wanyu/IteraTeR_v2 huggingface dataset:
Original:  a generalization and proof, in the context of the theory of branching processes, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct regimes :
Revised:  a generalization and proof, in the context of the theory of branching processes, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", 18 (2007) 2930--2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct regimes :
Edit intent: clarity
Original:  a generalization and proof, in the context of the theory of branching processes, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct regimes :
Revised:  a generalization and proof, in the context of the theory of branching processes, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct "stages" :
Edit intent: clarity
Original:  Math. Biol. 46 (1985) 239--262 ), in their study of polynucleotide evolution.
Revised:  Math. Biol. 46 (1985) 239-262 ), in their study of polynucleotide evolution.
Edit intent: fluency
Original:  a generalization and proof, in the context of the theory of branching processes , of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939 ), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in  four distinct "stages":
Revised:  a generalization and proof, for this particular class of models , of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939 ), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct "stages":
Edit intent: clarity
Original:  a generalization and proof, in the context of the theory of branching processes , of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939 ), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in  four distinct "stages":
Revised:  a generalization and proof, in the context of the theory of branching processes , of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939 ), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct "stages":
Edit intent: fluency
Original:  a generalization and proof, in the context of the theory of branching processes , of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939 ), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in  four distinct "stages":
Revised:  a generalization and proof, in the context of the theory of branching processes , of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930--2939 ), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in in four distinct "stages":
Edit intent: fluency
Original:  transient, " stationary "equilibrium , extinction threshold and lethal mutagenesis .
Revised:  extinction threshold, lethal mutagenesis, stationary "equilibrium , extinction threshold and lethal mutagenesis .
Edit intent: fluency
Original:  transient, " stationary "equilibrium , extinction threshold and lethal mutagenesis .
Revised:  transient, " stationary "equilibrium " and transient .
Edit intent: clarity
Original:  We compute the diffusion coefficient for bipedal spiders with an upper limit on the distance between the legs .
Revised:  We study the diffusion coefficient for bipedal spiders with an upper limit on the distance between the legs .
Edit intent: clarity
Original:  In experimental realizations legs usually convert substrates into the products (shorter segments ).
Revised:  In experimental realizations legs usually convert substrates into products (visited sites ).
Edit intent: clarity
Original:  The binding of legs to products is weaker, so the hopping rate from the substrates is slower .
Revised:  The binding of legs to products is weaker, so the hopping rate from the substrates is smaller .
Edit intent: clarity
Original:  We demonstrate the emergence of a very counter-intuitive behavior : the more spiders are slowed down on unvisited sites, the more motile they become.
Revised:  We demonstrate the emergence of a counter-intuitive behavior : the more spiders are slowed down on unvisited sites, the more motile they become.
Edit intent: clarity
Original:  We demonstrate the emergence of a very counter-intuitive behavior : the more spiders are slowed down on unvisited sites, the more motile they become.
Revised:  We demonstrate the emergence of a very counter-intuitive behavior - the more spiders are slowed down on unvisited sites, the more motile they become.
Edit intent: fluency
Original:  The tractability criterion can be intuitively stated as follows: the set F is tractable if (1) every function in F has arity at most 2 , or (2) F is transformable to an affine type, or (3) F is transformable to a product type, or (4) F is vanishing, combined with the right type of binary functions, or (5) F belongs to a special category of vanishing type Fibonacci gates.
Revised:  The tractability criterion can be intuitively stated as follows: A set F is tractable if (1) every function in F has arity at most 2 , or (2) F is transformable to an affine type, or (3) F is transformable to a product type, or (4) F is vanishing, combined with the right type of binary functions, or (5) F belongs to a special category of vanishing type Fibonacci gates.
Edit intent: fluency
Original:  The tractability criterion can be intuitively stated as follows: the set F is tractable if (1) every function in F has arity at most 2 , or (2) F is transformable to an affine type, or (3) F is transformable to a product type, or (4) F is vanishing, combined with the right type of binary functions, or (5) F belongs to a special category of vanishing type Fibonacci gates.
Revised:  The tractability criterion can be intuitively stated as follows: the set F is tractable if (1) every function in F has arity at most two , or (2) F is transformable to an affine type, or (3) F is transformable to a product type, or (4) F is vanishing, combined with the right type of binary functions, or (5) F belongs to a special category of vanishing type Fibonacci gates.
Edit intent: fluency
Original:  In this paper, we focus on k-mean clustering , and investigate its hardness and approximation solutions.
Revised:  In this paper, we focus on k-mean clustering , and investigate their hardness and approximation solutions.
Edit intent: fluency
Original:  The additional coloring requirement destroys some key properties used in existing k-mean clustering techniques (for the ordinary clustering problem ), and significantly complicates the problem.
Revised:  The additional coloring requirement destroys some key properties used in existing k-means techniques (for the ordinary clustering problem ), and significantly complicates the problem.
Edit intent: fluency
Original:  The additional coloring requirement destroys some key properties used in existing k-mean clustering techniques (for the ordinary clustering problem ), and significantly complicates the problem.
Revised:  The additional coloring requirement destroys some key properties used in existing k-mean clustering techniques (for ordinary points ), and significantly complicates the problem.
Edit intent: clarity
Original:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Revised:  %DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Edit intent: clarity
Original:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Revised:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Edit intent: clarity
Original:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Revised:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Edit intent: fluency
Original:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Revised:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, projective clustering is to find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Edit intent: clarity
Original:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Revised:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats so that the average distance (or squared distance) from points in P \setminus Q to their closest j-flats is minimized.
Edit intent: clarity
Original:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Revised:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P to their closest j-flats is minimized.
Edit intent: clarity
Original:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest j-flats is minimized.
Revised:  In this paper, we consider a new variant of the problem, called%DIFDELCMD < {\em %%% Robust Projective Clustering (RPC) : Given a set P of n points in R ^{d} space, two integers 2\leq k \leq n and 1 \leq j \leq d-1, and a small constant 0\leq \delta <1, find a set of k j-flats and a subset Q of P with cardinality no more than \delta n such that the total (or average) squared distancefrom all points in P \setminus Q to their closest flats is minimized.
Edit intent: fluency
Original:  For RPC, we first introduce a new geometric structure named%DIFDELCMD < {\em %%% shape kernel for a point set.
Revised:  %DIFDELCMD < {\em %%% shape kernel for a point set.
Edit intent: coherence
Original:  For RPC, we first introduce a new geometric structure named%DIFDELCMD < {\em %%% shape kernel for a point set.
Revised:  For RPC, we first introduce a new geometric structure named%DIFDELCMD < {\em %%% for a point set.
Edit intent: clarity
Original: We show that the depth of quantum circuits in a realistic architecture where a classical controller determines which local interactions to apply on the (k)D grid (%DIFDELCMD < \bbZ%%% ^k ) where ( k \geq 2 ) is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed.
Revised: We show that the depth of quantum circuits in a realistic architecture where a classical controller determines which local interactions to apply on the %DIFDELCMD < \bbZ%%% ^k ) where ( k \geq 2 ) is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed.
Edit intent: clarity
Original: We show that the depth of quantum circuits in a realistic architecture where a classical controller determines which local interactions to apply on the (k)D grid (%DIFDELCMD < \bbZ%%% ^k ) where ( k \geq 2 ) is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed.
Revised: We show that the depth of quantum circuits in a realistic architecture where a classical controller determines which local interactions to apply on the (k)D grid (%DIFDELCMD < \bbZ%%% ^k ) where ( k \geq 2 is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed.
Edit intent: fluency
Original:  We also present optimal non-adaptive quantum circuits for controlled operations and fan-outs on a (k)D grid.
Revised:  We also present optimal non-adaptive quantum circuits for controlled operations and fan-outs on a kD grid.
Edit intent: fluency
Original:  These circuits have depth ( \Theta(\sqrt[k]{n}) ), size ( \Theta(n) ) and width ( \Theta(n ) ).
Revised:  These circuits have depth \Theta(\sqrt[k]{n}) ), size ( \Theta(n) ) and width ( \Theta(n ) ).
Edit intent: fluency
Original:  These circuits have depth ( \Theta(\sqrt[k]{n}) ), size ( \Theta(n) ) and width ( \Theta(n ) ).
Revised:  These circuits have depth ( \Theta(\sqrt[k]{n}) , size \Theta(n) ) and width ( \Theta(n ) ).
Edit intent: fluency
Original:  These circuits have depth ( \Theta(\sqrt[k]{n}) ), size ( \Theta(n) ) and width ( \Theta(n ) ).
Revised:  These circuits have depth ( \Theta(\sqrt[k]{n}) ), size ( \Theta(n) and width \Theta(n ) ).
Edit intent: fluency
Original:  These circuits have depth ( \Theta(\sqrt[k]{n}) ), size ( \Theta(n) ) and width ( \Theta(n ) ).
Revised:  These circuits have depth ( \Theta(\sqrt[k]{n}) ), size ( \Theta(n) ) and width ( \Theta(n ).
Edit intent: fluency
Original: We show that the depth of quantum circuits in a realistic architecture where a classical controller determines which local interactions to apply on the kD grid \mathbb{Z ^k where k \geq 2 is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed.
Revised: We show that the depth of quantum circuits in the realistic architecture where a classical controller determines which local interactions to apply on the kD grid \mathbb{Z ^k where k \geq 2 is the same (up to a constant factor) as in the standard model where arbitrary interactions are allowed.
Edit intent: fluency
Original:  Our work therefore justifies the standard assumption that quantum algorithms can perform interactions between arbitrary pairs of qubits.
Revised:  Our work therefore justifies the standard assumption that interactions can be performed between arbitrary pairs of qubits.
Edit intent: clarity
Original:  In particular, our results imply that Shor's algorithm, controlled operations and fan-outs can be implemented in constant depth, polynomial size and polynomial width in this architecture.
Revised:  In particular, our results imply that Shor's algorithm, controlled operations and fanouts can be implemented in constant depth, polynomial size and polynomial width in this architecture.
Edit intent: fluency
Original:  We also present optimal non-adaptive quantum circuits for controlled operations and fan-outs on a kD grid.
Revised:  We also present optimal non-adaptive quantum circuits for controlled operations and fanouts on a kD grid.
Edit intent: fluency
Original:  These circuits have depth \Theta(\sqrt[k n%DIFDELCMD < }%%% ), size \Theta (n) and width \Theta (n).
Revised:  These circuits have depth \Theta(\sqrt[k %DIFDELCMD < }%%% ), size \Theta (n) and width \Theta (n).
Edit intent: clarity
Original:  These circuits have depth \Theta(\sqrt[k n%DIFDELCMD < }%%% ), size \Theta (n) and width \Theta (n).
Revised:  These circuits have depth \Theta(\sqrt[k n%DIFDELCMD < }%%% ), size \Theta (n) and width Theta (n).
Edit intent: fluency
Original:  Our lower bound is for a general class of operations which includes controlled operations and fan-outs as special cases .
Revised:  Our lower bound also applies to a more general class of operations which includes controlled operations and fan-outs as special cases .
Edit intent: clarity
Original:  Our lower bound is for a general class of operations which includes controlled operations and fan-outs as special cases .
Revised:  Our lower bound is for a general class of operations .
Edit intent: clarity
Original:  Dolphin whistles share various statistical properties with human words, i.e. Zipf's law for word frequencies (namely that the probability of the i-th most frequent word of a text is about i^{-\alpha}) and a parallel of the tendency of more frequent words to have more meanings.
Revised:  Dolphin whistles share various statistical properties with human words, i.e. Zipf's law for word frequencies (namely that the probability of the ith most frequent word of a text is about i^{-\alpha}) and a parallel of the tendency of more frequent words to have more meanings.
Edit intent: fluency
Original:  In this paper, we introduce  additional features into the model and consider two specific cases.
Revised:  In this paper, we introduce some additional features into the model and consider two specific cases.
Edit intent: clarity
Original: MicroRNA-mediated regulation of gene expression is characterised by some distinctive features which set it apart from unregulated and transcription factor-regulated gene expression.
Revised: MicroRNA-mediated regulation of gene expression is characterised by some distinctive features that set it apart from unregulated and transcription factor-regulated gene expression.
Edit intent: fluency
Original:  The model explains quite well the observations made in single cell experiments  .
Revised:  The model explains the observations made in single cell experiments .
Edit intent: clarity
Original:  In the first case we show that bistability is possible in a parameter regime  due to the presence of a non-linear protein decay term in the gene expression dynamics.
Revised:  In the first case we show that bistability is possible in a parameter regime , due to the presence of a non-linear protein decay term in the gene expression dynamics.
Edit intent: fluency
Original:  The theoretical predictions on binary gene expression are experimentally testable.
Revised:  The theoretical predictions relating to binary gene expression are experimentally testable.
Edit intent: clarity
Original:  While specific forms of social coordination can be seen in tools such as Evite, Meetup and Groupon, we introduce a more general model using what we call %DIFDELCMD < {\em %%% enmeshed queries .
Revised:  While specific forms of social coordination can be seen in tools such as Evite, Meetup and Groupon, we introduce a more general model using what we call %DIFDELCMD < {\em %%% enmeshed queries .
Edit intent: fluency
Original:  The n^(log n) barrier for group isomorphism has withstood all attacks - even for the special cases of p-groups and nilpotent groups - ever since Tarjan's n^(log n + O(1))  algorithm.
Revised:  The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the special cases of p-groups and nilpotent groups - ever since Tarjan's n^(log n + O(1)) algorithm.
Edit intent: fluency