wanyu/IteraTeR_v2 huggingface dataset:
Original:  We consider the approximate counting problem for Boolean CSPs with bounded-degree instances  for constraint languages containing the two unary constant relations {0} and {1}.
Revised:  We consider the approximate counting problem for Boolean CSPs with bounded-degree instances , for constraint languages containing the two unary constant relations {0} and {1}.
Edit intent: fluency
Original:  For lower degree bounds, additional cases arise in which the complexity is related to the complexity of approximately counting independent sets in hypergraphs.
Revised:  For lower degree bounds, additional cases arise , where the complexity is related to the complexity of approximately counting independent sets in hypergraphs.
Edit intent: fluency
Original:  Alignment spike metrics work by identifying ``equivalent'' spikes in one train and the other.
Revised:  Alignment spike metrics work by identifying "equivalent" spikes in one train and the other.
Edit intent: fluency
Original: Motivated by questions in nanotechnology, biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata.
Revised: Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata.
Edit intent: clarity
Original:  We devise a mathematical algorithm to recover the time-dependent transmission rate from epidemiological data.
Revised:  We derive an algorithm to recover the time-dependent transmission rate from epidemiological data.
Edit intent: clarity
Original:  We apply our algorithm to historic UK measles data and observe that for most cities the main spectral peak of the transmission rate has a two-year period.
Revised:  We apply our algorithm to historic UK measles data and discover that the two dominant spectral peaks of the transmission rate has a two-year period.
Edit intent: clarity
Original:  Our construction also illustrates the danger of overfitting an epidemic transmission modelwith a variable transmission rate function .
Revised:  Our construction also illustrates the danger of overfitting an SIR transmission model .
Edit intent: clarity
Original:  We derive an algorithm to recover the time-dependent transmission rate directly from infection data .
Revised:  We present an algorithm to recover the time-dependent transmission rate directly from infection data .
Edit intent: clarity
Original:  Conclusions/Significance: The main objective of this work is to provide a new algorithm to recover the transmission rate function from collectable infection data.
Revised:  Conclusions/Significance: The main objective of this work is to provide a new algorithm to recover the transmission rate function directly from infection data.
Edit intent: clarity
Original:  This clearly illustrates the danger of overfitting an SIR transmission model  .
Revised:  This clearly illustrates a serious danger of overfitting an SIR transmission model .
Edit intent: clarity
Original: Background: The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain.
Revised:  The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain.
Edit intent: coherence
Original:  The transmission rate has been thought impossible to measure directly.
Revised:  The transmission rate has been thought difficult to measure directly.
Edit intent: clarity
Original:  We present an algorithm to recover the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptibles , vital rates, etc.
Revised:  We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptibles , vital rates, etc.
Edit intent: clarity
Original:  Our algorithm also yields that almost any infection profile can be perfectly fitted by an SIR-type model with variable transmissibility .
Revised:  Our algorithm also yields that almost any infection profile can be perfectly fitted by an SIR model with variable transmissibility .
Edit intent: clarity
Original:  Our algorithm also yields that almost any infection profile can be perfectly fitted by an SIR-type model with variable transmissibility .
Revised:  Our algorithm also yields that almost any infection profile can be perfectly fitted by an SIR-type model with variable transmission rate .
Edit intent: clarity
Original:  This clearly illustrates a serious danger of overfitting an SIR transmission model with time-dependent transmission rate .
Revised:  This clearly shows a serious danger of overfitting an SIR transmission model with time-dependent transmission rate .
Edit intent: clarity
Original: We consider the noise complexity of differentially private mechanism in the setting where the user asks d linear queries f\colon \Re ^n\to \Re non-adaptively.
Revised: We consider the noise complexity of differentially private mechanisms in the setting where the user asks d linear queries f\colon \Re ^n\to \Re non-adaptively.
Edit intent: fluency
Original:  We show that the noise complexity is completely determined by two geometric parameters associated with the set of queries.
Revised:  We show that the noise complexity is determined by two geometric parameters associated with the set of queries.
Edit intent: clarity
Original:  We can achieve the same upper bound for non-random queries as well, assuming the truth of a deep conjecture from convex geometry, known as the Hyperplane conjecture  .
Revised:  Assuming the truth of a deep conjecture from convex geometry, known as the Hyperplane conjecture .
Edit intent: clarity
Original:  In contrast, our lower bound is strong enough to separate the notion of differential privacy from the weaker notion of approximate differential privacy where an upper bound of O(\sqrt{d}/\epsilon) can be achieved.
Revised:  In contrast, our lower bound is strong enough to separate the concept of differential privacy from the weaker notion of approximate differential privacy where an upper bound of O(\sqrt{d}/\epsilon) can be achieved.
Edit intent: fluency
Original:  In contrast, our lower bound is strong enough to separate the notion of differential privacy from the weaker notion of approximate differential privacy where an upper bound of O(\sqrt{d}/\epsilon) can be achieved.
Revised:  In contrast, our lower bound is strong enough to separate the notion of differential privacy from the notion of approximate differential privacy where an upper bound of O(\sqrt{d}/\epsilon) can be achieved.
Edit intent: clarity
Original: We consider the noise complexity of differentially private mechanisms in the setting where the user asks d linear queries f\colon \mathbb{R \Rn \to \mathbb{R non-adaptively.
Revised: We consider the noise complexity of differentially private mechanisms in the setting where the user asks d linear queries f\colon \Rn \to \mathbb{R non-adaptively.
Edit intent: fluency
Original: We consider the noise complexity of differentially private mechanisms in the setting where the user asks d linear queries f\colon \mathbb{R \Rn \to \mathbb{R non-adaptively.
Revised: We consider the noise complexity of differentially private mechanisms in the setting where the user asks d linear queries f\colon \mathbb{R \Rn \to \Re non-adaptively.
Edit intent: fluency
Original:  Here, the database is represented by a vector in \mathbb{R \Rn and proximity between databases is measured in the \ell_1-metric.
Revised:  Here, the database is represented by a vector in \Rn and proximity between databases is measured in the \ell_1-metric.
Edit intent: coherence
Original:  Our bound translates to error O(\min\{d/\epsilon, \sqrt{d\log (n/d) /\epsilon\}) per answer.
Revised:  Our bound translates to error O(\min\{d/\epsilon, \sqrt{d\log(n/d) /\epsilon\}) per answer.
Edit intent: fluency
Original:  The best previous upper bound (Laplacian mechanism) gives a bound of O(\min ( d/\eps ) ,n/\epsilon  ) per answer, while the best known lower bound was \Omega(d/\epsilon).
Revised:  The best previous upper bound (Laplacian mechanism) gives a bound of O(\min ( d/\eps ,n/\epsilon ) per answer, while the best known lower bound was \Omega(d/\epsilon).
Edit intent: fluency
Original:  The best previous upper bound (Laplacian mechanism) gives a bound of O(\min ( d/\eps ) ,n/\epsilon  ) per answer, while the best known lower bound was \Omega(d/\epsilon).
Revised:  The best previous upper bound (Laplacian mechanism) gives a bound of O(\min ( d/\eps ) ,n/\epsilon \ ) per answer, while the best known lower bound was \Omega(d/\epsilon).
Edit intent: fluency
Original: Diffusive processes describe a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks.
Revised: Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks.
Edit intent: clarity
Original:  The analysis of the simple random walk process reveals a strong departure of its behavior in quenched real scale-free networks from the mean-field predictions.
Revised:  The analysis of the simple random walk process , pointing out a strong departure of its behavior in quenched real scale-free networks from the mean-field predictions.
Edit intent: clarity
Original:  The analysis of the simple random walk process reveals a strong departure of its behavior in quenched real scale-free networks from the mean-field predictions.
Revised:  The analysis of the simple random walk process reveals a strong departure of the behavior observed in quenched real scale-free networks from the mean-field predictions.
Edit intent: clarity
Original:   Our work sheds light on mean-field theory on weighted networks and on its range of validity, warning about the reliability of mean-field results for more complex dynamics.
Revised:  Our work sheds light on mean-field theory on weighted networks and on its range of validity, and warns about the reliability of mean-field results for more complex dynamics.
Edit intent: coherence
Original:   Our work sheds light on mean-field theory on weighted networks and on its range of validity, warning about the reliability of mean-field results for more complex dynamics.
Revised:  Our work sheds light on mean-field theory on weighted networks and on its range of validity, warning about the reliability of mean-field results for complex dynamics.
Edit intent: clarity
Original: We present a mean-field dynamical theory for  semiflexible polymers which can precisely capture, without fitting parameters, recent fluorescence correlation spectroscopy results on single monomer kinetics of DNA strands in solution.
Revised: We present a mean-field dynamical theory for single semiflexible polymers which can precisely capture, without fitting parameters, recent fluorescence correlation spectroscopy results on single monomer kinetics of DNA strands in solution.
Edit intent: fluency
Original: Methods for specifying Moore type state machines (transducers) abstractly via primitive recursive functions and for definining parallel composition via simultaneous primitive recursion are discussed.
Revised: Methods for specifying Moore type state machines (transducers) abstractly via primitive recursive functions and for defining parallel composition via simultaneous primitive recursion are discussed.
Edit intent: fluency
Original:  The  semigroup is completely described whenever r=2 or r=3.
Revised:  The semigroup is completely described for r=2 or r=3.
Edit intent: clarity
Original:  The  semigroup is completely described whenever r=2 or r=3.
Revised:  The semigroup is completely described whenever r=2 and r=3.
Edit intent: fluency
Original: This thesis presents a two-layer uniform facet elastic ob ject for real-time simulation based on physics modeling method.
Revised: This thesis presents a two-layer uniform facet elastic object for real-time simulation based on physics modeling method.
Edit intent: fluency
Original:  It describes the elastic ob ject procedural modeling algorithm with particle system from the simplest one-dimensional object, to more complex two-dimensional and three-dimensional ob jects .
Revised:  It describes the elastic object procedural modeling algorithm with particle system from the simplest one-dimensional object, to more complex two-dimensional and three-dimensional ob jects .
Edit intent: fluency
Original:  It describes the elastic ob ject procedural modeling algorithm with particle system from the simplest one-dimensional object, to more complex two-dimensional and three-dimensional ob jects .
Revised:  It describes the elastic ob ject procedural modeling algorithm with particle system from the simplest one-dimensional object, to more complex two-dimensional and three-dimensional objects .
Edit intent: fluency
Original:  The construction of the double-layered elastic ob ject is closer to the real tissue's physical structure.
Revised:  The construction of the double-layered elastic object is closer to the real tissue's physical structure.
Edit intent: fluency
Original:  The inertial behavior of the elastic ob ject is well illustrated in environments with gravity and collisions with walls, ceiling, and floor.
Revised:  The inertial behavior of the elastic object is well illustrated in environments with gravity and collisions with walls, ceiling, and floor.
Edit intent: fluency
Original:  Users can interact with the modeled ob jects , deform them, and observe the response to their action in real time.
Revised:  Users can interact with the modeled objects , deform them, and observe the response to their action in real time.
Edit intent: fluency
Original: To determine if two given lists of numbers are the same set, we would sort both lists and see if we get the same result.
Revised: To determine if two lists of numbers are the same set, we would sort both lists and see if we get the same result.
Edit intent: clarity
Original: To determine if two given lists of numbers are the same set, we would sort both lists and see if we get the same result.
Revised: To determine if two given lists of numbers are the same set, we sort both lists and see if we get the same result.
Edit intent: clarity
Original:  Other canonical forms for equivalences arise in graph isomorphism and its variants , and the equality of permutation groups given by generators.
Revised:  Other canonical forms arise in graph isomorphism and its variants , and the equality of permutation groups given by generators.
Edit intent: clarity
Original:  Other canonical forms for equivalences arise in graph isomorphism and its variants , and the equality of permutation groups given by generators.
Revised:  Other canonical forms for equivalences arise in graph isomorphism algorithms , and the equality of permutation groups given by generators.
Edit intent: clarity
Original:  To determine if two given graphs are cospectral (have the same eigenvalues), however, we compute their characteristic polynomials and see if they are the same;
Revised:  To determine if two graphs are cospectral (have the same eigenvalues), however, we compute their characteristic polynomials and see if they are the same;
Edit intent: clarity
Original:  Specifically, we assume that for a fraction \rho of the nodes the true cluster assignments are known in advance.
Revised:  Specifically, we assume that for a fraction \rho of the nodes their true cluster assignments are known in advance.
Edit intent: clarity
Original:  For weighted graphs we show that a small semi--supervising can be used for a non--trivial definition of communities.
Revised:  For weighted graphs we show that a small semi--supervising can be used for a non-trivial definition of communities.
Edit intent: fluency
Original:  In this situation, when a node has a packet to forward to the sink, there is a trade-off between how long this node waits for a suitable neighbor to wake up and the progress the packet makes towards the sink once it is forwarded to this neighbour .
Revised:  In this situation, when a node has a packet to forward to the sink, there is a trade-off between how long this node waits for a suitable neighbor to wake up and the progress the packet makes towards the sink once it is forwarded to this neighbr .
Edit intent: fluency
Original:  Universality is detected in the local level statistics of noise-dressed eigenmodes, implying a novel quantitative criterion to single out the collective degrees of freedom of the protein from the majority of high-energy, localized vibrations.
Revised:  Bulk universality is detected in the local level statistics of noise-dressed eigenmodes, implying a novel quantitative criterion to single out the collective degrees of freedom of the protein from the majority of high-energy, localized vibrations.
Edit intent: clarity
Original:  For a set V of variables and set \mathcal C of constraints `` v_i {is between} v_j {and} v_k '' , decide whether there is a bijection from V to the set \{1, %DIFDELCMD < \hdots%%%  ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Revised:  For a set V of variables and set \mathcal C of constraints " v_i {is between} v_j {and} v_k '' , decide whether there is a bijection from V to the set \{1, %DIFDELCMD < \hdots%%% ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Edit intent: fluency
Original:  For a set V of variables and set \mathcal C of constraints `` v_i {is between} v_j {and} v_k '' , decide whether there is a bijection from V to the set \{1, %DIFDELCMD < \hdots%%%  ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Revised:  For a set V of variables and set \mathcal C of constraints `` v_i {is between} v_j {and} v_k " , decide whether there is a bijection from V to the set \{1, %DIFDELCMD < \hdots%%% ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Edit intent: fluency
Original:  For a set V of variables and set \mathcal C of constraints `` v_i {is between} v_j {and} v_k '' , decide whether there is a bijection from V to the set \{1, %DIFDELCMD < \hdots%%%  ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Revised:  For a set V of variables and set \mathcal C of constraints `` v_i {is between} v_j {and} v_k '' , decide whether there is a bijection from V to the set \{1, %DIFDELCMD < \hdots%%% ... ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Edit intent: fluency
Original:  Our result solves an open problem attributed to Benny Chor in Niedermeier's monograph `` Invitation to Fixed-Parameter Algorithms .''
Revised:  Our result solves an open problem attributed to Benny Chor in Niedermeier's monograph " Invitation to Fixed-Parameter Algorithms .''
Edit intent: fluency
Original:  We prove the existence of a quadratic kernel for the {\sc Betweenness} problem parameterized above  tight lower bound, which is stated as follows.
Revised:  We prove the existence of a quadratic kernel for the {\sc Betweenness} problem parameterized above its tight lower bound, which is stated as follows.
Edit intent: clarity
Original:  For a set V of variables and set \mathcal C of constraints "v_i is between v_j%DIFDELCMD < {%%% and v_k", decide whether there is a bijection from V to the set \{1, ... ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Revised:  For a set V of variables and set \mathcal C of constraints "v_i v_j%DIFDELCMD < {%%% and v_k", decide whether there is a bijection from V to the set \{1, ... ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Edit intent: clarity
Original:  For a set V of variables and set \mathcal C of constraints "v_i is between v_j%DIFDELCMD < {%%% and v_k", decide whether there is a bijection from V to the set \{1, ... ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Revised:  For a set V of variables and set \mathcal C of constraints "v_i is between %DIFDELCMD < {%%% and v_k", decide whether there is a bijection from V to the set \{1, ... ,|V|\} satisfying at least |\mathcal C|/3 + \kappa of the constraints in \mathcal C.
Edit intent: clarity
Original:  Our result solves an open problem attributed to Benny Chor in Niedermeier's monograph "Invitation to Fixed-Parameter Algorithms  "  . An approach developed in this paper can be used to determine parameterized complexity of a number of other optimization problems on permutations parameterized above or below tight bounds.
Revised:  Our result solves an open problem attributed to Benny Chor in Niedermeier's monograph "Invitation to Fixed-Parameter Algorithms . " . An approach developed in this paper can be used to determine parameterized complexity of a number of other optimization problems on permutations parameterized above or below tight bounds.
Edit intent: fluency
Original: A powerful embedding theorem in the context of dimension reduction is the \ell_2 flattening lemma of Johnson and Lindenstrauss   .
Revised: The l2 flattening lemma of Johnson and Lindenstrauss .
Edit intent: clarity
Original:  It has been conjectured that improved dimension bounds may be achievable for some data sets by bounding the target dimension  in terms of the intrinsic dimensionality of the data set (for example, the doubling dimension).
Revised:  It has been conjectured that the target dimension in terms of the intrinsic dimensionality of the data set (for example, the doubling dimension).
Edit intent: clarity
Original:  One such problem was proposed by Lang and Plaut  [ ,   and is still open.
Revised:  One such problem was proposed by Lang and Plaut [ , ), and is still open.
Edit intent: fluency
Original:  We pose another question in this line of work: Does the snowflake metric d^{1/2} of a doubling set S \subset \ell_2 always embed with distortion O(1) into \ell_2^D , for dimension D that depends solely on the doubling constant of the metric ?
Revised:  We prove another result in this line of work: Does the snowflake metric d^{1/2} of a doubling set S \subset \ell_2 always embed with distortion O(1) into \ell_2^D , for dimension D that depends solely on the doubling constant of the metric ?
Edit intent: clarity
Original:  We pose another question in this line of work: Does the snowflake metric d^{1/2} of a doubling set S \subset \ell_2 always embed with distortion O(1) into \ell_2^D , for dimension D that depends solely on the doubling constant of the metric ?
Revised:  We pose another question in this line of work: The snowflake metric d^{1/2} of a doubling set S \subset \ell_2 always embed with distortion O(1) into \ell_2^D , for dimension D that depends solely on the doubling constant of the metric ?
Edit intent: clarity
Original:  Moreover, our techniques are sufficiently robust to be applicable also to the more difficult spaces \ell_1 and \ell_\infty, although these extensions achieve dimension bounds that are quantitatively inferior than those for \ell_2 .
Revised:  Moreover, our techniques are sufficiently robust to be applicable also to the more difficult spaces \ell_1 and \ell_\infty, although these extensions achieve dimension bounds that are quantitatively inferior than those for l2 .
Edit intent: clarity
Original: The l2 flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction.
Revised: The l_2 flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction.
Edit intent: fluency
Original:  We prove another result in this line of work: The snowflake metric d^{1/2} of a doubling set S \subset l2 can be embedded with arbitrarily low distortion into l ^D2 , for dimension D that depends solely on the doubling constant of the metric.
Revised:  We prove another result in this line of work: The snowflake metric d^{1/2} of a doubling set S \subset l_2 embeds with constant distortion into l ^D2 , for dimension D that depends solely on the doubling constant of the metric.
Edit intent: clarity