wanyu/IteraTeR_v2 huggingface dataset:
Original:  We consider a threshold contagion  on a network whose nodes are embedded in a manifold and where the network has both `geometric edges', which respect the geometry of the underlying manifold, and ` non-geometric edges' that are not constrained by that geometry.
Revised:  We consider a threshold contagion model on a network whose nodes are embedded in a manifold and where the network has both `geometric edges', which respect the geometry of the underlying manifold, and ` non-geometric edges' that are not constrained by that geometry.
Edit intent: clarity
Original:  We consider a threshold contagion  on a network whose nodes are embedded in a manifold and where the network has both `geometric edges', which respect the geometry of the underlying manifold, and ` non-geometric edges' that are not constrained by that geometry.
Revised:  We consider a threshold contagion on a network whose nodes are embedded in a manifold and which has both `geometric edges', which respect the geometry of the underlying manifold, and ` non-geometric edges' that are not constrained by that geometry.
Edit intent: clarity
Original:  We consider a threshold contagion  on a network whose nodes are embedded in a manifold and where the network has both `geometric edges', which respect the geometry of the underlying manifold, and ` non-geometric edges' that are not constrained by that geometry.
Revised:  We consider a threshold contagion on a network whose nodes are embedded in a manifold and where the network has both `geometric edges', which respect the geometry of the underlying manifold, and ` nongeometric edges' that are not constrained by that geometry.
Edit intent: fluency
Original:  Taylor2015, we examine when a contagion propagates as a wave along a network whose nodes are embedded in a torus and when it jumps via long non-geometric edges to remote areas of the network.
Revised:  Taylor2015, we examine when a contagion propagates as a wave along a network whose nodes are embedded in a torus and when it jumps via long nongeometric edges to remote areas of the network.
Edit intent: fluency
Original:  We consider different probability distributions for constructing non-geometric edges --- reflecting different decay rates with respect to the distance between nodes in the underlying manifold --- and examine the effect of such choices on the qualitative properties of the spreading dynamics.
Revised:  We consider different probability distributions for constructing nongeometric edges -- reflecting different decay rates with respect to the distance between nodes in the underlying manifold --- and examine the effect of such choices on the qualitative properties of the spreading dynamics.
Edit intent: fluency
Original:  We consider different probability distributions for constructing non-geometric edges --- reflecting different decay rates with respect to the distance between nodes in the underlying manifold --- and examine the effect of such choices on the qualitative properties of the spreading dynamics.
Revised:  We consider different probability distributions for constructing non-geometric edges --- reflecting different decay rates with respect to the distance between nodes in the underlying manifold -- and examine the effect of such choices on the qualitative properties of the spreading dynamics.
Edit intent: fluency
Original: Recent attacks based on control flow speculation have broken process isolation through the exploitation of microarchitectural side channels that allow indirect access to shared microarchitectural state.
Revised: Recent attacks have broken process isolation through the exploitation of microarchitectural side channels that allow indirect access to shared microarchitectural state.
Edit intent: clarity
Original:  Enclaves  strengthen the process abstraction to restore isolation guarantees under a specified threat model that typically includes an untrusted operating system (OS) . We propose MI6, an architecture with an aggressive, speculative out-of-order processor capable of providing secure enclaves under a threat model that includes an untrusted OS and an attacker capable of mounting any software attack currently considered practical, including control flow speculation attacks such as Spectre.
Revised:  Enclaves aim to strengthen the process abstraction to restore isolation guarantees under a specified threat model that typically includes an untrusted operating system (OS) . We propose MI6, an architecture with an aggressive, speculative out-of-order processor capable of providing secure enclaves under a threat model that includes an untrusted OS and an attacker capable of mounting any software attack currently considered practical, including control flow speculation attacks such as Spectre.
Edit intent: clarity
Original:  Enclaves  strengthen the process abstraction to restore isolation guarantees under a specified threat model that typically includes an untrusted operating system (OS) . We propose MI6, an architecture with an aggressive, speculative out-of-order processor capable of providing secure enclaves under a threat model that includes an untrusted OS and an attacker capable of mounting any software attack currently considered practical, including control flow speculation attacks such as Spectre.
Revised:  Enclaves strengthen the process abstraction to restore isolation guarantees . We propose MI6, an architecture with an aggressive, speculative out-of-order processor capable of providing secure enclaves under a threat model that includes an untrusted OS and an attacker capable of mounting any software attack currently considered practical, including control flow speculation attacks such as Spectre.
Edit intent: clarity
Original:  The hardware area overhead of MI6 is 2.3\% for a core, not including an FPU, cache SRAMs, or a Last Level Cache (LLC) slice.
Edit intent: coherence
Original:  This open architecture and its study is the first step towards an open-source implementation of secure enclaves in an out-of-order machine that will be auditable by the architecture and the 
Revised:  This open architecture and its study is a first step towards an open-source implementation of secure enclaves in an out-of-order machine that will be auditable by the architecture and the 
Edit intent: fluency
Original:  This open architecture and its study is the first step towards an open-source implementation of secure enclaves in an out-of-order machine that will be auditable by the architecture and the 
Revised:  This open architecture and its study is the first step towards an open-source implementation of secure enclaves in an out-of-order machine that can be audited by the architecture and the 
Edit intent: clarity
Original: Recent attacks have broken process isolation through the exploitation of microarchitectural side channels that allow indirect access to shared microarchitectural state.
Revised: Recent attacks have broken process isolation by exploiting microarchitectural side channels that allow indirect access to shared microarchitectural state.
Edit intent: clarity
Original:  Enclaves aim to strengthen the process abstraction to restore isolation guarantees.
Revised:  Enclaves strengthen the process abstraction to restore isolation guarantees.
Edit intent: clarity
Original:  We propose MI6, an architecture with an aggressive, speculative out-of-order processor capable of providing secure enclaves under a threat model that includes an untrusted OS and an attacker capable of mounting any software attack currently considered practical, including control flow speculation attacks.
Revised:  We propose MI6, an aggressive, speculative out-of-order processor capable of providing secure enclaves under a threat model that includes an untrusted OS and an attacker capable of mounting any software attack currently considered practical, including control flow speculation attacks.
Edit intent: clarity
Original:  Security comes at the cost of approximately 16.4\% average slowdown for protected programs , and is slightly smaller for unprotected programs .
Revised:  Security comes at the cost of approximately 16.4\% average slowdown for protected programs .
Edit intent: coherence
Original:  In this paper, we shall develop an efficient model reduction method for solving viscous G-equations in incompressible steady and time-periodic cellular flows.
Revised:  In this paper, we develop an efficient model reduction method for solving viscous G-equations in incompressible steady and time-periodic cellular flows.
Edit intent: coherence
Original:  Our method is based on the Galerkin proper orthogonal decomposition (POD) methods .
Revised:  Our method is based on the Galerkin proper orthogonal decomposition (POD) method .
Edit intent: fluency
Original:  We also provide rigorous convergence analysis for our numerical method.
Revised:  We also provide rigorous convergence analysis for our method.
Edit intent: clarity
Original:  Specifically , we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows based on the POD method and fully resolved computations .
Revised:  In addition , we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows based on the POD method and fully resolved computations .
Edit intent: coherence
Original:  Specifically , we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows based on the POD method and fully resolved computations .
Revised:  Specifically , we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows .
Edit intent: coherence
Original:  Specifically, for a loss function with range bounded in [0,1], the generalization error of  \gamma-uniformly stable learning algorithm on n samples is known to be at most O((\gamma +1/n) n \log(1/\delta))  with probability at least 1-\delta.
Revised:  Specifically, for a loss function with range bounded in [0,1], the generalization error of a \gamma-uniformly stable learning algorithm on n samples is known to be at most O((\gamma +1/n) n \log(1/\delta)) with probability at least 1-\delta.
Edit intent: fluency
Original:  Specifically, for a loss function with range bounded in [0,1], the generalization error of  \gamma-uniformly stable learning algorithm on n samples is known to be at most O((\gamma +1/n) n \log(1/\delta))  with probability at least 1-\delta.
Revised:  Specifically, for a loss function with range bounded in [0,1], the generalization error of \gamma-uniformly stable learning algorithm on n samples is known to be within O((\gamma +1/n) n \log(1/\delta)) with probability at least 1-\delta.
Edit intent: clarity
Original:  Here we prove substantially stronger generalization bounds for uniformly stable algorithms without  any additional assumptions.
Revised:  We substantially improve generalization bounds for uniformly stable algorithms without any additional assumptions.
Edit intent: clarity
Original:  Here we prove substantially stronger generalization bounds for uniformly stable algorithms without  any additional assumptions.
Revised:  Here we prove substantially stronger generalization bounds for uniformly stable algorithms without making any additional assumptions.
Edit intent: clarity
Original:  First, we show that the generalization error in this setting is at most O((\gamma + 1/n) \log(1/\delta)) with probability at least 1-\delta.
Revised:  First, we show that the bound in this setting is at most O((\gamma + 1/n) \log(1/\delta)) with probability at least 1-\delta.
Edit intent: clarity
Original:  First, we show that the generalization error in this setting is at most O((\gamma + 1/n) \log(1/\delta)) with probability at least 1-\delta.
Revised:  First, we show that the generalization error in this setting is O((\gamma + 1/n) \log(1/\delta)) with probability at least 1-\delta.
Edit intent: clarity
Original:  In addition, we prove a tight bound of O(\gamma^2 + 1/n) on the second moment of the generalization error.
Revised:  In addition, we prove a tight bound of O(\gamma^2 + 1/n) on the second moment of the estimation error.
Edit intent: clarity
Original:  One can significantly improve the resolution of depth images by taking advantage of color information;
Revised:  One can significantly improve the resolution of depth maps by taking advantage of color information;
Edit intent: clarity
Original: In this note we present the formulation of the induction and co-induction principlesand related notions , such as fixed points, using the language and conventions of each of order theory, set theory, (first-order) logic, category theory, and the theory of types in (object-oriented and functional ) programming languages,  for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised: In this note we present the formulation of the induction and coinduction principles, and notions related to them such as fixed points, using the language and conventions of each of order theory, set theory, (first-order) logic, category theory, and the theory of types in (object-oriented and functional ) programming languages, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Edit intent: clarity
Original: In this note we present the formulation of the induction and co-induction principlesand related notions , such as fixed points, using the language and conventions of each of order theory, set theory, (first-order) logic, category theory, and the theory of types in (object-oriented and functional ) programming languages,  for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised: In this note we present the formulation of the induction and co-induction principlesand related notions , such as fixed points, using the language and conventions of each of order theory, set theory, the theory of types in (object-oriented and functional ) programming languages, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Edit intent: coherence
Original: In this note we present the formulation of the induction and co-induction principlesand related notions , such as fixed points, using the language and conventions of each of order theory, set theory, (first-order) logic, category theory, and the theory of types in (object-oriented and functional ) programming languages,  for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised: In this note we present the formulation of the induction and co-induction principlesand related notions , such as fixed points, using the language and conventions of each of order theory, set theory, (first-order) logic, category theory, and the theory of types in (object-oriented /OOP and functional/FP ) programming languages, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Edit intent: clarity
Original: In this note we present the formulation of the induction and co-induction principlesand related notions , such as fixed points, using the language and conventions of each of order theory, set theory, (first-order) logic, category theory, and the theory of types in (object-oriented and functional ) programming languages,  for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised: In this note we present the formulation of the induction and co-induction principlesand related notions , such as fixed points, using the language and conventions of each of order theory, set theory, (first-order) logic, category theory, and the theory of types in (object-oriented and functional ) programming languages, first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Edit intent: coherence
Original:  As a side-benefit that is of relevance to programming language researchers in particular, our comparison demonstrates one of the fundamental differences between structural typing (dominant in FP) and nominal typing ( dominant in mainstream OOP ).
Revised:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison demonstrates one of the fundamental differences between structural typing (dominant in FP) and nominal typing ( dominant in mainstream OOP ).
Edit intent: clarity
Original:  As a side-benefit that is of relevance to programming language researchers in particular, our comparison demonstrates one of the fundamental differences between structural typing (dominant in FP) and nominal typing ( dominant in mainstream OOP ).
Revised:  As a side-benefit that is of relevance to programming language researchers in particular, our comparison demonstrates one of the fundamental differences between nominal typing ( dominant in mainstream OOP ).
Edit intent: coherence
Original: In this note we present the formulation of the induction and coinduction principles, and notions related to them such as fixed points,  using the language and conventions of each of order theory, set theory, the theory of types in ( object-oriented /OOP and functional /FP) programming languages, first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised: In this paper we present the formulation of the induction and coinduction principles, and notions related to them such as fixed points, using the language and conventions of each of order theory, set theory, the theory of types in ( object-oriented /OOP and functional /FP) programming languages, first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Edit intent: clarity
Original: In this note we present the formulation of the induction and coinduction principles, and notions related to them such as fixed points,  using the language and conventions of each of order theory, set theory, the theory of types in ( object-oriented /OOP and functional /FP) programming languages, first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised: In this note we present the formulation of the induction and coinduction principles, and notions related to them such as fixed points, using the language and conventions of each of order theory, set theory, the theory of types of functional and object-oriented /OOP and functional /FP) programming languages, first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Edit intent: fluency
Original:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison  demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing (predominant in FP) .
Revised:  As a side-benefit of relevance to programming languages researchers in particular, our comparison demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing (predominant in FP) .
Edit intent: coherence
Original:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison  demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing (predominant in FP) .
Revised:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison also demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing (predominant in FP) .
Edit intent: clarity
Original:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison  demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing (predominant in FP) .
Revised:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison demonstrates one of the fundamental differences between nominal typing , predominant in mainstream OOP) and structural typing (predominant in FP) .
Edit intent: fluency
Original:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison  demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing (predominant in FP) .
Revised:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream object-oriented programming, and structural typing (predominant in FP) .
Edit intent: clarity
Original:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison  demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing (predominant in FP) .
Revised:  As a side-benefit that is relevant to programming languages researchers in particular, our comparison demonstrates one of the fundamental differences between nominal typing ( predominant in mainstream OOP) and structural typing , predominant in functional programming .
Edit intent: clarity
Original:  and notions related to them such as fixed points, pre-fixed points, and post-fixed points (plus inductive sets and types, coinductive sets and types, algebras and coalgebras), using the language and conventions of each of order theory, set theory, the theory of types of functional and object-oriented programming languages , first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised:  and notions related to them such as fixed points, pre-fixed points, and post-fixed points (plus inductive sets and types, coinductive sets and types, algebras and coalgebras), using the language and conventions of each of order theory, set theory, programming languages type theory , first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Edit intent: clarity
Original:  and notions related to them such as fixed points, pre-fixed points, and post-fixed points (plus inductive sets and types, coinductive sets and types, algebras and coalgebras), using the language and conventions of each of order theory, set theory, the theory of types of functional and object-oriented programming languages , first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these six mathematical subdisciplines.
Revised:  and notions related to them such as fixed points, pre-fixed points, and post-fixed points (plus inductive sets and types, coinductive sets and types, algebras and coalgebras), using the language and conventions of each of order theory, set theory, the theory of types of functional and object-oriented programming languages , first-order logic, and category theory, for the purpose of examining some of the similarities and dissimilarities between these mathematical subdisciplines.
Edit intent: clarity