wanyu/IteraTeR_v2 huggingface dataset:
Original:  Criterion for trajectories' "maximal smoothness " of arbitrary order n is employed, n = 3 is the case of the minimum-jerk model.
Revised:  Criterion for trajectories' maximal smoothness of arbitrary order n is employed, n = 3 is the case of the minimum-jerk model.
Edit intent: fluency
Original:  Corresponding counter-examples are provided.
Revised:  Counter-examples are provided.
Edit intent: clarity
Original:   The derived class of differential equation is a novel tool for discovering candidates for geometric movement primitives.
Revised:  The derived class of differential equations is a novel tool for discovering candidates for geometric movement primitives.
Edit intent: fluency
Original: Neuroscientific studies of the drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole.
Revised: Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole.
Edit intent: fluency
Original:  I derive a class of differential equations obeyed by movement paths for which nth order maximally smooth trajectories have constant rate of accumulating geometric measurement along the drawn path.
Revised:  I derive a class of differential equations obeyed by movement paths for which n-th order maximally smooth trajectories have constant rate of accumulating geometric measurement along the drawn path.
Edit intent: fluency
Original:  For example the two-thirds power-law model corresponds to piece-wise constant speed of accumulating equi-affine arc.
Edit intent: coherence
Original:  The second part is parametrization specific and is needed to identify whether a solution of the first part indeed represents a curve.
Revised:  The second part enforces consistency with desired (geometric) parametrization of curves on solutions of the first part indeed represents a curve.
Edit intent: clarity
Original:  A method for constructing trajectories based on primitives in different geometries is proposed .
Revised:  Connection between geometric invariance, motion smoothness, compositionality and performance of the compromised motor control system is discussed .
Edit intent: coherence
Original: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et  .\ al STOC 2011, Bl\"aser ICALP 2013  ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Revised: Motivated by the recent developments on the complexity of non-com\-mu\-ta\-tive determinant and permanent [Chien et .\ al STOC 2011, Bl\"aser ICALP 2013 ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Edit intent: clarity
Original: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et  .\ al STOC 2011, Bl\"aser ICALP 2013  ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Revised: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et al .\ al STOC 2011, Bl\"aser ICALP 2013 ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Edit intent: fluency
Original: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et  .\ al STOC 2011, Bl\"aser ICALP 2013  ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Revised: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et .\ STOC 2011, Bl\"aser ICALP 2013 ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Edit intent: clarity
Original: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et  .\ al STOC 2011, Bl\"aser ICALP 2013  ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Revised: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et .\ al STOC 2011, Bl\"aser ICALP 2013 ] Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Edit intent: coherence
Original: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et  .\ al STOC 2011, Bl\"aser ICALP 2013  ] and several lower bounds are known Nisan STOC 1991%DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Revised: Non-commutative arithmetic computations differ significantly from their commutative counterparts, in fact the determinant is known to have the same complexity as the permanent [Chien et .\ al STOC 2011, Bl\"aser ICALP 2013 ] and several lower bounds are known %DIFDELCMD < ]%%% . Looking to obtain tight characterizations for hard special cases of permanent , we observe the following:
Edit intent: clarity
Original:  1) We exhibit a parameter t for graphs of bounded component size so that there is an n^{O(t) complete on algebras that contain 2\times 2 matrices and the permutation group S_3} . Also, we prove a  2 ^{\Omega (n) computing the Cayley permanent on  graphs with component size bounded by two. 2)We show that non-commutative permanent over matrices of rank one is at least as hard as the commutative permanent.
Revised:  1) We exhibit a parameter t for graphs of bounded component size so that there is an n^{O(t) complete on algebras that contain 2\times 2 matrices and the permutation group S_3} . Also, we prove a lower bound of 2 ^{\Omega (n) computing the Cayley permanent on graphs with component size bounded by two. 2)We show that non-commutative permanent over matrices of rank one is at least as hard as the commutative permanent.
Edit intent: clarity
Original:  1) We exhibit a parameter t for graphs of bounded component size so that there is an n^{O(t) complete on algebras that contain 2\times 2 matrices and the permutation group S_3} . Also, we prove a  2 ^{\Omega (n) computing the Cayley permanent on  graphs with component size bounded by two. 2)We show that non-commutative permanent over matrices of rank one is at least as hard as the commutative permanent.
Revised:  1) We exhibit a parameter t for graphs of bounded component size so that there is an n^{O(t) complete on algebras that contain 2\times 2 matrices and the permutation group S_3} . Also, we prove a 2 ^{\Omega(n) computing the Cayley permanent on graphs with component size bounded by two. 2)We show that non-commutative permanent over matrices of rank one is at least as hard as the commutative permanent.
Edit intent: fluency
Original:  This is in sharp contrast to the commutative case where the best known upper bound for DegSLP is%DIFDELCMD < {\sf %%% co-RP ^{\sf PP and CoeffSLP is known to be \# }%DIFDELCMD < {\sf %%% P complete .
Revised:  This is in sharp contrast to the commutative case where the best known upper bound for DegSLP is%DIFDELCMD < {\sf %%% ^{\sf PP and CoeffSLP is known to be \# }%DIFDELCMD < {\sf %%% P complete .
Edit intent: clarity
Original:  This is in sharp contrast to the commutative case where the best known upper bound for DegSLP is%DIFDELCMD < {\sf %%% co-RP ^{\sf PP and CoeffSLP is known to be \# }%DIFDELCMD < {\sf %%% P complete .
Revised:  This is in sharp contrast to the commutative case where the best known upper bound for DegSLP is%DIFDELCMD < {\sf %%% co-RP and CoeffSLP is known to be \# }%DIFDELCMD < {\sf %%% P complete .
Edit intent: coherence
Original:  This is in sharp contrast to the commutative case where the best known upper bound for DegSLP is%DIFDELCMD < {\sf %%% co-RP ^{\sf PP and CoeffSLP is known to be \# }%DIFDELCMD < {\sf %%% P complete .
Revised:  This is in sharp contrast to the commutative case where the best known upper bound for DegSLP is%DIFDELCMD < {\sf %%% co-RP ^{\sf PP and CoeffSLP is known to be \# }%DIFDELCMD < {\sf %%% complete .
Edit intent: fluency
Original:  We also numerically evaluate the "generalized" (strong) stochastic burstiness bound based on publicly posted data describing an actual MapReduce workload of a Facebook datacenter.
Edit intent: coherence
Original:  Because of the complexity of interactions, the differential impacts with respect to a baseline, i.e., a business-as-usual  , are commonly considered in relative comparison with various projects.
Revised:  Because of the complexity of interactions, the differential impacts with respect to a baseline, i.e., a business-as-usual (BAU) scenario , are commonly considered in relative comparison with various projects.
Edit intent: clarity
Original:  Because of the complexity of interactions, the differential impacts with respect to a baseline, i.e., a business-as-usual  , are commonly considered in relative comparison with various projects.
Revised:  Because of the complexity of interactions, the differential impacts with respect to a baseline, i.e., a business-as-usual , are commonly considered to relatively compare various projects.
Edit intent: clarity
Original:  Although various mythologies have been successfully proposed and used to contain such a side effect, their bottom-up nature, which initiates  from the project itself and ultimately widens the scope, could easily fail to maintain critical modifications to the baseline.
Revised:  Although various mythologies have been successfully proposed and used to contain such a side effect, the bottom-up nature, which initiates from the project itself and ultimately widens the scope, could easily fail to maintain critical modifications to the baseline.
Edit intent: clarity
Original:  Although various mythologies have been successfully proposed and used to contain such a side effect, their bottom-up nature, which initiates  from the project itself and ultimately widens the scope, could easily fail to maintain critical modifications to the baseline.
Revised:  Although various mythologies have been successfully proposed and used to contain such a side effect, their bottom-up nature, which initiates the assessment from the project itself and ultimately widens the scope, could easily fail to maintain critical modifications to the baseline.
Edit intent: clarity
Original:  Although various mythologies have been successfully proposed and used to contain such a side effect, their bottom-up nature, which initiates  from the project itself and ultimately widens the scope, could easily fail to maintain critical modifications to the baseline.
Revised:  Although various mythologies have been successfully proposed and used to contain such a side effect, their bottom-up nature, which initiates from the project itself and ultimately widens the scope, could easily fail to acknowledge critical modifications to the baseline.
Edit intent: clarity
Original: For a wireless communications network, Local Pooling (LoP) is a desirable property due to its sufficiency for the optimality of low-complexity greedy scheduling techniques.
Revised: The study of the optimality of low-complexity greedy scheduling techniques in wireless communications networks is a very complex problem. The Local Pooling (LoP) is a desirable property due to its sufficiency for the optimality of low-complexity greedy scheduling techniques.
Edit intent: coherence
Original:  We then use simulation to explore this problem in the regime of small network sizes, which suggests the probability that an ER or RG graph satisfies LoP and contains a giant component decays quickly with the size of the network .
Revised:  We then use simulation to explore this problem in the regime of small networks, which suggest the probability that an ER or RG graph satisfies LoP and contains a giant component decays quickly with the size of the network .
Edit intent: clarity
Original:  We then use simulation to explore this problem in the regime of small network sizes, which suggests the probability that an ER or RG graph satisfies LoP and contains a giant component decays quickly with the size of the network .
Revised:  We then use simulation to explore this problem in the regime of small network sizes, which suggests the probability that an ER or RG graph satisfies LoP and is connected decays quickly in network size .
Edit intent: clarity
Original:  We model the Dengue as a stochastic Cellular Automata (CA) process following Susceptible, Exposed, Infected, Recovered (SEIR) -Susceptible, Exposed, Infected (SEI)- for human and vector dynamics respectively in each cell, and analyze the spatial and temporal spreading  disease using parameters from field studies.
Revised:  We model the Dengue as a stochastic Cellular Automata (CA) with human and vector dynamics respectively in each cell, and analyze the spatial and temporal spreading disease using parameters from field studies.
Edit intent: clarity
Original:  We model the Dengue as a stochastic Cellular Automata (CA) process following Susceptible, Exposed, Infected, Recovered (SEIR) -Susceptible, Exposed, Infected (SEI)- for human and vector dynamics respectively in each cell, and analyze the spatial and temporal spreading  disease using parameters from field studies.
Revised:  We model the Dengue as a stochastic Cellular Automata (CA) process following Susceptible, Exposed, Infected, Recovered (SEIR) -Susceptible, Exposed, Infected (SEI)- for human and vector dynamics and analyze the spatial and temporal spreading disease using parameters from field studies.
Edit intent: coherence
Original:  We model the Dengue as a stochastic Cellular Automata (CA) process following Susceptible, Exposed, Infected, Recovered (SEIR) -Susceptible, Exposed, Infected (SEI)- for human and vector dynamics respectively in each cell, and analyze the spatial and temporal spreading  disease using parameters from field studies.
Revised:  We model the Dengue as a stochastic Cellular Automata (CA) process following Susceptible, Exposed, Infected, Recovered (SEIR) -Susceptible, Exposed, Infected (SEI)- for human and vector dynamics respectively in each cell, and analyze the spatial and temporal spreading of the disease using parameters from field studies.
Edit intent: fluency
Original:  We use the data on mosquito density from Ahmedabad city of India as input to our model to predict the dynamics of Dengue incidence and compare it to the reported data on the prevalence of the disease from 2006-2012.
Revised:  Mosquito density data from Ahmedabad city of India as input to our model to predict the dynamics of Dengue incidence and compare it to the reported data on the prevalence of the disease from 2006-2012.
Edit intent: coherence
Original:  We use the data on mosquito density from Ahmedabad city of India as input to our model to predict the dynamics of Dengue incidence and compare it to the reported data on the prevalence of the disease from 2006-2012.
Revised:  We use the data on mosquito density from Ahmedabad city of India as input to our model . We predict the dynamics of Dengue incidence and compare it to the reported data on the prevalence of the disease from 2006-2012.
Edit intent: fluency
Original:  We used data based statistical models of human mobility such as exponential step length and super diffusive L\'evy flight to study mobility effects on Dengue spreading within the city.
Revised:  We have used statistical model of human mobility such as exponential step length and super diffusive L\'evy flight to study mobility effects on Dengue spreading within the city.
Edit intent: clarity
Original:  We used data based statistical models of human mobility such as exponential step length and super diffusive L\'evy flight to study mobility effects on Dengue spreading within the city.
Revised:  We used data based statistical models of human mobility with exponential step length and super diffusive L\'evy flight to study mobility effects on Dengue spreading within the city.
Edit intent: clarity
Original:  We used data based statistical models of human mobility such as exponential step length and super diffusive L\'evy flight to study mobility effects on Dengue spreading within the city.
Revised:  We used data based statistical models of human mobility such as exponential step length distribution to study mobility effects on Dengue spreading within the city.
Edit intent: clarity
Original: We propose and prove completeness of logic for reasoning with functional dependencies (FDs) with semantics defined by general non-idempotent aggregation functions.
Revised: We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined by general non-idempotent aggregation functions.
Edit intent: clarity
Original:  Our approach is based on the idea of preserving similarity of attribute values and allows us to express and reason with stronger relationships between attribute values than the ordinary FDs.
Revised:  Our approach is based on the idea of preserving similarity of attribute values and allows us to express stronger relationships between attribute values than the ordinary FDs.
Edit intent: clarity
Original:  In our setting, the FDs not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes , formalizing a type of continuity of FDs .
Revised:  In our setting, the dependencies not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes , formalizing a type of continuity of FDs .
Edit intent: clarity
Original:  In our setting, the FDs not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes , formalizing a type of continuity of FDs .
Revised:  In our setting, the FDs not only express that certain values are determined by others but also express that similar values of attributes imply similar values of other attributes .
Edit intent: clarity
Original:  We also comment on the related computational issues,  the relational vs. propositional semantics of the monoidal FDs, and the relationship to the ordinary FDs .
Revised:  We also comment on the related computational issues, and the relational vs. propositional semantics of the monoidal FDs, and the relationship to the ordinary FDs .
Edit intent: coherence
Original: Geometric data analysis, which is multivariate data analysis , is an approach for what has been referred to as the visualisation and verbalisation of data.
Revised: We use geometric multivariate data analysis , is an approach for what has been referred to as the visualisation and verbalisation of data.
Edit intent: coherence
Original: Geometric data analysis, which is multivariate data analysis , is an approach for what has been referred to as the visualisation and verbalisation of data.
Revised: Geometric data analysis, which is multivariate data analysis which has been termed a methodology for both the visualization and verbalization of data.
Edit intent: clarity
Original:  In our previous work we noted the following, which we address in an innovative way in this new work: "top-down communication campaigns in social media%DIFDELCMD < ] %%% both predominate and are advised by those involved in `social marketing' ... . However, this rarely manifests itself through measurable behaviour change. .." We visualise and we show how we can quantify change in Twitter narrative.
Revised:  In our previous work we noted the following, which we address in an innovative way in this new work: "top-down communication campaigns %DIFDELCMD < ] %%% both predominate and are advised by those involved in `social marketing' ... . However, this rarely manifests itself through measurable behaviour change. .." We visualise and we show how we can quantify change in Twitter narrative.
Edit intent: clarity
Original:  In our previous work we noted the following, which we address in an innovative way in this new work: "top-down communication campaigns in social media%DIFDELCMD < ] %%% both predominate and are advised by those involved in `social marketing' ... . However, this rarely manifests itself through measurable behaviour change. .." We visualise and we show how we can quantify change in Twitter narrative.
Revised:  In our previous work we noted the following, which we address in an innovative way in this new work: "top-down communication campaigns in social media%DIFDELCMD < ] %%% Unlike current marketing, political and other communication campaigns using Twitter, we develop an innovative approach to measuring bevavioural change. We show also how we can quantify change in Twitter narrative.
Edit intent: coherence
Original:  Potentially too, we show how we can assess statistical significance of these social media events .
Revised:  Potentially too, we show how we can assess statistical significance of social media behaviour .
Edit intent: clarity
Original:  Unfortunately, exact simulation results in simulating every reaction that occurs which may preclude the use of exact simulators for models of any realistic size . Approximate simulation techniques therefore become important.
Revised:  Unfortunately, exact simulation results in simulating every reaction that occurs . This will preclude the use of exact simulators for models of any realistic size . Approximate simulation techniques therefore become important.
Edit intent: coherence
Original:  Unfortunately, exact simulation results in simulating every reaction that occurs which may preclude the use of exact simulators for models of any realistic size . Approximate simulation techniques therefore become important.
Revised:  Unfortunately, exact simulation results in simulating every reaction that occurs which may preclude the use of exact simulators for models of any realistic size and so approximate algorithms become important.
Edit intent: clarity
Original:  We describe a general framework to assess approximate stochastic simulators .
Revised:  In this paper we describe a general framework to assess approximate stochastic simulators .
Edit intent: clarity
Original: Mutually connected components (MCCs) play an important role as a measure of resilience in the study of interconnected networks.
Revised: Mutually connected components (MCCs) play an important role as a measure of resilience in the study of interdependent networks.
Edit intent: clarity
Original:  Despite their importance, an efficient algorithm to obtain physical properties of all MCCs during the removals of links is not available .
Revised:  Despite their importance, an efficient algorithm to obtain the statistics of all MCCs during the removals of links is not available .
Edit intent: clarity