wanyu/IteraTeR_v2 huggingface dataset:
Original:  In particular, even in the presence of severe ill-conditioning, frames impose sufficient mathematical structure so as to give rise to good accuracy in finite precision calculations .
Revised:  In particular, even in the presence of severe ill-conditioning, frames impose sufficient mathematical structure in order to give rise to good accuracy in finite precision calculations .
Edit intent: clarity
Original:  In particular, even in the presence of severe ill-conditioning, frames impose sufficient mathematical structure so as to give rise to good accuracy in finite precision calculations .
Revised:  In particular, even in the presence of severe ill-conditioning, frames impose sufficient mathematical structure so as to give rise to accurate, well-conditioned approximations .
Edit intent: clarity
Original: Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans an appropriate function space.
Revised: Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space.
Edit intent: clarity
Original:  For instance, we exhibit a frame which yields simple, high-order approximations of smooth functions in arbitrary geometries.
Edit intent: coherence
Original:  We demonstrate the existence of such representations for all our examples.
Revised:  We demonstrate the existence of such representations in all of our examples.
Edit intent: clarity
Original: To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network is an attractive solution for the urban deployment of  5G wireless networks.
Revised: The wireless backhaul network is an attractive solution for the urban deployment of 5G wireless networks.
Edit intent: coherence
Original: To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network is an attractive solution for the urban deployment of  5G wireless networks.
Revised: To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network provides an attractive solution for the urban deployment of 5G wireless networks.
Edit intent: clarity
Original: To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network is an attractive solution for the urban deployment of  5G wireless networks.
Revised: To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network is an attractive solution for the urban deployment of fifth generation ( 5G wireless networks.
Edit intent: fluency
Original:  Optimization of 5G wireless backhaul networks is a key issue.
Revised:  Optimization of 5G wireless backhaul networks is an interesting and challenging issue.
Edit intent: clarity
Original:   Specifically, the number and positions of gateways are optimized in the long time scale of 5G wireless backhaul networks.
Revised:  Specifically, the number and locations of gateways are optimized in the long time scale of 5G wireless backhaul networks.
Edit intent: clarity
Original:  Numerical results show the  cost efficiency of  proposed optimization algorithm is better than the cost efficiency of conventional and most widely used shortest path (SP) algorithm in 5G wireless backhaul networks.
Revised:  Numerical results show the cost efficiency of 5G wireless backhaul networks. Moreover, the cost efficiency of proposed optimization algorithm is better than the cost efficiency of conventional and most widely used shortest path (SP) algorithm in 5G wireless backhaul networks.
Edit intent: coherence
Original:  Numerical results show the  cost efficiency of  proposed optimization algorithm is better than the cost efficiency of conventional and most widely used shortest path (SP) algorithm in 5G wireless backhaul networks.
Revised:  Numerical results show the cost efficiency of proposed optimization algorithm is better than that of conventional and most widely used shortest path (SP) algorithm in 5G wireless backhaul networks.
Edit intent: clarity
Original:  The method is described and analyzed in details , and then applied to both synthetic and real graphs, showing its potential.
Revised:  The method is described and analyzed in detail , and then applied to both synthetic and real graphs, showing its potential.
Edit intent: fluency
Original: Community detection is a task of fundamental importance in social network analysis . Community structures enable us to discover the hidden interactions among the network members that can be used in many knowledge-based domains such as bioinformatics, computer networks, e-commerce and forensic science .
Revised: Community detection is a task of fundamental importance in social network analysis that can be used in many knowledge-based domains such as bioinformatics, computer networks, e-commerce and forensic science .
Edit intent: clarity
Original: Community detection is a task of fundamental importance in social network analysis . Community structures enable us to discover the hidden interactions among the network members that can be used in many knowledge-based domains such as bioinformatics, computer networks, e-commerce and forensic science .
Revised: Community detection is a task of fundamental importance in social network analysis . Community structures enable us to discover the hidden interactions among the network members that can be used in a variety of knowledge-based domains such as bioinformatics, computer networks, e-commerce and forensic science .
Edit intent: clarity
Original: Community detection is a task of fundamental importance in social network analysis . Community structures enable us to discover the hidden interactions among the network members that can be used in many knowledge-based domains such as bioinformatics, computer networks, e-commerce and forensic science .
Revised: Community detection is a task of fundamental importance in social network analysis . Community structures enable us to discover the hidden interactions among the network members that can be used in many knowledge-based domains .
Edit intent: clarity
Original:  While there exist many works on community detection based on connectivity structure , they suffer from either considering the overlapping or non-overlapping community structures .
Revised:  While there exist many works on community detection based on connectivity structures , they suffer from either considering the overlapping or non-overlapping community structures .
Edit intent: fluency
Original:  While there exist many works on community detection based on connectivity structure , they suffer from either considering the overlapping or non-overlapping community structures .
Revised:  While there exist many works on community detection based on connectivity structure , they suffer from either considering the overlapping or non-overlapping communities .
Edit intent: clarity
Original:  In this work, we propose a novel approach for general community detection through an integrated framework to extract the overlapping and non-overlapping community structures without assuming prior structural connectivity on the networks.
Revised:  In this work, we propose a novel approach for general community detection through an integrated framework to extract the overlapping and non-overlapping community structures without assuming prior structural connectivity on networks.
Edit intent: fluency
Original:  Our general framework is based on a primary node based criterion which consists up the internal association degree along with the external association degree to compute the criterion in the proposed approach .
Revised:  Our general framework is based on a primary node based criterion which consists of the internal association degree along with the external association degree to compute the criterion in the proposed approach .
Edit intent: fluency
Original:  Our general framework is based on a primary node based criterion which consists up the internal association degree along with the external association degree to compute the criterion in the proposed approach .
Revised:  Our general framework is based on a primary node based criterion which consists up the internal association degree along with the external association degree .
Edit intent: coherence
Original:  The evaluation of the proposed method is investigated through the extensive simulation experiments and several benchmark real network data-sets .
Revised:  The evaluation of the proposed method is investigated through the extensive simulation experiments and several benchmark real network datasets .
Edit intent: clarity
Original: One of the major characteristics of living organisms is metabolic rate - the amount of energy produced per unit time.
Revised: One of the major characteristics of living organisms is metabolic rate - amount of energy produced per unit time.
Edit intent: fluency
Original:  When the size of organisms increases, the metabolic rate increases slower than organisms' mass , which has important implications for the evolutionary and ontogenetic development.
Revised:  When the size of organisms increases, the metabolic rate increases slower than organisms' mass , which has important implications for the individual and population organismal development.
Edit intent: clarity
Original:  Here, we study the fundamental causes of this phenomenon on the basis of metabolic properties of unicellular organisms (Amoeba Proteus, fission yeast S. pombe, E. coli, B. subtilis, Staphylococcus).
Revised:  Here, we study the causes of this phenomenon on the basis of metabolic properties of unicellular organisms (Amoeba Proteus, fission yeast S. pombe, E. coli, B. subtilis, Staphylococcus).
Edit intent: clarity
Original:  Here, we study the fundamental causes of this phenomenon on the basis of metabolic properties of unicellular organisms (Amoeba Proteus, fission yeast S. pombe, E. coli, B. subtilis, Staphylococcus).
Revised:  Here, we study the fundamental causes of this phenomenon considering metabolic properties of unicellular organisms (Amoeba Proteus, fission yeast S. pombe, E. coli, B. subtilis, Staphylococcus).
Edit intent: clarity
Original:  The study discovered that the metabolic properties and allometric scaling of unicellular organisms are defined by at least two primary factors.
Revised:  The study discovered that the metabolic properties of unicellular organisms are defined by at least two primary factors.
Edit intent: clarity
Original:  The study discovered that the metabolic properties and allometric scaling of unicellular organisms are defined by at least two primary factors.
Revised:  The study discovered that the metabolic properties and allometric scaling of unicellular organisms are defined by two primary factors.
Edit intent: clarity
Original:  One is the acquisition of nutrients through the surface in a common nutritional environment, which forms the base part of 2/3 of an allometric exponent.
Revised:  One is the need to acquire nutrients through the surface in a common nutritional environment, which forms the base part of 2/3 of an allometric exponent.
Edit intent: clarity
Original:  The other factor is a regular increase of nutrient influx per unit surface when one ascends the food chain and organisms' mass increases.
Revised:  The other factor is a regular increase of nutrient influx per unit surface , when organisms' mass increases.
Edit intent: clarity
Original:  Accounting for the increase of nutrient influx and its variations , we obtained allometric exponents close to values obtained in experiments.
Revised:  Accounting for the increase of nutrient influx , we obtained allometric exponents close to values obtained in experiments.
Edit intent: clarity
Original: We consider the model of interacting neurons proposed in 8%DIFDELCMD < ] %%% and use the statistical selection procedure proposed in 4%DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Revised:  8%DIFDELCMD < ] %%% and use the statistical selection procedure proposed in 4%DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Edit intent: clarity
Original: We consider the model of interacting neurons proposed in 8%DIFDELCMD < ] %%% and use the statistical selection procedure proposed in 4%DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Revised: We consider the model of interacting neurons proposed in %DIFDELCMD < ] %%% and use the statistical selection procedure proposed in 4%DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Edit intent: style
Original: We consider the model of interacting neurons proposed in 8%DIFDELCMD < ] %%% and use the statistical selection procedure proposed in 4%DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Revised: We consider the model of interacting neurons proposed in 8%DIFDELCMD < ] %%% 4%DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Edit intent: coherence
Original: We consider the model of interacting neurons proposed in 8%DIFDELCMD < ] %%% and use the statistical selection procedure proposed in 4%DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Revised: We consider the model of interacting neurons proposed in 8%DIFDELCMD < ] %%% and use the statistical selection procedure proposed in %DIFDELCMD < ] %%% to infer the interaction graph from observed neural activity (spike trains ) of the first olfactory relay of an insect.
Edit intent: style
Original:  We propose a pruning method to deal with  small sample sizes  .
Revised:  We propose a pruning method to deal with the small sample sizes .
Edit intent: fluency
Original:  We use simulations to test the efficiency of the estimator and to fix the parameters involved in its construction.
Revised:  We evaluate the estimator and to fix the parameters involved in its construction.
Edit intent: clarity
Original:  In order to test the performance of the proposed estimator on our spike train data, the data set is split in two parts and the resulting connection graphs are compared .
Revised:  In order to test the performance of both original and improved procedures through simulation studies, which are also used for parameter tuning and for exploring the effect of recording only a small subset of the neurons of a network .
Edit intent: coherence
Original:  Incidentally, we develop an algorithm for computing the gcrd of a family of linear Mahler operators with nonzero constant terms .
Revised:  Incidentally, we develop an algorithm for computing the gcrd of a family of linear Mahler operators .
Edit intent: clarity
Original:  However , recent work shows that exact backpropagated weights are not essential for learning deep representations.
Revised:  However , recent work showed that exact backpropagated weights are not essential for learning deep representations.
Edit intent: coherence
Original:  Random backpropagation replaces feedback weights with random ones and encourages the network to adjust its feed-forward weights to learn pseudo-inverses of the (random) feedback weights.
Revised:  Random BP replaces feedback weights with random ones and encourages the network to adjust its feed-forward weights to learn pseudo-inverses of the (random) feedback weights.
Edit intent: clarity
Original:  Here , we demonstrate an event-driven random backpropagation (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations in neuromorphic computing hardware.
Revised:  Building on these results , we demonstrate an event-driven random backpropagation (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations in neuromorphic computing hardware.
Edit intent: clarity
Original:  Here , we demonstrate an event-driven random backpropagation (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations in neuromorphic computing hardware.
Revised:  Here , we demonstrate an event-driven random BP (eRBP) rule that uses an error-modulated synaptic plasticity for learning deep representations in neuromorphic computing hardware.
Edit intent: clarity
Original:  The rule is very suitable for implementation in neuromorphic hardware using a two-compartment leaky integrate & fire neuronand a membrane-voltage modulated, spike-driven plasticity rule  .
Revised:  The rule is very suitable for implementation in neuromorphic hardware using a two-compartment leaky Integrate & fire neuronand a membrane-voltage modulated, spike-driven plasticity rule .
Edit intent: fluency
Original:  The rule is very suitable for implementation in neuromorphic hardware using a two-compartment leaky integrate & fire neuronand a membrane-voltage modulated, spike-driven plasticity rule  .
Revised:  The rule is very suitable for implementation in neuromorphic hardware using a two-compartment leaky integrate & Fire (I .
Edit intent: clarity
Original:  Our results show that using eRBP, deep representations are rapidly learned without using backpropagated gradients , achieving nearly identical classification accuracies compared to artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning.
Revised:  Our results show that using eRBP, deep representations are rapidly learned , achieving nearly identical classification accuracies compared to artificial neural network simulations on GPUs, while being robust to neural and synaptic state quantizations during learning.
Edit intent: clarity
Original:  In particular, Curto, Itskov, Veliz-Cuba, and Youngs recently introduced the concept of neural ideal , which is an algebraic object that encodes the full combinatorial data of a neural code .
Revised:  In particular, Curto, Itskov, Veliz-Cuba, and Youngs recently introduced the concept of neural ideal , which is an algebraic object that can be used to better understand the combinatorial structure of neural codes .
Edit intent: clarity
Original: In this paper we introduce an interface for supporting ordered maps that are augmented to support quick "sums" of values over ranges of the keys.
Revised: In this paper we introduce an interface for supporting ordered maps that is augmented to support quick "sums" of values over ranges of the keys.
Edit intent: fluency
Original:  This library supports a wide variety of functions on  maps ranging from basic insertion and deletion to more interesting functions such as union, intersection, difference, filtering, extracting ranges, splitting, and range-sums.
Revised:  This library supports a wide variety of functions on maps ranging from basic insertion and deletion to more interesting functions such as union, intersection, filtering, extracting ranges, splitting, and range-sums.
Edit intent: clarity
Original:  With this augmentation the library can be directly applied to many settings such as to 2D range trees , interval trees,  word index searching , and segment trees .
Revised:  With this augmentation the library can be directly applied to many settings such as to 2D range trees , interval trees, 2D range trees, and word index searching , and segment trees .
Edit intent: coherence
Original:  With this augmentation the library can be directly applied to many settings such as to 2D range trees , interval trees,  word index searching , and segment trees .
Revised:  With this augmentation the library can be directly applied to many settings such as to 2D range trees , interval trees, word index searching .
Edit intent: clarity
Original: Ordered (key-value) maps are an important and widely-used data structure for large-scale data processing frameworks.
Revised: Ordered (key-value) maps are an important and widely-used data type for large-scale data processing frameworks.
Edit intent: clarity
Original:  As examples of the use of the interface and the performance of PAM  we apply the library to four applications: simple range sums, interval trees, 2D range trees, and  word index searching.
Revised:  As examples of the use of the interface and the performance of PAM , we apply the library to four applications: simple range sums, interval trees, 2D range trees, and word index searching.
Edit intent: fluency
Original:  Sequentially the code achieves performance that matches or exceeds exiting libraries designed specially for a single application, and in parallel our implementation gets speedups ranging from 40 to 90 on 72 cores with 2-way hyperthreading.
Revised:  Sequentially the code achieves performance that matches or exceeds existing libraries designed specially for a single application, and in parallel our implementation gets speedups ranging from 40 to 90 on 72 cores with 2-way hyperthreading.
Edit intent: fluency
Original: In this paper, we study the properties of nonlinear BSDEs driven by a Brownian motion and a martingale measure associated with a default jump with intensity process (\lambda_t).
Revised: We study the properties of nonlinear BSDEs driven by a Brownian motion and a martingale measure associated with a default jump with intensity process (\lambda_t).
Edit intent: clarity
Original:  We then apply these results to nonlinear pricing of European contingent claims in an imperfect financial market with a  defaultable risky asset.
Revised:  We then apply these results to nonlinear pricing of European contingent claims in an imperfect financial market with a totally defaultable risky asset.
Edit intent: clarity
Original:  The case of claims paying dividends is also included via the singular process.
Revised:  The case of claims paying dividends is also studied via a singular process.
Edit intent: clarity
Original: This paper presents a novel canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures.
Revised: This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures.
Edit intent: clarity
Original:  We first show that by using finite element method, this most challenging problem can be formulated as a bi-level mixed integer nonlinear programming problem  , i.e. for a given deformation, the upper-level optimization is a typical linear constrained 0-1 programming problem, while for a given structure, the lower-level optimization is a general nonlinear continuous minimization problem in computational nonlinear elasticity.
Revised:  By using finite element method, this most challenging problem can be formulated as a bi-level mixed integer nonlinear programming problem , i.e. for a given deformation, the upper-level optimization is a typical linear constrained 0-1 programming problem, while for a given structure, the lower-level optimization is a general nonlinear continuous minimization problem in computational nonlinear elasticity.
Edit intent: coherence
Original:  We first show that by using finite element method, this most challenging problem can be formulated as a bi-level mixed integer nonlinear programming problem  , i.e. for a given deformation, the upper-level optimization is a typical linear constrained 0-1 programming problem, while for a given structure, the lower-level optimization is a general nonlinear continuous minimization problem in computational nonlinear elasticity.
Revised:  We first show that by using finite element method, this most challenging problem can be formulated as a mixed integer nonlinear programming problem , i.e. for a given deformation, the upper-level optimization is a typical linear constrained 0-1 programming problem, while for a given structure, the lower-level optimization is a general nonlinear continuous minimization problem in computational nonlinear elasticity.
Edit intent: clarity