wanyu/IteraTeR_v2 huggingface dataset:
Original:  Recently, the author introduced the Partial Searchlight Scheduling Problem, in which only a given subregion of the environment has to be searched, and proved that its 3-dimensional decisional version is PSPACE-hard, even when restricted to orthogonal polyhedra.
Revised:  Recently, the author introduced the Partial Searchlight Scheduling Problem, in which only a given subregion of the environment has to be searched, and proved that its 3-dimensional decision version is PSPACE-hard, even when restricted to orthogonal polyhedra.
Edit intent: fluency
Original:  Here we extend and refine this result, by proving that 2-dimensional Partial Searchlight Scheduling is strongly PSPACE-complete, both in general and restricted to orthogonal polygons in which the region to be searched is a rectangle  .
Revised:  Here we extend and refine this result, by proving that 2-dimensional Partial Searchlight Scheduling is strongly PSPACE-complete, both in general and restricted to orthogonal polygons where the region to be searched is a rectangle .
Edit intent: clarity
Original:  We confirm analytical results by numerical simulation  .
Revised:  We illustrate analytical results by numerical simulation .
Edit intent: clarity
Original:  The second scenario is given by CBOE option price data for S& P 500 index options at a large number of strikes.
Revised:  The second scenario is given by CBOE option price data for S& P500 index options at a large number of strikes.
Edit intent: fluency
Original:  For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains whose convergence is rather well-understood in terms of their spectral gap.
Revised:  For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains whose convergence is fairly well-understood in terms of their spectral gap.
Edit intent: coherence
Original:  However, since for many applications load items cannot be divided arbitrarily , we focus on the discrete case where the load is composed of indivisible tokens.
Revised:  However, in many applications load items cannot be divided arbitrarily , we focus on the discrete case where the load is composed of indivisible tokens.
Edit intent: coherence
Original:  However, since for many applications load items cannot be divided arbitrarily , we focus on the discrete case where the load is composed of indivisible tokens.
Revised:  However, since for many applications load items cannot be divided arbitrarily and we need to deal with the discrete case where the load is composed of indivisible tokens.
Edit intent: clarity
Original:  Unfortunately, this discretization entails a non-linear behavior due to its rounding errors, which makes the analysis much harder than in the continuous case.
Revised:  This discretization entails a non-linear behavior due to its rounding errors, which makes the analysis much harder than in the continuous case.
Edit intent: coherence
Original:  Our results demonstrate that there is almost no deviation between the discrete and continuous case.
Revised:  Our results demonstrate that there is almost no difference between the discrete and continuous case.
Edit intent: clarity
Original:  For instance, for any regular network in the matching-based model, all nodes have the same load up to a constant additive error in (asymptotically) the same number of rounds required in the continuous case.
Revised:  For instance, for any regular network in the matching model, all nodes have the same load up to a constant additive error in (asymptotically) the same number of rounds required in the continuous case.
Edit intent: clarity
Original:  For instance, for any regular network in the matching-based model, all nodes have the same load up to a constant additive error in (asymptotically) the same number of rounds required in the continuous case.
Revised:  For instance, for any regular network in the matching-based model, all nodes have the same load up to an additive constant in (asymptotically) the same number of rounds required in the continuous case.
Edit intent: clarity
Original:  This generalizes and tightens the previous best result, which only holds for expander graphs and whose number of rounds is sub-optimal (STOC'09).
Revised:  This generalizes and tightens the previous best result, which only holds for expander graphs (STOC'09).
Edit intent: clarity
Original: We consider the problem of balancing load items (tokens) on networks.
Revised: We consider the problem of balancing load items (tokens) in networks.
Edit intent: clarity
Original:  Starting with an arbitrary load distribution, we allow in each round nodes to exchange tokens with their neighbors  .
Revised:  Starting with an arbitrary load distribution, we allow nodes to exchange tokens with their neighbors .
Edit intent: clarity
Original:  Starting with an arbitrary load distribution, we allow in each round nodes to exchange tokens with their neighbors  .
Revised:  Starting with an arbitrary load distribution, we allow in each round nodes to exchange tokens with their neighbors in each round .
Edit intent: clarity
Original:  For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains  whose convergence is fairly well-understood in terms of their spectral gap.
Revised:  For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains , whose convergence is fairly well-understood in terms of their spectral gap.
Edit intent: fluency
Original:  However, in many applications  load items cannot be divided arbitrarily  and we need to deal with the discrete case where the load is composed of indivisible tokens.
Revised:  However, in many applications , load items cannot be divided arbitrarily and we need to deal with the discrete case where the load is composed of indivisible tokens.
Edit intent: fluency
Original:  However, in many applications  load items cannot be divided arbitrarily  and we need to deal with the discrete case where the load is composed of indivisible tokens.
Revised:  However, in many applications load items cannot be divided arbitrarily , and we need to deal with the discrete case where the load is composed of indivisible tokens.
Edit intent: fluency
Original:  This discretization entails a non-linear behavior due to its rounding errors, which makes the analysis much harder than in the continuous case.
Revised:  This discretization entails a non-linear behavior due to its rounding errors, which makes this analysis much harder than in the continuous case.
Edit intent: fluency
Original:  Therefore, it has been a major open problem to understand the limitations of discrete load balancing and its relation to the continuous case.
Edit intent: coherence
Original:  For instance, for any regular network in the matching model, all nodes have the same load up to an additive constant in (asymptotically) the same number of rounds  required in the continuous case.
Revised:  For instance, for any regular network in the matching model, all nodes have the same load up to an additive constant in (asymptotically) the same number of rounds as required in the continuous case.
Edit intent: clarity
Original: Observational and analytical research of results of studies on etiology and pathogenesis of psoriatic disease is carried out.
Revised: Analytical research of results of studies on etiology and pathogenesis of psoriatic disease is carried out.
Edit intent: clarity
Original:  Y-model of pathogenesis of psoriasis - skin reaction to systemic psoriatic process SPP is formulated.
Revised:  The new model of pathogenesis - skin reaction to systemic psoriatic process SPP is formulated.
Edit intent: clarity
Original:   Psoriatic inflammation is regarded as a reaction of the skin immune system to activity of reprogrammed monocytes Mo-R and dendritic cells DC-R involved in derma from blood flow.
Revised:  ... Psoriatic inflammation is regarded as a reaction of the skin immune system to activity of reprogrammed monocytes Mo-R and dendritic cells DC-R involved in derma from blood flow.
Edit intent: fluency
Original:   Psoriatic inflammation is regarded as a reaction of the skin immune system to activity of reprogrammed monocytes Mo-R and dendritic cells DC-R involved in derma from blood flow.
Revised:  Psoriatic inflammation is regarded as a reaction of the skin immune system to activity of Mo-R and dendritic cells DC-R involved in derma from blood flow.
Edit intent: clarity
Original:   Psoriatic inflammation is regarded as a reaction of the skin immune system to activity of reprogrammed monocytes Mo-R and dendritic cells DC-R involved in derma from blood flow.
Revised:  Psoriatic inflammation is regarded as a reaction of the skin immune system to activity of reprogrammed monocytes Mo-R and DC-R involved in derma from blood flow.
Edit intent: clarity
Original:  Blood Mo-R and DC-R contain Y-antigen and, getting to derma, can be transformed in mature maDC-Y and present this antigen to Y-specific T-lymphocytes as well as activate them.
Revised:  They contain Y-antigen and, getting to derma, can be transformed in mature maDC-Y and present this antigen to Y-specific T-lymphocytes as well as activate them.
Edit intent: coherence
Original:  The severity of plaque is determined by intensity of Y-antigen income into derma (inside Mo-R and DC-R) , which depends on SPP severity.
Revised:  Existence and severity of psoriatic plaque is determined by intensity of Y-antigen income into derma (inside Mo-R and DC-R) , which depends on SPP severity.
Edit intent: clarity
Original:  The severity of plaque is aggravated by LP2 inflammation if it persists after this plaque initiation.
Revised:  The severity of plaque is aggravated by LP2-inflammation if it persists after this plaque initiation.
Edit intent: fluency
Original:  New  Mo-R, DC-R  and Y-specific T-lymphocytes are constantly attracted into plaques from blood flow, and so support vicious cycles.
Revised:  New Mo-R, DC-R ) and Y-specific T-lymphocytes are constantly attracted into plaques from blood flow, and so support vicious cycles.
Edit intent: fluency
Original:  " Part 1. Systemic psoriatic process." - arxiv.org/abs/ 1110.0584 v1
Revised:  Part 1. Systemic psoriatic process." - arxiv.org/abs/ 1110.0584 v1
Edit intent: fluency
Original:  " Part 1. Systemic psoriatic process." - arxiv.org/abs/ 1110.0584 v1
Revised:  " Part 1. arXiv: 1110.0584 v1
Edit intent: clarity
Original:  We derive tight bounds on the critical threshold, p_c(\theta), such that for all p > p  _c(\theta) full percolation takes place, whereas for p < p  _c(\theta) it does not.
Revised:  We derive bounds on the critical threshold, p_c(\theta), such that for all p > p _c(\theta) full percolation takes place, whereas for p < p _c(\theta) it does not.
Edit intent: clarity
Original:  We derive tight bounds on the critical threshold, p_c(\theta), such that for all p > p  _c(\theta) full percolation takes place, whereas for p < p  _c(\theta) it does not.
Revised:  We derive tight bounds on the critical threshold, p_c(\theta), such that for all p > p " _c(\theta) full percolation takes place, whereas for p < p _c(\theta) it does not.
Edit intent: fluency
Original:  We derive tight bounds on the critical threshold, p_c(\theta), such that for all p > p  _c(\theta) full percolation takes place, whereas for p < p  _c(\theta) it does not.
Revised:  We derive tight bounds on the critical threshold, p_c(\theta), such that for all p > p _c(\theta) full percolation takes place, whereas for p < p ' _c(\theta) it does not.
Edit intent: fluency
Original: We study the scalability of multihop wireless communications, a major concern in networking, for the case that users access content replicated across the nodes.
Revised: We investigate on the scalability of multihop wireless communications, a major concern in networking, for the case that users access content replicated across the nodes.
Edit intent: clarity
Original:  Our study begins with the detailed joint content replication and delivery problem  , a hard combinatorial optimization , which is reduced to the simpler replication density problem whose performance is of the same order as the original.
Revised:  Our study begins with the detailed joint content replication and delivery problem , a hard combinatorial optimization . This is reduced to the simpler replication density problem whose performance is of the same order as the original.
Edit intent: coherence
Original:  Our study begins with the detailed joint content replication and delivery problem  , a hard combinatorial optimization , which is reduced to the simpler replication density problem whose performance is of the same order as the original.
Revised:  Our study begins with the detailed joint content replication and delivery problem , a hard combinatorial optimization , which is reduced to a simpler problem based on replication density, whose performance is of the same order as the original.
Edit intent: clarity
Original:  Assuming a Zipf popularity law, and letting the number of files and network nodes both go to infinity, we identify scaling capacity laws from O(N) down to O(1).
Revised:  Assuming a Zipf popularity law, and letting the size of content and network both go to infinity, we identify scaling capacity laws from O(N) down to O(1).
Edit intent: clarity
Original:  The paper also discusses the use of Gaussian quadrature rules for calculating hub and authority scores  .
Revised:  The paper also discusses the use of Gaussian quadrature rules for calculating hub and authority scores is discussed .
Edit intent: clarity
Original: Bone is a continuously renewed biomaterial .
Revised: Bone is a biomaterial undergoing continuous renewal .
Edit intent: clarity
Original:  Therefore, we develop a  mathematical model of bone cell interactions that takes into account both biochemicaland biomechanical regulations, and investigate numerically the influence of the specific surface (surface density) on bone remodelling within a small bone tissue sample.
Revised:  Therefore, we develop a sophisticated mathematical model of bone cell interactions that takes into account both biochemicaland biomechanical regulations, and investigate numerically the influence of the specific surface (surface density) on bone remodelling within a small bone tissue sample.
Edit intent: clarity
Original:  Therefore, we develop a  mathematical model of bone cell interactions that takes into account both biochemicaland biomechanical regulations, and investigate numerically the influence of the specific surface (surface density) on bone remodelling within a small bone tissue sample.
Revised:  Therefore, we develop a mathematical model of bone cell interactions that takes into account both biochemicaland biomechanical regulations, and investigate numerically the influence of bone surface availability in bone remodelling within a small bone tissue sample.
Edit intent: clarity
Original:  Therefore, we develop a  mathematical model of bone cell interactions that takes into account both biochemicaland biomechanical regulations, and investigate numerically the influence of the specific surface (surface density) on bone remodelling within a small bone tissue sample.
Revised:  Therefore, we develop a mathematical model of bone cell interactions that takes into account both biochemicaland biomechanical regulations, and investigate numerically the influence of the specific surface (surface density) on bone remodelling within a representative bone tissue sample.
Edit intent: clarity
Original:  A multiscale homogenisation scheme is used for the calculation of microstrains at the cellular level.
Edit intent: coherence
Original:  The interdependence between the bone cells' activity, which modifies the bone microstructure, and changes in the specific surface is implemented using a known experimental relationship between bone specific surface and bone porosity.
Revised:  The interdependence between the bone cells' activity, which modifies the bone microstructure, and changes in the specific surface is implemented using a remarkable experimental relationship between bone specific surface and bone porosity.
Edit intent: clarity
Original:  Our model suggests that geometrical regulation of the activation of new remodelling events has a significant effect on bone porosity and bone stiffness.
Revised:  Our model suggests that geometrical regulation of the activation of new remodelling events could have a significant effect on bone porosity and bone stiffness.
Edit intent: clarity
Original:  For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that even around a contractile inclusion or molecular motor there is a compressed region ;
Revised:  For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that even around a contractile inclusion or molecular motor there is radial compression ;
Edit intent: clarity
Original:  We extend this algorithm to solve a weighted version of the problem in which vertices have integer weights and  can be split into differently colored parts, so that the total weight of a monochromatic component does not exceed C.
Revised:  We extend this algorithm to solve a weighted version of the problem in which vertices have integer weights and can be split into differently colored parts, however, the total weight of a monochromatic component does not exceed C.
Edit intent: coherence
Original:  We extend this algorithm to solve a weighted version of the problem in which vertices have integer weights and  can be split into differently colored parts, so that the total weight of a monochromatic component does not exceed C.
Revised:  We extend this algorithm to solve a weighted version of the problem in which vertices have integer weights and can be split into differently colored parts, so that the total weight of a monochromatic component cannot exceed C.
Edit intent: clarity
Original: This article discusses the performance of several spectral numerical methods to solve the time evolution of a convection problem with viscosity strongly dependent on temperature.
Revised: This article proposes spectral numerical methods to solve the time evolution of a convection problem with viscosity strongly dependent on temperature.
Edit intent: clarity
Original:  The setup is a 2D domain with periodic boundary conditions along the horizontal coordinate.
Revised:  The set-up is a 2D domain with periodic boundary conditions along the horizontal coordinate.
Edit intent: fluency
Original:  Stable stationary solutions become unstable through a Hopf bifurcation, after which the time-dependent regime is solved by the spectral techniques proposed for that purpose in this article .
Revised:  Stable stationary solutions become unstable through a Hopf bifurcation, after which the time-dependent regime is solved by the spectral techniques proposed in this article .
Edit intent: clarity
Original:  Our main theorem states that q-holonomicity is preserved under twisting, i.e., replacing q by \omega q where \omega is a complex root of unity .
Revised:  Our main theorems state that q-holonomicity is preserved under twisting, i.e., replacing q by \omega q where \omega is a complex root of unity .
Edit intent: fluency
Original:  Our proofs are constructive, work } in the multivariate setting of \partial-finite sequences and is implemented in the Mathematica package HolonomicFunctions.
Revised:  Our proofs are constructive, work } in the multivariate setting of \partial-finite sequences and are implemented in the Mathematica package HolonomicFunctions.
Edit intent: fluency
Original: Benford's law states that in many data sets the overall distribution of the significant digits tends to be logarithmic so that the occurrence of numbers beginning with smaller first significant digits is more often than those with larger ones.
Revised: Benford's law states that in many data sets the overall distribution of the significant digits tends to be logarithmic so that the numbers beginning with smaller first significant digits is more often than those with larger ones.
Edit intent: clarity
Original: Benford's law states that in many data sets the overall distribution of the significant digits tends to be logarithmic so that the occurrence of numbers beginning with smaller first significant digits is more often than those with larger ones.
Revised: Benford's law states that in many data sets the overall distribution of the significant digits tends to be logarithmic so that the occurrence of numbers beginning with smaller significant digits occur more often than those with larger ones.
Edit intent: clarity
Original:  Further, the general improvement in the statistical accuracy which we observed supports the applicability of the normalization process used to limit the inclusion of the countries in the database for which the illicit financial flows are not substantial.
Revised:  Further, the general improvement in the statistical accuracy we find here supports the applicability of the normalization process used to limit the inclusion of the countries in the database for which the illicit financial flows are not substantial.
Edit intent: clarity
Original:  Further, the general improvement in the statistical accuracy which we observed supports the applicability of the normalization process used to limit the inclusion of the countries in the database for which the illicit financial flows are not substantial.
Revised:  Further, the general improvement in the statistical accuracy which we observed supports the applicability of the two stage normalization in filtering out countries from database for which the illicit financial flows are not substantial.
Edit intent: clarity
Original:  Further, the general improvement in the statistical accuracy which we observed supports the applicability of the normalization process used to limit the inclusion of the countries in the database for which the illicit financial flows are not substantial.
Revised:  Further, the general improvement in the statistical accuracy which we observed supports the applicability of the normalization process used to limit the inclusion of the countries in the database for which illicit financial flows are not substantial.
Edit intent: clarity
Original: Benford's law states that in many data sets the overall distribution of the significant digits tends to be logarithmic so that the numbers beginning with smaller significant digits occur more often than those with larger ones.
Revised: Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller significant digits occur more often than those with larger ones.
Edit intent: clarity
Original: Benford's law states that in many data sets the overall distribution of the significant digits tends to be logarithmic so that the numbers beginning with smaller significant digits occur more often than those with larger ones.
Revised: Benford's law states that in many data sets the overall distribution of the significant digits tends to be logarithmic so that the numbers beginning with smaller digits occur more often than those with larger ones.
Edit intent: fluency
Original:  We show that One-clock priced timed games can be solved in time m 12^n poly(n ), where n is the number of states and m is the number of actions.
Revised:  We show that one-clock priced timed games can be solved in time m 12^n poly(n ), where n is the number of states and m is the number of actions.
Edit intent: fluency
Original:  For our improvement, we introduce and study a new algorithm for solving One-clock Priced Timed Games , based on the sweep-line technique from computational geometry .
Revised:  For our improvement, we introduce and study a new algorithm for solving one-clock priced timed games , based on the sweep-line technique from computational geometry .
Edit intent: fluency