wanyu/IteraTeR_v2 huggingface dataset:
Original:  When r=2 and A is equivalent to a nonnegativematrix by signing rows and columns, we again demonstrate how minimizing the (vector) 1-norm of H among generalized inverses can be achieved by a particular reflexive generalized inverse following our block construction.
Revised:  When r=2 with A nonnegative, we demonstrate how to minimize the (vector) 1-norm of H among generalized inverses can be achieved by a particular reflexive generalized inverse following our block construction.
Edit intent: clarity
Original:  Finally, for general r, we demonstrate how to efficiently find a reflexive generalized inverse following our block construction that is within approximately a factor of r^2 of the (vector) 1-norm of the generalized inversehaving minimum (vector) 1-norm .
Revised:  Finally, for general r, we efficiently find reflexive generalized inverses with 1-norm within approximately a factor of r^2 of the (vector) 1-norm of the generalized inversehaving minimum (vector) 1-norm .
Edit intent: clarity
Original:  Finally, for general r, we demonstrate how to efficiently find a reflexive generalized inverse following our block construction that is within approximately a factor of r^2 of the (vector) 1-norm of the generalized inversehaving minimum (vector) 1-norm .
Revised:  Finally, for general r, we demonstrate how to efficiently find a reflexive generalized inverse following our block construction that is within approximately a factor of r^2 of the minimum 1-norm of the generalized inversehaving minimum (vector) 1-norm .
Edit intent: fluency
Original:  Finally, for general r, we demonstrate how to efficiently find a reflexive generalized inverse following our block construction that is within approximately a factor of r^2 of the (vector) 1-norm of the generalized inversehaving minimum (vector) 1-norm .
Revised:  Finally, for general r, we demonstrate how to efficiently find a reflexive generalized inverse following our block construction that is within approximately a factor of r^2 of the (vector) 1-norm generalized inverse .
Edit intent: clarity
Original:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Revised:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% %DIFDELCMD < \xx%%% ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Edit intent: fluency
Original:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Revised:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% ( ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Edit intent: fluency
Original:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Revised:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% %DIFDELCMD < \xx%%% _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Edit intent: fluency
Original:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%%  _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Revised:  If %DIFDELCMD < \sss %%% is the solution to the system of equations %DIFDELCMD < \xx%%% = %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% ), first, a vector sequence \{ %DIFDELCMD < \xx%%% _m\} is generated via the fixed-point iterative scheme %DIFDELCMD < \xx%%% _{m+1}= %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% ( _m), m=0,1,\ldots, and next, RRE is applied to this sequence to accelerate its convergence.
Edit intent: clarity
Original:  RRE produces approximations %DIFDELCMD < \sss%%% _{n,k to }%DIFDELCMD < \sss %%%  to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% _n,%DIFDELCMD < \xx%%% \boldsymbol{x}\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Revised:  RRE produces approximations %DIFDELCMD < \sss%%% to }%DIFDELCMD < \sss %%% to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% _n,%DIFDELCMD < \xx%%% \boldsymbol{x}\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Edit intent: fluency
Original:  RRE produces approximations %DIFDELCMD < \sss%%% _{n,k to }%DIFDELCMD < \sss %%%  to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% _n,%DIFDELCMD < \xx%%% \boldsymbol{x}\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Revised:  RRE produces approximations %DIFDELCMD < \sss%%% _{n,k to }%DIFDELCMD < \sss %%% _{n,k to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% _n,%DIFDELCMD < \xx%%% \boldsymbol{x}\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Edit intent: fluency
Original:  RRE produces approximations %DIFDELCMD < \sss%%% _{n,k to }%DIFDELCMD < \sss %%%  to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% _n,%DIFDELCMD < \xx%%% \boldsymbol{x}\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Revised:  RRE produces approximations %DIFDELCMD < \sss%%% _{n,k to }%DIFDELCMD < \sss %%% to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% %DIFDELCMD < \xx%%% \boldsymbol{x}\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Edit intent: coherence
Original:  RRE produces approximations %DIFDELCMD < \sss%%% _{n,k to }%DIFDELCMD < \sss %%%  to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% _n,%DIFDELCMD < \xx%%% \boldsymbol{x}\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Revised:  RRE produces approximations %DIFDELCMD < \sss%%% _{n,k to }%DIFDELCMD < \sss %%% to }\boldsymbol{s} that are of the form %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k}=\sum^k_{i=0}\gamma_i %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+i} for some scalars \gamma_i depending (nonlinearly) on %DIFDELCMD < \xx%%% _n,%DIFDELCMD < \xx%%% \boldsymbol{x}_n,\boldsymbol{x} _{n+1},\ldots, %DIFDELCMD < \xx%%% \boldsymbol{x} _{n+k+1} and satisfying \sum^k_{i=0}\gamma_i=1.
Edit intent: clarity
Original:  The convergence properties of RRE when applied in conjunction with linear %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% \boldsymbol{f}\boldsymbol{x} ) have been analyzed in different publications.
Revised:  The convergence properties of RRE when applied in conjunction with linear %DIFDELCMD < \ff%%% %DIFDELCMD < \xx%%% \boldsymbol{f}\boldsymbol{x} ) have been analyzed in different publications.
Edit intent: fluency
Original:  The convergence properties of RRE when applied in conjunction with linear %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% \boldsymbol{f}\boldsymbol{x} ) have been analyzed in different publications.
Revised:  The convergence properties of RRE when applied in conjunction with linear %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% \boldsymbol{f}(\boldsymbol{x} ) have been analyzed in different publications.
Edit intent: coherence
Original:  In this work, we discuss the convergence of the %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k} obtained from RRE with nonlinear %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% \boldsymbol{f}\boldsymbol{x} ) (i)\,when n\to\infty with fixed k, and (ii)\,in two so-called {\em cycling} modes.
Revised:  In this work, we discuss the convergence of the %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k} obtained from RRE with nonlinear %DIFDELCMD < \ff%%% %DIFDELCMD < \xx%%% \boldsymbol{f}\boldsymbol{x} ) (i)\,when n\to\infty with fixed k, and (ii)\,in two so-called {\em cycling} modes.
Edit intent: fluency
Original:  In this work, we discuss the convergence of the %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k} obtained from RRE with nonlinear %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% \boldsymbol{f}\boldsymbol{x} ) (i)\,when n\to\infty with fixed k, and (ii)\,in two so-called {\em cycling} modes.
Revised:  In this work, we discuss the convergence of the %DIFDELCMD < \sss%%% \boldsymbol{s} _{n,k} obtained from RRE with nonlinear %DIFDELCMD < \ff%%% (%DIFDELCMD < \xx%%% \boldsymbol{f}(\boldsymbol{x} ) (i)\,when n\to\infty with fixed k, and (ii)\,in two so-called {\em cycling} modes.
Edit intent: clarity
Original:  It relies on the tactics of ethical investments for sustainable development and low-carbon energy, and voluntary donations for a low-carbon fund to allow adaption to climate change.
Revised:  It relies on ethical investments for sustainable development and low-carbon energy, and voluntary donations for a low-carbon fund to allow adaption to climate change.
Edit intent: clarity
Original:  It relies on the tactics of ethical investments for sustainable development and low-carbon energy, and voluntary donations for a low-carbon fund to allow adaption to climate change.
Revised:  It relies on the tactics of ethical investments for sustainable development and low-carbon energy, and a voluntarily financed low-carbon fund to allow adaption to climate change.
Edit intent: clarity
Original:  It relies on the tactics of ethical investments for sustainable development and low-carbon energy, and voluntary donations for a low-carbon fund to allow adaption to climate change.
Revised:  It relies on the tactics of ethical investments for sustainable development and low-carbon energy, and voluntary donations for a low-carbon fund for adaptation to climate change.
Edit intent: clarity
Original:  With OECD household savings worth over 5\% GDP , ethical savings alone have considerable potential.
Revised:  With OECD savings exceeding 5\% GDP , ethical savings alone have considerable potential.
Edit intent: clarity
Original:  With OECD household savings worth over 5\% GDP , ethical savings alone have considerable potential.
Revised:  With OECD household savings worth over 5\% of disposable household income , ethical savings alone have considerable potential.
Edit intent: clarity
Original:  To prove our results, we formulate several new versions of the variable drift theorems which might be of independent interest.
Revised:  To prove our results, we formulate several new versions of the variable drift theorems , which also might be of independent interest.
Edit intent: clarity
Original: Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that maintain a stochastic model of the solution space.
Revised: Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that maintain a probabilistic model of the solution space.
Edit intent: clarity
Original:  This model is updated from iteration to iteration  based on the quality of the solutions sampled according to the model.
Revised:  This model is updated from iteration to iteration , based on the quality of the solutions sampled according to the model.
Edit intent: fluency
Original:  We prove that this significance-based compact genetic algorithm (sig-cGA) optimizes the common benchmark functions OneMax and LeadingOnesboth in O(n\log n) time, a result shown for no other EDA or evolutionary algorithm so far.
Revised:  We prove that this significance-based compact genetic algorithm (sig-cGA) optimizes the commonly regarded benchmark functions OneMax and LeadingOnesboth in O(n\log n) time, a result shown for no other EDA or evolutionary algorithm so far.
Edit intent: clarity
Original: Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that maintain a probabilistic model of the solution space .
Revised: Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that create a probabilistic model of the solution space .
Edit intent: clarity
Original:  Such frequencies take long to be moved back to the middle range, leading to significant performance losses.
Edit intent: coherence
Original:  For the recently proposed scGA -- an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model -- we prove that it optimizes OneMax only in a time exponential in the hypothetical population size 1/\rho . Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.
Revised:  For the recently proposed scGA -- an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model -- we prove that it optimizes OneMax only in a time exponential in its hypothetical population size 1/\rho . Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.
Edit intent: clarity
Original:  For the recently proposed scGA -- an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model -- we prove that it optimizes OneMax only in a time exponential in the hypothetical population size 1/\rho . Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.
Revised:  For the recently proposed scGA -- an EDA that tries to prevent erratic model updates by imposing a bias to the uniformly distributed model -- we prove that it optimizes OneMax only in a time exponential in the hypothetical population size . Similarly, we show that the convex search algorithm cannot optimize OneMax in polynomial time.
Edit intent: clarity
Original:  For the \v{C and Rips filtrations, we characterize the weight functions for which the corresponding feature maps converge as n approaches infinity, and by doing so, we prove laws of large numbers for the total persistences of such diagrams.
Revised:  For the Cech and Rips filtrations, we characterize the weight functions for which the corresponding feature maps converge as n approaches infinity, and by doing so, we prove laws of large numbers for the total persistences of such diagrams.
Edit intent: fluency
Original: Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence diagnosis based on MRI is challenging.
Revised: Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence MRI based diagnosis is challenging.
Edit intent: coherence
Original:  In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissues in vivo .
Revised:  In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissue .
Edit intent: clarity
Original:  Analysing white matter structures of 32 subjects we incorporated our in vivo findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis.
Revised:  Analysing white matter structures of 32 subjects we incorporated our findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis.
Edit intent: clarity
Original:  Incorporating these alterations in a classification framework, we found that patients and controls are linearly separable with 81.3\% accuracy and 83.3\% sensitivity .
Revised:  Combining these alterations in a classification framework, we found that patients and controls are linearly separable with 81.3\% accuracy and 83.3\% sensitivity .
Edit intent: clarity
Original:  Incorporating these alterations in a classification framework, we found that patients and controls are linearly separable with 81.3\% accuracy and 83.3\% sensitivity .
Revised:  Incorporating these alterations in a classification framework, we found that patients and controls .
Edit intent: clarity
Original:  We suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit to reverse the mechanisms leading to epileptogenesis.
Revised:  We suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit for reversing the mechanisms leading to epileptogenesis.
Edit intent: fluency
Original:  We propose a Mckean-Vlasov type integro differential equation to analyze the multi-individual system analytically , and prove that the model has the ability of representing the scaling limit behavior for the large number individuals system in which the interaction is a multivariate self excitation process with exponential function weight .
Revised:  We propose a Mckean-Vlasov type integro differential equation to analyze the multi-individual system analytically , and prove that the asymptotic behaviors of the model in which the interaction is a multivariate self excitation process with exponential function weight .
Edit intent: clarity
Original:  We show that the coupling between the model and the initial distribution in the equation captures the influence of self excitation process, which decribes the mutually- exicting and recurrent nature of individuals.
Revised:  We show that the coupling between the model and the initial distribution captures the influence of self excitation process, which decribes the mutually- exicting and recurrent nature of individuals.
Edit intent: clarity
Original: A patient is more than one number, yet most approaches to machine learning from electronic health data can only predict a single endpoint.
Revised: Most approaches to machine learning from electronic health data can only predict a single endpoint.
Edit intent: coherence
Original:  Here, we present an alternative -- using unsupervised deep learning to simulate detailed patient trajectories.
Revised:  Here, we present an alternative that uses unsupervised deep learning to simulate detailed patient trajectories.
Edit intent: fluency
Original:  Even though it is not trained to predict changes in disease severity, our unsupervised model predicts changes in total ADAS-Cog scores with the same accuracy as specifically trained supervised models .
Revised:  Our unsupervised model predicts changes in total ADAS-Cog scores with the same accuracy as specifically trained supervised models .
Edit intent: clarity
Original:  Our model's ability to simultaneously predict dozens of characteristics of a patient at any point in the future is a crucial step forward in computational precision medicine .
Revised:  Our model's ability to simultaneously simulate dozens of patient characteristics is a crucial step forward in computational precision medicine .
Edit intent: clarity
Original:  Our model's ability to simultaneously predict dozens of characteristics of a patient at any point in the future is a crucial step forward in computational precision medicine .
Revised:  Our model's ability to simultaneously predict dozens of characteristics of a patient at any point in the future is a crucial step towards personalized medicine for Alzheimer's Disease .
Edit intent: clarity
Original:  We propose to modify RS  into a new indicator (DIV) which operationalizes "variety, " "balance, " and "disparity " independently and then combines them ex post.
Revised:  We propose to modify RS into a new indicator (DIV) which operationalizes variety, balance, and disparity independently and then combines them ex post.
Edit intent: fluency
Original:  We apply DIV to the aggregated citation patterns of 11,487 journals covered by the Journal Citation Reports 2016 of the Science Citation Index and the Social Sciences Citation Index as an empirical domain and, in more detail, to the citation patterns of 86 journals assigned to the Web-of-Science category "information science and library science" in both the cited and citing directions.
Revised:  We apply DIV to the aggregated citation patterns of 11,487 journals covered by the Journal Citation Reports 2016 of the Science Citation Index and the Social Sciences Citation Index as an empirical domain and, in more detail, to the citation patterns of 85 journals assigned to the Web-of-Science category "information science and library science" in both the cited and citing directions.
Edit intent: clarity
Original:  We apply DIV to the aggregated citation patterns of 11,487 journals covered by the Journal Citation Reports 2016 of the Science Citation Index and the Social Sciences Citation Index as an empirical domain and, in more detail, to the citation patterns of 86 journals assigned to the Web-of-Science category "information science and library science" in both the cited and citing directions.
Revised:  We apply DIV to the aggregated citation patterns of 11,487 journals covered by the Journal Citation Reports 2016 of the Science Citation Index and the Social Sciences Citation Index as an empirical domain and, in more detail, to the citation patterns of 86 journals assigned to the Web-of-Science category "information science library science" in both the cited and citing directions.
Edit intent: fluency
Original:  A routine for the measurement of the various operationalizations of diversity (in any data matrix or vector ) is made available online.
Revised:  A routine for the measurement of the various operationalizations of diversity (in any data matrix ) is made available online.
Edit intent: clarity