wanyu/IteraTeR_v2 huggingface dataset:
Original:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) recently proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets of F ^*_q needed to cover the roots of f in \mathbf{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ (t-2)/t } +...
Revised:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets of F ^*_q needed to cover the roots of f in \mathbf{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ (t-2)/t } +...
Edit intent: clarity
Original:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) recently proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets of F ^*_q needed to cover the roots of f in \mathbf{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ (t-2)/t } +...
Revised:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) recently proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets in F ^*_q needed to cover the roots of f in \mathbf{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ (t-2)/t } +...
Edit intent: fluency
Original:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) recently proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets of F ^*_q needed to cover the roots of f in \mathbf{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ (t-2)/t } +...
Revised:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) recently proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets of F ^*_q needed to cover the roots of f in \mathbb{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ (t-2)/t } +...
Edit intent: clarity
Original:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) recently proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets of F ^*_q needed to cover the roots of f in \mathbf{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ (t-2)/t } +...
Revised:  To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) recently proved an upper bound of 2(q-1)^{ (t-2)/(t-1) } on the number of cosets of F ^*_q needed to cover the roots of f in \mathbf{F ^*_q. Here, we give explicit f with root structure approaching this bound: For q a t-th power we give an explicit t-nomial vanishing on q^{ \frac{t-2 } +...
Edit intent: clarity
Original: +q^{1/t distinct cosets of \mathbf{F ^*_q.
Revised: +q^{1/t distinct cosets of \mathbb{F ^*_q.
Edit intent: fluency
Original:  Over prime fields \mathbf{F _p, computational data we provide suggests that it is harder to construct explicit sparse polynomials with many cosets of roots.
Revised:  Over prime fields \mathbf{F _p, computational data we provide suggests that it is harder to construct explicit sparse polynomials with many roots.
Edit intent: clarity
Original:  Nevertheless, we find trinomials vanishing on \Omega(\frac{\log \log p{\log \log \log p}) distinct cosets in \mathbf{F}^*_p and, } assuming the Generalized Riemann Hypothesis, \Omega(\left( \frac{\log p}{\log \log p} ) distinct cosets in \mathbf{F \right)  _p.
Revised:  Nevertheless, {\log \log \log p}) distinct cosets in \mathbf{F}^*_p and, } assuming the Generalized Riemann Hypothesis, \Omega(\left( \frac{\log p}{\log \log p} ) distinct cosets in \mathbf{F \right) _p.
Edit intent: coherence
Original:  Nevertheless, we find trinomials vanishing on \Omega(\frac{\log \log p{\log \log \log p}) distinct cosets in \mathbf{F}^*_p and, } assuming the Generalized Riemann Hypothesis, \Omega(\left( \frac{\log p}{\log \log p} ) distinct cosets in \mathbf{F \right)  _p.
Revised:  Nevertheless, we find trinomials vanishing on \Omega(\frac{\log \log p{\log \log \log p}) distinct cosets in \mathbf{F}^*_p and, } assuming the Generalized Riemann Hypothesis, \Omega(\left( \frac{\log p}{\log \log p} \right) _p.
Edit intent: coherence
Original: We show that the 2D local Hamiltonian problem with the restriction that the ground state satisfies area laws is QMA-complete.
Revised: We show that the 2D local Hamiltonian problem with the constraint that the ground state satisfies area laws is QMA-complete.
Edit intent: fluency
Original: We show that the 2D local Hamiltonian problem with the restriction that the ground state satisfies area laws is QMA-complete.
Revised: We show that the 2D local Hamiltonian problem with the restriction that the ground state obeys area laws is QMA-complete.
Edit intent: clarity
Original:  We also prove similar results in 2D translationally invariant systems and for the 3D Heisenberg and Hubbard models  . Consequently, in general the ground states of local Hamiltonians satisfying area laws do not have efficient classical representations that support efficient computation of local expectation values unless QMA=NP.
Revised:  We also prove similar results in 2D translation-invariant systems and for the 3D Heisenberg and Hubbard models . Consequently, in general the ground states of local Hamiltonians satisfying area laws do not have efficient classical representations that support efficient computation of local expectation values unless QMA=NP.
Edit intent: clarity
Original:  We also prove similar results in 2D translationally invariant systems and for the 3D Heisenberg and Hubbard models  . Consequently, in general the ground states of local Hamiltonians satisfying area laws do not have efficient classical representations that support efficient computation of local expectation values unless QMA=NP.
Revised:  We also prove similar results in 2D translationally invariant systems and for the 3D Heisenberg and Hubbard models . Consequently, in general the ground states of 2D local Hamiltonians with area laws have efficient classical representations that support efficient computation of local expectation values unless QMA=NP.
Edit intent: clarity
Original:  Conceptually , even if in the future area laws are proved for the ground state in 2D gapped systems, there is still a long way to go towards understanding the computational complexity of 2D gapped systems .
Revised:  Conceptually , even if area laws are proved for the ground state in 2D gapped systems, there is still a long way to go towards understanding the computational complexity of 2D gapped systems .
Edit intent: clarity
Original:  Conceptually , even if in the future area laws are proved for the ground state in 2D gapped systems, there is still a long way to go towards understanding the computational complexity of 2D gapped systems .
Revised:  Conceptually , even if in the future area laws are proved for ground states of 2D gapped systems, there is still a long way to go towards understanding the computational complexity of 2D gapped systems .
Edit intent: fluency
Original:  Conceptually , even if in the future area laws are proved for the ground state in 2D gapped systems, there is still a long way to go towards understanding the computational complexity of 2D gapped systems .
Revised:  Conceptually , even if in the future area laws are proved for the ground state in 2D gapped systems, the computational complexity of 2D gapped systems .
Edit intent: clarity
Original: We show that the  2D  local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete.
Revised: We show that the two-dimensional ( 2D local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete.
Edit intent: clarity
Original: We show that the  2D  local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete.
Revised: We show that the 2D ) local Hamiltonian problem with the constraint that the ground state obeys area laws is QMA-complete.
Edit intent: fluency
Original: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total .
Revised: We Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total .
Edit intent: clarity
Original: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total .
Revised: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in rka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total .
Edit intent: coherence
Original: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total .
Revised: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% introduce the quasiminimal subshifts, having finitely many subsystems in total .
Edit intent: clarity
Original: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total .
Revised: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, subshifts having only finitely many subsystems in total .
Edit intent: clarity
Original: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems in total .
Revised: We show that there exists a universal subshift having only a finite number of minimal subsystems, refuting a conjecture in Delvenne, K\r{urka, Blondel, '05}%DIFDELCMD < ]%%% . We then introduce the still smaller class of quasiminimal subshifts, having finitely many subsystems .
Edit intent: clarity
Original:  We construct a universal system in this class, and show examples of such systems generated by substitutions.
Revised:  We show many examples of such systems generated by substitutions.
Edit intent: clarity
Original:  In fact, while [ Delvenne, K\r{u shows that minimal systems have a decidable model-checking problem for regular languages, we show that one (proper nontrivial) subsystem, which can be chosen more or less arbitrarily among minimal systems, is enough to make this problem \Sigma^0_1-complete, even when also restricting to a small subclass of the regular languages.
Revised:  In fact, while [ shows that minimal systems have a decidable model-checking problem for regular languages, we show that one (proper nontrivial) subsystem, which can be chosen more or less arbitrarily among minimal systems, is enough to make this problem \Sigma^0_1-complete, even when also restricting to a small subclass of the regular languages.
Edit intent: coherence
Original: We study the class of 1-perfectly orientable (1-p.o.) graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-p.o. graphs form a common generalization of chordal graphs and circular arc graphs.
Revised: We study the class of 1-perfectly orientable graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-p.o. graphs form a common generalization of chordal graphs and circular arc graphs.
Edit intent: clarity
Original: We study the class of 1-perfectly orientable (1-p.o.) graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-p.o. graphs form a common generalization of chordal graphs and circular arc graphs.
Revised: We study the class of 1-perfectly orientable (1-p.o.) graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-perfectly orientable graphs form a common generalization of chordal graphs and circular arc graphs.
Edit intent: fluency
Original:  Even though 1-p.o. graphs can be recognized in polynomial time, little is known about their structure.
Revised:  Even though they can be recognized in polynomial time, little is known about their structure.
Edit intent: clarity
Original:  This includes : (i)  a characterization of 1-p.o. graphs in terms of edge clique covers, (ii) identification of several graph transformations preserving the class of 1-p.o. graphs, (iii) a complete characterization of 1-p.o. cographs and of 1-p.o. complements of forests, and (iv) an infinite family of minimal forbidden induced minors for the class of 1-p. o. graphs.
Revised:  This includes : (i) give a characterization of 1-p.o. graphs in terms of edge clique covers, (ii) identification of several graph transformations preserving the class of 1-p.o. graphs, (iii) a complete characterization of 1-p.o. cographs and of 1-p.o. complements of forests, and (iv) an infinite family of minimal forbidden induced minors for the class of 1-p. o. graphs.
Edit intent: clarity
Original:  This includes : (i)  a characterization of 1-p.o. graphs in terms of edge clique covers, (ii) identification of several graph transformations preserving the class of 1-p.o. graphs, (iii) a complete characterization of 1-p.o. cographs and of 1-p.o. complements of forests, and (iv) an infinite family of minimal forbidden induced minors for the class of 1-p. o. graphs.
Revised:  This includes : (i) a characterization of 1-p.o. graphs in terms of edge clique covers, (ii) identify several graph transformations preserving the class of 1-p.o. graphs, (iii) a complete characterization of 1-p.o. cographs and of 1-p.o. complements of forests, and (iv) an infinite family of minimal forbidden induced minors for the class of 1-p. o. graphs.
Edit intent: fluency
Original:  This includes : (i)  a characterization of 1-p.o. graphs in terms of edge clique covers, (ii) identification of several graph transformations preserving the class of 1-p.o. graphs, (iii) a complete characterization of 1-p.o. cographs and of 1-p.o. complements of forests, and (iv) an infinite family of minimal forbidden induced minors for the class of 1-p. o. graphs.
Revised:  This includes : (i) a characterization of 1-p.o. graphs in terms of edge clique covers, (ii) identification of several graph transformations preserving the class of 1-p.o. graphs, (iii) exhibit an infinite family of minimal forbidden induced minors for the class of 1-p. o. graphs.
Edit intent: coherence
Original: Summarising the new orphan works law  , we show how they make the public interest prevail and allow libraries and other beneficiaries to improve their services.
Revised: Summarising the new orphan works law , we show how it makes the public interest prevail and allow libraries and other beneficiaries to improve their services.
Edit intent: fluency
Original: Summarising the new orphan works law  , we show how they make the public interest prevail and allow libraries and other beneficiaries to improve their services.
Revised: Summarising the new orphan works law , we show how they make the public interest prevail and allows libraries and other beneficiaries to improve their services.
Edit intent: fluency
Original:  Failing that, european culture will disappear. -- Sintetizzando le nuove norme sulle opere orfane, mostriamo come esse affermino la prevalenza dell'interesse pubblico e consentano a biblioteche e altri enti beneficiari di migliorare i propri servizi.
Revised:  Failing that, European culture will disappear. -- Sintetizzando le nuove norme sulle opere orfane, mostriamo come esse affermino la prevalenza dell'interesse pubblico e consentano a biblioteche e altri enti beneficiari di migliorare i propri servizi.
Edit intent: fluency
Original: Recent experimental studies confirm the prevalence of the widely known performance anomaly problem and the severe network utility degradation this inflicts on current Wi-Fi networks .
Revised: Recent experimental studies confirm the prevalence of the widely known performance anomaly problem in current Wi-Fi networks, and report on the severe network utility degradation this inflicts on current Wi-Fi networks .
Edit intent: clarity
Original: Recent experimental studies confirm the prevalence of the widely known performance anomaly problem and the severe network utility degradation this inflicts on current Wi-Fi networks .
Revised: Recent experimental studies confirm the prevalence of the widely known performance anomaly problem and the severe network utility degradation caused by this phenomenon .
Edit intent: clarity
Original:  Although a large body of work addressed this issue, we attribute  refusal of prior solutions to their poor implementation feasibility with off-the-shelf hardware and their imprecise modelling of the 802.11 protocol.
Revised:  Although a large body of work addressed this issue, we attribute the refusal of prior solutions to their poor implementation feasibility with off-the-shelf hardware and their imprecise modelling of the 802.11 protocol.
Edit intent: fluency
Original:  We present a fully functional light-weight implementation of our scheme on commodity access points and evaluate this extensively via experiments in a real deployment  over a broad range of network conditions.
Revised:  We present a fully functional light-weight implementation of our scheme on commodity access points and evaluate this extensively via experiments in a real deployment , over a broad range of network conditions.
Edit intent: fluency
Original:  Results demonstrate  our proposal achieves up to 100\\% utility gains, can double video streaming goodput and reduces TCP download times by 8x.
Revised:  Results demonstrate that our proposal achieves up to 100\\% utility gains, can double video streaming goodput and reduces TCP download times by 8x.
Edit intent: fluency
Original:  Known examples show that this is no longer true if any of the two conditions ( odd number of vertices or a forbidden subdivision) on the class \mathcal{G is dropped.
Revised:  Known examples show that this is no longer true if any of the two conditions on the class \mathcal{G odd number of vertices or a forbidden subdivision) on the class \mathcal{G is dropped.
Edit intent: fluency
Original:  Known examples show that this is no longer true if any of the two conditions ( odd number of vertices or a forbidden subdivision) on the class \mathcal{G is dropped.
Revised:  Known examples show that this is no longer true if any of the two conditions ( odd number of vertices or a forbidden subdivision) is dropped.
Edit intent: clarity
Original:  The main ingredient in the proof is a  structural result on weighted graphs with a forbidden subdivision , which may be of independent interest .
Revised:  The main ingredient in the proof is a new structural result on weighted graphs with a forbidden subdivision , which may be of independent interest .
Edit intent: clarity
Original:  The main ingredient in the proof is a  structural result on weighted graphs with a forbidden subdivision , which may be of independent interest .
Revised:  The main ingredient in the proof is a structural result on weighted graphs with a forbidden subdivision .
Edit intent: clarity
Original: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered  .
Revised: In the graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered .
Edit intent: coherence
Original: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered  .
Revised: The graph sharing game , two players share a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered .
Edit intent: clarity
Original: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered  .
Revised: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices , claiming and collecting the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered .
Edit intent: clarity
Original: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, in each move keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered  .
Revised: The graph sharing game is played by two players , Alice and Bob, on a connected graph G with non-negative weights assigned to the vertices . Starting with Alice, the players take the vertices of G one by one, while keeping the set of all taken vertices connected , until the whole G has been taken . Each player wants to maximize the total weight of the vertices they have gathered .
Edit intent: clarity