wanyu/IteraTeR_v2 huggingface dataset:
Original:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes ) . Somewhat surprisingly, we retain most other properties from the convex setting for the decentralized consensus algorithms  DGD and Prox-DGD, such as convergence to a (  neighborhood of) consensus stationary solution and the rates of convergence when diminishing (constant) step sizes are used .
Revised:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes . Somewhat surprisingly, we retain most other properties from the convex setting for the decentralized consensus algorithms DGD and Prox-DGD, such as convergence to a ( neighborhood of) consensus stationary solution and the rates of convergence when diminishing (constant) step sizes are used .
Edit intent: fluency
Original:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes ) . Somewhat surprisingly, we retain most other properties from the convex setting for the decentralized consensus algorithms  DGD and Prox-DGD, such as convergence to a (  neighborhood of) consensus stationary solution and the rates of convergence when diminishing (constant) step sizes are used .
Revised:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes ) . Somewhat surprisingly, the decentralized consensus algorithms DGD and Prox-DGD, such as convergence to a ( neighborhood of) consensus stationary solution and the rates of convergence when diminishing (constant) step sizes are used .
Edit intent: clarity
Original:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes ) . Somewhat surprisingly, we retain most other properties from the convex setting for the decentralized consensus algorithms  DGD and Prox-DGD, such as convergence to a (  neighborhood of) consensus stationary solution and the rates of convergence when diminishing (constant) step sizes are used .
Revised:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes ) . Somewhat surprisingly, we retain most other properties from the convex setting for the decentralized consensus algorithms , DGD and Prox-DGD, such as convergence to a ( neighborhood of) consensus stationary solution and the rates of convergence when diminishing (constant) step sizes are used .
Edit intent: fluency
Original:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes ) . Somewhat surprisingly, we retain most other properties from the convex setting for the decentralized consensus algorithms  DGD and Prox-DGD, such as convergence to a (  neighborhood of) consensus stationary solution and the rates of convergence when diminishing (constant) step sizes are used .
Revised:  When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we still do sometimes ) . Somewhat surprisingly, we retain most other properties from the convex setting for the decentralized consensus algorithms DGD and Prox-DGD, such as convergence to a ( neighborhood of) consensus stationary solution and have guaranteed rates of convergence when diminishing (constant) step sizes are used .
Edit intent: clarity
Original:  It is worth noting that the Prox-DGD algorithm can handle nonconvex nonsmooth functions assume that their proximal operators can be computed.
Revised:  It is worth noting that Prox-DGD algorithm can handle nonconvex nonsmooth functions assume that their proximal operators can be computed.
Edit intent: fluency
Original:  It is worth noting that the Prox-DGD algorithm can handle nonconvex nonsmooth functions assume that their proximal operators can be computed.
Revised:  It is worth noting that the Prox-DGD can handle nonconvex nonsmooth functions assume that their proximal operators can be computed.
Edit intent: clarity
Original:  It is worth noting that the Prox-DGD algorithm can handle nonconvex nonsmooth functions assume that their proximal operators can be computed.
Revised:  It is worth noting that the Prox-DGD algorithm can handle nonconvex nonsmooth functions if their proximal operators can be computed.
Edit intent: clarity
Original:  To establish some of  these properties, the existing proofs from the convex setting need changes, and some results require a completely different line of analysis  .
Revised:  To establish some of these properties, we have to introduce a completely different line of analysis .
Edit intent: coherence
Original: Using fundamental ideas from Brattka%DIFDELCMD < &%%% Hertling'98 and by means of object-oriented overloading of operators, the iRRAM library supports imperative programming over the reals with a both sound and computable, multivalued semantics of tests.
Revised:  Brattka%DIFDELCMD < &%%% Hertling'98 and by means of object-oriented overloading of operators, the iRRAM library supports imperative programming over the reals with a both sound and computable, multivalued semantics of tests.
Edit intent: clarity
Original: Using fundamental ideas from Brattka%DIFDELCMD < &%%% Hertling'98 and by means of object-oriented overloading of operators, the iRRAM library supports imperative programming over the reals with a both sound and computable, multivalued semantics of tests.
Revised: Using fundamental ideas from %DIFDELCMD < &%%% Hertling'98 and by means of object-oriented overloading of operators, the iRRAM library supports imperative programming over the reals with a both sound and computable, multivalued semantics of tests.
Edit intent: coherence
Original: Using fundamental ideas from Brattka%DIFDELCMD < &%%% Hertling'98 and by means of object-oriented overloading of operators, the iRRAM library supports imperative programming over the reals with a both sound and computable, multivalued semantics of tests.
Revised: Using fundamental ideas from Brattka%DIFDELCMD < &%%% and by means of object-oriented overloading of operators, the iRRAM library supports imperative programming over the reals with a both sound and computable, multivalued semantics of tests.
Edit intent: coherence
Original: Inspired and guided by the iRRAM C++ library (M\"uller 2001), we formally specify a programming language for the paradigm of EXACT REAL COMPUTATION ( ERC) : reliably operating on encapsulated CONTINUOUS data types such as (not necessarily algebraic) real numbers -- imperatively and exactly (no rounding errors) with primitives COMPUTABLE in the sense of Recursive Analysis including a necessarily modified multivalued (=non-functional) semantics of tests.
Revised: This work formalizes "Exact Real Computation" ( ERC) : reliably operating on encapsulated CONTINUOUS data types such as (not necessarily algebraic) real numbers -- imperatively and exactly (no rounding errors) with primitives COMPUTABLE in the sense of Recursive Analysis including a necessarily modified multivalued (=non-functional) semantics of tests.
Edit intent: clarity
Original: Inspired and guided by the iRRAM C++ library (M\"uller 2001), we formally specify a programming language for the paradigm of EXACT REAL COMPUTATION ( ERC) : reliably operating on encapsulated CONTINUOUS data types such as (not necessarily algebraic) real numbers -- imperatively and exactly (no rounding errors) with primitives COMPUTABLE in the sense of Recursive Analysis including a necessarily modified multivalued (=non-functional) semantics of tests.
Revised: Inspired and guided by the iRRAM C++ library (M\"uller 2001), we formally specify a programming language for the paradigm of EXACT REAL COMPUTATION ( ERC) : a paradigm combining (i) ALGEBRAIC imperative programming of/over abstract data types (ADTs) for CONTINUOUS structures with (ii) a selection and sound semantics of primitives computable in the sense of Recursive Analysis including a necessarily modified multivalued (=non-functional) semantics of tests.
Edit intent: clarity
Original:  We establish Turing-COMPLETENESS over the reals: a partial function f:R^d x Z -> R is computable ( in the sense of Recursive Analysis ) iff it can be expressed in ERC . For rigorously specifying and arguing about such computations in Mathematical Logic, we then propose a DECIDABLE first-order theory over two sorts , integers and real numbers.
Revised:  We establish Turing-COMPLETENESS over the reals: a partial real function is computable in the sense of Recursive Analysis ) iff it can be expressed in ERC . For rigorously specifying and arguing about such computations in Mathematical Logic, we then propose a DECIDABLE first-order theory over two sorts , integers and real numbers.
Edit intent: clarity
Original:  We establish Turing-COMPLETENESS over the reals: a partial function f:R^d x Z -> R is computable ( in the sense of Recursive Analysis ) iff it can be expressed in ERC . For rigorously specifying and arguing about such computations in Mathematical Logic, we then propose a DECIDABLE first-order theory over two sorts , integers and real numbers.
Revised:  We establish Turing-COMPLETENESS over the reals: a partial function f:R^d x Z -> R is computable ( in the sense of Recursive Analysis iff it can be expressed in ERC . For rigorously specifying and arguing about such computations in Mathematical Logic, we then propose a DECIDABLE first-order theory over two sorts , integers and real numbers.
Edit intent: fluency
Original:  We  extend the rules of Hoare Logic to support the formal derivation of correctness proofs in ERC;
Revised:  We accordingly extend the rules of Hoare Logic to support the formal derivation of correctness proofs in ERC;
Edit intent: coherence
Original:  We  extend the rules of Hoare Logic to support the formal derivation of correctness proofs in ERC;
Revised:  We extend the rules of Hoare Logic to support formal correctness proofs in ERC;
Edit intent: clarity
Original:  and we have them, including their real quantification, verified in the Coq Proof Assistant.
Revised:  and formally verify the aforementioned example programs with the Coq Proof Assistant.
Edit intent: clarity
Original:  yet REALIZING a function (again like e^x) requires only to APPROXIMATE its return value up to guaranteed absolute error 2 ^{p for any given integer p: closure under composition is implicit.
Revised:  yet REALIZING a function (again like e^x) requires only to APPROXIMATE its return value up to guaranteed absolute error 2 ^p for any given integer p: closure under composition is implicit.
Edit intent: fluency
Original:  Three simple numerical problems demonstrate both the convenience and novel control-flow considerations of this approach to Reliable Numerics: multivalued integer rounding, solving systems of linear equations, and simple root finding.
Revised:  Three basic numerical problems demonstrate both the convenience and novel control-flow considerations of this approach to Reliable Numerics: multivalued integer rounding, solving systems of linear equations, and simple root finding.
Edit intent: clarity
Original:  We accordingly extend the rules of Hoare Logic  to support formal correctness proofs in ERC ;
Revised:  Rules of Hoare Logic to support formal correctness proofs in ERC ;
Edit intent: coherence
Original: - with partial inequality predicate and multivalued binary SELECT and continuous conditional (aka PARALLEL-IF) operations -- yet REALIZING a function (again like e^x) requires only to APPROXIMATE its return value up to guaranteed absolute error 2^p for any given integer p:\to closure under composition is implicit.
Revised: - with partial inequality predicate and multivalued binary SELECT and continuous conditional (aka PARALLEL-IF) operations -- yet REALIZING a function (again like e^x) requires only to APPROXIMATE its return value up to guaranteed absolute error 2^p with respect to an additionally given integer parameter p\to closure under composition is implicit.
Edit intent: clarity
Original:  Programs thus operate on a many-sorted structure involving real numbers and integers,  connected via the 'error' embedding Z\ni p\mapsto 2^p\in R, whose first-order theory is proven decidable and model-complete.
Revised:  Programs thus operate on a many-sorted structure involving real numbers and integers, the latter connected via the 'error' embedding Z\ni p\mapsto 2^p\in R, whose first-order theory is proven decidable and model-complete.
Edit intent: clarity
Original:  Special features of MANET like hop-by-hop communications, dynamic topology  and open network boundary made security highly challengeable.
Revised:  Special features of MANET like hop-by-hop communications, dynamic topology , and open network boundary made security highly challengeable.
Edit intent: fluency
Original:  In this paper, a novel approach called Detection and Elimination Black Holes DEBH is proposed, which uses a data control packet and an additional Black hole Check BCh table for detecting and eliminating malicious nodes.
Revised:  In this paper, a novel approach called Detecting and Eliminating Black Holes (DEBH) is proposed that uses a data control packet and an additional Black hole Check BCh table for detecting and eliminating malicious nodes.
Edit intent: clarity
Original:  In this paper, a novel approach called Detection and Elimination Black Holes DEBH is proposed, which uses a data control packet and an additional Black hole Check BCh table for detecting and eliminating malicious nodes.
Revised:  In this paper, a novel approach called Detection and Elimination Black Holes DEBH is proposed, which uses a data control packet and an additional Black hole Check (BCh) table for detecting and eliminating malicious nodes.
Edit intent: clarity
Original: Across many scientific domains, there is  common need to automatically extract a simplified view or a coarse-graining of how a complex system's components interact.
Revised: Across many scientific domains, there is a common need to automatically extract a simplified view or a coarse-graining of how a complex system's components interact.
Edit intent: fluency
Original: Across many scientific domains, there is  common need to automatically extract a simplified view or a coarse-graining of how a complex system's components interact.
Revised: Across many scientific domains, there is common need to automatically extract a simplified view or coarse-graining of how a complex system's components interact.
Edit intent: fluency
Original:  It is common to evaluate the performance of community detection algorithms by their ability to find so-called ground truth communities.
Revised:  It is common to evaluate the performance of community detection algorithms by their ability to find so-called "ground truth" communities.
Edit intent: fluency
Original:  This works well in synthetic networks with planted communities because such networks' links are formed explicitly based on the planted communities.
Revised:  This works well in synthetic networks with planted communities because such networks' links are formed explicitly based on those known communities.
Edit intent: clarity
Original:  We prove that no algorithm can uniquely solve community detection, and we prove a general No Free Lunch theorem for community detection, which implies that no algorithm can perform better than any other across all inputs .
Revised:  We prove that no algorithm can uniquely solve community detection, and we prove a general No Free Lunch theorem for community detection, which implies that there can be no algorithm that is optimal for all possible community detection tasks .
Edit intent: clarity
Original:  However,  node metadata still have value and a careful exploration of their relationship with network structure can yield insights of genuine worth.
Revised:  However, node metadata still have value so a careful exploration of their relationship with network structure can yield insights of genuine worth.
Edit intent: coherence
Original:  We illustrate this point by introducing two statistical techniques that can quantify the relationship between metadata and community structure for a broad class  models.
Revised:  We illustrate this point by introducing two statistical techniques that can quantify the relationship between metadata and community structure for a broad class of models.
Edit intent: fluency
Original: In the year of 2016, there were more than 24 million Indonesian twitter users sharing news, events, as well as personal feelings and experiences on Twitter.
Edit intent: coherence
Original:  This study seeks to validate a search protocol of  health-related terms using real-time Twitter data which can later be used to understand if, and how, twitter can reveal information on the current health situation in Indonesia.
Revised:  This study seeks to validate a search protocol of health-related terms using Twitter data which can later be used to understand if, and how, twitter can reveal information on the current health situation in Indonesia.
Edit intent: clarity
Original:  This study seeks to validate a search protocol of  health-related terms using real-time Twitter data which can later be used to understand if, and how, twitter can reveal information on the current health situation in Indonesia.
Revised:  This study seeks to validate a search protocol of health-related terms using real-time Twitter data which can later be used to understand if, and how, Twitter can reveal information on the current health situation in Indonesia.
Edit intent: fluency
Original:  In this validation study of mining protocols, we extracted geo-located conversations related to health and disease postings on Twitter using a set of pre-defined keywords, assessed the prevalence, frequency  and timing of such content in these conversations, and validated how this search protocol was able to detect relevant disease tweets.
Revised:  In this validation study of mining protocols, we extracted geo-located conversations related to health and disease postings on Twitter using a set of pre-defined keywords, assessed the prevalence, frequency , and timing of such content in these conversations, and validated how this search protocol was able to detect relevant disease tweets.
Edit intent: fluency
Original:  The accuracy of predictions of mined hits versus expert validated hits using the CART algorithm showed good validity with AUC beyond 0.8.
Revised:  The accuracy of predictions showed a good validity with AUC beyond 0.8.
Edit intent: clarity
Original:  Our study shows that monitoring of public sentiment on Twitter , combined with contextual knowledge about the disease, can detect health and disease tweets and potentially be used as a valuable real-time proxy for health events over space and time .
Revised:  Our study shows that monitoring of public sentiment on Twitter can be used as a valuable real-time proxy for health events over space and time .
Edit intent: coherence
Original:  Our study shows that monitoring of public sentiment on Twitter , combined with contextual knowledge about the disease, can detect health and disease tweets and potentially be used as a valuable real-time proxy for health events over space and time .
Revised:  Our study shows that monitoring of public sentiment on Twitter , combined with contextual knowledge about the disease, can detect health and disease tweets and potentially be used as a real-time proxy for health events over space and time .
Edit intent: clarity
Original:  Our study shows that monitoring of public sentiment on Twitter , combined with contextual knowledge about the disease, can detect health and disease tweets and potentially be used as a valuable real-time proxy for health events over space and time .
Revised:  Our study shows that monitoring of public sentiment on Twitter , combined with contextual knowledge about the disease, can detect health and disease tweets and potentially be used as a valuable real-time proxy for health events .
Edit intent: clarity
Original:  Agents then perform a Bayesian update of their beliefs followed by a local averaging of the log beliefs  .
Revised:  Agents then perform a Bayesian update of their beliefs followed by an averaging of the log beliefs .
Edit intent: clarity
Original:  ODs  subsume FDs, however, not vice versa as ODs can additionally express business rules involving order , e.g., an employee never has a higher salary while paying lower taxes compared with another employee.
Revised:  ODs subsume FDs, as they can additionally express business rules involving order , e.g., an employee never has a higher salary while paying lower taxes compared with another employee.
Edit intent: coherence
Original:  ODs  subsume FDs, however, not vice versa as ODs can additionally express business rules involving order , e.g., an employee never has a higher salary while paying lower taxes compared with another employee.
Revised:  ODs subsume FDs, however, not vice versa as ODs can additionally express business rules involving order ; e.g., an employee never has a higher salary while paying lower taxes compared with another employee.
Edit intent: fluency
Original:  We address the limitations of prior work on OD discovery which has factorial complexity in the number of attributes, is incomplete (i.e., it does not discover valid ODs that cannot be inferred from the ones found) and is not concise (i.e.,  can result in "redundant" discovery and overly large discovery sets).
Revised:  We address the limitations of prior work on OD discovery which has factorial complexity in the number of attributes, is incomplete (i.e., it does not discover valid ODs that cannot be inferred from the ones found) and is not concise (i.e., can result in "redundant" discovery and overly large discovery sets).
Edit intent: fluency
Original:  We address the limitations of prior work on OD discovery which has factorial complexity in the number of attributes, is incomplete (i.e., it does not discover valid ODs that cannot be inferred from the ones found) and is not concise (i.e.,  can result in "redundant" discovery and overly large discovery sets).
Revised:  We address the limitations of prior work on OD discovery which has factorial complexity in the number of attributes, is incomplete (i.e., it does not discover valid ODs that cannot be inferred from the ones found) and is not concise (i.e., it can result in "redundant" discovery and overly large discovery sets).
Edit intent: fluency
Original:  This includes a novel polynomial mapping to a canonical form for ODs, and a sound and complete set of axioms (inference rules) for canonical ODs.
Revised:  This is based on a novel polynomial mapping to a canonical form for ODs, and a sound and complete set of axioms (inference rules) for canonical ODs.
Edit intent: clarity
Original: Reaction prediction remains one of the great challenges for organic chemistry . Solving this problem computationally requires the programming of a vast amount of knowledge and intuition of the rules of organic chemistry and the development of algorithms for their application .
Revised: Reaction prediction remains one of the major challenges for organic chemistry . Solving this problem computationally requires the programming of a vast amount of knowledge and intuition of the rules of organic chemistry and the development of algorithms for their application .
Edit intent: clarity
Original:  We test this capability on problems from a popular organic chemistry textbook.
Revised:  We test this method on problems from a popular organic chemistry textbook.
Edit intent: clarity
Original:  The first algorithm uses this Morse function to identify handles that are glued systematically to obtain a pant decomposition.
Revised:  The first algorithm uses this Morse function to identify handles that are glued systematically to obtain a pant decomposition.
Edit intent: fluency
Original: A network is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree.
Revised: A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree.
Edit intent: clarity