wanyu/IteraTeR_v2 huggingface dataset:
Original:  We identify the loop regions of the S protein , and examine their structural variability across the PDB .
Revised:  This paper identifies the S protein loops and studies their conformational variability based on the available Protein Data Bank (PDB) structures .
Edit intent: clarity
Original:  As artificial intelligence technologies -- in education and beyond -- have led to inequitable outcomes for marginalized communities, various approaches have been developed to evaluate and mitigate AI systems' disparate impact .
Revised:  As artificial intelligence technologies -- in education and beyond -- may contribute to inequitable outcomes for marginalized communities, various approaches have been developed to evaluate and mitigate AI systems' disparate impact .
Edit intent: clarity
Original:  As artificial intelligence technologies -- in education and beyond -- have led to inequitable outcomes for marginalized communities, various approaches have been developed to evaluate and mitigate AI systems' disparate impact .
Revised:  As artificial intelligence technologies -- in education and beyond -- have led to inequitable outcomes for marginalized communities, various approaches have been developed to evaluate and mitigate the harmful impacts of AI .
Edit intent: clarity
Original:  However, we argue in this paper that the dominant paradigm of evaluating fairness on the basis of performance disparities in AI models is inadequate for confronting the structural inequities that educational AI systems (re)produce.
Revised:  However, we argue in this paper that the dominant paradigm of evaluating fairness on the basis of performance disparities in AI models is inadequate for confronting the systemic inequities that educational AI systems (re)produce.
Edit intent: clarity
Original:  We draw on a lens of structural injustice informed by critical theory and Black feminist scholarship to critically interrogate several widely-studied and widely-adopted categories of educational AI systems and demonstrate how educational AI technologies are bound up in and reproduce historical legacies of structural injustice and inequity, regardless of the parity of their models' performance.
Revised:  We draw on a lens of structural injustice informed by critical theory and Black feminist scholarship to critically interrogate several widely-studied and widely-adopted categories of educational AI and explore how they are bound up in and reproduce historical legacies of structural injustice and inequity, regardless of the parity of their models' performance.
Edit intent: clarity
Original:  We close with alternative visions for a more equitable future for educational AI research .
Revised:  We close with alternative visions for a more equitable future for educational AI .
Edit intent: clarity
Original:  A variety of accompanying numerical experiments demonstrates the quadrature algorithm on two- and three-dimensional problems, including  randomly generated geometry involving multiple high curvature pieces;
Revised:  A variety of numerical experiments demonstrates the quadrature algorithm on two- and three-dimensional problems, including randomly generated geometry involving multiple high curvature pieces;
Edit intent: clarity
Original:  A variety of accompanying numerical experiments demonstrates the quadrature algorithm on two- and three-dimensional problems, including  randomly generated geometry involving multiple high curvature pieces;
Revised:  A variety of accompanying numerical experiments demonstrates the quadrature algorithm on two- and three-dimensional problems, including : randomly generated geometry involving multiple high curvature pieces;
Edit intent: fluency
Original:  A variety of accompanying numerical experiments demonstrates the quadrature algorithm on two- and three-dimensional problems, including  randomly generated geometry involving multiple high curvature pieces;
Revised:  A variety of accompanying numerical experiments demonstrates the quadrature algorithm on two- and three-dimensional problems, including randomly generated geometry involving multiple high-curvature pieces;
Edit intent: fluency
Original:  adaptation to simplex constraint cells in addition to hyper-rectangular constraint cells;
Revised:  adaptation to simplex constraint cells in addition to hyperrectangular constraint cells;
Edit intent: fluency
Original: Although many researchers have studied false data injection (FDI) attacks in power state estimation, current state estimation approaches are still highly vulnerable to FDI attacks.
Revised: Many researchers have studied false data injection (FDI) attacks in power state estimation, current state estimation approaches are still highly vulnerable to FDI attacks.
Edit intent: coherence
Original: Although many researchers have studied false data injection (FDI) attacks in power state estimation, current state estimation approaches are still highly vulnerable to FDI attacks.
Revised: Although many researchers have studied false data injection (FDI) attacks in power state estimation, but existing state estimation approaches are still highly vulnerable to FDI attacks.
Edit intent: coherence
Original:  Our time complexity analysis shows that the proposed two robust defense approaches are efficient.
Revised:  Our time complexity analysis shows that the two proposed robust defense approaches are efficient.
Edit intent: fluency
Original:  Moreover,  to demonstrate the effectiveness of the proposed approaches, we compare them with the three well-known approaches: the least square approach, the Imhotep-SMT approach, and the MEE-UKF approach.
Revised:  Moreover, in order to demonstrate the effectiveness of the proposed approaches, we compare them with the three well-known approaches: the least square approach, the Imhotep-SMT approach, and the MEE-UKF approach.
Edit intent: fluency
Original:  Experiments show that the proposed approaches further reduce the estimation error by two orders of magnitude and four orders of magnitude compared to the Imhotep-SMT approach and the least square approach, respectively.
Revised:  Our extensive experiments show that the proposed approaches further reduce the estimation error by two orders of magnitude and four orders of magnitude compared to the Imhotep-SMT approach and the least square approach, respectively.
Edit intent: clarity
Original:  Whereas our approach has a similar root mean square error as the Imhotep-SMT approach has , our approach provides a more stable result .
Revised:  Moreover , our approach provides a more stable result .
Edit intent: coherence
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% \forall \alpha R(\alpha ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Edit intent: fluency
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Edit intent: fluency
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A \times B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Edit intent: clarity
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set \mathbb{B (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Edit intent: fluency
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Edit intent: fluency
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig \"o} 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Edit intent: fluency
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig }nig 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Edit intent: fluency
Original:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = Bool (up to weak classical reasoning) -
Revised:  \Rightarrow\exists\alpha %DIFDELCMD < \foralla %%% R(a ,\alpha(a)) ) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, \bullet the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), \bullet the axiom of dependent choice if A = N, \bullet Weak K\"onig } 's Lemma if A = \mathbb{N} and B = \mathbb{B (up to weak classical reasoning) -
Edit intent: fluency
Original:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Revised:  GBI(A,B,T) intuitionistically captures the strength of \bullet G } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Edit intent: fluency
Original:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Revised:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel \"o} 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Edit intent: clarity
Original:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Revised:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel }del 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Edit intent: fluency
Original:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Revised:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC _{A,B,T smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Edit intent: coherence
Original:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool ^\mathbb{N} and B is \mathbb{N}.
Revised:  GBI(A,B,T) intuitionistically captures the strength of \bullet G\"odel } 's completeness theorem in the form validity implies provability for entailment relations if B = Bool , \bullet bar induction when A = \mathbb{N}, \bullet the Weak Fan Theorem when A = \mathbb{N} and B = Bool . Contrastingly, even though GDC (A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is \mathbb{B ^\mathbb{N} and B is \mathbb{N}.
Edit intent: fluency
Original:  We develop our method based on a state-of-the-art active V-SLAM approach for omnidirectional robots , and evaluate it through rigorous simulation and real robot experiments.
Revised:  We develop our method based on a state-of-the-art active V-SLAM approach for omnidirectional robots and evaluate it through rigorous simulation and real robot experiments.
Edit intent: fluency
Original:  We publish it to allow other researchers to compare their approaches transparently and we will publish our code.
Revised:  We published it to allow other researchers to compare their approaches transparently and we will publish our code.
Edit intent: fluency
Original:  We publish it to allow other researchers to compare their approaches transparently and we will publish our code.
Revised:  We publish it to allow other researchers to compare their approaches transparently and we furthermore published our code.
Edit intent: coherence
Original:  For two-phase flows, the recent work of Kromer and Bothe (arXiv:2101.03861 ) addresses the positioning of a single plane by combining an implicit bracketing of the sought position with up to third-order derivatives of the volume fraction.
Revised:  For two-phase flows, the recent work of Kromer Bothe (doi.org/10.1016/j.jcp.2021.110776 ) addresses the positioning of a single plane by combining an implicit bracketing of the sought position with up to third-order derivatives of the volume fraction.
Edit intent: clarity
Original:  In comparison to an existing decomposition-based approach, the number of truncations was reduced by up to an order of magnitude , further highlighting the superiority of the divergence-based volume computation .
Revised:  In comparison to an existing decomposition-based approach, the number of truncations was reduced by up to an order of magnitude .
Edit intent: coherence
Original:  For the model-aided method, we derive closed-form expressions when using maximum ratio or zero-forcing precoding  .
Revised:  For the model-aided method, we derive all expressions in closed form for the case when maximum ratio or zero-forcing precoding .
Edit intent: clarity
Original:  For the model-aided method, we derive closed-form expressions when using maximum ratio or zero-forcing precoding  .
Revised:  For the model-aided method, we derive closed-form expressions when using maximum ratio or zero-forcing precoding is used .
Edit intent: clarity
Original: A reconfigurable intelligent surface (RIS) is a  flat layer made of sub-wavelength-sized reflective elements capable of adding a tunable phase shift to the impinging electromagnetic wave  .
Revised: A reconfigurable intelligent surface (RIS) is a flat layer made of inexpensive elements that can add a tunable phase shift to the impinging electromagnetic wave .
Edit intent: clarity
Original:  This paper considers the fundamental problem of target detection in a RIS-aided multiple-input multiple-output (MIMO) radar system .
Revised:  This paper considers the fundamental problem of target detection in a RIS-aided multiple-input multiple-output (MIMO) radar .
Edit intent: clarity
Original:  At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the  transmitter and one close to the  receiver) and subsumes both a mono-static and a bi-static radar configuration with or without a line-of-sight (LOS) view of the prospective target.
Revised:  At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the radar transmitter and one close to the receiver) and subsumes both a mono-static and a bi-static radar configuration with or without a line-of-sight (LOS) view of the prospective target.
Edit intent: fluency
Original:  At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the  transmitter and one close to the  receiver) and subsumes both a mono-static and a bi-static radar configuration with or without a line-of-sight (LOS) view of the prospective target.
Revised:  At first, a general signal model is introduced, which includes the possibility of using up to two RISs (one close to the transmitter and one close to the radar receiver) and subsumes both a mono-static and a bi-static radar configuration with or without a line-of-sight (LOS) view of the prospective target.
Edit intent: fluency