wanyu/IteraTeR_v2 huggingface dataset:
Original:  The graph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Revised:  The graph realization problemgraph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Edit intent: fluency
Original:  The graph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Revised:  The graph realization problem is to find for given nonnegative integers a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Edit intent: clarity
Original:  The graph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Revised:  The graph realization problem is to find for a given integer sequence s:=( a_1, \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Edit intent: coherence
Original:  The graph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Revised:  The graph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n a simple graph (no loops or multiple edges) such that we have for the vertex degrees d(v_i )= a_i.
Edit intent: clarity
Original:  The graph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that we have for the vertex degrees d(v_i )= a_i.
Revised:  The graph realization problem is to find for a given integer sequence s:=( a_1, ... \dots ,a_n ) a labeled graph G=(V,E) (without loops and parallel edges) such that each vertex v_i has degree a_i.
Edit intent: clarity
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A) ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Edit intent: clarity
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= %DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A) ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Edit intent: fluency
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dotsbipartite realization problem ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A) ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Edit intent: fluency
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots ..., %DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A) ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Edit intent: fluency
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots ..., a_n%DIFDELCMD < \choose %%% a) a labeled digraph G=(V,A) ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Edit intent: clarity
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A) is to find a digraph ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Edit intent: fluency
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A) ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that each vertex v_i has indegree a_i and for the vertex outdegrees d^+(v_i)= b_i.
Edit intent: clarity
Original:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots  ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A)  ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and for the vertex outdegrees d^+(v_i)= b_i.
Revised:  The loop-digraph realization problem (bipartite graph realization problem)or the digraph realization problem is to find for a given sequence S:= a_1%DIFDELCMD < \choose %DIFDELCMD < %%% b_1 , \dots ..., a_n%DIFDELCMD < \choose %%% b_n a) a labeled digraph G=(V,A) ( without parallel arcs) with at most one loop per vertex or b) a labeled digraph G=(V,A) (without parallel arcs and loops ) such that we have for the vertex indegrees d^-(v_i )= a_i and outdegree b_i.
Edit intent: fluency
Original:  Mahadev and Peled (1995) extended the classic approach to a more general result for graphs  leading to an efficient realization algorithm  .
Revised:  Mahadev and Peled (1995) extended the classic approach to a more general result for graphs , leading to an efficient realization algorithm .
Edit intent: fluency
Original:  Our main invention \\  is the connection between majorization and the number of realizations for an (integer) sequence.
Revised:  \\ is the connection between majorization and the number of realizations for an (integer) sequence.
Edit intent: coherence
Original:  In all three cases we showfor two (integer) sequences S' ,S where S' majorizes S in a certain sense, that S possesses more realizations than S'.
Revised:  In all three cases we showfor two (integer) sequences S' ,S where S' majorizes S in a certain sense, then S possesses more realizations than S'.
Edit intent: coherence
Original:  For the first time, we give a precise characterization which (integer) sequences possess the most realizations for fixed n and  fixed number of arcs m :=\sum_{i=1\emph{ \emph{  .
Revised:  For the first time, we give a precise characterization which (integer) sequences possess the most realizations for fixed n and a fixed number of arcs m :=\sum_{i=1\emph{ \emph{ .
Edit intent: fluency
Original: This paper classifies and evaluates existing and emerging telecommunications technologies based on their relative economic value for network operators.
Revised: This paper evaluates and classifies existing and emerging telecommunications technologies based on their relative economic value for network operators.
Edit intent: fluency
Original: Various biological sensory systems exhibit a response to the relative change of the stimulus, often reffered to as fold-change detection.
Revised: Various biological sensory systems exhibit a response to the relative change of the stimulus, often referred to as fold-change detection.
Edit intent: fluency
Original:  Here, we present a mechanism consisting of two interacting proteins, able to detect a fold-change effectively .
Revised:  Here, we present a mechanism consisting of two interacting proteins, that effectively detects a fold-change effectively .
Edit intent: clarity
Original:  Here, we present a mechanism consisting of two interacting proteins, able to detect a fold-change effectively .
Revised:  Here, we present a mechanism consisting of two interacting proteins, able to detect a fold-change of the stimulus .
Edit intent: clarity
Original:  This mechanism, in contrast to other proposed mechanisms, does not consume chemical energy and is not subject to transcriptional and translational noise.
Revised:  This mechanism, in contrast to previously proposed mechanisms, does not consume chemical energy and is not subject to transcriptional and translational noise.
Edit intent: clarity
Original:  We show by analytical and numerical calculations that the mechanism can have a fast, precise and efficient response for parameters that are relevant to eukaryotic cells.
Revised:  We show by analytical and numerical calculations that the mechanism can have a fast, precise and effcient response for parameters that are relevant to eukaryotic cells.
Edit intent: fluency
Original: Various biological sensory systems exhibit a response to the relative change of the stimulus, often referred to as fold-change detection.
Revised: Various biological sensory systems exhibit a response to a relative change of the stimulus, often referred to as fold-change detection.
Edit intent: fluency
Original:  Here, we present a mechanism consisting of two interacting proteins , that effectively detects a fold-change of the stimulus .
Revised:  Here, we present a mechanism consisting of two interacting proteins .
Edit intent: clarity
Original:  We show by analytical and numerical calculations  that the mechanism can have a fast, precise and effcient response for parameters that are relevant to eukaryotic cells.
Revised:  We show by analytical and numerical calculations , that the mechanism can have a fast, precise and effcient response for parameters that are relevant to eukaryotic cells.
Edit intent: fluency
Original:  We show by analytical and numerical calculations  that the mechanism can have a fast, precise and effcient response for parameters that are relevant to eukaryotic cells.
Revised:  We show by analytical and numerical calculations that the mechanism can have a fast, precise and efficient response for parameters that are relevant to eukaryotic cells.
Edit intent: fluency
Original:  Our method uses cost functions which can be freely chosen to combine costs for distances between spots in space and time and which can account for the reliability of positioning a molecule.
Revised:  Our method works with cost functions which can be freely chosen to combine costs for distances between spots in space and time and which can account for the reliability of positioning a molecule.
Edit intent: clarity
Original:  Furthermore, we derive an unbiased estimator for diffusion coefficients of blinking molecules, which proves well in our experimental evaluation of our approach .
Revised:  Our method can be applied to 2D and 3D tracking .
Edit intent: clarity
Original:  We also prove the decidability of the injectivity problem for cellular automata defined on tree shifts of finite type.
Revised:  We also prove the decidability of the injectivity problem for cellular automata defined on a tree shift of finite type.
Edit intent: fluency
Original: We apply the objective method of Aldous to the problem of finding the minimum cost edge-cover of the complete graph with random independent and identically distributed edge-costs .
Revised: We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge-costs .
Edit intent: fluency
Original: We apply the objective method of Aldous to the problem of finding the minimum cost edge-cover of the complete graph with random independent and identically distributed edge-costs .
Revised: We apply the objective method of Aldous to the problem of finding the minimum cost edge-cover of the complete graph with random independent and identically distributed edge costs .
Edit intent: fluency
Original:  A proof via the objective method is useful because it provides us  more information on the nature of the edges incident on a typical root in the minimum cost edge cover.
Revised:  A proof via the objective method is useful because it provides us with more information on the nature of the edges incident on a typical root in the minimum cost edge cover.
Edit intent: fluency
Original:  A proof via the objective method is useful because it provides us  more information on the nature of the edges incident on a typical root in the minimum cost edge cover.
Revised:  A proof via the objective method is useful because it provides us more information on the nature of the edge's incident on a typical root in the minimum cost edge cover.
Edit intent: fluency
Original:  A proof via the objective method is useful because it provides us  more information on the nature of the edges incident on a typical root in the minimum cost edge cover.
Revised:  A proof via the objective method is useful because it provides us more information on the nature of the edges incident on a typical root in the minimum-cost edge cover.
Edit intent: fluency
Original:  This finds application in a computational linguistics problem of semantic projection.
Revised:  This can be applied in a computational linguistics problem of semantic projection.
Edit intent: clarity
Original:  These theoretical study gives us algorithms of transforming a given A-hypergeometric system into a Pfaffian system.
Edit intent: coherence
Original:  The size of the Pfaffian system associated to a subclass of the order polytopes has the growth rate of the polynomial order.
Revised:  The size of the bases associated to a subclass of the order polytopes has the growth rate of the polynomial order.
Edit intent: clarity
Original:  The size of the Pfaffian system associated to a subclass of the order polytopes has the growth rate of the polynomial order.
Revised:  The size of the Pfaffian system associated to a subclass of the order polytopes have the growth rate of the polynomial order.
Edit intent: fluency
Original: We consider the stability of robust scheduling policies for Lu-Kumar networks.
Revised: We consider the stability of robust scheduling policies for multiclass queueing networks.
Edit intent: clarity
Original:  These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time in each group .
Revised:  These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time .
Edit intent: clarity
Original:  We also prove the throughput optimality of longest-dominating-queue scheduling when the network topology is acyclic, for an arbitrary number of groups and queues.
Revised:  We also prove the throughput-optimality of longest-dominating-queue scheduling when the network topology is acyclic, for an arbitrary number of groups and queues.
Edit intent: fluency
Original: We study a variation of the minority game , in which each agent uses a probabilistic strategy, and tries to optimize her total expected weighted future payoff, the weight of the payoff after \tau days being (1 - \lambda) \lambda^\tau, with \lambda < 1. We show that standard Nash equilibrium concept is unsatisfactory in this case, and propose an alternative, called co-action equilibrium .
Revised: We propose a variation of the minority game , in which each agent uses a probabilistic strategy, and tries to optimize her total expected weighted future payoff, the weight of the payoff after \tau days being (1 - \lambda) \lambda^\tau, with \lambda < 1. We show that standard Nash equilibrium concept is unsatisfactory in this case, and propose an alternative, called co-action equilibrium .
Edit intent: clarity
Original: We study a variation of the minority game , in which each agent uses a probabilistic strategy, and tries to optimize her total expected weighted future payoff, the weight of the payoff after \tau days being (1 - \lambda) \lambda^\tau, with \lambda < 1. We show that standard Nash equilibrium concept is unsatisfactory in this case, and propose an alternative, called co-action equilibrium .
Revised: We study a variation of the minority game , in which each agent uses a probabilistic strategy, and tries to optimize her total expected weighted future payoff, the weight of the payoff after \tau days being (1 - \lambda) \lambda^\tau, with \lambda < 1. We show that standard Nash equilibrium , called co-action equilibrium .
Edit intent: coherence
Original:  We study the co-action equilibrium steady state of the system as \lambda is varied from 0 to 1, and show that it gives a higher expected payoff than the Nash equilibrium for all agents.
Revised:  We study the co-action equilibrium steady state of the system as \lambda is varied from 0 to 1, and show that it gives a higher expected payoff for all agents.
Edit intent: clarity
Original:  Parameters of the optimal strategy depend on  \lambda, and can change discontinuously as%DIFDELCMD < \lambdais %%% varied , even for a finite number of agents.
Revised:  Parameters of the optimal strategy depend on \lambda, and %DIFDELCMD < \lambdais %%% varied , even for a finite number of agents.
Edit intent: clarity
Original:  We analyse in detail the optimal strategies when the number of agents N \leq 7 , and they decide selfishly, using only previous day's outcome .
Revised:  The solution for N \leq 7 , and they decide selfishly, using only previous day's outcome .
Edit intent: clarity
Original: We propose a variation of the minority game in which N rational agents use probabilistic strategies.
Revised: We propose a variation of the minority game in which rational agents use probabilistic strategies.
Edit intent: clarity
Original:  We propose an alternative to the standard Nash equilibrium, called co-action equilibrium, which gives higher expected payoff for all agents.
Revised:  We propose an alternative to the standard Nash equilibrium, called co-action equilibrium, which gives higher expected pay-off for all agents.
Edit intent: fluency
Original:  It has been conjectured that there exists a dichotomy for the complexity of CERTAINTY(Q) for conjunctive queries: it is either in PTIME or coNP-complete.
Revised:  It has been conjectured that there exists a dichotomy on the complexity of CERTAINTY(Q) for conjunctive queries: it is either in PTIME or coNP-complete.
Edit intent: fluency
Original:  In this paper, we prove that the conjecture is indeed true for the case of conjunctive queries without self-joins, where each atom has as a key either a single attribute (simple key) or all attributes of the atom (no key violations) .
Revised:  In this paper, we prove that the conjecture is indeed true for the case of conjunctive queries without self-joins, where each atom has as a key either a single attribute (simple key) or all attributes of the atom .
Edit intent: coherence
Original:  We observe that turning off the post-smoothing in SMG dramatically slows down the standard PCG-SMG. For the flexible PCG and LOBPCG, our numerical results show that post-smoothing can be avoided, resulting in overall acceleration, due to the high costs of smoothing and relatively insignificant decrease in convergence speed.
Revised:  We observe that turning off the post-smoothing in SMG dramatically slows down the standard PCG-SMG. For flexible PCG and LOBPCG, our numerical results show that post-smoothing can be avoided, resulting in overall acceleration, due to the high costs of smoothing and relatively insignificant decrease in convergence speed.
Edit intent: fluency