wanyu/IteraTeR_v2 huggingface dataset:
Original:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant  \left(\right) \geqslant  and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant  consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left(  ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Revised:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant \left(\right) \geqslant and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left( i=3 ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Edit intent: fluency
Original:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant  \left(\right) \geqslant  and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant  consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left(  ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Revised:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant \left(\right) \geqslant and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left( ^{k}{p \_i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Edit intent: fluency
Original:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant  \left(\right) \geqslant  and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant  consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left(  ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Revised:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant \left(\right) \geqslant and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left( ^{k}{p _i }^{\alpha \_i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Edit intent: fluency
Original:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant  \left(\right) \geqslant  and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant  consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left(  ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Revised:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant \left(\right) \geqslant and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left( ^{k}{p _i }^{\alpha _i } \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Edit intent: fluency
Original:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant  \left(\right) \geqslant  and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant  consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left(  ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Revised:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant \left(\right) \geqslant and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left( ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \_i\geqslant 0 for all i, lined in the increasing order.
Edit intent: fluency
Original:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant  \left(\right) \geqslant  and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant  consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left(  ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, lined in the increasing order.
Revised:  + q _3 , for two sequences of arbitrary positive integers (p_i)_{i \ge 3 and (q_i)_{i \ge 3} } \left(\right) \geqslant \left(\right) \geqslant and we show that the sequence of differences \left(\_k(n)- \mathrm{G}\_k} ( G_k(n)-G_k( n-1) )_{n \ge 1 \right) \geqslant consists of numbers of the form (\prod_{i=3^{k}q_i) \cdot (\prod_{i=3}} \left( }q\_i}\right) \left( ^{k}{p _i }^{\alpha _i } ) \right) , with \alpha _i%DIFDELCMD < \ge %%% \geqslant 0 for all i, arranged in nondecreasing order.
Edit intent: clarity
Original:  Based on the intersection theory, the Chow form for an irreducible differential variety is defined and most of the properties of the Chow form in the algebraic case are extended to its differential counterpart.
Revised:  Based on the intersection theory, the Chow form for an irreducible differential variety is defined and most of the properties of the Chow form in the algebraic case are established for its differential counterpart.
Edit intent: clarity
Original:  Rapidly growing overhead associated with the primary function of the Internet---routing information packets between any two computers in the world---causes concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade ;
Revised:  Rapidly growing overheads associated with the primary function of the Internet---routing information packets between any two computers in the world---causes concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade ;
Edit intent: fluency
Original:  Rapidly growing overhead associated with the primary function of the Internet---routing information packets between any two computers in the world---causes concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade ;
Revised:  Rapidly growing overhead associated with the primary function of the Internet---routing information packets between any two computers in the world---cause concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade ;
Edit intent: fluency
Original:  We develop new general models for  multi-cell SINR using stochastic geometry.
Revised:  We develop new general models for the multi-cell SINR using stochastic geometry.
Edit intent: fluency
Original:  When the rate of immigration is either zero or proportional to the birth rate, we use Kendall's generating function method to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one dimensional integration.
Revised:  When birth rate is zero or immigration rate is either zero or proportional to the birth rate, we use Kendall's generating function method to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one dimensional integration.
Edit intent: clarity
Original:  This reduction results in  simple and fast implementation of the EM algorithm.
Revised:  This reduction results in a simple and fast implementation of the EM algorithm.
Edit intent: fluency
Original:  We test our algorithms on simulated data and then use our new methods to explore  birth and death rates of a transposable element in the genome of Mycobacterium tuberculosis, the causative agent of tuberculosis.
Revised:  We test our algorithms on simulated data and then use our new methods to explore the birth and death rates of a transposable element in the genome of Mycobacterium tuberculosis, the causative agent of tuberculosis.
Edit intent: fluency
Original:  When birth rate is zero or immigration rate is either zero or proportional to the birth rate, we use Kendall's generating function method to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one dimensional integration.
Revised:  When birth rate is zero or immigration rate is either zero or proportional to the birth rate, we use Kendall's method. Using the generating function, we reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one dimensional integration.
Edit intent: fluency
Original:  We test our algorithms on simulated data and then use our new methods to explore the birth and death rates of a transposable element in the genome of Mycobacterium tuberculosis, the causative agent of  tuberculosis.
Revised:  We test our algorithms on simulated data , we apply it to DNA fingerprinting of Mycobacterium tuberculosis, the causative agent of tuberculosis.
Edit intent: clarity
Original:  We derive a closed-form expression of the joint generating function of the BD process and some of its statistics using Kendall's method.
Revised:  We derive a closed-form expression for the joint generating function of the BD process and some of its statistics using Kendall's method.
Edit intent: fluency
Original:  Our analysis reveals previously undocumented differences in death rates of IS6110  among three major lineages of Mycobacterium tuberculosis .
Revised:  Our analysis reveals previously undocumented differences in IS6110 among three major lineages of Mycobacterium tuberculosis .
Edit intent: clarity
Original:  Fitting linear BDI processes to panel data is a nontrivial optimization problem , because birth and death rates can be functions of many parameters related to the covariates of interest.
Revised:  Fitting linear BDI processes to panel data is a nontrivial optimization problem because birth and death rates can be functions of many parameters related to the covariates of interest.
Edit intent: fluency
Original:  We propose a novel expectation-maximization (EM) algorithm for fitting linear BDI models with covariates to panel data.
Revised:  We propose a novel expectation--maximization (EM) algorithm for fitting linear BDI models with covariates to panel data.
Edit intent: fluency
Original:  We derive a closed-form expression for the joint generating function of some of the BDI process statistics and use this generating function to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one dimensional integration.
Revised:  We derive a closed-form expression for the joint generating function of some of the BDI process statistics and use this generating function to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one-dimensional integration.
Edit intent: fluency
Original: Aim: To assess the capability of  monocyte-derived dendritic cells (DCs) to take Fe3O4 magnetic nanoparticles (MNPs) , keeping their viability.
Revised: In this work, the capability of monocyte-derived dendritic cells (DCs) to take Fe3O4 magnetic nanoparticles (MNPs) , keeping their viability.
Edit intent: clarity
Original:  To provoke cell death on these MNPs-loaded DCs using an external alternating magnetic field (AMF) . Material methods: Peripheral blood mononuclear cells were isolated from normal blood and platelets removed by centrifugation.
Revised:  To provoke cell death on these MNPs-loaded DCs using an external alternating magnetic methods: Peripheral blood mononuclear cells were isolated from normal blood and platelets removed by centrifugation.
Edit intent: clarity
Original:  However, we found that the amount of incorporated magnetic material within the cytoplasm (1 to 5 pg/cell) was unable to raise the temperature of the cell culture.
Revised:  However, we found that the amount of incorporated magnetic particles did not raise the temperature of the cell culture.
Edit intent: clarity
Original:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under  AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Revised:  Conclusion: Our results point to local damage produced by the MNPs could be the main mechanism for the selective cell death of MNP-loaded DCs under AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Edit intent: clarity
Original:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under  AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Revised:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under an AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Edit intent: fluency
Original:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under  AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Revised:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under AMF. Based on the ability of these cells to evade the reticuloendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Edit intent: fluency
Original:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under  AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Revised:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes combined with an AMF should be considered as a potentially powerful tool for tumor therapy.
Edit intent: fluency
Original:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under  AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumor therapy.
Revised:  Conclusion: Our results point to local damage produced by the MNPs as the main mechanism for the selective cell death of MNP-loaded DCs under AMF. Based on the ability of these cells to evade the rethiculoendothelial system, these complexes in combination with AMF should be considered as a potentially powerful tool for tumour therapy.
Edit intent: fluency
Original:  Database states form a boolean topos of which the classical "relational algebra" is a fragment.
Revised:  Database states form a topos of which the classical "relational algebra" is a fragment.
Edit intent: clarity
Original:  A database schema is a category and a state is a set-valued functor  .
Revised:  A database schema is a category and a state is a set-valued functor on it .
Edit intent: clarity
Original:  We show that morphisms of schemas induce three "data migration functors" that translate states from one schema to the other in canonical ways.
Revised:  We show that morphisms of schemas induce three "data migration functors" , which translate instances from one schema to the other in canonical ways.
Edit intent: clarity
Original:  We  provide a generic outer bound to the capacity of this system and propose a coding algorithm that achieves this bound for an arbitrary number of users and symmetric channel conditions , assuming that instantaneous feedback is known to all users.
Revised:  We first provide a generic outer bound to the capacity of this system and propose a coding algorithm that achieves this bound for an arbitrary number of users and symmetric channel conditions , assuming that instantaneous feedback is known to all users.
Edit intent: coherence
Original:  Removing this assumption results in a rate region which differs from the outer bound by a factor O(N ^2 /L), where L is  packet length.
Revised:  Removing this assumption results in a throughput region that differs from the outer bound by a factor O(N ^2 /L), where L is packet length.
Edit intent: clarity
Original:  For the case of non-symmetric channels , we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N > = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) when each user knows only its own ACK.
Revised:  For the case of arbitrary channel statistics , we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N > = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) when each user knows only its own ACK.
Edit intent: clarity
Original:  For the case of non-symmetric channels , we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N > = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) when each user knows only its own ACK.
Revised:  For the case of non-symmetric channels , we present a modification of the previous algorithm whose throughput region is identical to the outer bound for N > = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) when each user knows only its own ACK.
Edit intent: clarity
Original:  For the case of non-symmetric channels , we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N > = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) when each user knows only its own ACK.
Revised:  For the case of non-symmetric channels , we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) when each user knows only its own ACK.
Edit intent: clarity
Original:  For the case of non-symmetric channels , we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N > = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) when each user knows only its own ACK.
Revised:  For the case of non-symmetric channels , we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N > = 3, when instant feedback is known to all users, and differs from the bound by O( N^2 /L) , when all 3 users know only their own ACK.
Edit intent: clarity
Original: We consider the N-user broadcast erasure channel with N unicast sessions (one for each user) where receiver feedback is  sent to the transmitter in the form of ACK/NACK messages.
Revised: We consider the N-user broadcast erasure channel with N unicast sessions (one for each user) where receiver feedback is regularly sent to the transmitter in the form of ACK/NACK messages.
Edit intent: clarity
Original:  For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose throughput region is identical to the outer bound for N = 3, when instant feedback is known to all users, and differs from the bound by O(1/L), when all 3 users know only their own ACK.
Revised:  For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose throughput region is identical to the outer bound for N = 3, when instant feedback is known to all users, and differs from the bound by O(1/L), when the 3 users know only their own ACK.
Edit intent: clarity
Original:  we then propose a virtual-queue-based inter-session mixing coding algorithm, determine its throughput region and show that it achieves capacity under certain conditions on channel statistics, assuming that instantaneous feedback is known to all users.
Revised:  we then propose a virtual-queue-based inter-session mixing coding algorithm, determine its rate region and show that it achieves capacity under certain conditions on channel statistics, assuming that instantaneous feedback is known to all users.
Edit intent: clarity
Original:  For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose throughput region is identical to the outer bound for N=3, when instant feedback is known to all users, and differs from the bound by O( 1 /L)\to  , when the 3 users know only their own ACK.
Revised:  For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose rate region is identical to the outer bound for N=3, when instant feedback is known to all users, and differs from the bound by O( 1 /L)\to , when the 3 users know only their own ACK.
Edit intent: clarity
Original:  For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose throughput region is identical to the outer bound for N=3, when instant feedback is known to all users, and differs from the bound by O( 1 /L)\to  , when the 3 users know only their own ACK.
Revised:  For the case of arbitrary channel statistics, we present a modification of the previous algorithm whose throughput region is identical to the outer bound for N=3, when instant feedback is known to all users, and differs from the bound by 1 /L)\to , when the 3 users know only their own ACK.
Edit intent: clarity
Original: The Ising Model , a pairwise binary maximum entropy model, has recently received much attention for the statistical description of neural spike train data.
Revised: The Ising Model has recently received much attention for the statistical description of neural spike train data.
Edit intent: clarity
Original:  In particular, we demonstrate decoding of spatial patterns of activity comprised of over 700 neurons with the TAP algorithm.
Edit intent: coherence