wanyu/IteraTeR_v2 huggingface dataset:
Original: A weak odd dominated (WOD) set is a set B of vertices for which there exists a subset C of V%DIFDELCMD < \B %%%  }  such that every vertex in B has an odd number of neighbors in C. Given a graph G of order n, \kappa(G) denotes the size of the greatest WOD set, and \kappa'(G) the size of the smallest non-WOD set.
Revised: A weak odd dominated (WOD) set is a set B of vertices for which there exists a subset C of V%DIFDELCMD < \B %%% } such that every vertex in B has an odd number of neighbors in C. Given a graph G of order n, \kappa(G) denotes the size of the largest WOD set, and \kappa'(G) the size of the smallest non-WOD set.
Edit intent: clarity
Original:  The decision problems associated with  \kappa, \kappa' and \kappa_Q have been proved to be NP-Complete.
Revised:  The decision problems associated with the quantities \kappa, \kappa' and \kappa_Q have been proved to be NP-Complete.
Edit intent: clarity
Original:  The decision problems associated with  \kappa, \kappa' and \kappa_Q have been proved to be NP-Complete.
Revised:  The decision problems associated with \kappa, \kappa' and \kappa_Q are known to be NP-Complete.
Edit intent: clarity
Original:  In this paper, we prove that depending on the parametrization, the WOD problemsare either FPT or equivalent to Oddset, and as a consequence, hard for W 1%DIFDELCMD < ]%%% . We also prove that the three WOD problems are hard for W[1] even for bipartite graphs .
Revised:  In this paper, we 1%DIFDELCMD < ]%%% . We also prove that the three WOD problems are hard for W[1] even for bipartite graphs .
Edit intent: coherence
Original:  In this paper, we prove that depending on the parametrization, the WOD problemsare either FPT or equivalent to Oddset, and as a consequence, hard for W 1%DIFDELCMD < ]%%% . We also prove that the three WOD problems are hard for W[1] even for bipartite graphs .
Revised:  In this paper, we prove that depending on the parametrization, the WOD problemsare either FPT or equivalent to Oddset, and as a consequence, hard for W %DIFDELCMD < ]%%% . We also prove that the three WOD problems are hard for W[1] even for bipartite graphs .
Edit intent: fluency
Original:  Homology detection is critical to genomics.
Revised: Emerging high-throughput technologies have led to a deluge of putative non-coding RNA (ncRNA) sequences identified in a wide variety of organisms. Systematic characterization of these transcripts will be a tremendous challenge. Homology detection is critical to genomics.
Edit intent: clarity
Original:  Non-coding RNA (ncRNA ) presents a challenge for homology detection, as the primary sequence is often poorly conserved and de novo structure prediction remains difficult.
Revised:  ncRNA presents a challenge for homology detection, as the primary sequence is often poorly conserved and de novo structure prediction remains difficult.
Edit intent: clarity
Original:  Here we infer a large fitness landscape from high-throughput sequence data from the E. coli lac promoter regionwith ~200, 000 mutanegized sequences of 75 nucleotides.
Revised:  Here we construct such a map using the recently collected corpora of high-throughput sequence data from the E. coli lac promoter regionwith ~200, 000 mutanegized sequences of 75 nucleotides.
Edit intent: clarity
Original:  Here we infer a large fitness landscape from high-throughput sequence data from the E. coli lac promoter regionwith ~200, 000 mutanegized sequences of 75 nucleotides.
Revised:  Here we infer a large fitness landscape from high-throughput sequence data from the promoter regionwith ~200, 000 mutanegized sequences of 75 nucleotides.
Edit intent: clarity
Original:  Here we infer a large fitness landscape from high-throughput sequence data from the E. coli lac promoter regionwith ~200, 000 mutanegized sequences of 75 nucleotides.
Revised:  Here we infer a large fitness landscape from high-throughput sequence data from the E. coli lac 75 nucleotides.
Edit intent: clarity
Original:  We find that the additive (non-epistatic) components account for about 2/3 of the explainable variance in the data, while the epistatic components explain on the order of 10\% . We find the fitness landscape to be essentially single peaked, with a small amount of antagonistic epistasis.
Revised:  We find that the additive (non-epistatic) components account for about two-thirds of the explainable variance in the data, while the epistatic components explain on the order of 10\% . We find the fitness landscape to be essentially single peaked, with a small amount of antagonistic epistasis.
Edit intent: clarity
Original:  By comparison to neutrally evolved randomly generated sequences, we deduce a significant amount of selective pressure on the wild type .
Revised:  There is a significant selective pressure on the wild type .
Edit intent: clarity
Original:  Our method also reveals the binding sites and their interactions , without any difficult optimization steps.
Revised:  Our method also reveals the binding sites and their interactions without difficult optimization steps.
Edit intent: coherence
Original:  To illustrate our results, we use example ensembles of time-dependent networks from neuroscience that exhibit properties likely to be important in a variety of other networks .
Revised:  To illustrate our results, we employ ensembles of time-dependent networks from neuroscience that exhibit properties likely to be important in a variety of other networks .
Edit intent: clarity
Original: We construct a model of a lattice polymer which describes secondary structures of proteins .
Revised: In the standard approach to lattice proteins the models based on nearest neighbor interaction are used. In this kind of models it is difficult to explain the existence of secondary structures --- special preferred conformations of protein chains. In the present paper a new lattice model of proteins is proposed which is based on non-local cooperative interactions .
Edit intent: coherence
Original:  In this model the energy of a conformation of a polymer is equal to a sum of energies of conformations of segments of the polymer chain of the length five.
Revised:  In this model the energy of a conformation of a polymer is equal to the sum of energies of conformations of segments of the polymer chain of the length five.
Edit intent: fluency
Original:  In this model the energy of a conformation of a polymer is equal to a sum of energies of conformations of segments of the polymer chain of the length five.
Revised:  In this model the energy of a conformation of a polymer is equal to a sum of energies of conformations of fragments of the polymer chain of the length five.
Edit intent: clarity
Original:  We show that for this model with cooperative interaction all conformations with minimal energy are combinations of lattice models of alpha-helix and beta-strand.
Revised:  We show that for this model all conformations with minimal energy are combinations of lattice models of alpha-helix and beta-strand.
Edit intent: clarity
Original: We introduce a rigorous and powerful method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions  .
Revised: We introduce a rigorous method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions .
Edit intent: clarity
Original:  This allows for an accurate and computationally very efficient reconstruction of the free-energy profile as a function of an arbitrarily chosen reaction coordinate .
Revised:  This allows for a computationally efficient reconstruction of the free-energy profile as a function of an arbitrarily chosen reaction coordinate .
Edit intent: clarity
Original:  Minimal prefix tree to distinguish elements turns out to require asymptotically only about 2.77544 bits per element, while standard approaches use a few times more.
Revised:  Minimal prefix tree which distinguish elements turns out to require asymptotically only about 2.77544 bits per element, while standard approaches use a few times more.
Edit intent: fluency
Original:  In this paper there will be analyzed informational content of such  task and how to practically approach this lower boundary . Minimal prefix tree which distinguish elements turns out to require asymptotically only about 2.77544 bits per element, while standard approaches use a few times more  .
Revised:  In this paper there will be analyzed informational content of such general task and how to practically approach this lower boundary . Minimal prefix tree which distinguish elements turns out to require asymptotically only about 2.77544 bits per element, while standard approaches use a few times more .
Edit intent: clarity
Original:  In this paper there will be analyzed informational content of such  task and how to practically approach this lower boundary . Minimal prefix tree which distinguish elements turns out to require asymptotically only about 2.77544 bits per element, while standard approaches use a few times more  .
Revised:  In this paper there will be analyzed informational content of such task and how to practically approach such found lower boundaries . Minimal prefix tree which distinguish elements turns out to require asymptotically only about 2.77544 bits per element, while standard approaches use a few times more .
Edit intent: clarity
Original:  The detection of these IBD segments is now feasible, enabling a wide range of applications from phasing and imputation to demographic inference.
Revised:  The detection of these IBD segments has recently become feasible, enabling a wide range of applications from phasing and imputation to demographic inference.
Edit intent: clarity
Original:  Using coalescent theory, we calculate the mean and variance of the total sharing between arbitrary pairs of individuals.
Revised:  Specifically, using coalescent theory, we calculate the mean and variance of the total sharing between arbitrary pairs of individuals.
Edit intent: coherence
Original:  Using coalescent theory, we calculate the mean and variance of the total sharing between arbitrary pairs of individuals.
Revised:  Using coalescent theory, we calculate the variance of the total sharing between arbitrary pairs of individuals.
Edit intent: clarity
Original:  Using coalescent theory, we calculate the mean and variance of the total sharing between arbitrary pairs of individuals.
Revised:  Using coalescent theory, we calculate the mean and variance of the total sharing between random pairs of individuals.
Edit intent: clarity
Original:  We then study the cohort-averaged sharing: the average total sharing between one individual to the rest of the cohort.
Revised:  We then investigate the cohort-averaged sharing: the average total sharing between one individual to the rest of the cohort.
Edit intent: clarity
Original:  We then study the cohort-averaged sharing: the average total sharing between one individual to the rest of the cohort.
Revised:  We then study the cohort-averaged sharing: the average total sharing between one individual and the rest of the cohort.
Edit intent: fluency
Original:  Surprisingly, the variance of this distribution remains large even for large cohorts, implying the existence of "hyper-sharing" individuals.
Revised:  Surprisingly, the variance of this distribution does not vanish even for large cohorts, implying the existence of "hyper-sharing" individuals.
Edit intent: clarity
Original:  The presence of such individuals bears important consequences to the design of sequencing studies, since, if they are selected for whole-genome sequencing, a larger fraction of the cohort can be subsequently imputed.
Revised:  The presence of such individuals has consequences for the design of sequencing studies, since, if they are selected for whole-genome sequencing, a larger fraction of the cohort can be subsequently imputed.
Edit intent: clarity
Original:  We calculate the expected gain in power of imputation by IBD, and subsequently, in power to detect an association, when individuals are either randomly selected or are specifically the hyper-sharing individuals.
Revised:  We calculate the expected gain in power of imputation by IBD, and subsequently, in power to detect an association, when individuals are either randomly selected or specifically chosen to be the hyper-sharing individuals.
Edit intent: fluency
Original:  We show that the independent set problem on edge-clique graphs of cographs and of distance-hereditary graphs can be solved in polynomial time .
Revised:  We show that the independent set problem on edge-clique graphs of cographs .
Edit intent: clarity
Original:  We used turn-based stochastic parity games to define acceptance of Markov chains by a special subclass of p-automata.
Revised:  We used turn-based stochastic parity games to define acceptance of Markov chains by a subclass of p-automata.
Edit intent: clarity
Original:  Acceptance by general p-automata  was left undefined as there was no notion of games that supported it.
Revised:  Acceptance by general p-automata , which was left undefined as there was no notion of games that supported it.
Edit intent: coherence
Original:  Obligations are orthogonal to the linear winning conditions that define whether a play is winning.
Revised:  Obligations are orthogonal to the linear winning conditions that define winning.
Edit intent: clarity
Original:  We define and show that Blackwell games with Borel objectives and obligations are determined by a reduction similar to Martin's proof of determinacy of Blackwell games with Borel objectives.
Revised:  We define value via a reduction to turn-based games similar to Martin's proof of determinacy of Blackwell games with Borel objectives.
Edit intent: clarity
Original:   We show that for Markov chains with Borel objectives and obligations  and finite turn-based stochastic parity games with obligations there exists an alternative and simpler characterization of the value function without going through a Martin-like reduction . Based on this simpler characterization we give an  algorithm to analyze finite turn-based stochastic parity games with obligations in exponential time .
Revised:  We show that for Markov chains with Borel objectives and obligations , and finite turn-based stochastic parity games with obligations there exists an alternative and simpler characterization of the value function without going through a Martin-like reduction . Based on this simpler characterization we give an algorithm to analyze finite turn-based stochastic parity games with obligations in exponential time .
Edit intent: fluency
Original:   We show that for Markov chains with Borel objectives and obligations  and finite turn-based stochastic parity games with obligations there exists an alternative and simpler characterization of the value function without going through a Martin-like reduction . Based on this simpler characterization we give an  algorithm to analyze finite turn-based stochastic parity games with obligations in exponential time .
Revised:  We show that for Markov chains with Borel objectives and obligations and finite turn-based stochastic parity games with obligations there exists an alternative and simpler characterization of the value function . Based on this simpler characterization we give an algorithm to analyze finite turn-based stochastic parity games with obligations in exponential time .
Edit intent: coherence
Original:   We show that for Markov chains with Borel objectives and obligations  and finite turn-based stochastic parity games with obligations there exists an alternative and simpler characterization of the value function without going through a Martin-like reduction . Based on this simpler characterization we give an  algorithm to analyze finite turn-based stochastic parity games with obligations in exponential time .
Revised:  We show that for Markov chains with Borel objectives and obligations and finite turn-based stochastic parity games with obligations there exists an alternative and simpler characterization of the value function without going through a Martin-like reduction . Based on this simpler definition we give an algorithm to analyze finite turn-based stochastic parity games with obligations in exponential time .
Edit intent: clarity
Original:  Finally, we show that obligation games provide the necessary framework for reasoning about p-automata and that they indeed generalize the previous definition.
Revised:  Finally, we show that obligation games provide the necessary framework for reasoning about p-automata and that they generalize the previous definition.
Edit intent: coherence
Original:  We generalize these characterizations for { ] k-chordal graphs by introducing the notions of k-simplicial vertexand k-simplicial ordering ]  .
Revised:  We generalize these characterizations for { ]. We give a characterization of k-chordal graphs by introducing the notions of k-simplicial vertexand k-simplicial ordering ] .
Edit intent: clarity
Original:  This question is motivated by the problem of characterising algebras of almost minimal rank studied by Blaeser and de Voltaire in [1]  This paper is a translation of a report submitted by the author to the XI international Lupanov Seminar "Discrete mathematics and applications" (in Russian).
Revised:  This question is motivated by the problem of characterising algebras of almost minimal rank studied by Blaeser and de Voltaire in [1] . This paper is a translation of a report submitted by the author to the XI international Lupanov Seminar "Discrete mathematics and applications" (in Russian).
Edit intent: fluency
Original:  This generates a significant traffic from the satellite to the ground stations, and, thus, image downlinking may become a bottleneck in the efficiency of the whole system.
Revised:  This generates significant communication traffic from the satellite to the ground stations, and, thus, image downlinking may become a bottleneck in the efficiency of the whole system.
Edit intent: clarity
Original:  This generates a significant traffic from the satellite to the ground stations, and, thus, image downlinking may become a bottleneck in the efficiency of the whole system.
Revised:  This generates a significant traffic from the satellite to the ground stations, and, thus, image downlinking often becomes the bottleneck in the efficiency of the whole system.
Edit intent: clarity
Original:  In this paper we address the downlink scheduling problem for the Canada's Earth observing SAR satellite, RADARSAT-2.
Revised:  In this paper we address the downlink scheduling problem for Canada's Earth observing SAR satellite, RADARSAT-2.
Edit intent: fluency
Original:  Being an applied problem, downlink scheduling is characterized with a number of constraints that make it difficult not only to optimize the schedule but even to produce a feasible solution.
Revised:  Being an applied problem, downlink scheduling is characterised with a number of constraints that make it difficult not only to optimize the schedule but even to produce a feasible solution.
Edit intent: fluency
Original:  Being an applied problem, downlink scheduling is characterized with a number of constraints that make it difficult not only to optimize the schedule but even to produce a feasible solution.
Revised:  Being an applied problem, downlink scheduling is characterized with a number of constraints that make it difficult not only to optimise the schedule but even to produce a feasible solution.
Edit intent: fluency
Original:  The produced Eiffel code is functionally equivalent to the original C code, and takes advantage of some of Eiffel's object-oriented features to produce readable, maintainable, and easy-to-debug translations.
Revised:  The produced Eiffel code is functionally equivalent to the original C code, and takes advantage of some of Eiffel's object-oriented features to produce safe and easy-to-debug translations.
Edit intent: clarity
Original: In this research paper, the problem of minimization of quadratic forms associated with the dynamics of Hopfield-Amari neural network is considered.
Revised: In this research paper, the problem of optimization of quadratic forms associated with the dynamics of Hopfield-Amari neural network is considered.
Edit intent: clarity
Original:  A theorem associated with local/global minimization of quadratic energy function using the Hopfield- Amari neural network is discussed.
Revised:  A theorem associated with local/global minimization of quadratic energy function using the Hopfield-Amari neural network is discussed.
Edit intent: fluency
Original: We study physical limits of chemical sensing by a single chemotactic cell with cooperative chemoreceptors on the cell surface .
Revised: Most sensory cells use cross-membrane chemoreceptors to detect chemical signals in the environment. The biochemical properties and spatial organization of chemoreceptors play important roles in achieving and maintaining sensitivity and accuracy of chemical sensing. Here we investigate the effects of receptor cooperativity and adaptation on the limits of gradient sensing. We study a single cell with aggregated chemoreceptor arrays on the cell surface .
Edit intent: clarity
Original:  Our results also show that isotropic receptor aggregate layout  represents an optimal configuration to gradient sensing and that anisotropy does not change the effect of receptor cooperativity on the sensing limit .
Revised:  Our results also show that isotropic receptor aggregate layout represents an optimal configuration to gradient sensing .
Edit intent: coherence
Original: Representations are internal models of the world that provide context to a sensory stream and are formed over evolutionary time as well as learned .
Revised: Representations are internal models of the environment that can provide guidance to a behaving agent, even in the absence of sensory information. It is not clear how representations are developed and whether or not they are necessary or even essential for intelligent behavior .
Edit intent: clarity
Original:  We argue here that representations are the expected consequence of an adaptive process, give a formal definition of representation based on information theory, and quantify it using our new measure R.
Revised:  We argue here that representations are the expected consequence of an adaptive process, give a formal definition of representation based on information theory, and quantify it with a measure R.
Edit intent: clarity
Original:  To measure how R changes over time, we evolve two types of networks---a recurrent artificial neural network and a network of hidden Markov gates---to solve a categorization task using a Genetic Algorithm .
Revised:  To measure how R changes over time, we evolve two types of networks---an artificial neural network and a network of hidden Markov gates---to solve a categorization task using a Genetic Algorithm .
Edit intent: clarity
Original:  To measure how R changes over time, we evolve two types of networks---a recurrent artificial neural network and a network of hidden Markov gates---to solve a categorization task using a Genetic Algorithm .
Revised:  To measure how R changes over time, we evolve two types of networks---a recurrent artificial neural network and a network of hidden Markov gates---to solve a categorization task using a genetic algorithm .
Edit intent: fluency
Original:  We find that the capacity to represent increases during evolutionary adaptation and that representations build up during the lifetimeof these agents .
Revised:  We find that the capacity to represent increases during evolutionary adaptation , and that agents form representations of their environment during their lifetime. This ability allows the agents to act on sensorial inputs in the context of their acquired representations and enables complex and context-dependent behavior .
Edit intent: coherence
Original:  We conclude that any successful cognitive systemthat represents its environment within internal states should have a positive R .
Revised:  We conclude that R should be able to quantify the representations within any cognitive system, and should be predictive of an agent's long-term adaptive success .
Edit intent: clarity