:  2) if k<\eps d/ \ln d, then the information of the colouring of the root affects the distribution of the colouring of the leaves regardless of the height of the tree.
Revised:  2) if k<\eps d/ \ln d, then the information of the colouring of the root biases the distribution of the colouring of the leaves regardless of the height of the tree.
Edit intent: clarity
Original:  Despite this threshold, there is no apparent combinatorial reason why such a result should be true.
Revised:  There is no apparent combinatorial reason why such a result should be true.
Edit intent: clarity
Original:  Searching for an explanation, we note that the above implies that for k>\eps d/ \ln dand two broadcasting processes that assign the root different colours the following holds: There is a coupling such that the probability of having vertices which take different colour assignments in the two processes reduces as we move away from the root.
Revised:  Searching for an explanation, we note that the above implies that for k>\eps d/ \ln dand two broadcasting processes that assign the root different colours such that the probability of having vertices which take different colour assignments in the two processes reduces as we move away from the root.
Edit intent: clarity
Original:  Devising one calls for understanding a complex combinatorial problem and it is a  non-trivial task to achieve for any k < d. In this work we provide a coupling which has the aforementioned properties for k> 2d / \ln d(much below d).
Revised:  Devising one calls for understanding a complex combinatorial problem and it is a non-trivial task to accomplish for any k < d. In this work we provide a coupling which has the aforementioned properties for k> 2d / \ln d(much below d).
Edit intent: clarity
Original:  Devising one calls for understanding a complex combinatorial problem and it is a  non-trivial task to achieve for any k < d. In this work we provide a coupling which has the aforementioned properties for k> 2d / \ln d(much below d).
Revised:  Devising one calls for understanding a complex combinatorial problem and it is a non-trivial task to achieve for any k < d. In this work we obtain a coupling which has the aforementioned properties for k> 2d / \ln d(much below d).
Edit intent: clarity
Original:  Devising one calls for understanding a complex combinatorial problem and it is a  non-trivial task to achieve for any k < d. In this work we provide a coupling which has the aforementioned properties for k> 2d / \ln d(much below d).
Revised:  Devising one calls for understanding a complex combinatorial problem and it is a non-trivial task to achieve for any k < d. In this work we provide a coupling which has the aforementioned property for any k> 2d / \ln d(much below d).
Edit intent: fluency