wanyu/IteraTeR_v2 huggingface dataset:
Original:  Formally, given a connected graph G (V,E) with vertices labeled from [1,...,n] and a permutation \pi the problem is to find a routing scheme with minimum number of steps which routes a pebble from vertex i to \pi(i) for all i.
Revised:  Formally, given a connected graph G with vertices labeled from [1,...,n] and a permutation \pi the problem is to find a routing scheme with minimum number of steps which routes a pebble from vertex i to \pi(i) for all i.
Edit intent: coherence
Original:  The minimum number of steps to route all vertices given a permutation is called the routing time rt(G,\pi) and the maximum number of steps necessary to route any permutation for a given graph G is called the routing number rt(G) of G . In this paper we present  following new results, which answer some of the open problems posed in \cite{5}:
Revised:  The minimum number of steps to route all vertices given a permutation is called the routing time rt(G,\pi) of G given \pi . In this paper we present following new results, which answer some of the open problems posed in \cite{5}:
Edit intent: clarity
Original:  The minimum number of steps to route all vertices given a permutation is called the routing time rt(G,\pi) and the maximum number of steps necessary to route any permutation for a given graph G is called the routing number rt(G) of G . In this paper we present  following new results, which answer some of the open problems posed in \cite{5}:
Revised:  The minimum number of steps to route all vertices given a permutation is called the routing time rt(G,\pi) and the maximum number of steps necessary to route any permutation for a given graph G is called the routing number rt(G) of G . In this paper we present the following new results, which answer some of the open problems posed in \cite{5}:
Edit intent: fluency
Original:  The minimum number of steps to route all vertices given a permutation is called the routing time rt(G,\pi) and the maximum number of steps necessary to route any permutation for a given graph G is called the routing number rt(G) of G . In this paper we present  following new results, which answer some of the open problems posed in \cite{5}:
Revised:  The minimum number of steps to route all vertices given a permutation is called the routing time rt(G,\pi) and the maximum number of steps necessary to route any permutation for a given graph G is called the routing number rt(G) of G . In this paper we present following new results, which answer one of the open problems posed in \cite{5}:
Edit intent: fluency
Original:  1) Determining whether rt(G,\pi) is \le 2 can be done in O( m\sqrt{n time for any arbitrary graph G with m edges . 2) Determining whether rt(G,\pi) is \le k for any k \ge 3 is NP-Complete.
Revised:  1) Determining whether rt(G,\pi) is \le 2 can be done in O( m\sqrt{n time for any arbitrary connected graph G . 2) Determining whether rt(G,\pi) is \le k for any k \ge 3 is NP-Complete.
Edit intent: clarity
Original:  In the second half we study a analogous property of graphs, which we termed as sorting numbers .
Revised:  In the second part we study a analogous property of graphs, which we termed as sorting numbers .
Edit intent: clarity
Original:  In the second half we study a analogous property of graphs, which we termed as sorting numbers .
Revised:  In the second half we study a related property of graphs, which we termed as sorting numbers .
Edit intent: fluency
Original:  Informally, \textit{sorting number} of  graph is the minimum depth sorting network that only uses edges of the graph.
Revised:  Informally, \textit{sorting number} of a graph is the minimum depth sorting network that only uses edges of the graph.
Edit intent: fluency
Original:   We show that a T with maximum degree \Delta can accommodate a O(\min(n\Delta^2,n^2)) depth sorting network.
Revised:  We show that a tree with maximum degree \Delta can accommodate a O(\min(n\Delta^2,n^2)) depth sorting network.
Edit intent: clarity
Original:  Additionally  we give two instance of trees for which this upper bound is tight.
Revised:  Additionally , we give two instance of trees for which this upper bound is tight.
Edit intent: fluency
Original:  Additionally  we give two instance of trees for which this upper bound is tight.
Revised:  Additionally we give two instance of trees for which this bound is tight.
Edit intent: clarity
Original: This paper presents a novel reversible data hiding (RDH) algorithm for gray-scaled images, in which the prediction-error of prediction error (PPE) of the pixels are used to accommodate the secret message bits .
Revised: This paper presents a novel reversible data hiding (RDH) algorithm for gray-scaled images, in which the prediction-error of prediction error (PPE) of a pixel is used to carry the secret data .
Edit intent: clarity
Original:  By reversibly shifting the PPE histogram (PPEH) with optimized parameters, the pixels corresponding to the altered PPEH bins can be finally modified so as to carry the secret data.
Revised:  By reversibly shifting the PPE histogram (PPEH) with optimized parameters, the pixels corresponding to the altered PPEH bins can be finally modified to carry the secret data.
Edit intent: clarity
Original:  Experimental results have implied that the proposed method can benefit from the prediction procedure of the PEs  as well as the sorting technique, and ;
Revised:  Experimental results have implied that the proposed method can benefit from the prediction procedure of the PEs , sorting technique as well as the sorting technique, and ;
Edit intent: fluency
Original: There is a remarkable consensus that human and non-human subjects experience temporal distortions in many stages of their perceptual and decision-making systems.
Revised: There is a consensus that human and non-human subjects experience temporal distortions in many stages of their perceptual and decision-making systems.
Edit intent: clarity
Original:  This article develops a  haircut model by treating repos as debt investments and seeks haircuts to control counterparty contingent exposure to asset price gap risk.
Revised:  This article develops a repo haircut model by treating repos as debt investments and seeks haircuts to control counterparty contingent exposure to asset price gap risk.
Edit intent: fluency
Original:  Using the unhedgeable gap risk during a margin period of risk as a starting point , this article introduces a reserve capital approach to the hedging error and its inclusion in derivatives pricing and valuation.
Revised:  Starting with the gap risk during a margin period of risk as a starting point , this article introduces a reserve capital approach to the hedging error and its inclusion in derivatives pricing and valuation.
Edit intent: clarity
Original:  For a repurchase agreement , economic capital is computed under a double-exponential jump-diffusion model , either estimated from historical data or calibrated to options smile.
Revised:  For a repurchase agreement , economic capital is computed under a double-exponential jump-diffusion model estimated from historical data or calibrated to options smile.
Edit intent: fluency
Original:  An extended partial differential equation is derived with two new terms for expected gap loss and economic capital charge, leading to the gap risk economic value adjustment (GAP_EVA) and capital valuation adjustment (KVA) respectively.
Revised:  An extended partial differential equation is derived with two new terms for expected gap loss and economic capital charge, leading to the gap risk economic value adjustment and capital valuation adjustment (KVA) respectively.
Edit intent: clarity
Original:  By introducing an enlarged canonical space, we reformulate the superhedging problem for American options as a problem for European options .
Revised:  By introducing an enlarged canonical space, we can see American options as a problem for European options .
Edit intent: clarity
Original: We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness centrality .
Revised: We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness .
Edit intent: clarity
Original:  In particular, in the vast majority of simulated networks, the nodes with maximum decay centrality are characterized by a threshold on the decay parameter below which they belong to the set of nodes with maximum degree and above which they belong to the set of nodes with maximum closeness.
Revised:  In particular, in the vast majority of networks, the nodes with maximum decay centrality are characterized by a threshold on the decay parameter below which they belong to the set of nodes with maximum degree and above which they belong to the set of nodes with maximum closeness.
Edit intent: clarity
Original: We address the problem of a participatory decision-making process where a shared priority list of alternatives has to be obtained while avoiding inconsistent decisions , related to the "Condorcet paradox" .
Revised: We address the problem of a participatory decision-making process where a shared priority list of alternatives has to be obtained while avoiding inconsistent decisions .
Edit intent: coherence
Original:  Simulations' results show the efficacy of interaction in avoiding the paradox and finding a transitive and, above all, shared decision.
Revised:  Simulations' results show the efficacy of interaction in finding a transitive and, above all, shared decision.
Edit intent: clarity
Original: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Revised: The Maximum Carpool Matching problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Edit intent: fluency
Original: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Revised: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graphs . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Edit intent: fluency
Original: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Revised: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : A \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Edit intent: clarity
Original: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Revised: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Edit intent: clarity
Original: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Revised: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M is a subset of A \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Edit intent: clarity
Original: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, d_{out (p) \leq 1.
Revised: The MAXIMUM CARPOOL MATCHING problem is a star packing problem in directed graph . Formally, given a directed graph G = (V, E ), a capacity function c: V \to N , and a weight function w : E \to R , a feasible carpool matching \emph{ is a triple (P, D, M), where P and D form a partition of V, and M \subseteq E \cap (P \times D), under the constraints that for every vertex d \in D, d_{in (d) \leq c(d), and for every vertex p \in P, dout (p) \leq 1.
Edit intent: fluency
Original:  In the MAXIMUM CARPOOL MATCHING problem we seek for a matching (P, D, M) that maximizes the total weight of M.
Revised:  In the Maximum Carpool Matching problem we seek for a matching (P, D, M) that maximizes the total weight of M.
Edit intent: fluency
Original:  We also present 2-approximation algorithms for the unweighted and for the uncapacitated variants of the problem.
Revised:  We also present 2-approximation algorithm for the unweighted and for the uncapacitated variants of the problem.
Edit intent: fluency
Original:  In this paper  we link FPT results to classic artificial intelligence  techniques to show how they complement each other.
Revised:  In this paper , we link FPT results to classic artificial intelligence techniques to show how they complement each other.
Edit intent: fluency
Original:  In this paper  we link FPT results to classic artificial intelligence  techniques to show how they complement each other.
Revised:  In this paper we link FPT results to classic artificial intelligence (AI) techniques to show how they complement each other.
Edit intent: clarity
Original:  We show that the FPT nature of  WSP with UI constraints  decomposes the problem into two levels , and exploit this in a new FPT algorithm that is by many orders of magnitude faster then the previous state-of-the-art WSP algorithm .
Revised:  We show that the FPT nature of the WSP with UI constraints decomposes the problem into two levels , and exploit this in a new FPT algorithm that is by many orders of magnitude faster then the previous state-of-the-art WSP algorithm .
Edit intent: fluency
Original:  We show that the FPT nature of  WSP with UI constraints  decomposes the problem into two levels , and exploit this in a new FPT algorithm that is by many orders of magnitude faster then the previous state-of-the-art WSP algorithm .
Revised:  We show that the FPT nature of WSP with UI constraints decomposes the problem into two levels . Exploiting this two-level split, we develop a new FPT algorithm that is by many orders of magnitude faster then the previous state-of-the-art WSP algorithm .
Edit intent: clarity
Original:  We show that the FPT nature of  WSP with UI constraints  decomposes the problem into two levels , and exploit this in a new FPT algorithm that is by many orders of magnitude faster then the previous state-of-the-art WSP algorithm .
Revised:  We show that the FPT nature of WSP with UI constraints decomposes the problem into two levels , and exploit this in a new FPT algorithm that is by many orders of magnitude faster than the previous state-of-the-art WSP algorithm .
Edit intent: fluency
Original:  Inspired by a classic graph colouring method called Zykov's Contraction, we designed a new pseudo-boolean (PB) formulation of  WSP with UI constraints that also exploits the two-level split of the problem  .
Revised:  Inspired by a classic graph colouring method called Zykov's Contraction, we designed a new pseudo-boolean (PB) formulation of the WSP with UI constraints that also exploits the two-level split of the problem .
Edit intent: fluency
Original:  Inspired by a classic graph colouring method called Zykov's Contraction, we designed a new pseudo-boolean (PB) formulation of  WSP with UI constraints that also exploits the two-level split of the problem  .
Revised:  Inspired by a classic graph colouring method called Zykov's Contraction, we designed a new pseudo-boolean (PB) formulation of WSP with UI constraints which exploits this new decomposition of the problem .
Edit intent: clarity
Original:  Our experiments showed that , in many cases, this formulation being solved with a general purpose PB solver demonstrated performance comparable to that of our bespoke FPT algorithm .
Revised:  Our experiments show that efficiency of solving this new PB formulation of the problem by a general purpose PB solver demonstrated performance comparable to that of our bespoke FPT algorithm .
Edit intent: clarity
Original:  Our experiments showed that , in many cases, this formulation being solved with a general purpose PB solver demonstrated performance comparable to that of our bespoke FPT algorithm .
Revised:  Our experiments showed that , in many cases, this formulation being solved with a general purpose PB solver can be close to the bespoke FPT algorithm .
Edit intent: clarity
Original:  We also study the practical, average-case, performance of various algorithms .
Revised:  We also study the computational performance of various algorithms .
Edit intent: clarity
Original:  We give a new view of the FPT nature of the WSP with UI constraints , showing that it decomposes the problem into two levels.
Revised:  We give a new view of the FPT nature of the WSP with UI constraints giving a decomposition of the problem into two levels.
Edit intent: coherence
Original:  and it also has only polynomial space complexitywhereas the old algorithm takes memory exponential in k, which limits its application .
Revised:  and it also has only polynomial-space complexity .
Edit intent: coherence
Original:  We also provide a new pseudo-boolean (PB) formulation of the WSP with UI constraints which exploits this new decomposition of the problem into two levels.
Revised:  We also introduce new pseudo-Boolean (PB) formulation of the WSP with UI constraints which exploits this new decomposition of the problem into two levels.
Edit intent: clarity
Original:  We also provide a new pseudo-boolean (PB) formulation of the WSP with UI constraints which exploits this new decomposition of the problem into two levels.
Revised:  We also provide a new pseudo-boolean (PB) formulation of the WSP with UI constraints which efficiently exploit this new decomposition of the problem into two levels.
Edit intent: clarity
Original: Finite element methods were shown to achieve high accuracies in numerically solving the EEG forward problem , while enabling to realistically incorporate important conductive features such as complicatedly shaped geometrical structures and anisotropic conductivities.
Revised: Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem , while enabling to realistically incorporate important conductive features such as complicatedly shaped geometrical structures and anisotropic conductivities.
Edit intent: style
Original: Finite element methods were shown to achieve high accuracies in numerically solving the EEG forward problem , while enabling to realistically incorporate important conductive features such as complicatedly shaped geometrical structures and anisotropic conductivities.
Revised: Finite element methods were shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as complicatedly shaped geometrical structures and anisotropic conductivities.
Edit intent: clarity
Original: Finite element methods were shown to achieve high accuracies in numerically solving the EEG forward problem , while enabling to realistically incorporate important conductive features such as complicatedly shaped geometrical structures and anisotropic conductivities.
Revised: Finite element methods were shown to achieve high accuracies in numerically solving the EEG forward problem , while enabling to realistically incorporate important conductive features such as anisotropic conductivities.
Edit intent: clarity
Original:  To date, most  presented approaches rely on the same underlying formulation, a continuous Galerkin (CG)-FEM.
Revised:  To date, most of the presented approaches rely on the same underlying formulation, a continuous Galerkin (CG)-FEM.
Edit intent: fluency
Original:  To date, most  presented approaches rely on the same underlying formulation, a continuous Galerkin (CG)-FEM.
Revised:  To date, most presented approaches rely on the same underlying formulation, the continuous Galerkin (CG)-FEM.
Edit intent: fluency
Original:  Thereby , a higher simulation accuracy can be achieved in certain scenarios, e.g., when the diameter of thin insulating structures  such as the skull  is in the range of the mesh resolution.
Revised:  Thereby , a higher simulation accuracy can be achieved in certain scenarios, e.g., when the diameter of thin insulating structures , such as the skull is in the range of the mesh resolution.
Edit intent: fluency
Original:  Thereby , a higher simulation accuracy can be achieved in certain scenarios, e.g., when the diameter of thin insulating structures  such as the skull  is in the range of the mesh resolution.
Revised:  Thereby , a higher simulation accuracy can be achieved in certain scenarios, e.g., when the diameter of thin insulating structures such as the skull , is in the range of the mesh resolution.
Edit intent: fluency