wanyu/IteraTeR_full_sent huggingface dataset:
Original:  In this we are inspired by the analogous results for ]  P-matrices (matrices with all principal minors positive) .
Revised:  We do away with the former, and show that A is TP_k if and only if every contiguous submatrix of size \leq k has the sign non-reversal property. In fact this can be strengthened to only consider test vectors in \mathbb{R ] P-matrices (matrices with all principal minors positive) .
Edit intent: meaning-changed
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive.
Revised:  and B = (b_{ij}) . This is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for an entire class of matrices simultaneously to be totally positive.
Edit intent: clarity
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive.
Revised:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of =t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for an entire class of matrices simultaneously to be totally positive.
Edit intent: clarity
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive.
Revised:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% C \in \mathbb{R^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for an entire class of matrices simultaneously to be totally positive.
Edit intent: meaning-changed
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive.
Revised:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a two-element subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for an entire class of matrices simultaneously to be totally positive.
Edit intent: meaning-changed
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive.
Revised:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the TP_k property for all of \mathbb{I}(A,B) . This provides a test for an entire class of matrices simultaneously to be totally positive.
Edit intent: meaning-changed
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive.
Revised:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) for arbitrary k \geq 1. In particular, this provides a test for an entire class of matrices simultaneously to be totally positive.
Edit intent: meaning-changed
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive.
Revised:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for total positivity (of any order), simultaneously for an entire class of matrices simultaneously to be totally positive.
Edit intent: meaning-changed
Original:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for  an entire class of matrices simultaneously to be totally positive. We also establish analogous results for other classes of matrices: almost P-matrices, N-matrices and (minimally) semipositive matrices.
Revised:  and B = (b_{ij}) , denoted by \mathbb{I is the collection of all matrices C such that c_{ij=t_{ij}a_{ij} +(1-t_{ij})b_{ij}for all i,j, where t_{ij} \in }%DIFDELCMD < [%%% 0,1^{m \times n} such that each c_{ij} is between a_{ij} and b_{ij}} . Using the sign non-reversal property, we identify a finite subset of \mathbb{I}(A,B) that detects the total positivity of all of \mathbb{I}(A,B) . This provides a test for an entire class of rectangular matrices.
Edit intent: meaning-changed
Original: Mean-modulated flicker -- wherein luminance increments and decrements of equal magnitude are applied, over time, to a test field -- is commonly used in both clinical assessment of vision and experimental studies of visual systems.
Revised: Achromatic, mean-modulated flicker ( wherein luminance increments and decrements of equal magnitude are applied, over time, to a test field -- is commonly used in both clinical assessment of vision and experimental studies of visual systems.
Edit intent: meaning-changed
Original: Mean-modulated flicker -- wherein luminance increments and decrements of equal magnitude are applied, over time, to a test field -- is commonly used in both clinical assessment of vision and experimental studies of visual systems.
Revised: Mean-modulated flicker -- wherein luminance increments and decrements of equal magnitude are applied, over time, to a test field ) is commonly used in both clinical assessment of vision and experimental studies of visual systems.
Edit intent: fluency
Original:  The CG247X's response times depended on both source and destination luminance . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X was artifact-free , that is, the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Revised:  The CG247X's rise and fall times depended on both source and destination luminance . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X was artifact-free , that is, the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Edit intent: meaning-changed
Original:  The CG247X's response times depended on both source and destination luminance . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X was artifact-free , that is, the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Revised:  The CG247X's response times depended on both the luminance from which, and to which, it responded, as is to be generally expected from LCDs . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X was artifact-free , that is, the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Edit intent: meaning-changed
Original:  The CG247X's response times depended on both source and destination luminance . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X was artifact-free , that is, the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Revised:  The CG247X's response times depended on both source and destination luminance . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X appeared largely artifact-free , that is, the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Edit intent: clarity
Original:  The CG247X's response times depended on both source and destination luminance . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X was artifact-free , that is, the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Revised:  The CG247X's response times depended on both source and destination luminance . Despite this nonlinear behaviour, we were able to define a contrast and frequency range wherein the CG247X was artifact-free ; the relationship between nominal luminance and displayed luminance was accurately modelled using a causal, linear time-invariant system.
Edit intent: coherence
Original:  The ability to discover an applicant's likelihood towards job-hopping can URLanizations make informed hiring decisions benefiting both parties. In this work , we show that the language one uses when responding to interview questions related to situational judgment and past behaviour is predictive of their likelihood to job hop.
Revised:  Our work shows that language used in responding to interview questions related to situational judgment and past behaviour is predictive of their likelihood to job hop.
Edit intent: clarity
Original:  In this work , we show that the language one uses when responding to interview questions related to situational judgment and past behaviour is predictive of their likelihood to job hop. We used responses from over 45,000 job applicants who completed an online chat interview and also self-rated themselves on a job-hopping motive scale to analyse the correlation between the two.
Revised:  In this work , we show that the language one uses when responding to interview questions related to situational judgment and past behaviour is predictive of job-hopping motive as measured by the Job-Hopping Motives (JHM) Scale. The study is based on responses from over 45,000 job applicants who completed an online chat interview and also self-rated themselves on a job-hopping motive scale to analyse the correlation between the two.
Edit intent: meaning-changed
Original:  We used responses from over 45,000 job applicants who completed an online chat interview and also self-rated themselves on a job-hopping motive scale to analyse the correlation between the two. We evaluated five different methods of text representation  , namely four open-vocabulary approaches (TF-IDF, LDA, Glove word embeddings and Doc2Vec document embeddings) and one closed-vocabulary approach (LIWC).
Revised:  We used responses from over 45,000 job applicants who completed an online chat interview and also self-rated themselves on JHM Scale. Five different methods of text representation , namely four open-vocabulary approaches (TF-IDF, LDA, Glove word embeddings and Doc2Vec document embeddings) and one closed-vocabulary approach (LIWC).
Edit intent: coherence
Original:  We evaluated five different methods of text representation  , namely four open-vocabulary approaches (TF-IDF, LDA, Glove word embeddings and Doc2Vec document embeddings) and one closed-vocabulary approach (LIWC).
Revised:  We evaluated five different methods of text representation were evaluated , namely four open-vocabulary approaches (TF-IDF, LDA, Glove word embeddings and Doc2Vec document embeddings) and one closed-vocabulary approach (LIWC).
Edit intent: meaning-changed
Original:  The Glove embeddings provided the best results with a positive correlation of r = 0.35 between sequences of words used and the job-hopping likelihood. With further analysis , we also found that there is a positive correlation of r = 0.25 between  job-hopping likelihood and the HEXACO personality trait Openness to experience .
Revised:  The Glove embeddings provided the best results with a positive correlation of r = 0.35 between sequences of words used and the JHM Scale. Further analysis also showed a correlation of r = 0.25 between job-hopping likelihood and the HEXACO personality trait Openness to experience .
Edit intent: meaning-changed
Original:  With further analysis , we also found that there is a positive correlation of r = 0.25 between  job-hopping likelihood and the HEXACO personality trait Openness to experience . In other words, the more open a candidate is to new experiences, the more likely they are to job hop. The ability to objectively infer a candidate's likelihood towards job hopping presents significant opportunities, especially when assessing candidates with no prior work history. On the other hand, experienced candidates who come across as job hoppers, based purely on their resume, get an opportunity to indicate otherwise .
Revised:  With further analysis , we also found that there is a positive correlation of r = 0.25 between job-hopping likelihood and the HEXACO personality trait Openness to experience and a correlation of r = -0.09 with the trait Agreeableness .
Edit intent: meaning-changed
Original:  First, we show that a polynomial matrix P(x) with chordal sparsity is positive semidefinite for all x\in R^n if and only if there exists a sum-of-squares (SOS) polynomial \sigma(x) such that \sigma (x)P (x) can be decomposed into a sum of sparse SOS matrices , each of which is zero outside a small principal submatrix .
Revised:  First, we establish that a polynomial matrix P(x) with chordal sparsity is positive semidefinite for all x\in R^n if and only if there exists a sum-of-squares (SOS) polynomial \sigma(x) such that \sigma (x)P (x) can be decomposed into a sum of sparse SOS matrices , each of which is zero outside a small principal submatrix .
Edit intent: clarity
Original:  First, we show that a polynomial matrix P(x) with chordal sparsity is positive semidefinite for all x\in R^n if and only if there exists a sum-of-squares (SOS) polynomial \sigma(x) such that \sigma (x)P (x) can be decomposed into a sum of sparse SOS matrices , each of which is zero outside a small principal submatrix .
Revised:  First, we show that a polynomial matrix P(x) with chordal sparsity is positive semidefinite for all x\in R^n if and only if there exists a sum-of-squares (SOS) polynomial \sigma(x) such that \sigma P is a sum of sparse SOS matrices , each of which is zero outside a small principal submatrix .
Edit intent: clarity
Original:  First, we show that a polynomial matrix P(x) with chordal sparsity is positive semidefinite for all x\in R^n if and only if there exists a sum-of-squares (SOS) polynomial \sigma(x) such that \sigma (x)P (x) can be decomposed into a sum of sparse SOS matrices , each of which is zero outside a small principal submatrix .
Revised:  First, we show that a polynomial matrix P(x) with chordal sparsity is positive semidefinite for all x\in R^n if and only if there exists a sum-of-squares (SOS) polynomial \sigma(x) such that \sigma (x)P (x) can be decomposed into a sum of sparse SOS matrices .
Edit intent: meaning-changed
Original:  Second, we establish that setting \sigma(x)=(x_1^2 + \cdots + x_n^2)^\nu for some integer \nu suffices if P (x) is even, homogeneous , and positive definite  .
Revised:  Second, we show that setting \sigma(x)=(x_1^2 + \cdots + x_n^2)^\nu for some integer \nu suffices if P (x) is even, homogeneous , and positive definite .
Edit intent: clarity
Original:  Second, we establish that setting \sigma(x)=(x_1^2 + \cdots + x_n^2)^\nu for some integer \nu suffices if P (x) is even, homogeneous , and positive definite  .
Revised:  Second, we establish that setting \sigma(x)=(x_1^2 + \cdots + x_n^2)^\nu for some integer \nu suffices if P is homogeneous and positive definite .
Edit intent: clarity
Original:  Second, we establish that setting \sigma(x)=(x_1^2 + \cdots + x_n^2)^\nu for some integer \nu suffices if P (x) is even, homogeneous , and positive definite  .
Revised:  Second, we establish that setting \sigma(x)=(x_1^2 + \cdots + x_n^2)^\nu for some integer \nu suffices if P (x) is even, homogeneous , and positive definite globally .
Edit intent: meaning-changed
Original:  Third, we prove a sparse-matrix version of Putinar's Positivstellensatz: if P (x) has chordal sparsity and is positive definite on a compact semialgebraic set \mathcal{K}=\{x:
Revised:  Third, we prove that if P is positive definite on a compact semialgebraic set \mathcal{K}=\{x:
Edit intent: coherence
Original:  that are sums of sparse SOS matrices , each of which is zero outside a small principal submatrix is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these decomposition results, we obtain sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables .
Revised:  that are sums of sparse SOS matrices . Finally, if \mathcal{K is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these decomposition results, we obtain sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables .
Edit intent: meaning-changed
Original:  that are sums of sparse SOS matrices , each of which is zero outside a small principal submatrix is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these decomposition results, we obtain sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables .
Revised:  that are sums of sparse SOS matrices , each of which is zero outside a small principal submatrix is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these results, we obtain sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables .
Edit intent: fluency
Original:  that are sums of sparse SOS matrices , each of which is zero outside a small principal submatrix is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these decomposition results, we obtain sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables .
Revised:  that are sums of sparse SOS matrices , each of which is zero outside a small principal submatrix is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for (x_1^2 + \ldots + x_n^2)^\nu P(x) with some integer \nu\geq 0 when P and g_1,\ldots,g_m are homogeneous of even degree} . Using these decomposition results, we find sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables .
Edit intent: clarity