wanyu/IteraTeR_v2 huggingface dataset:
Original:  Importantly, even when assuming that all cells in a tissue  molecularly equivalent, the model predicts a common ("universal") functional dependence of the long-term clonal survival probability on the position within the niche, as well as the emergence of a well-defined number of "functional " stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Revised:  Importantly, even when assuming that all cells in a tissue molecularly equivalent, the model predicts a common ("universal") functional dependence of the long-term clonal survival probability on the position within the niche, as well as the emergence of a well-defined number of functional stem cells, dependent only on the rate of random movements vs. mitosis-driven advection.
Edit intent: fluency
Original:  We test the predictions of this theory on datasets on pubertal mammary gland tips, embryonic kidney tips as well homeostatic intestinal crypt , and find good quantitative agreement for the number of functional stem cells in each organ , as well as the predicted functional dependence of the competition .
Revised:  We test the predictions of this theory on datasets on pubertal mammary gland tips, embryonic kidney tips as well homeostatic intestinal crypt . Importantly, we find good agreement for the number of functional stem cells in each organ , as well as the predicted functional dependence of the competition .
Edit intent: coherence
Original:  Multicompartment models of nonlinear dendrites and related neuromorphic circuit designs enable faithful imitation of such dynamic integration processes, but these approaches are also associated with a relatively high computing cost or circuit size.
Revised:  Multicompartment models of non-linear dendrites and related neuromorphic circuit designs enable faithful imitation of such dynamic integration processes, but these approaches are also associated with a relatively high computing cost or circuit size.
Edit intent: fluency
Original:  Here, we investigate synaptic integration of spatiotemporal spike patterns with multiple dynamic synapses on point-neurons in the DYNAP-SE neuromorphic processor, which can offer a complementary resource-efficient, albeit less flexible, approach to feature detection.
Revised:  Here, we investigate synaptic integration of spatiotemporal spike patterns with multiple dynamic synapses on point-neurons in the DYNAP-SE neuromorphic processor, which offers a complementary resource-efficient, albeit less flexible, approach to feature detection.
Edit intent: clarity
Original: There are n \ge 2 stacks, each filled with d items (its full capacity) , and one empty stack with capacity d . A robot arm, in one stack operation ( move ), may pop one item from the top of a non-empty stack and subsequently push it into a stack that is not at capacity.
Revised: There are n \ge 2 stacks, each filled with d items , and one empty stack with capacity d . A robot arm, in one stack operation ( move ), may pop one item from the top of a non-empty stack and subsequently push it into a stack that is not at capacity.
Edit intent: clarity
Original: There are n \ge 2 stacks, each filled with d items (its full capacity) , and one empty stack with capacity d . A robot arm, in one stack operation ( move ), may pop one item from the top of a non-empty stack and subsequently push it into a stack that is not at capacity.
Revised: There are n \ge 2 stacks, each filled with d items (its full capacity) , and one empty stack with capacity d . A robot arm, in one stack operation ( step ), may pop one item from the top of a non-empty stack and subsequently push it into a stack that is not at capacity.
Edit intent: clarity
Original: There are n \ge 2 stacks, each filled with d items (its full capacity) , and one empty stack with capacity d . A robot arm, in one stack operation ( move ), may pop one item from the top of a non-empty stack and subsequently push it into a stack that is not at capacity.
Revised: There are n \ge 2 stacks, each filled with d items (its full capacity) , and one empty stack with capacity d . A robot arm, in one stack operation ( move ), may pop one item from the top of a non-empty stack and subsequently push it onto a stack not at capacity.
Edit intent: clarity
Original:  The items must be rearranged using pop-and-push moves so that at the end, the k^{\rm th} stack holds items (k-1)d +1, \ldots, kd, in that order, from the top to the bottom for all 1 \le k \le n.
Revised:  The items must be rearranged using pop-and-pushs so that in the end, the k^{\rm th} stack holds items (k-1)d +1, \ldots, kd, in that order, from the top to the bottom for all 1 \le k \le n.
Edit intent: clarity
Original:  Our main contribution is the design of an algorithm with a guaranteed upper bound of O(nd) for both versions when d \le cn \lceil \rceil for arbitrary fixed positive number c.
Revised:  Our main contribution is the design of an algorithm with a guaranteed upper bound of O(nd) for both versions when d \le \lceil \rceil for arbitrary fixed positive number c.
Edit intent: clarity
Original: Applications related to artificial intelligence, machine learning  and system identification simulations essentially use eigenvectors.
Revised: Applications related to artificial intelligence, machine learning , and system identification simulations essentially use eigenvectors.
Edit intent: fluency
Original:  Calculating eigenvectors for very large matrices using conventional methods is compute intensive and renders the applications slow.
Revised:  Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and renders the applications slow.
Edit intent: fluency
Original:  Recently, Eigenvector-Eigenvalue Identity formula promising significant speed up was identified.
Revised:  Recently, Eigenvector-Eigenvalue Identity formula promising significant speedup was identified.
Edit intent: fluency
Original:  We provide a first of it's kind systematic study of the implementation of the formula.
Revised:  We provide a first of its kind systematic study of the implementation of the formula.
Edit intent: fluency
Original:  We demonstrate further improvements using high performance computing concepts over native NumPy eigenvector implementation which uses LAPACK and BLAS.
Revised:  We demonstrate further improvements using high-performance computing concepts over native NumPy eigenvector implementation which uses LAPACK and BLAS.
Edit intent: fluency
Original: Abstract Hypergraphs were introduced in 1973 by Berg\'e.
Revised:  Hypergraphs were introduced in 1973 by Berg\'e.
Edit intent: style
Original:  However, simple contagion models cannot reproduce the complex features observed in real world data, leading to research on more complicated complex contagion models.
Revised:  However, simple contagion models cannot reproduce the complex features observed in real-world data, leading to research on more complicated complex contagion models.
Edit intent: fluency
Original:  A noted feature of complex contagion is social reinforcement , that individuals require multiple exposures to information before they begin to spread it themselves.
Revised:  A noted feature of complex contagion is social reinforcement that individuals require multiple exposures to information before they begin to spread it themselves.
Edit intent: fluency
Original:  We show that in general this problem is undecidable and formulate a number of sufficient conditions, which guarantee decidability and polynomial boundedness of effects of transactions.
Revised:  We show that in general this problem is undecidable and formulate sufficient conditions, which guarantee decidability and polynomial boundedness of effects of transactions.
Edit intent: clarity
Original:  One encounters thecurse of dimensionality , and working with vectorized data fails to preserve the data structure.
Revised:  One encounters the , and working with vectorized data fails to preserve the data structure.
Edit intent: clarity
Original:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Revised:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{ . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Edit intent: clarity
Original:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Revised:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Edit intent: coherence
Original:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Revised:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data ( ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Edit intent: coherence
Original:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Revised:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine SVM ) Kernel for revealing nonlinear relationships.
Edit intent: fluency
Original:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine (SVM ) Kernel for revealing nonlinear relationships.
Revised:  To mitigate the nonlinear relationship of tensor data more economically, we propose the\emph{Tensor Train Multi-way Multi-level Kernel (TT-MMK) . This technique combines kernel filtering of the initial input data (Kernelized Tensor Train (KTT) ) , stable reparametrization of the KTT in the Canonical Polyadic (CP) format, and the Dual Structure-preserving Support Vector Machine ( ) Kernel for revealing nonlinear relationships.
Edit intent: clarity
Original:  We demonstrate numerically that the TT-MMK method is more reliable computationally, is less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification compared to similar tensorised SVM methods .
Revised:  We demonstrate numerically that the TT-MMK method is more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification compared to similar tensorised SVM methods .
Edit intent: fluency
Original:  We demonstrate numerically that the TT-MMK method is more reliable computationally, is less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification compared to similar tensorised SVM methods .
Revised:  We demonstrate numerically that the TT-MMK method is more reliable computationally, is less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques .
Edit intent: clarity
Original: An increasing amount of collected data are high-dimensional  and it is crucial for efficient learning algorithms to exploit the tensorial structure as much as possible.
Revised: An increasing amount of collected data are high-dimensional and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible.
Edit intent: fluency
Original:  The ever present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor  methods.
Revised:  The ever-present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor methods.
Edit intent: fluency
Original:  The ever present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor  methods.
Revised:  The ever present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor classification methods.
Edit intent: clarity
Original:  In the presence of small amounts of training data  kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary.
Revised:  In the presence of small amounts of training data , kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary.
Edit intent: fluency
Original:  We introduce the Tensor Train Multi-way Multi-level Kernel (TT-MMK) as a method that combines the simplicity of Canonical Polyadic (CP) with the robustness of the tensor train (TT) decomposition.
Revised:  We develop the Tensor Train Multi-way Multi-level Kernel (TT-MMK) as a method that combines the simplicity of Canonical Polyadic (CP) with the robustness of the tensor train (TT) decomposition.
Edit intent: clarity
Original:  We introduce the Tensor Train Multi-way Multi-level Kernel (TT-MMK) as a method that combines the simplicity of Canonical Polyadic (CP) with the robustness of the tensor train (TT) decomposition.
Revised:  We introduce the Tensor Train Multi-way Multi-level Kernel (TT-MMK) , which combines the simplicity of Canonical Polyadic (CP) with the robustness of the tensor train (TT) decomposition.
Edit intent: clarity
Original: Dynamic algorithms capable of supporting batches of updates are increasingly relevant today due to the emergence of rapidly-evolving dynamic datasets.
Revised: Dynamic algorithms capable of supporting batches of updates are increasingly relevant today due to the emergence of rapidly evolving dynamic datasets.
Edit intent: fluency
Original:  Since processing updates on a single processor is often unrealistic for large batches of updates, designing parallel dynamic algorithms that achieve provably low span is important for many applications.
Revised:  Since processing updates on a single processor is often unrealistic for large batches of updates, designing parallel batch-dynamic algorithms that achieve provably low span is important for many applications.
Edit intent: fluency
Original: We give the first efficient algorithm for the problem of list-decodable subspace recovery .
Revised: In list-decodable subspace recovery .
Edit intent: clarity
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) of which are drawn i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } and the rest are arbitrary, potentially adversarial outliers.
Edit intent: clarity
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } inliers and the rest are arbitrary, potentially adversarial outliers.
Edit intent: fluency
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } ) and the rest are arbitrary, potentially adversarial outliers.
Edit intent: fluency
Original:  Our algorithm takes input n samples \alpha n (  \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r }  and the rest are arbitrary, potentially adversarial outliers.
Revised:  Our algorithm takes input n samples \alpha n ( \alpha \ll 1/2) are generated i.i.d. from Gaussian distribution \mathcal{N(0,\Sigma_*) on R^d with covariance \Sigma_* of rank r } and the rest are arbitrary, potential adversarial outliers.
Edit intent: fluency
Original:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\Pi  satisfies certifiable anti-concentration.
Revised:  The goal is to recover a O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\Pi satisfies certifiable anti-concentration.
Edit intent: clarity
Original:  It outputs a list of O(1/\alpha) projection matrices guaranteed to contain a projection matrix%DIFDELCMD < \Pisuch %%% that\Pi  satisfies certifiable anti-concentration.
Revised:  It outputs a list of O(1/\alpha) %DIFDELCMD < \Pisuch %%% that\Pi satisfies certifiable anti-concentration.
Edit intent: clarity
Original:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The algorithm needs n=d ^{ O ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi} 1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: fluency
Original:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The algorithm needs n=d ^{ \log ( 1 ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi} 1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: clarity
Original:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% time algorithm that outputs a list containing a\hat{\Pi} \hat{\Pi} 1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: clarity
Original:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi} 1/ %DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: clarity
Original:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi}  1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% samples and runs in time n^{\log (r \kappa) \tilde{O(1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Revised:  The algorithm needs n=d ^{ \log ( r \kappa ) %DIFDELCMD < \tilde{O}%%% (\hat{\Pi} \hat{\Pi} 1/ \alpha^2)%DIFDELCMD < \MBLOCKRIGHTBRACE %%% (1/\alpha^4)} time where \kappa is the ratio of the largest to smallest non-zero eigenvalues of \Sigma_*.
Edit intent: coherence
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever D satisfies certifiable anti-concentration.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari 2020) ) gave algorithms for this problem that work whenever D satisfies certifiable anti-concentration.
Edit intent: fluency
Original:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) ) gave algorithms for this problem that work whenever D satisfies certifiable anti-concentration.
Revised:  Two recent independent works (Raghavendra-Yau, Bakshi-Kothari ( 2020) gave the first efficient algorithm for this problem that work whenever D satisfies certifiable anti-concentration.
Edit intent: clarity
Original:  The running time of both these algorithms , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ] \emph{ - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  The running time of both these algorithms , however, and the error bounds on \|\Pi} ] \emph{ - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: coherence