wanyu/IteraTeR_v2 huggingface dataset:
Original:  The result is a type of constrained Bayesian network, which we dub Suppes-Bayes Causal Network (%DIFDELCMD < \SBCN%%%  ). Next, we develop a toolkit of methods based on random walks on top of the %DIFDELCMD < \SBCN%%%  , addressing different anti-discrimination legal concepts, such as direct and indirect discrimination, group and individual discrimination, genuine requirement, and favoritism.
Revised:  The result is a type of constrained Bayesian network, which we dub Suppes-Bayes Causal Network %DIFDELCMD < \SBCN%%% ). Next, we develop a toolkit of methods based on random walks on top of the %DIFDELCMD < \SBCN%%% , addressing different anti-discrimination legal concepts, such as direct and indirect discrimination, group and individual discrimination, genuine requirement, and favoritism.
Edit intent: fluency
Original:  The result is a type of constrained Bayesian network, which we dub Suppes-Bayes Causal Network (%DIFDELCMD < \SBCN%%%  ). Next, we develop a toolkit of methods based on random walks on top of the %DIFDELCMD < \SBCN%%%  , addressing different anti-discrimination legal concepts, such as direct and indirect discrimination, group and individual discrimination, genuine requirement, and favoritism.
Revised:  The result is a type of constrained Bayesian network, which we dub Suppes-Bayes Causal Network (%DIFDELCMD < \SBCN%%% Suppes-Bayes Causal Network (SBCN ). Next, we develop a toolkit of methods based on random walks on top of the %DIFDELCMD < \SBCN%%% , addressing different anti-discrimination legal concepts, such as direct and indirect discrimination, group and individual discrimination, genuine requirement, and favoritism.
Edit intent: clarity
Original:  In 1999 Merino and Welsh conjectured that \max(T _M(2,0),T_M(0,2))\geq T_M(1,1) for graphic matroids.
Revised:  In 1999 Merino and Welsh conjectured that \max(T (M;2,0), T(M;0,2))\geq T(M;1,1) holds for graphic matroids.
Edit intent: clarity
Original:  In order to do this, we introduce and study a particular class of lattice path matroids, called %DIFDELCMD < {\em %%% snakes .
Revised:  In order to do this, we introduce and study particular lattice path matroids, called %DIFDELCMD < {\em %%% snakes .
Edit intent: clarity
Original:  In order to do this, we introduce and study a particular class of lattice path matroids, called %DIFDELCMD < {\em %%% snakes .
Revised:  In order to do this, we introduce and study a particular class of lattice path matroids, called %DIFDELCMD < {\em %%% .
Edit intent: fluency
Original:  Snakes are used as building bricks to establish a stronger inequality implying the above multiplicative conjecture as well as to characterize the cases in which equality holds.
Revised:  Snakes are used as building bricks to indeed establish a strengthening of the multiplicative conjecture as well as to characterize the cases in which equality holds.
Edit intent: clarity
Original:  Snakes are used as building bricks to establish a stronger inequality implying the above multiplicative conjecture as well as to characterize the cases in which equality holds.
Revised:  Snakes are used as building bricks to establish a stronger inequality implying the above multiplicative conjecture as well as a complete characterization of the cases in which equality holds.
Edit intent: clarity
Original: Consumer foraging behaviors are dynamic, changing in response to prey availability, seasonality, competition, and even the physiological states of the consumers .
Revised: Consumer foraging behaviors are dynamic, changing in response to prey availability, seasonality, competition, and even the consumer's physiological state .
Edit intent: clarity
Original:  The isotopic composition of a consumer is a product of these factors as well as the isotopic landscape of its prey, i.e. the isotopic mixing space.
Revised:  The isotopic composition of a consumer is a product of these factors as well as the isotopic 'landscape' of its prey, i.e. the isotopic mixing space.
Edit intent: clarity
Original:  Here we build a mechanistic framework that links the ecological and physiological processes of an individual consumer to the isotopic distribution that describes its diet, and ultimately to the isotopic composition of its own tissues, defined as its isotopic niche .
Revised:  Here we build a mechanistic framework that links the ecological and physiological processes of an individual consumer to the isotopic distribution that describes its diet, and ultimately to the isotopic composition of its own tissues, defined as its 'isotopic niche' .
Edit intent: clarity
Original:  Results of our analytical derivations reveal general insight into the conditions that impact isotopic niche width as a function of consumer specialization on prey, as well as its ability to transition between diets over time.
Revised:  Results of our derivations reveal general insight into the conditions that impact isotopic niche width as a function of consumer specialization on prey, as well as its ability to transition between diets over time.
Edit intent: clarity
Original:  Results of our analytical derivations reveal general insight into the conditions that impact isotopic niche width as a function of consumer specialization on prey, as well as its ability to transition between diets over time.
Revised:  Results of our analytical derivations reveal general insight into the conditions impacting isotopic niche width as a function of consumer specialization on prey, as well as its ability to transition between diets over time.
Edit intent: fluency
Original:  Results of our analytical derivations reveal general insight into the conditions that impact isotopic niche width as a function of consumer specialization on prey, as well as its ability to transition between diets over time.
Revised:  Results of our analytical derivations reveal general insight into the conditions that impact isotopic niche width as a function of consumer specialization on prey, as well as the consumer's ability to transition between diets over time.
Edit intent: fluency
Original:  The notion of combinatorial expanders of graphs (i.e. the Cheeger constant of a graph) has seen two generalizations to high dimensional simplicial complexes.
Revised:  The notion of combinatorial expansion of graphs (i.e. the Cheeger constant of a graph) has seen two generalizations to high dimensional simplicial complexes.
Edit intent: fluency
Original:  One generalization, known as %DIFDELCMD < {\em %%% coboundary expansion is due to Linial and Meshulem;
Revised:  One generalization, known as %DIFDELCMD < {\em %%% coboundary expansion, is due to Linial and Meshulem;
Edit intent: fluency
Original:  No construction (either random or explicit) of %DIFDELCMD < {\em %%% bounded degree combinational expanders (according to either definition) were known until a recent work of~KKL.
Revised:  No construction (either random or explicit) of %DIFDELCMD < {\em %%% bounded degree combinational expanders (according to either definition) were known until a recent work of~KKL.
Edit intent: fluency
Original:  In this work we show explicit {\em bounded degree} systolic expanders of%DIFDELCMD < {\em %DIFDELCMD < %%% every dimension .
Revised:  In this work we present explicit {\em bounded degree} systolic expanders of%DIFDELCMD < {\em %DIFDELCMD < %%% every dimension .
Edit intent: clarity
Original:  Moreover, we provide a local to global criteria on a complex that implies systolic expansion: Namely, if the 1-skeleton graph underlying a d-dimensional complex  is a good expander graph and all its links are both coboundary expanders and good expander graphs, then the (d-1)-dimensional skeleton of the complex is a systolic expander.
Revised:  Moreover, we provide a local to global criterion on a complex that implies systolic expansion: Namely, if the 1-skeleton graph underlying a d-dimensional complex is a good expander graph and all its links are both coboundary expanders and good expander graphs, then the (d-1)-dimensional skeleton of the complex is a systolic expander.
Edit intent: fluency
Original:  Moreover, we provide a local to global criteria on a complex that implies systolic expansion: Namely, if the 1-skeleton graph underlying a d-dimensional complex  is a good expander graph and all its links are both coboundary expanders and good expander graphs, then the (d-1)-dimensional skeleton of the complex is a systolic expander.
Revised:  Moreover, we provide a local to global criteria on a complex that implies cosystolic expansion: Namely, if the 1-skeleton graph underlying a d-dimensional complex is a good expander graph and all its links are both coboundary expanders and good expander graphs, then the (d-1)-dimensional skeleton of the complex is a systolic expander.
Edit intent: fluency
Original:  Moreover, we provide a local to global criteria on a complex that implies systolic expansion: Namely, if the 1-skeleton graph underlying a d-dimensional complex  is a good expander graph and all its links are both coboundary expanders and good expander graphs, then the (d-1)-dimensional skeleton of the complex is a systolic expander.
Revised:  Moreover, we provide a local to global criteria on a complex that implies systolic expansion: Namely, if the 1-skeleton graph underlying a d-dimensional complex is a good expander graph and all its links are both coboundary expanders and good expander graphs, then the (d-1)-dimensional skeleton of the complex is a cosystolic expander.
Edit intent: clarity
Original:  No construction (either random or explicit) of bounded degree combinational expanders (according to either definition) were known until a recent work of~\mbox{ KKL0pt .
Revised:  0pt .
Edit intent: coherence
Original:  We model the joint resource allocation and mobile user association as a matching game with complementarities , peer effects and selfish players\footnote{Merely interested in maximizing their own individual throughput .
Revised:  We model the joint resource allocation and user association as a matching game with complementarities , peer effects and selfish players\footnote{Merely interested in maximizing their own individual throughput .
Edit intent: clarity
Original:  We model the joint resource allocation and mobile user association as a matching game with complementarities , peer effects and selfish players\footnote{Merely interested in maximizing their own individual throughput .
Revised:  We model the joint resource allocation and mobile user association as a matching game with complementarities \footnote{Merely interested in maximizing their own individual throughput .
Edit intent: clarity
Original:  We model the joint resource allocation and mobile user association as a matching game with complementarities , peer effects and selfish players\footnote{Merely interested in maximizing their own individual throughput .
Revised:  We model the joint resource allocation and mobile user association as a matching game with complementarities , peer effects and selfish players\footnote{ .
Edit intent: clarity
Original:  We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as the anomalyin IEEE 802.11 . The mechanism can be used at the connectivity management layer to achieve efficient APs-mobile user associations without modification of the MAC layer.
Revised:  We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as its MAC anomaly . The mechanism can be used at the connectivity management layer to achieve efficient APs-mobile user associations without modification of the MAC layer.
Edit intent: clarity
Original:  We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as the anomalyin IEEE 802.11 . The mechanism can be used at the connectivity management layer to achieve efficient APs-mobile user associations without modification of the MAC layer.
Revised:  We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as the anomalyin IEEE 802.11 . The mechanism can be implemented as a virtual connectivity management layer to achieve efficient APs-mobile user associations without modification of the MAC layer.
Edit intent: clarity
Original:  We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as the anomalyin IEEE 802.11 . The mechanism can be used at the connectivity management layer to achieve efficient APs-mobile user associations without modification of the MAC layer.
Revised:  We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as the anomalyin IEEE 802.11 . The mechanism can be used at the connectivity management layer to achieve efficient APs-user associations without modification of the MAC layer.
Edit intent: clarity
Original: In order to understand the evolution of social networks in terms of perception-based strategic link formation , we numerically study a perception-based network formation model .
Revised: In order to understand the evolution of social networks in terms of perception-based strategic link formation .
Edit intent: clarity
Original:  Here each individual is assumed to have his/ her own perception of the actual network, and use it to decide whether to create a link to other individual.
Revised:  Here each individual has her own perception of the actual network, and use it to decide whether to create a link to other individual.
Edit intent: clarity
Original:  Here each individual is assumed to have his/ her own perception of the actual network, and use it to decide whether to create a link to other individual.
Revised:  Here each individual is assumed to have his/ her own perception of the actual network, and use it to decide whether to create a link to another individual.
Edit intent: fluency
Original:  An individual with the least perception accuracy can benefit from updating his/ her perception using that of the most accurate individual via a new link.
Revised:  An individual with the least perception accuracy can benefit from updating her perception using that of the most accurate individual via a new link.
Edit intent: clarity
Original:  The effect of initial conditions on the complexity of the dynamics is discussed in terms of the number of jumps.
Revised:  The effect of initial conditions on the number of jumps.
Edit intent: clarity
Original:  Here each individual has her own perception of the actual network, and use it to decide whether to create a link to another individual.
Revised:  Here each individual has her own perception of the actual network, and uses it to decide whether to create a link to another individual.
Edit intent: fluency
Original: Let S  be a set of n sites in the plane .
Revised: Let S be a set of n sites .
Edit intent: clarity
Original:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label \ell(t)  , the scheme R may consult the current routing table \rho(r) to compute a new site r' and a new header h', where r'is a neighbor of r.
Revised:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the label \ell(t) , the scheme R may consult the current routing table \rho(r) to compute a new site r' and a new header h', where r'is a neighbor of r.
Edit intent: clarity
Original:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label \ell(t)  , the scheme R may consult the current routing table \rho(r) to compute a new site r' and a new header h', where r'is a neighbor of r.
Revised:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label \ell(t) of the target , the scheme R may consult the current routing table \rho(r) to compute a new site r' and a new header h', where r'is a neighbor of r.
Edit intent: clarity
Original:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label \ell(t)  , the scheme R may consult the current routing table \rho(r) to compute a new site r' and a new header h', where r'is a neighbor of r.
Revised:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label \ell(t) , the scheme R consults the routing table \rho(r) to compute a new site r' and a new header h', where r'is a neighbor of r.
Edit intent: clarity
Original:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label \ell(t)  , the scheme R may consult the current routing table \rho(r) to compute a new site r' and a new header h', where r'is a neighbor of r.
Revised:  For any two sites s, t \in S, the scheme R must be able to route a packet from s to t in the following way: given a current site r (initially, r = s), a header h (initially empty), and the target label \ell(t) , the scheme R may consult the current routing table \rho(r) to compute a neighbor r' of r, a new header h', where r'is a neighbor of r.
Edit intent: coherence
Original:  The packet is then routed to r', and the process is repeated until the packet reaches t.
Revised:  The packet is then routed to r', and the procedure is repeated until the packet reaches t.
Edit intent: clarity
Original:  Here, based only on sequences, we use a global statistical probability model of  co-variation to detect 3D contacts, in analogy to recently developed breakthrough methods for computational protein folding.
Revised:  Using a global probability model of co-variation to detect 3D contacts, in analogy to recently developed breakthrough methods for computational protein folding.
Edit intent: clarity
Original:  Here, based only on sequences, we use a global statistical probability model of  co-variation to detect 3D contacts, in analogy to recently developed breakthrough methods for computational protein folding.
Revised:  Here, based only on sequences, we use a global statistical probability model of sequence co-variation to detect 3D contacts, in analogy to recently developed breakthrough methods for computational protein folding.
Edit intent: fluency
Original: RNA genes are ubiquitousin cell physiology , but the vast majority of non-coding RNAs are poorly understood.
Revised: Non-coding RNAs are ubiquitous , but the vast majority of non-coding RNAs are poorly understood.
Edit intent: clarity
Original: We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of semidefinite and sum of squares (SOS) programs .
Revised: We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of semidefinite and sum of squares (SOS) program .
Edit intent: fluency
Original:  While the approach is applicable to semidefinite relaxations of general polynomial programs, we apply it to two problems of discrete optimization: the maximum independent set problem and the partition problem.
Revised:  While the approach is applicable to SDP relaxations of general polynomial programs, we apply it to two problems of discrete optimization: the maximum independent set problem and the partition problem.
Edit intent: clarity
Original:  Finally , we consider investors with additional information and, for specific types of extra information, we characterize the models that are semi-statically complete for the informed investors  .
Revised:  Furthermore , we consider investors with additional information and, for specific types of extra information, we characterize the models that are semi-statically complete for the informed investors .
Edit intent: fluency
Original:  Our results give an algorithm for deciding isomorphism of PCCs in time \exp( (n^{1/3)), the first improvement over Babai's \exp(}%DIFDELCMD < O%%% (n^{1/2 .
Revised:  Our results give an algorithm for deciding isomorphism of PCCs in time \exp( )), the first improvement over Babai's \exp(}%DIFDELCMD < O%%% (n^{1/2 .
Edit intent: clarity
Original:  We prove that a (banner, odd hole)-free graph is either perfect, or does not contain a stable set on three vertices, or contains a homogeneous set.
Revised:  We prove that a (banner, odd hole)-free graph is perfect, or does not contain a stable set on three vertices, or contains a homogeneous set.
Edit intent: clarity
Original:  In spite of serious attention paid to networks of pulse coupled oscillators, there is a lack of mathematical results, addressing networks with general communication topologies and  phase-response curves  .
Revised:  In spite of serious attention paid to networks of pulse coupled oscillators, there is a lack of mathematical results, addressing networks with general communication topologies and general phase-response curves .
Edit intent: fluency
Original:  In spite of serious attention paid to networks of pulse coupled oscillators, there is a lack of mathematical results, addressing networks with general communication topologies and  phase-response curves  .
Revised:  In spite of serious attention paid to networks of pulse coupled oscillators, there is a lack of mathematical results, addressing networks with general communication topologies and phase-response curves of the oscillators .
Edit intent: clarity
Original:  A hypergraph%DIFDELCMD < {\cal %%% H is said to be 1-Sperner if every two distinct hyperedges e,f of%DIFDELCMD < {\cal %%% H satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences , including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Revised:  A hypergraph%DIFDELCMD < {\cal %%% is said to be 1-Sperner if every two distinct hyperedges e,f of%DIFDELCMD < {\cal %%% H satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences , including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Edit intent: fluency
Original:  A hypergraph%DIFDELCMD < {\cal %%% H is said to be 1-Sperner if every two distinct hyperedges e,f of%DIFDELCMD < {\cal %%% H satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences , including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Revised:  A hypergraph%DIFDELCMD < {\cal %%% H %DIFDELCMD < {\cal %%% H satisfy \min\{|e\setminus f|,|f\setminus e|\ a decomposition theorem for 1-Sperner hypergraphs and examine several of its consequences , including bounds on the size of 1-Sperner hypergraphs and a new, constructive proof of the fact that every 1-Sperner hypergraph is threshold.
Edit intent: clarity