wanyu/IteraTeR_v2 huggingface dataset:
Original:  We introduce a class of sequences  simple constructible sheaves, that could be seen as the sheaf-theoretic analog of the Blum-Shub-Smale class P_{R}.
Revised:  We introduce a class of sequences of simple constructible sheaves, that could be seen as the sheaf-theoretic analog of the Blum-Shub-Smale class P_{R}.
Edit intent: fluency
Original:  We also define a hierarchy of complexity classes of sheaves mirroring the polynomial hierarchy, PH_{R}  in the B-S-S theory.
Revised:  We also define a hierarchy of complexity classes of sheaves mirroring the polynomial hierarchy, PH_{R} , in the B-S-S theory.
Edit intent: fluency
Original:  Finally, we pose the natural sheaf-theoretic analogs of the classical \mathbf{P} vs  \mathbf{NP} question, and also discuss a connection with Toda's theorem from discrete complexity theory in the context of constructible sheaves  .
Revised:  We pose the natural sheaf-theoretic analogs of the classical \mathbf{P} vs \mathbf{NP} question, and also discuss a connection with Toda's theorem from discrete complexity theory in the context of constructible sheaves .
Edit intent: coherence
Original:  Finally, we pose the natural sheaf-theoretic analogs of the classical \mathbf{P} vs  \mathbf{NP} question, and also discuss a connection with Toda's theorem from discrete complexity theory in the context of constructible sheaves  .
Revised:  Finally, we pose the natural sheaf-theoretic analogs of the classical \mathbf{P} vs . \mathbf{NP} question, and also discuss a connection with Toda's theorem from discrete complexity theory in the context of constructible sheaves .
Edit intent: fluency
Original:  Because gene regulatory networks (GRN) govern phenotypic adaptations , they reflect the trade-offs between these different forces .
Revised:  Because gene regulatory networks (GRN) govern phenotypic adaptations and reflect the trade-offs between these different forces .
Edit intent: coherence
Original:  We examined the responses of 32,423 expressed sequences to drought and to the hormone abscisic acid and selected 145 co-expressed transcripts.
Revised:  We examined the responses of 32,423 expressed sequences to drought and to abscisic acid and selected 145 co-expressed transcripts.
Edit intent: clarity
Original:  From this, we inferred a GRN by meta-analyses of a Gaussian Graphical model and a Random Forest algorithm and studied the genetic diversity of its nodes.
Revised:  From this, we inferred a GRN by meta-analyses of a Gaussian graphical model and a Random Forest algorithm and studied the genetic diversity of its nodes.
Edit intent: fluency
Original:  From this, we inferred a GRN by meta-analyses of a Gaussian Graphical model and a Random Forest algorithm and studied the genetic diversity of its nodes.
Revised:  From this, we inferred a GRN by meta-analyses of a Gaussian Graphical model and a random forest algorithm and studied the genetic diversity of its nodes.
Edit intent: fluency
Original:  This suggests that this function is key in sunflower physiological response to drought.
Revised:  This suggests that nitrate transport is a critical aspect of sunflower physiological response to drought.
Edit intent: clarity
Original:  Among Helianthus populations, we observed that more highly connected nodes in the GRN had lower genetic diversity .
Revised:  We observed that differentiation of the network genes in elite sunflower cultivars is correlated with their position and connectivity .
Edit intent: clarity
Original:  At the evolutionary level, we propose that network topology constrained adaptation to dry environment and thus speciation .
Revised:  At the evolutionary level, we propose that network topology constrained adaptation to dry environments .
Edit intent: clarity
Original:  This model is  motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible.
Revised:  This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible.
Edit intent: clarity
Original:  We show tight bounds for a number of problems, specifically Theta((n/p)^{2/3}) p-parallel queries for element distinctness and Theta((n/p)^{k/(k+1)} for k-SUM . Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs.
Revised:  We show tight bounds for a number of problems, specifically Theta((n/p)^{2/3}) p-parallel queries for element distinctness and Theta((n/p)^{k/(k+1)} for k-sum . Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs.
Edit intent: clarity
Original:  Given street maps of the same city collected from different sources, researchers often need to know how  they differ.
Revised:  Given street maps of the same city collected from different sources, researchers often need to know how and where they differ.
Edit intent: clarity
Original:   Likewise, many current street map comparison algorithms focus on the spatial embeddings only but do not take structural properties into account  .
Revised:  Likewise, many current street map comparison algorithms focus on the spatial embeddings only and do not take structural properties into account .
Edit intent: fluency
Original:  We propose a new path-based distance measure to compare two planar geometric graphs that are embedded in the same plane.
Revised:  We propose a new path-based distance measure to compare two planar geometric graphs embedded in the same plane.
Edit intent: clarity
Original:  We propose a new path-based distance measure to compare two planar geometric graphs that are embedded in the same plane.
Revised:  We propose a new path-based distance measure to compare two planar geometric graphs that are embedded in the plane.
Edit intent: clarity
Original:  We show that it can be approximated in polynomial time and that it preserves structural and spatial properties of the graphs.
Revised:  We show that this distance can be approximated in polynomial time and that it preserves structural and spatial properties of the graphs.
Edit intent: clarity
Original: This paper extends results from Mortimer and Williams (1991) about changes of probability measure up to random times.
Revised: This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to random times.
Edit intent: fluency
Original:  This work presents a highly scalable neuromorphic hardware based on crossbar array of 1-bit resistive cross points as distributed synapses with in-situ stochastic characteristic .
Revised:  This work presents a highly scalable neuromorphic hardware based on crossbar array of 1-bit resistive crosspoints as distributed stochastic synapses .
Edit intent: clarity
Original:  As medical applications drove the datasets therein, all studies were based on protein-coding genes, in which variants are also impacted by natural selection.
Revised:  All these studies were based on protein-coding genes, in which variants are also impacted by natural selection.
Edit intent: clarity
Original:  We sequenced putatively neutral loci that are very far from genes and that meet a wide array of additional criteria  .
Revised:  We sequenced loci very far from genes and that meet a wide array of additional criteria .
Edit intent: clarity
Original:  We sequenced putatively neutral loci that are very far from genes and that meet a wide array of additional criteria  .
Revised:  We sequenced putatively neutral loci that are very far from genes that meet a wide array of additional criteria .
Edit intent: coherence
Original:  We investigate the amount of randomness (that is, the number of random bits used by the robots) that is necessary to achieve scattering.
Revised:  We investigate the amount of randomness (that is, the number of random bits used by the robots) that is required to achieve scattering.
Edit intent: fluency
Original:  We give a non-adaptive full-sensing algorithm for channels with collision detection and an adaptive full-sensing algorithm for channels without collision detection that achieve O( min (n+w,w\log n)) packet latency.
Revised:  We give a non-adaptive algorithm for channels with collision detection and an adaptive full-sensing algorithm for channels without collision detection that achieve O( min (n+w,w\log n)) packet latency.
Edit intent: fluency
Original:  We give a non-adaptive full-sensing algorithm for channels with collision detection and an adaptive full-sensing algorithm for channels without collision detection that achieve O( min (n+w,w\log n)) packet latency.
Revised:  We give a non-adaptive full-sensing algorithm for channels with collision detection and an adaptive algorithm for channels without collision detection that achieve O( min (n+w,w\log n)) packet latency.
Edit intent: fluency
Original:  We give a non-adaptive full-sensing algorithm for channels with collision detection and an adaptive full-sensing algorithm for channels without collision detection that achieve O( min (n+w,w\log n)) packet latency.
Revised:  We give a non-adaptive full-sensing algorithm for channels with collision detection and an adaptive full-sensing algorithm for channels without collision detection that achieve O( \min (n+w,w\log n)) packet latency.
Edit intent: fluency
Original:  We develop a non-adaptive full-sensing algorithm for channels without collision detection that achieves O(n+w) queue size and O( n w ) packet latency.
Revised:  We develop a non-adaptive algorithm for channels without collision detection that achieves O(n+w) queue size and O( n w ) packet latency.
Edit intent: clarity
Original:  We develop a non-adaptive full-sensing algorithm for channels without collision detection that achieves O(n+w) queue size and O( n w ) packet latency.
Revised:  We develop a non-adaptive full-sensing algorithm for channels without collision detection that achieves O(n+w) queue size and O( nw ) packet latency.
Edit intent: fluency
Original:  This is in contrast with the adversarial model of global injection rates, in which non-adaptive full-sensing algorithms with bounded packet latency do not exist [ 15 ].
Revised:  This is in contrast with the adversarial model of global injection rates, in which non-adaptive algorithms with bounded packet latency do not exist [ 15 ].
Edit intent: clarity
Original: Finding a maximum independent set  of a given family of axis-parallel rectangles is a basic problem in computational geometry and combinatorics.
Revised: Finding a maximum independent set of a given fam- ily of axis-parallel rectangles is a basic problem in computational geometry and combinatorics.
Edit intent: fluency
Original: Finding a maximum independent set  of a given family of axis-parallel rectangles is a basic problem in computational geometry and combinatorics.
Revised: Finding a maximum independent set of a given family of axis-parallel rectangles is a basic problem in computational geom- etry and combinatorics.
Edit intent: fluency
Original:  This problem has attracted attention since the sixties, when Wegner conjectured that the corresponding duality gap, i.e., the  ratio between the maximum independent set and the minimum hitting set  , is bounded by a universal constant.
Revised:  This problem has attracted significant atten- tion since the sixties, when Wegner conjectured that the corresponding duality gap, i.e., the ratio between the maximum independent set and the minimum hitting set , is bounded by a universal constant.
Edit intent: clarity
Original:  This problem has attracted attention since the sixties, when Wegner conjectured that the corresponding duality gap, i.e., the  ratio between the maximum independent set and the minimum hitting set  , is bounded by a universal constant.
Revised:  This problem has attracted attention since the sixties, when Wegner conjectured that the corresponding duality gap, i.e., the maximum possible ratio between the maximum independent set and the minimum hitting set , is bounded by a universal constant.
Edit intent: clarity
Original:  From a computational complexity perspective, although for general rectangle families the problem is known to be NP-hard , we derive an O(n^2)  algorithm for the maximum weight independent set when, in addition to intersecting a diagonal, the rectangles intersect below it .
Revised:  From a computational complexity perspective, although for general rectangle families the problem is known to be NP-hard , we derive an O(n^2) -time algorithm for the maximum weight independent set when, in addition to intersecting a diagonal, the rectangles intersect below it .
Edit intent: clarity
Original:  From a computational complexity perspective, although for general rectangle families the problem is known to be NP-hard , we derive an O(n^2)  algorithm for the maximum weight independent set when, in addition to intersecting a diagonal, the rectangles intersect below it .
Revised:  From a computational complexity perspective, although for general rectangle families the problem is known to be NP-hard , we derive an O(n^2) algorithm for the maximum weight independent set when, in addition the rectangles intersect below it .
Edit intent: clarity
Original:  From a computational complexity perspective, although for general rectangle families the problem is known to be NP-hard , we derive an O(n^2)  algorithm for the maximum weight independent set when, in addition to intersecting a diagonal, the rectangles intersect below it .
Revised:  From a computational complexity perspective, although for general rectangle families the problem is known to be NP-hard , we derive an O(n^2) algorithm for the maximum weight independent set when, in addition to intersecting a diagonal, the rectangles intersect below the diagonal .
Edit intent: clarity
Original:  As a consequence, we obtain a 2-approximation algorithm for the maximum weight independent set of rectangles intersecting a diagonal  .
Revised:  As a consequence, we obtain a 2-approximation algo- rithm for the maximum weight independent set of rectangles intersecting a diagonal .
Edit intent: fluency
Original: This paper is about \mu-limit sets of cellular automata , i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution , starting from an initial \mu-random confi guration .
Revised: This paper concerns \mu-limit sets of cellular automata , i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution , starting from an initial \mu-random confi guration .
Edit intent: clarity
Original: This paper is about \mu-limit sets of cellular automata , i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution , starting from an initial \mu-random confi guration .
Revised: This paper is about \mu-limit sets of cellular automata : sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution , starting from an initial \mu-random confi guration .
Edit intent: coherence
Original: This paper is about \mu-limit sets of cellular automata , i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution , starting from an initial \mu-random confi guration .
Revised: This paper is about \mu-limit sets of cellular automata , i.e. sets of configurations made of words whose probability to appear arbitrarily late in the evolution , starting from an initial \mu-random confi guration .
Edit intent: clarity
Original: This paper is about \mu-limit sets of cellular automata , i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution , starting from an initial \mu-random confi guration .
Revised: This paper is about \mu-limit sets of cellular automata , i.e. sets of configurations made of words which have a positive probability to appear arbitrarily late in the evolution , starting from an initial \mu-random configuration .
Edit intent: fluency
Original:  Our main resultsare : first, that such a set can have a %DIFDELCMD < \Signma%%% _3 -hard language, second that it can contain only \alpha-complex confi gurations and thirdthat any non-trivial property concerning these sets is at least \Pi _3 -hard.
Revised:  Our main resultsare : first, that such a set can have a %DIFDELCMD < \Signma%%% _3 -hard language, second , they can contain only \alpha-complex confi gurations and thirdthat any non-trivial property concerning these sets is at least \Pi _3 -hard.
Edit intent: clarity
Original:  Our main resultsare : first, that such a set can have a %DIFDELCMD < \Signma%%% _3 -hard language, second that it can contain only \alpha-complex confi gurations and thirdthat any non-trivial property concerning these sets is at least \Pi _3 -hard.
Revised:  Our main resultsare : first, that such a set can have a %DIFDELCMD < \Signma%%% _3 -hard language, second that it can contain only \alpha-complex configurations, third, any non-trivial property concerning these sets is at least \Pi _3 -hard.
Edit intent: fluency
Original:  Our main resultsare : first, that such a set can have a %DIFDELCMD < \Signma%%% _3 -hard language, second that it can contain only \alpha-complex confi gurations and thirdthat any non-trivial property concerning these sets is at least \Pi _3 -hard.
Revised:  Our main resultsare : first, that such a set can have a %DIFDELCMD < \Signma%%% _3 -hard language, second that it can contain only \alpha-complex confi gurations and thirdthat any non-trivial property concerning them is at least \Pi _3 -hard.
Edit intent: fluency
Original:  We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the probability of appearance of a word in the evolution.
Revised:  We prove complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the probability of appearance of a word in the evolution.
Edit intent: clarity
Original:  We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the probability of appearance of a word in the evolution.
Revised:  We also prove various complexity upper bounds, study restrictions of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the probability of appearance of a word in the evolution.
Edit intent: clarity
Original:  We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the probability of appearance of a word in the evolution.
Revised:  We also prove various complexity upper bounds, study some restriction of these questions to particular classes of CA, and different types of (non-)convergence of the probability of appearance of a word in the evolution.
Edit intent: clarity
Original:  We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the probability of appearance of a word in the evolution.
Revised:  We also prove various complexity upper bounds, study some restriction of these questions to particular classes of cellular automata, and study different types of (non-)convergence of the measure of a word during the evolution.
Edit intent: clarity
Original:  Given a heterogeneous pool of network switches, through experiments and analysis, we explore how the distribution of servers across switches and the interconnection of switches impact on network throughput.
Revised:  Given a heterogeneous pool of network switches, through experiments and analysis, we explore how the distribution of servers across switches and the interconnection of switches affect network throughput.
Edit intent: clarity
Original:  In our experiment, ten years data (from January 1st, 2002 to January 1st, 2012) are collected and schemed by rolling windows to predict one-day-ahead directions.
Edit intent: coherence
Original:  The results also varify theco-movement effect between the Korean (Hong Kong) stock market and the American stock market .
Revised:  The results also varify the effect between the Korean (Hong Kong) stock market and the American stock market .
Edit intent: clarity
Original:  The results also varify theco-movement effect between the Korean (Hong Kong) stock market and the American stock market .
Revised:  The results also varify theco-movement HIS .
Edit intent: clarity
Original:  Two connected results describe the eigenvalue distribution of large matrices with random coefficients: Wigner's semicircle law (for symmetric matrices), and Girko's circular law (for asymmetric ones).
Revised:  Two connected results describe the eigenvalue distribution of large matrices with random coefficients: Wigner's semicircular law and Girko's circular law (for asymmetric ones).
Edit intent: fluency
Original:  We also propose a new method to accurately approximate the dominant eigenvalue of a complex network, with applications in epidemiology .
Revised:  We also propose a new method to accurately approximate the dominant eigenvalue of complex networks .
Edit intent: clarity
Original: This paper studies online shortest path routing over dynamic multi-hop networks.
Revised: This paper studies online shortest-path routing over dynamic multi-hop networks.
Edit intent: fluency
Original:  Link costs or delays are time-varying and modelled by independent and identically distributed random processes, whose parameters are initially unknown.
Revised:  Link costs or delays are time-varying and modeled by independent and identically distributed random processes, whose parameters are initially unknown.
Edit intent: fluency
Original: This paper studies online shortest-path routing over dynamic multi-hop networks.
Revised: This paper studies online shortest path routing over multi-hop networks.
Edit intent: clarity
Original:  We formulate the problem as a combinatorial bandit optimization problem and consider several scenarios that differ in where routing decisions are made and in the information available when making the decision .
Revised:  We formulate the problem as a combinatorial bandit optimization problem and consider several scenarios that differ in where routing decisions are made and in the information available when making the decisions .
Edit intent: fluency
Original:  For each scenario, we derive the tight asymptotic lower bound on the regret that has to be satisfied by any online routing policy.
Revised:  For each scenario, we derive a tight asymptotic lower bound on the regret that has to be satisfied by any online routing policy.
Edit intent: fluency
Original:  These bounds help us to understand the performance improvements we can expect when (i) taking routing decisions at each hop rather than at the source only, and (ii) observing per-link costs rather than aggregate path costs .
Revised:  These bounds help us to understand the performance improvements we can expect when (i) taking routing decisions at each hop rather than at the source only, and (ii) observing per-link delays rather than end-to-end path delays .
Edit intent: clarity
Original:  The regret upper bounds of these algorithm improve over those of the existing algorithms, and they significantly outperform the-state-of-art algorithm in numerical experiments.
Revised:  The regret upper bounds of these algorithms improve over those of the existing algorithms, and they significantly outperform the-state-of-art algorithm in numerical experiments.
Edit intent: fluency