wanyu/IteraTeR_v2 huggingface dataset:
Original:  This paper focuses on the problem of counting list M-partitions, given a graph G and given lists for each vertex of G. We  give an algorithm that solves this problem in polynomial time for every (fixed) matrix M for which the problem is tractable .
Revised:  This paper focuses on the problem of counting list M-partitions, given a graph G and given lists for each vertex of G. We give an algorithm that counts list M-partitions in polynomial time for every (fixed) matrix M for which the problem is tractable .
Edit intent: clarity
Original:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Revised:  The algorithm uses data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Edit intent: clarity
Original:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Revised:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Edit intent: fluency
Original:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Revised:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Edit intent: fluency
Original:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Revised:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists restrict access to portions of M in which the interactions of 0s and 1s is controlled.
Edit intent: clarity
Original:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interactions of 0s and 1s is controlled.
Revised:  The algorithm relies on data structures such as sparse-dense partitions and subcube decompositions to reduce each problem instance to a sequence of problem instances in which the lists have a certain useful structure that restricts access to portions of M in which the interaction of 0s and 1s is controlled.
Edit intent: fluency
Original:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Revised:  We solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Edit intent: fluency
Original:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Revised:  We show how to solve the resulting restricted instances by converting them into counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Edit intent: clarity
Original:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Revised:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we solve using arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Edit intent: clarity
Original:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Revised:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Edit intent: fluency
Original:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that the problem of counting list M-partitions is #P-complete.
Revised:  We show how to solve the resulting restricted instances by converting them into particular counting constraint satisfaction problems (#CSPs) which we show how to solve using a constraint satisfaction technique known as " arc-consistency " . For every matrix M for which our algorithm fails, we show that counting list M-partitions is #P-complete.
Edit intent: clarity
Original:  Furthermore , we give an explicit characterisation of the dichotomy theorem: counting list M-partitions is tractable (in FP ) if and only if the matrix M has a structure called a derectangularising sequence  .
Revised:  Further , we give an explicit characterisation of the dichotomy theorem: counting list M-partitions is tractable (in FP ) if and only if the matrix M has a structure called a derectangularising sequence .
Edit intent: fluency
Original:  Furthermore , we give an explicit characterisation of the dichotomy theorem: counting list M-partitions is tractable (in FP ) if and only if the matrix M has a structure called a derectangularising sequence  .
Revised:  Furthermore , we give an explicit characterisation of the dichotomy theorem: counting list M-partitions is in FP if M has a structure called a derectangularising sequence .
Edit intent: clarity
Original:  Alternatively, for each coordinate system  we observe the coordinates of a subset of the points.
Revised:  Alternatively, for each coordinate system , we observe the coordinates of a subset of the points.
Edit intent: fluency
Original:  We study the problem of estimating the global coordinates  (up to a global rigid transform) of the points from such measurements .
Revised:  The problem of estimating the global coordinates (up to a global rigid transform) of the points from such measurements .
Edit intent: clarity
Original:  We study the problem of estimating the global coordinates  (up to a global rigid transform) of the points from such measurements .
Revised:  We study the problem of estimating the global coordinates (up to a rigid transform) of the points from such measurements .
Edit intent: clarity
Original:  We study the problem of estimating the global coordinates  (up to a global rigid transform) of the points from such measurements .
Revised:  We study the problem of estimating the global coordinates (up to a global rigid transform) from such measurements .
Edit intent: clarity
Original:  This problem comes up in distributed approaches to molecular conformation (determination of molecular structures using NMR) and sensor network localization, and also in computer vision and graphics applications.
Revised:  This problem comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics applications.
Edit intent: clarity
Original:  We perform some numerical simulations to validate the algorithm and confirm the theoretical findings  .
Revised:  We perform numerical experiments on simulated data to confirm the theoretical findings .
Edit intent: clarity
Original:  The least-squares formulation  , though non-convex, has a well known closed-form solution for the case M=2 (based on the singular value decomposition).
Revised:  The least-squares formulation of this problem , though non-convex, has a well known closed-form solution for the case M=2 (based on the singular value decomposition).
Edit intent: clarity
Original:  The least-squares formulation  , though non-convex, has a well known closed-form solution for the case M=2 (based on the singular value decomposition).
Revised:  The least-squares formulation , though non-convex, has a well known closed-form solution when M=2 (based on the singular value decomposition).
Edit intent: clarity
Original:  In this paper, we propose a semidefinite relaxation of the least-squares formulation , and prove conditions for exact and stable recovery for both this relaxationand for a previously proposed spectral relaxation .
Revised:  In this paper, we demonstrate how the least-squares formulation , and prove conditions for exact and stable recovery for both this relaxationand for a previously proposed spectral relaxation .
Edit intent: clarity
Original:  In particular, using results from rigidity theory and the theory of semidefinite programming, we prove that the semidefinite relaxation can guarantee recovery under more adversarial measurements compared to the spectral counterpart.
Revised:  In particular, we prove that the semidefinite relaxation can guarantee recovery under more adversarial measurements compared to the spectral counterpart.
Edit intent: clarity
Original: Studies of thousands of individuals have found genetic evidence for dramatic population growth in recent human history.
Revised: Population genetic studies have found evidence for dramatic population growth in recent human history.
Edit intent: clarity
Original:  These studies have also documents high numbers of amino acid changing polymorphisms that are likely evolutionarily important and may be of medic relevance .
Revised:  It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequencies, and effect sizes of mutations that contribute risk to complex traits .
Edit intent: clarity
Original:  Here I use  population genetic models to demonstrate how the recent population growth has directly led to the accumulation of deleterious amino acid changing polymorphism .
Revised:  Here I use simulations under population genetic models to demonstrate how the recent population growth has directly led to the accumulation of deleterious amino acid changing polymorphism .
Edit intent: clarity
Original:  I show that recent  growth increases the proportion of non synonymous SNPs and that the average mutation is more deleterious in an expanding populationthan in a non-exanded population.
Revised:  I show that recent population growth increases the proportion of non synonymous SNPs and that the average mutation is more deleterious in an expanding populationthan in a non-exanded population.
Edit intent: fluency
Original:  If a mutation's effect on disease status is correlated with its effect on fitness, then rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand.
Revised:  If a mutation's effect on a trait is correlated with its effect on fitness, then rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand.
Edit intent: clarity
Original:  If a mutation's effect on disease status is correlated with its effect on fitness, then rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand.
Revised:  If a mutation's effect on disease status is correlated with its effect on fitness, rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand.
Edit intent: coherence
Original:  These findings suggest careful consideration of recent population history will be essential for designing optimal association studies for low-frequency and rare variants .
Revised:  These findings suggest careful consideration of recent population history may be an important factor influencing the power of association tests in accounting for the missing heritability of certain complex traits .
Edit intent: clarity
Original: It is well known that temperature affects both the timing and outcome of animal development, and there is considerable evidence that species have adapted so that their embryos develop appropriately in the climates in which they live.
Revised: Temperature affects both the timing and outcome of animal development, and there is considerable evidence that species have adapted so that their embryos develop appropriately in the climates in which they live.
Edit intent: coherence
Original:  To determine the species-specific impact of temperature on the rate, order , and proportionality of major stages of embryonic development , we used time-lapse imaging to track the developmental progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C , and used a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Revised:  To determine the impact of temperature on the rate, order , and proportionality of major stages of embryonic development , we used time-lapse imaging to track the developmental progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C , and used a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Edit intent: clarity
Original:  To determine the species-specific impact of temperature on the rate, order , and proportionality of major stages of embryonic development , we used time-lapse imaging to track the developmental progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C , and used a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Revised:  To determine the species-specific impact of temperature on the order and timing of events during Drosophila melanogaster embryogenesis , we used time-lapse imaging to track the developmental progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C , and used a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Edit intent: clarity
Original:  To determine the species-specific impact of temperature on the rate, order , and proportionality of major stages of embryonic development , we used time-lapse imaging to track the developmental progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C , and used a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Revised:  To determine the species-specific impact of temperature on the rate, order , and proportionality of major stages of embryonic development , we used time-lapse imaging to track the progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C , and used a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Edit intent: clarity
Original:  To determine the species-specific impact of temperature on the rate, order , and proportionality of major stages of embryonic development , we used time-lapse imaging to track the developmental progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C , and used a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Revised:  To determine the species-specific impact of temperature on the rate, order , and proportionality of major stages of embryonic development , we used time-lapse imaging to track the developmental progress of embryos in 11 Drosophila species at seven precisely maintained temperatures between 17.5C and 32.5C . We employed a combination of automated and manual annotation to determine the timing of 34 milestones during embryogenesis.
Edit intent: coherence
Original:  D. mojavensis, a sub-tropical fly, exhibits an amplified slow-down with lower temperatures, while  D. virilis , a temperate fly, exhibits slower growth than tropical species at all temperatures.
Revised:  D. mojavensis, a sub-tropical D. mojavensis develops slower than tropical species at low temperatures, while D. virilis , a temperate fly, exhibits slower growth than tropical species at all temperatures.
Edit intent: clarity
Original:  D. mojavensis, a sub-tropical fly, exhibits an amplified slow-down with lower temperatures, while  D. virilis , a temperate fly, exhibits slower growth than tropical species at all temperatures.
Revised:  D. mojavensis, a sub-tropical fly, exhibits an amplified slow-down with lower temperatures, while D. virilis develops slower at all temperatures.
Edit intent: clarity
Original:  The alpine  species D. persimilis and D. pseudoobscura grow as rapidly as tropical flies at cooler temperatures, but exhibit diminished acceleration above 22.5C and have drastically slowed development by 30C.
Revised:  The alpine species D. persimilis and D. pseudoobscura develop as rapidly as tropical flies at cooler temperatures, but exhibit diminished acceleration above 22.5C and have drastically slowed development by 30C.
Edit intent: clarity
Original:  Six of these are of tropical origin like D. melanogaster and have similar temperature responses.
Revised:  Six of these species, like D. melanogaster and have similar temperature responses.
Edit intent: clarity
Original:  The sub-tropical D. mojavensis  develops slower than  tropical species at low temperatures, while the temperate D. virilis develops slower at all temperatures.
Revised:  The sub-tropical D. mojavensis develops slower than the tropical species at low temperatures, while the temperate D. virilis develops slower at all temperatures.
Edit intent: fluency
Original:  The sub-tropical D. mojavensis  develops slower than  tropical species at low temperatures, while the temperate D. virilis develops slower at all temperatures.
Revised:  The sub-tropical D. mojavensis develops slower than tropical species at lower temperatures, while the temperate D. virilis develops slower at all temperatures.
Edit intent: clarity
Original:  The sub-tropical D. mojavensis  develops slower than  tropical species at low temperatures, while the temperate D. virilis develops slower at all temperatures.
Revised:  The sub-tropical D. mojavensis develops slower than tropical species at low temperatures, while D. virilis develops slower at all temperatures.
Edit intent: clarity
Original:  Despite ranging from 13  to 46 hours  , the relative timing of events from cellularization to hatching is constant across all of the species and temperatures examined , suggesting the existence of a previously unrecognized timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Revised:  Despite ranging from 13 to 46 hours , the relative timing of events from cellularization through hatching is constant across all of the species and temperatures examined , suggesting the existence of a previously unrecognized timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Edit intent: fluency
Original:  Despite ranging from 13  to 46 hours  , the relative timing of events from cellularization to hatching is constant across all of the species and temperatures examined , suggesting the existence of a previously unrecognized timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Revised:  Despite ranging from 13 to 46 hours , the relative timing of events from cellularization to hatching is constant across all species and temperatures examined , suggesting the existence of a previously unrecognized timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Edit intent: clarity
Original:  Despite ranging from 13  to 46 hours  , the relative timing of events from cellularization to hatching is constant across all of the species and temperatures examined , suggesting the existence of a previously unrecognized timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Revised:  Despite ranging from 13 to 46 hours , the relative timing of events from cellularization to hatching is constant across all of the species and temperatures , suggesting the existence of a previously unrecognized timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Edit intent: clarity
Original:  Despite ranging from 13  to 46 hours  , the relative timing of events from cellularization to hatching is constant across all of the species and temperatures examined , suggesting the existence of a previously unrecognized timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Revised:  Despite ranging from 13 to 46 hours , the relative timing of events from cellularization to hatching is constant across all of the species and temperatures examined , suggesting the existence of a timer controlling embryogenesis progress and tuned by natural selection in response to the thermal environment of each species .
Edit intent: clarity