wanyu/IteraTeR_v2 huggingface dataset:
Original:  For all positive integers m,n , B and every m x n (0,1)-matrix M with zeta_s( m )Bn 1-entries, the rows of M can be partitioned into s intervals so that some Bn/m-tuple of columns contains at least B 1-entries in each of the intervals.
Revised:  For all positive integers n and B and every m x n (0,1)-matrix M with zeta_s( m )Bn 1-entries, the rows of M can be partitioned into s intervals so that some Bn/m-tuple of columns contains at least B 1-entries in each of the intervals.
Edit intent: clarity
Original:  For all positive integers m,n , B and every m x n (0,1)-matrix M with zeta_s( m )Bn 1-entries, the rows of M can be partitioned into s intervals so that some Bn/m-tuple of columns contains at least B 1-entries in each of the intervals.
Revised:  For all positive integers m,n , B and every n x n (0,1)-matrix M with zeta_s( m )Bn 1-entries, the rows of M can be partitioned into s intervals so that some Bn/m-tuple of columns contains at least B 1-entries in each of the intervals.
Edit intent: fluency
Original:  For all positive integers m,n , B and every m x n (0,1)-matrix M with zeta_s( m )Bn 1-entries, the rows of M can be partitioned into s intervals so that some Bn/m-tuple of columns contains at least B 1-entries in each of the intervals.
Revised:  For all positive integers m,n , B and every m x n (0,1)-matrix M with zeta_s( n )Bn 1-entries, the rows of M can be partitioned into s intervals so that some Bn/m-tuple of columns contains at least B 1-entries in each of the intervals.
Edit intent: fluency
Original:  For all positive integers m,n , B and every m x n (0,1)-matrix M with zeta_s( m )Bn 1-entries, the rows of M can be partitioned into s intervals so that some Bn/m-tuple of columns contains at least B 1-entries in each of the intervals.
Revised:  For all positive integers m,n , B and every m x n (0,1)-matrix M with zeta_s( m )Bn 1-entries, the rows of M can be partitioned into s intervals so that at least B columns contain at least B 1-entries in each of the intervals.
Edit intent: clarity
Original: Hard combinatorial optimisation problems deal with the search for the ground state of discrete systems under strong frustration such as spin glasses . A transformation of state variables may enhance computational tractability.
Revised: Hard combinatorial optimization problems deal with the search for the ground state of discrete systems under strong frustration such as spin glasses . A transformation of state variables may enhance computational tractability.
Edit intent: fluency
Original: Hard combinatorial optimisation problems deal with the search for the ground state of discrete systems under strong frustration such as spin glasses . A transformation of state variables may enhance computational tractability.
Revised: Hard combinatorial optimisation problems deal with the search for the ground state of discrete systems under strong constraints . A transformation of state variables may enhance computational tractability.
Edit intent: clarity
Original:  Here we show how redundant non-invertible encodings enhance optimisation by enriching the density of low-energy states.
Revised:  Here we show how redundant non-invertible encodings enhance optimization by enriching the density of low-energy states.
Edit intent: fluency
Original:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Revised:  Finding an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Edit intent: fluency
Original:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Revised:  As an exact solution to MEI is NP-hard for general F . We present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Edit intent: fluency
Original:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Revised:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI that achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Edit intent: fluency
Original:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Revised:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation guarantee -- depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Edit intent: clarity
Original:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G ) in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Revised:  As an exact solution to MEI is NP-hard for general F , we present the first approximation algorithm for MEI which achieves an additive approximation factor ( depending only on the size of F and the maximum degree of G , in the case of connected G. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion.
Edit intent: fluency
Original:  It is also known that an (even approximate) solution to the MEI problem would approximate the crossing number of the F-almost-planar graph G+F, while computing the crossing number of G+F exactly is NP-hard already when |F|=1.
Revised:  It is also known that an (even approximate) solution to the MEI problem would approximate the crossing number of the F-almost-planar graph G+F, while computing the crossing number of G+F exactly is NP-hard already when |F|=1.
Edit intent: fluency
Original:  The model is motivated by {\em  experiments on organelle motility along a microtubule (MT),  where particles are propelled by molecular motors (dynein and kinesin) along the thirteen protofilaments of the MT . In the model, particles can switch directions of motion due to "tug-of-war" events between counteracting motors.
Revised:  The model is motivated by {\em experiments on organelle motility along a microtubule (MT), consisting of thirteen protofilaments, where particles are propelled by molecular motors (dynein and kinesin) along the thirteen protofilaments of the MT . In the model, particles can switch directions of motion due to "tug-of-war" events between counteracting motors.
Edit intent: clarity
Original:  The model is motivated by {\em  experiments on organelle motility along a microtubule (MT),  where particles are propelled by molecular motors (dynein and kinesin) along the thirteen protofilaments of the MT . In the model, particles can switch directions of motion due to "tug-of-war" events between counteracting motors.
Revised:  The model is motivated by {\em experiments on organelle motility along a microtubule (MT), where particles are propelled by molecular motors (dynein and kinesin) . In the model, particles can switch directions of motion due to "tug-of-war" events between counteracting motors.
Edit intent: clarity
Original:  The model is motivated by {\em  experiments on organelle motility along a microtubule (MT),  where particles are propelled by molecular motors (dynein and kinesin) along the thirteen protofilaments of the MT . In the model, particles can switch directions of motion due to "tug-of-war" events between counteracting motors.
Revised:  The model is motivated by {\em experiments on organelle motility along a microtubule (MT), where particles are propelled by molecular motors (dynein and kinesin) along the thirteen protofilaments of the MT . In the model, organelles (particles) can switch directions of motion due to "tug-of-war" events between counteracting motors.
Edit intent: clarity
Original:  Collisions of particles on the same lane can be cleared by switching to adjacent filaments (lane changes).
Revised:  Collisions of particles on the same lane can be cleared by switching to adjacent protofilaments (lane changes).
Edit intent: clarity
Original:  We analyze transport properties of the model with no-flux boundary conditions at the end of a MT ("plus-end" or tip).
Revised:  We analyze transport properties of the model with no-flux boundary conditions at one end of a MT ("plus-end" or tip).
Edit intent: clarity
Original:  In particular, the main causes of the diverse phenomenology of these diseases, of which measles and pertussis dynamics are two extreme examples, have been a subject of debate in the literature .
Revised:  In particular, different models of immunity waning and degree of protection applied to disease and vaccine induced immunity have been debated in the literature .
Edit intent: clarity
Original:  This issue is addressed here through the comparison of five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection based on susceptible-infective-recovered (SIR) dynamics in a closed population.
Revised:  This issue is addressed here through the comparison of five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection based on susceptible-infective-recovered dynamics in a closed population.
Edit intent: clarity
Original: Motivated by the dynamics of cultural change and diversity, we consider a generalization of the three-species constrained voter model on a complete graph introduced in [J. Phys.
Revised: Motivated by the dynamics of cultural change and diversity, we generalize the three-species constrained voter model on a complete graph introduced in [J. Phys.
Edit intent: clarity
Original:  In this opinion dynamics model, a population of total size N is composed of "leftists" and "rightists" that interact with "centrists": a leftist and centrist can both become leftists with rate (1+q)/2 or centrists with rate (1-q)/2 (and similarly for rightists and centrists), where q denotes the bias towards extremism (q>0) or centrism (q<0).
Revised:  In this opinion dynamics model, a population of size N is composed of "leftists" and "rightists" that interact with "centrists": a leftist and centrist can both become leftists with rate (1+q)/2 or centrists with rate (1-q)/2 (and similarly for rightists and centrists), where q denotes the bias towards extremism (q>0) or centrism (q<0).
Edit intent: clarity
Original:  This system admits three absorbing fixed points and a "polarization" line along which a frozen mixture of leftists and rightists coexists .
Revised:  This system admits three absorbing fixed points and a "polarization" line along which a frozen mixture of leftists and rightists coexist .
Edit intent: fluency
Original: Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple Access Channels (GMAC) have been recently reported, wherein introducing appropriate rotation between the constellations of the two users is shown to maximally enlarge the CC capacity region.
Revised: Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple Access Channels (GMAC) have been recently reported, wherein an appropriate angle of rotation between the constellations of the two users is shown to maximally enlarge the CC capacity region.
Edit intent: clarity
Original: Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple Access Channels (GMAC) have been recently reported, wherein introducing appropriate rotation between the constellations of the two users is shown to maximally enlarge the CC capacity region.
Revised: Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple Access Channels (GMAC) have been recently reported, wherein introducing appropriate rotation between the constellations of the two users is shown to enlarge the CC capacity region.
Edit intent: clarity
Original:  Such a Non-Orthogonal Multiple Access (NO-MA) method of enlarging the CC capacity region is referred to as Constellation Rotation (CR) scheme.
Revised:  We refer to such a scheme as the Constellation Rotation (CR) scheme.
Edit intent: clarity
Original:  In this paper, we propose a novel NO-MA technique called Constellation Power Allocation (CPA) scheme to enlarge the CC capacity region of two-user GMAC . We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced ML decoding complexity for some QAM constellations.
Revised:  In this paper, we propose a novel scheme called the Constellation Power Allocation (CPA) scheme to enlarge the CC capacity region of two-user GMAC . We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced ML decoding complexity for some QAM constellations.
Edit intent: clarity
Original:  In this paper, we propose a novel NO-MA technique called Constellation Power Allocation (CPA) scheme to enlarge the CC capacity region of two-user GMAC . We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced ML decoding complexity for some QAM constellations.
Revised:  In this paper, we propose a novel NO-MA technique called Constellation Power Allocation (CPA) scheme to enlarge the CC capacity region of two-user GMAC . We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced decoding complexity for some QAM constellations.
Edit intent: clarity
Original:  In this paper, we propose a novel NO-MA technique called Constellation Power Allocation (CPA) scheme to enlarge the CC capacity region of two-user GMAC . We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced ML decoding complexity for some QAM constellations.
Revised:  In this paper, we propose a novel NO-MA technique called Constellation Power Allocation (CPA) scheme to enlarge the CC capacity region of two-user GMAC . We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced ML decoding complexity for QAM constellations.
Edit intent: clarity
Original:  Further, the CPA scheme used for two-user GMAC with random phase offsets is shown to provide larger CC sum capacities at high SNR values compared to the CR scheme.
Revised:  Further, the CPA scheme is more than the CR scheme at high SNR values compared to the CR scheme.
Edit intent: clarity
Original: We study the wireless scheduling problem in the physically realistic SINR model.
Revised: We study the wireless scheduling problem in the SINR model.
Edit intent: clarity
Original:  More specifically : we are given a set of n links, each a sender-receiver pair .
Revised:  More specifically , given a set of n links, each a sender-receiver pair .
Edit intent: clarity
Original:  We would like to schedule the links using the minimum number of slots, using the SINR model of interference among simultaneously transmitting links .
Revised:  We would like to schedule the links usingschedule the minimum number of slots, using the SINR model of interference among simultaneously transmitting links .
Edit intent: clarity
Original:  We would like to schedule the links using the minimum number of slots, using the SINR model of interference among simultaneously transmitting links .
Revised:  We would like to schedule the links using) the links into the minimum number of slots, using the SINR model of interference among simultaneously transmitting links .
Edit intent: clarity
Original:  We would like to schedule the links using the minimum number of slots, using the SINR model of interference among simultaneously transmitting links .
Revised:  We would like to schedule the links using the minimum number of slots, each satisfying interference constraints allowing simultaneous transmission .
Edit intent: clarity
Original:  In this work, we provide a distributed O(\log n)-approximation  for the scheduling problem, matching the best ratio known for centralized algorithms.
Revised:  We give a distributed O(\log n)-approximation for the scheduling problem, matching the best ratio known for centralized algorithms.
Edit intent: clarity
Original:  In this work, we provide a distributed O(\log n)-approximation  for the scheduling problem, matching the best ratio known for centralized algorithms.
Revised:  In this work, we provide a distributed O(\log n)-approximation algorithm for the scheduling problem, matching the best ratio known for centralized algorithms.
Edit intent: fluency
Original:  This is based on an algorithm studied by Kesselheim and V\"ocking, improving their analysis by a logarithmic factor.
Revised:  This is based on an algorithm of Kesselheim and V\"ocking, improving their analysis by a logarithmic factor.
Edit intent: clarity
Original:  This is based on an algorithm studied by Kesselheim and V\"ocking, improving their analysis by a logarithmic factor.
Revised:  This is based on an algorithm studied by Kesselheim and V\"ocking, whose analysis we improve by a logarithmic factor.
Edit intent: clarity
Original:  Our aim is to provide not only the fastest  implementation but also compare to performance models and hardware counter data in order to fully understand the results.
Revised:  Our aim is to provide not only the fastest possible implementation but also compare to performance models and hardware counter data in order to fully understand the results.
Edit intent: clarity
Original:  In comparison with these problems, surjective homomorphism problems seem to be harder to classify and we examine especially three concrete problems of open complexity that have arisen from the literature  .
Revised:  In comparison with these problems, surjective homomorphism problems seem to be harder to classify and we examine especially three concrete problems that have arisen from the literature .
Edit intent: clarity
Original:  This result is the 2-d analogue of the jump from the optimum binary search trees of Knuth in 1971 which required that the distribution be provided, to the splay trees of Sleator and Tarjan in 1985 where in the static optimality theorem it was proven that splay trees had the same asymptotic performance of optimum search trees without being provided the probability distribution.
Revised:  This result is the 2D analogue of the jump from the optimum binary search trees of Knuth in 1971 which required that the distribution be provided, to the splay trees of Sleator and Tarjan in 1985 where in the static optimality theorem it was proven that splay trees had the same asymptotic performance of optimum search trees without being provided the probability distribution.
Edit intent: fluency
Original: In the past ten years , there have been a number of data structures that, given a distribution of planar point location queries, produce a planar point location data structure that is tuned for the provided distribution.
Revised: Over the last decade , there have been a number of data structures that, given a distribution of planar point location queries, produce a planar point location data structure that is tuned for the provided distribution.
Edit intent: fluency
Original: In the past ten years , there have been a number of data structures that, given a distribution of planar point location queries, produce a planar point location data structure that is tuned for the provided distribution.
Revised: In the past ten years , there have been several data structures that, given a distribution of planar point location queries, produce a planar point location data structure that is tuned for the provided distribution.
Edit intent: style
Original:  These structures all suffer from the requirement that the query distribution be provided in advance.
Revised:  These structures all suffer from the requirement that the query distribution must be known in advance.
Edit intent: clarity
Original:  For the problem of point location in a triangulation, a data structure is presented that performs asymptotically as well as these structures, but does not require the distribution to be provided in advance.
Revised:  We present a new data structure for point location queries in planar triangulations. Our structure is asymptotically as fast as the optimal structures, but does not require the distribution to be provided in advance.
Edit intent: clarity
Original:  This result is the 2D analogue of the jump from the optimum binary search trees of Knuth in 1971 which required that the distribution be provided, to the splay trees of Sleator and Tarjan in 1985 where in the static optimality theorem it was proven that splay trees had the same asymptotic performance of optimum search trees without being provided the probability distribution .
Revised:  This result is the 2D analogue of the jump from Knuth's optimum binary search trees of Knuth in 1971 which required that the distribution be provided, to the splay trees of Sleator and Tarjan in 1985 where in the static optimality theorem it was proven that splay trees had the same asymptotic performance of optimum search trees without being provided the probability distribution .
Edit intent: clarity
Original:  This result is the 2D analogue of the jump from the optimum binary search trees of Knuth in 1971 which required that the distribution be provided, to the splay trees of Sleator and Tarjan in 1985 where in the static optimality theorem it was proven that splay trees had the same asymptotic performance of optimum search trees without being provided the probability distribution .
Revised:  This result is the 2D analogue of the jump from the optimum binary search trees of Knuth in 1971 ) to the splay trees of Sleator and Tarjan in 1985 where in the static optimality theorem it was proven that splay trees had the same asymptotic performance of optimum search trees without being provided the probability distribution .
Edit intent: coherence