wanyu/IteraTeR_v2 huggingface dataset:
Original: We define generalized standard triples X,  zC_{1} - C_{0}, \mathbf{Y P(z) \in C^{n \times n}[z]  in order to use the representation X(z C_{1}~-~C_{0})^{-1}Y~=~P^{-1}(z) except if z is an eigenvalue  .
Revised: We define generalized standard triples X, zC_{1} - C_{0}, \mathbf{Y P(z) \in C^{n \times n}[z] , in order to use the representation X(z C_{1}~-~C_{0})^{-1}Y~=~P^{-1}(z) except if z is an eigenvalue .
Edit intent: fluency
Original: We define generalized standard triples X,  zC_{1} - C_{0}, \mathbf{Y P(z) \in C^{n \times n}[z]  in order to use the representation X(z C_{1}~-~C_{0})^{-1}Y~=~P^{-1}(z) except if z is an eigenvalue  .
Revised: We define generalized standard triples X, zC_{1} - C_{0}, \mathbf{Y P(z) \in C^{n \times n}[z] in order to use the representation X(z C_{1}~-~C_{0})^{-1}Y~=~P^{-1}(z) which holds except when z is an eigenvalue .
Edit intent: clarity
Original: We define generalized standard triples X,  zC_{1} - C_{0}, \mathbf{Y P(z) \in C^{n \times n}[z]  in order to use the representation X(z C_{1}~-~C_{0})^{-1}Y~=~P^{-1}(z) except if z is an eigenvalue  .
Revised: We define generalized standard triples X, zC_{1} - C_{0}, \mathbf{Y P(z) \in C^{n \times n}[z] in order to use the representation X(z C_{1}~-~C_{0})^{-1}Y~=~P^{-1}(z) except if z is an eigenvalue of \mathbf{P .
Edit intent: clarity
Original: We investigate stochastic, distributedalgorithms that can accomplish separation and integration behaviors in self-organizing particle systems, an abstraction of programmable matter.
Revised: We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration behaviors in self-organizing particle systems, an abstraction of programmable matter.
Edit intent: clarity
Original: We investigate stochastic, distributedalgorithms that can accomplish separation and integration behaviors in self-organizing particle systems, an abstraction of programmable matter.
Revised: We investigate stochastic, distributedalgorithms that can accomplish separation and integration in self-organizing particle systems, an abstraction of programmable matter.
Edit intent: clarity
Original:  These particle systems are composed of individual computational units known as particles that each have limited memory, strictly local communication abilities, and modest computational power , and which collectively solve system-wide problems of movement and coordination.
Revised:  Such systems are composed of individual computational units known as particles that each have limited memory, strictly local communication abilities, and modest computational power , and which collectively solve system-wide problems of movement and coordination.
Edit intent: clarity
Original:  These particle systems are composed of individual computational units known as particles that each have limited memory, strictly local communication abilities, and modest computational power , and which collectively solve system-wide problems of movement and coordination.
Revised:  These particle systems are composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational power , and which collectively solve system-wide problems of movement and coordination.
Edit intent: clarity
Original:  With the same frequency of trials and feedback, about half the participants succeeded in learning the categories (learners: criterion 80\% accuracy) and the rest did not (non-learners).
Revised:  With the same number of trials and feedback, about half the participants succeeded in learning the categories (learners: criterion 80\% accuracy) and the rest did not (non-learners).
Edit intent: clarity
Original:  The lower the proportion of features distinguishing category members from non-members (i.e., greater difficulty), the fewer the learners and the more trials it took them to learn.
Edit intent: coherence
Original: We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as the trapped ions.
Revised: We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as trapped ions.
Edit intent: fluency
Original:  Our focus is on the co-design of a problem, its solution, and quantum hardware capable of executing the solution at the minimal cost expressed in terms of the quantum computing resources used , while demonstrating the solution of an instance of a scientifically interesting problem that is intractable classically.
Revised:  Our focus is on the co-design of a problem, its solution, and quantum hardware capable of executing the solution at the minimal cost expressed in terms of the quantum computing resources used while demonstrating the solution of an instance of a scientifically interesting problem that is intractable classically.
Edit intent: fluency
Original:  and, last but not least, (iii) a } formal semantic framework that allows for efficient execution and yet a precise way to describe standard components of a compiler together with additional validationcomponents for programs in the language being compiled.
Revised:  and, last but not least, (iii) a }, a formal semantic framework that allows for efficient execution and yet a precise way to describe standard components of a compiler together with additional validationcomponents for programs in the language being compiled.
Edit intent: fluency
Original:  Our formal framework  is comprised by Generalized Interpreting { Automata, an automata-based formalism to describe the operational semantics of programming languages  that generalizes Gordon Plotkin's Interpreting Automata approach, and the Basic Programming Languages Constructs (BPLC) library, a set of programming languages constructs inspired by Peter Mosses' Component-Based Semantics .
Revised:  Our formal framework \pi is comprised by Generalized Interpreting { Automata, an automata-based formalism to describe the operational semantics of programming languages that generalizes Gordon Plotkin's Interpreting Automata approach, and the Basic Programming Languages Constructs (BPLC) library, a set of programming languages constructs inspired by Peter Mosses' Component-Based Semantics .
Edit intent: fluency
Original:  Our formal framework  is comprised by Generalized Interpreting { Automata, an automata-based formalism to describe the operational semantics of programming languages  that generalizes Gordon Plotkin's Interpreting Automata approach, and the Basic Programming Languages Constructs (BPLC) library, a set of programming languages constructs inspired by Peter Mosses' Component-Based Semantics .
Revised:  Our formal framework is comprised by Generalized Interpreting {\pi Automata, an automata-based formalism to describe the operational semantics of programming languages that generalizes Gordon Plotkin's Interpreting Automata approach, and the Basic Programming Languages Constructs (BPLC) library, a set of programming languages constructs inspired by Peter Mosses' Component-Based Semantics .
Edit intent: fluency
Original:  Our formal framework  is comprised by Generalized Interpreting { Automata, an automata-based formalism to describe the operational semantics of programming languages  that generalizes Gordon Plotkin's Interpreting Automata approach, and the Basic Programming Languages Constructs (BPLC) library, a set of programming languages constructs inspired by Peter Mosses' Component-Based Semantics .
Revised:  Our formal framework is comprised by Generalized Interpreting { Automata, an automata-based formalism to describe the operational semantics of programming languages , that generalizes Gordon Plotkin's Interpreting Automata approach, and the Basic Programming Languages Constructs (BPLC) library, a set of programming languages constructs inspired by Peter Mosses' Component-Based Semantics .
Edit intent: fluency
Original:  Our formal framework  is comprised by Generalized Interpreting { Automata, an automata-based formalism to describe the operational semantics of programming languages  that generalizes Gordon Plotkin's Interpreting Automata approach, and the Basic Programming Languages Constructs (BPLC) library, a set of programming languages constructs inspired by Peter Mosses' Component-Based Semantics .
Revised:  Our formal framework is comprised by Generalized Interpreting { Automata, an automata-based formalism to describe the operational semantics of programming languages that generalizes Gordon Plotkin's Interpreting Automata .
Edit intent: clarity
Original: We study a discrete optimization problem over a dynamical system that consists of several linear subsystems .
Revised: We study the following optimization problem over a dynamical system that consists of several linear subsystems .
Edit intent: clarity
Original:  In particular, we aim to find a sequence of K matrices, each chosen from a given finite set of square matrices, to maximize a convex function over the product of the K matrices and a given vector.
Revised:  In particular, we aim to find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and a given vector.
Edit intent: clarity
Original:  In particular, we aim to find a sequence of K matrices, each chosen from a given finite set of square matrices, to maximize a convex function over the product of the K matrices and a given vector.
Revised:  In particular, we aim to find a sequence of K matrices, each chosen from a given finite set of square matrices, to maximize a convex function over the product of the K matrices and the given vector.
Edit intent: fluency
Original:  This problem models many applications in operations research and control .
Revised:  This simple problem has many applications in operations research and control .
Edit intent: clarity
Original:  We propose a polynomial-time exact algorithm for the problem when the given set of matrices has the oligo-vertex property, a concept we introduce to characterize the numbers of extreme points of certain polytopes related to the given matrices.
Revised:  We propose a simple exact algorithm for the problem when the given set of matrices has the oligo-vertex property, a concept we introduce to characterize the numbers of extreme points of certain polytopes related to the given matrices.
Edit intent: clarity
Original:  We propose a polynomial-time exact algorithm for the problem when the given set of matrices has the oligo-vertex property, a concept we introduce to characterize the numbers of extreme points of certain polytopes related to the given matrices.
Revised:  We propose a polynomial-time exact algorithm for the problem when the given set of matrices has the oligo-vertex property, a concept we introduce in this paper for a set of matrices.
Edit intent: clarity
Original:  We derive a set of sufficient conditions for a pair of matrices to have the oligo-vertex property.
Revised:  We derive several sufficient conditions for a pair of matrices to have the oligo-vertex property.
Edit intent: clarity
Original:  We derive a set of sufficient conditions for a pair of matrices to have the oligo-vertex property.
Revised:  We derive a set of sufficient conditions for a set of matrices to have the oligo-vertex property.
Edit intent: fluency
Original:  We also pose several open questions on the oligo-vertex property and discuss its potential connection with the finiteness property of a set of matrices, which may be of independent interest.
Revised:  We also propose several open questions on the oligo-vertex property and discuss its potential connection with the finiteness property of a set of matrices, which may be of independent interest.
Edit intent: fluency
Original: An indexing of a finite set S is a bijection D : \{1,...,|S|\} \rightarrow S.
Revised: An indexing of a finite set S is a bijection D : \{1,...,|S|\} \rightarrow S.
Edit intent: fluency
Original: Social networks continuously change as people create new ties and break existing ones .
Revised: Social networks continuously change as new ties are created and existing ones fade .
Edit intent: clarity
Original:  It is widely noted that our social embedding exerts  strong influence on what information we receive , and how we form beliefs and make decisions.
Revised:  It is widely noted that our social embedding exerts a strong influence on what information we receive , and how we form beliefs and make decisions.
Edit intent: fluency
Original:  It is widely noted that our social embedding exerts  strong influence on what information we receive , and how we form beliefs and make decisions.
Revised:  It is widely noted that our social embedding exerts strong influence on what information we receive and how we form beliefs and make decisions.
Edit intent: fluency
Original:  However, most studies overlook the dynamic nature of social networks , and its role in fostering adaptive collective intelligence.
Revised:  However, most empirical studies on the role of social networks in collective intelligence have overlooked the dynamic nature of social networks , and its role in fostering adaptive collective intelligence.
Edit intent: clarity
Original:  However, most studies overlook the dynamic nature of social networks , and its role in fostering adaptive collective intelligence.
Revised:  However, most studies overlook the dynamic nature of social networks and its role in fostering adaptive collective intelligence.
Edit intent: fluency
Original:  It remains unknown (1) how network structures adapt to the performances of individuals, and (2) whether this adaptation promotes the accuracy of individual and collective decisions.
Revised:  It remains unknown (1) how network structures adapt to the attributes of individuals, and (2) whether this adaptation promotes the accuracy of individual and collective decisions.
Edit intent: clarity
Original:  Our results reveal that groups of people embedded in dynamic social networks can adapt to biased and non-stationary information environments.
Revised:  Our results reveal that social network plasticity in the presence of feedback, can adapt to biased and non-stationary information environments.
Edit intent: clarity
Original: Fostering technological innovation is intimately related to knowledge creation and recombination.
Revised: Technological innovation is intimately related to knowledge creation and recombination.
Edit intent: clarity
Original:  Here, we map research efforts in Greece within the domain of renewable energy technology and its intersections with the domains of nanoscience and nanotechnology with focus on materials, and electrical engineering and computer science by means of a combined statistical and network-based approach to studying collaboration in scientific authorship.
Revised:  In this work we introduce a combined statistical and network-based approach to study collaboration in scientific authorship. We apply it to characterize recent research efforts in Greece within the domain of renewable energy technology and its intersections with the domains of nanoscience and nanotechnology with focus on materials, and electrical engineering and computer science by means of a combined statistical and network-based approach to studying collaboration in scientific authorship.
Edit intent: coherence
Original:  Here, we map research efforts in Greece within the domain of renewable energy technology and its intersections with the domains of nanoscience and nanotechnology with focus on materials, and electrical engineering and computer science by means of a combined statistical and network-based approach to studying collaboration in scientific authorship.
Revised:  Here, we map research efforts in renewable energy technology and its intersections with the domains of nanoscience and nanotechnology with focus on materials, and electrical engineering and computer science by means of a combined statistical and network-based approach to studying collaboration in scientific authorship.
Edit intent: clarity
Original:  We specifically examine the content, organizational make-up and geographic trace of scientific collaboration, how these have evolved over the sixteen-year period 2000-2015, and we attempt to illuminate the processes underlying knowledge creation and diversification .
Revised:  We specifically examine the content, organizational make-up and geographic trace of scientific collaboration, how these have evolved over the sixteen-year period 2000-2015, and we attempt to illuminate the processes which underlie knowledge creation and diversification .
Edit intent: clarity
Original:  We propose a modeling framework, referred to as Evo-Lexis, that provides insight to some general and fundamental queries about evolving hierarchical systems.
Revised:  We propose a modeling framework, referred to as Evo-Lexis, that provides insight to some fundamental questions about evolving hierarchical systems.
Edit intent: clarity
Original:  Evo-Lexis computes the optimized adjustment of a given hierarchy when the set of targets changes over time by additions and removals (  "incremental design").
Revised:  Evo-Lexis computes the optimized adjustment of a given hierarchy when the set of targets changes over time by additions and removals ( a process referred to as "incremental design").
Edit intent: clarity
Original:  4. Which are the differences in terms of cost and structure between the incrementally designed and the corresponding  clean-slate designed hierarchies ?
Revised:  4. Which are the differences in terms of cost and structure between incrementally designed hierarchies and the corresponding clean-slate designed hierarchies ?
Edit intent: fluency
Original:  4. Which are the differences in terms of cost and structure between the incrementally designed and the corresponding  clean-slate designed hierarchies ?
Revised:  4. Which are the differences in terms of cost and structure between the incrementally designed and the corresponding " clean-slate designed hierarchies ?
Edit intent: fluency
Original:  We present a fully automatic pipeline for same-subject-MRI guided reconstruction of image volumes from a series of histological sections of different modalities, followed by diffeomorphic mapping to a reference atlas.
Revised:  We present a fully automatic pipeline for same-subject-MRI guided reconstruction of a histological series, jointly with diffeomorphic mapping to a reference atlas.
Edit intent: clarity
Original: We elucidate the structure of (P_6,C_4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes whose structure is completely characterized . Using this result, we show that for any (P_6,C_4)-free graph G, the following hold: (i) \lceil5\omega(G){4}\rceil and \lceil\Delta(G) + \omega(G) +1{2}\rceil are  upper bounds for the chromatic number of G. Moreover, these bounds are tight.
Revised: We elucidate the structure of (P_6,C_4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes of graphs . Using this result, we show that for any (P_6,C_4)-free graph G, the following hold: (i) \lceil5\omega(G){4}\rceil and \lceil\Delta(G) + \omega(G) +1{2}\rceil are upper bounds for the chromatic number of G. Moreover, these bounds are tight.
Edit intent: clarity
Original: We elucidate the structure of (P_6,C_4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes whose structure is completely characterized . Using this result, we show that for any (P_6,C_4)-free graph G, the following hold: (i) \lceil5\omega(G){4}\rceil and \lceil\Delta(G) + \omega(G) +1{2}\rceil are  upper bounds for the chromatic number of G. Moreover, these bounds are tight.
Revised: We elucidate the structure of (P_6,C_4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes whose structure is completely characterized . Using this result, we show that for any (P_6,C_4)-free graph G, \lceil5\omega(G){4}\rceil and \lceil\Delta(G) + \omega(G) +1{2}\rceil are upper bounds for the chromatic number of G. Moreover, these bounds are tight.
Edit intent: coherence
Original: We elucidate the structure of (P_6,C_4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes whose structure is completely characterized . Using this result, we show that for any (P_6,C_4)-free graph G, the following hold: (i) \lceil5\omega(G){4}\rceil and \lceil\Delta(G) + \omega(G) +1{2}\rceil are  upper bounds for the chromatic number of G. Moreover, these bounds are tight.
Revised: We elucidate the structure of (P_6,C_4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes whose structure is completely characterized . Using this result, we show that for any (P_6,C_4)-free graph G, the following hold: (i) \lceil5\omega(G){4}\rceil and \lceil\Delta(G) + \omega(G) +1{2}\rceil are tight upper bounds for the chromatic number of G. Moreover, these bounds are tight.
Edit intent: fluency
Original: Physical annealing systems provide a heuristic approach to solve NP-hard Ising optimization problems.
Revised: Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems.
Edit intent: fluency
Original:  In this paper we study the performance of two types of annealing machines that have very different connectivity -- a commercially available quantum annealer built by %DIFDELCMD < \dwave %%% Systems, which has sparse connectivity, and coherent Ising machines  based on optical parametric oscillator networks, which have all-to-all connectivity.
Revised:  In this paper we study the performance of two types of annealing machines--a commercially available quantum annealer built by %DIFDELCMD < \dwave %%% Systems, which has sparse connectivity, and coherent Ising machines based on optical parametric oscillator networks, which have all-to-all connectivity.
Edit intent: clarity
Original:  In this paper we study the performance of two types of annealing machines that have very different connectivity -- a commercially available quantum annealer built by %DIFDELCMD < \dwave %%% Systems, which has sparse connectivity, and coherent Ising machines  based on optical parametric oscillator networks, which have all-to-all connectivity.
Revised:  In this paper we study the performance of two types of annealing machines that have very different connectivity -- a commercially available quantum annealer built by %DIFDELCMD < \dwave %%% Systems, which has sparse connectivity, and coherent Ising machines (CIMs) based on optical parametric oscillator networks, which have all-to-all connectivity.
Edit intent: clarity
Original:  This leads to a several-orders-of-magnitude time-to-solution difference between coherent Ising machines and the%DIFDELCMD < \dwave %%% system for problems with over 50 vertices.
Revised:  This leads to a several-orders-of-magnitude time-to-solution difference %DIFDELCMD < \dwave %%% system for problems with over 50 vertices.
Edit intent: clarity
Original:  Our results provide strong experimental support to efforts to increase the connectivity of physical annealers.
Revised:  Our results provide strong experimental support for efforts to increase the connectivity of physical annealers.
Edit intent: fluency
Original: Clinically-relevant forms of acute cell injury, which include stroke and myocardial infarction, have been of long-lasting challenge in terms of successful intervention and treatments.
Revised: Medical conditions due to acute cell injury, which include stroke and myocardial infarction, have been of long-lasting challenge in terms of successful intervention and treatments.
Edit intent: clarity