wanyu/IteraTeR_v2 huggingface dataset:
Original: In a previous work we introduced slice graphs with the aim to specify both infinite languages of of directed acyclic graphs (DAGs ) and infinite languages of partial orders.
Revised: In a previous work we introduced slice graphs as a way to specify both infinite languages of of directed acyclic graphs (DAGs ) and infinite languages of partial orders.
Edit intent: clarity
Original: In a previous work we introduced slice graphs with the aim to specify both infinite languages of of directed acyclic graphs (DAGs ) and infinite languages of partial orders.
Revised: In a previous work we introduced slice graphs with the aim to specify both infinite languages of DAGs and infinite languages of partial orders.
Edit intent: clarity
Original:  In the present work we prove that every slice graph SG may be effectively transformed into a Hasse diagram generator HG representing the same partial order language.
Revised:  In this work we prove that every slice graph SG may be effectively transformed into a Hasse diagram generator HG representing the same partial order language.
Edit intent: coherence
Original:  In the present work we prove that every slice graph SG may be effectively transformed into a Hasse diagram generator HG representing the same partial order language.
Revised:  In the present work we prove that any slice graph slice graph SG can be effectively transformed into a Hasse diagram generator HG representing the same partial order language.
Edit intent: clarity
Original:  Finally we prove that the intersection of partial order languages represented by saturated slice graphs is computable and that their inclusion is decidable .
Revised:  Finally we identify the class of saturated slice graphs. The class of partial order lang. represented by saturated slice graphs is computable and that their inclusion is decidable .
Edit intent: clarity
Original:  Therein we focused on the study of Hasse diagram generators, i.e., slice graphs that generate only transitive reduced DAGs . In this work we prove that any slice graph slice graph SG can be effectively transformed into a Hasse diagram generator HG representing the same set of partial orders.
Revised:  Therein we focused on the study of Hasse diagram generators, i.e., slice graphs that generate only transitive reduced DAGs . In this work we prove that any slice graph SG can be effectively transformed into a Hasse diagram generator HG representing the same set of partial orders.
Edit intent: fluency
Original:  The class of partial order lang. represented by saturated SG's is closed under union, intersection and even under a suitable notion of complementation  .
Revised:  The class of partial order languages representable by saturated slice graphs is closed under union, intersection and even under a suitable notion of complementation .
Edit intent: clarity
Original:  Furthermore partial order lang. belonging to this class can be tested for inclusion and admit a canonical representation in terms of HDG's . As an evidence that saturation is a very natural property, we point out that for any bounded p/t-net N there is a canonical saturated HDG representing precisely the partial order behavior of N .
Revised:  Furthermore partial order languages belonging to this class can be tested for inclusion and admit a canonical representation in terms of HDG's . As an evidence that saturation is a very natural property, we point out that for any bounded p/t-net N there is a canonical saturated HDG representing precisely the partial order behavior of N .
Edit intent: fluency
Original:  Furthermore partial order lang. belonging to this class can be tested for inclusion and admit a canonical representation in terms of HDG's . As an evidence that saturation is a very natural property, we point out that for any bounded p/t-net N there is a canonical saturated HDG representing precisely the partial order behavior of N .
Revised:  Furthermore partial order lang. belonging to this class can be tested for inclusion and admit canonical representatives in terms of HDG's . As an evidence that saturation is a very natural property, we point out that for any bounded p/t-net N there is a canonical saturated HDG representing precisely the partial order behavior of N .
Edit intent: fluency
Original:  We define a  notion of flip which transforms a pseudoline arrangement with contact points into another one with the same support, and we study the graph of these flips.
Revised:  We define a notion of flip between these arrangements and study the graph of these flips.
Edit intent: clarity
Original:  In particular, we provide an enumeration algorithm for arrangements with a given support, based on the properties of certain greedy pseudoline arrangements and on their relationship with sorting networks.
Revised:  In particular, we provide an enumeration algorithm for arrangements with a given support, based on the properties of certain greedy pseudoline arrangements and on their connection with sorting networks.
Edit intent: fluency
Original:  Our algorithm requires a polynomial running time per arrangement and its working space is polynomial.
Revised:  Both the running time per arrangement and its working space is polynomial.
Edit intent: clarity
Original:  Our algorithm requires a polynomial running time per arrangement and its working space is polynomial.
Revised:  Our algorithm requires a polynomial running time per arrangement and the working space of our algorithm are polynomial.
Edit intent: clarity
Original:  As the motivation for this work, we provide in this paper a new interpretation of both pseudotriangulations and multitriangulations in terms of pseudoline arrangements with contact points covering a certain support .
Revised:  As the motivation for this work, we provide in this paper a new interpretation of both pseudotriangulations and multitriangulations in terms of pseudoline arrangements on specific supports .
Edit intent: clarity
Original:  This interpretation explains their common properties and leads to a natural definition of multipseudotriangulations, which generalizes them .
Revised:  This interpretation explains their common properties and leads to a natural definition of multipseudotriangulations, which generalizes both .
Edit intent: clarity
Original:  We study the elementary properties of these multipseudotriangulations and compare them to iterations of pseudotriangulations.
Revised:  We study elementary properties of these multipseudotriangulations and compare them to iterations of pseudotriangulations.
Edit intent: fluency
Original:  We study the elementary properties of these multipseudotriangulations and compare them to iterations of pseudotriangulations.
Revised:  We study the elementary properties of multipseudotriangulations and compare them to iterations of pseudotriangulations.
Edit intent: clarity
Original:  Forensic Lucid, a Lucid dialect, is a language to specify and reason about cyberforensics cases.
Revised:  Forensic Lucid, a Lucid dialect, is a language to specify and reason about cyberforensic cases.
Edit intent: fluency
Original: Nonparametric statistical methods developed for analyzing data for high numbers of genes, SNPs, or other biological features tend to overfit data with smaller numbers of features such as proteins, metabolites, or, when expression is measured with conventional instruments, genes.
Revised: Nonparametric statistical methods developed for analyzing data for large numbers of genes, SNPs, or other biological features tend to overfit data with smaller numbers of features such as proteins, metabolites, or, when expression is measured with conventional instruments, genes.
Edit intent: clarity
Original: Let the chromatic index of a hypergraph be the smallest number of colours needed to colourthe edges such that similarly-coloured edges are disjoint.
Revised: A colouring of a hypergraph be the smallest number of colours needed to colourthe edges such that similarly-coloured edges are disjoint.
Edit intent: clarity
Original:  the polychromatic number is the maximum number of colours in any polychromatic colouring.
Revised:  the polychromatic number is the maximum number of colours in such a colouring.
Edit intent: clarity
Original:  Its dual is the cover-decomposition number : the maximum number of disjoint hyperedge-covers.
Revised:  Its dual , the cover-decomposition number : the maximum number of disjoint hyperedge-covers.
Edit intent: fluency
Original:  Its dual is the cover-decomposition number : the maximum number of disjoint hyperedge-covers.
Revised:  Its dual is the cover-decomposition number , is the maximum number of disjoint hyperedge-covers.
Edit intent: coherence
Original:  In geometric settings , there is extensive work on lower-bounding these numbers in terms of their trivial upper bounds (minimum hyperedge size and minimum degree).
Revised:  In geometric hypergraphs , there is extensive work on lower-bounding these numbers in terms of their trivial upper bounds (minimum hyperedge size and minimum degree).
Edit intent: clarity
Original:  We obtain algorithms yielding near-tight bounds for three hypergraph families : those with bounded hyperedge size, those representing paths in trees, and those with bounded VC-dimension.
Revised:  We obtain algorithms yielding near-tight bounds for three families of hypergraphs: bounded hyperedge size, those representing paths in trees, and those with bounded VC-dimension.
Edit intent: fluency
Original:  We obtain algorithms yielding near-tight bounds for three hypergraph families : those with bounded hyperedge size, those representing paths in trees, and those with bounded VC-dimension.
Revised:  We obtain algorithms yielding near-tight bounds for three hypergraph families : those with bounded hyperedge size, paths in trees, and those with bounded VC-dimension.
Edit intent: clarity
Original:  We obtain algorithms yielding near-tight bounds for three hypergraph families : those with bounded hyperedge size, those representing paths in trees, and those with bounded VC-dimension.
Revised:  We obtain algorithms yielding near-tight bounds for three hypergraph families : those with bounded hyperedge size, those representing paths in trees, and bounded VC-dimension.
Edit intent: fluency
Original:  One new technique we use is a link between cover-decomposition and iterated relaxation of linear programs .
Revised:  This reveals that discrepancy theory and iterated linear program relaxation are useful for cover-decomposition. Finally, we discuss the generalization of cover-decomposition to sensor cover .
Edit intent: coherence
Original:  Let k\geq 1 and partition the vertices of a graph G into sets V_1, \ldots , V_r, such that for 1\leq i \leq r every vertex in V_i has at most \max\{k, |V_i|-k \} neighbours outside V_i.
Revised:  Let k\geq 1 and partition the vertices of a graph G into sets V_1, ... , V_r, such that for 1\leq i \leq r every vertex in V_i has at most \max\{k, |V_i|-k \} neighbours outside V_i.
Edit intent: clarity
Original: We present an analytical framework which enables performance evaluation of different multi-channel multi-stage spectrum sensing protocols for Opportunistic Spectrum Access networks.
Revised: We present an analytical framework which enables performance evaluation of different multi-channel multi-stage spectrum sensing algorithms for Opportunistic Spectrum Access networks.
Edit intent: clarity
Original:   Analyzed performance metrics include the average secondary user throughput and the average collision probability between the primary and secondary users.
Revised:  Analyzed performance metrics include the average secondary user throughput and the average collision probability between primary and secondary users.
Edit intent: fluency
Original:  The main results show that when a constraint is given upon the probability of primary user mis-detection , multi-stage sensing is in most cases superior to the single stage sensing counterpart.
Revised:  The main results show that when the probability of primary user mis-detection , multi-stage sensing is in most cases superior to the single stage sensing counterpart.
Edit intent: clarity
Original:  The main results show that when a constraint is given upon the probability of primary user mis-detection , multi-stage sensing is in most cases superior to the single stage sensing counterpart.
Revised:  The main results show that when a constraint is given upon the probability of primary user mis-detection is constrained, the performance of multi-stage sensing is in most cases superior to the single stage sensing counterpart.
Edit intent: clarity
Original:  Further , prolonged channel observation at the first sensing stage decreases the collision probability considerably  while keeping the throughput at an acceptable level.
Revised:  Besides , prolonged channel observation at the first sensing stage decreases the collision probability considerably while keeping the throughput at an acceptable level.
Edit intent: coherence
Original:  Further , prolonged channel observation at the first sensing stage decreases the collision probability considerably  while keeping the throughput at an acceptable level.
Revised:  Further , prolonged channel observation at the first stage of sensing decreases the collision probability considerably while keeping the throughput at an acceptable level.
Edit intent: clarity
Original:  Further , prolonged channel observation at the first sensing stage decreases the collision probability considerably  while keeping the throughput at an acceptable level.
Revised:  Further , prolonged channel observation at the first sensing stage decreases the collision probability considerably , while keeping the throughput at an acceptable level.
Edit intent: fluency
Original:  Finally, in most network scenariosconsidered in this work, two stages of sensing are enough to obtain the maximum throughput in Opportunistic Spectrum Access communication.
Revised:  Finally, in realistic primary user traffic scenarios, using two stages of sensing are enough to obtain the maximum throughput in Opportunistic Spectrum Access communication.
Edit intent: clarity
Original:  Finally, in most network scenariosconsidered in this work, two stages of sensing are enough to obtain the maximum throughput in Opportunistic Spectrum Access communication.
Revised:  Finally, in most network scenariosconsidered in this work, two stages of sensing maximizes throughput while meeting constraints subjected by Opportunistic Spectrum Access communication.
Edit intent: clarity
Original:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques  , single and parallel channel access, primary and secondary user traffic, as well as buffering of incoming secondary user traffic  .
Revised:  The analytical framework models the following : number of sensing stages, physical layer sensing techniques , single and parallel channel access, primary and secondary user traffic, buffering of incoming secondary user traffic .
Edit intent: coherence
Original:  Our results show that when the probability of primary user mis-detection is constrained, the performance of multi-stage sensing is  in most cases  superior to the single stage sensing counterpart.
Revised:  Our results show that when the probability of primary user mis-detection is constrained, the performance of multi-stage sensing is , in most cases superior to the single stage sensing counterpart.
Edit intent: fluency
Original:  Our results show that when the probability of primary user mis-detection is constrained, the performance of multi-stage sensing is  in most cases  superior to the single stage sensing counterpart.
Revised:  Our results show that when the probability of primary user mis-detection is constrained, the performance of multi-stage sensing is in most cases , superior to the single stage sensing counterpart.
Edit intent: fluency
Original: Options that allow the holder to extend the  maturity by paying an additional fixed amount found many applications in finance.
Revised: Financial contracts with options that allow the holder to extend the maturity by paying an additional fixed amount found many applications in finance.
Edit intent: clarity
Original: Options that allow the holder to extend the  maturity by paying an additional fixed amount found many applications in finance.
Revised: Options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance.
Edit intent: clarity
Original:  This technique should provide some guidance into the type of probability density functions that can be derived from particular economic agent exchange rules, or for that matter, any other kinetic model of gases with particular collision physics.
Revised:  This should provide some guidance into the type of probability density functions that can be derived from particular economic agent exchange rules, or for that matter, any other kinetic model of gases with particular collision physics.
Edit intent: clarity
Original:  The algorithm achieves a constant time cost for processing cluster association and a cost between O (\log M) and O (M) for processing bond dissociation in clusters with M bonds. we apply the method to simulate a trivalent ligand and a bivalent receptor clustering system and obtain an average scaling of O (M^{0.45}) for processing bond dissociation in acyclic aggregation, compared to a linear scaling with the cluster size in standard methods  .
Revised:  The algorithm achieves a constant time cost for processing cluster association and a cost between O (\log M) and O (M) for processing bond dissociation in clusters with M bonds. we apply the method to simulate a trivalent ligand and a bivalent receptor clustering system and obtained an average scaling of O (M^{0.45}) for processing bond dissociation in acyclic aggregation, compared to a linear scaling with the cluster size in standard methods .
Edit intent: fluency
Original: Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with complementary analytical results we show evidence for anomalous diffusion and weak ergodicity breaking.
Revised: Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking.
Edit intent: clarity
Original: We show that the maximization of the sum degrees-of-freedom for the static flat-fading multiple-input multiple-output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem  , when the signal spaces span all available dimensions.
Revised: We show that the maximization of the sum degrees-of-freedom for the static flat-fading multiple-input multiple-output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem (RCRM) , when the signal spaces span all available dimensions.
Edit intent: clarity
Original:  The rank minimization corresponds to maximizing interference alignment (IA) such that interference spans the lowest dimensional subspace possible.
Revised:  The rank minimization corresponds to maximizing interference alignment (IA) so that interference spans the lowest dimensional subspace possible.
Edit intent: fluency
Original:  We also show that our heuristic relaxation can be also tuned to the multi-cell interference channel.
Revised:  We also show that our heuristic relaxation can be tuned for the multi-cell interference channel.
Edit intent: fluency
Original:  We show new tight characterizations of public coin one-way communication complexity which strengthen on the tight characterization shown in [J., Klauck, Nayak 08].
Revised:  We show a new tight characterization of public coin one-way communication complexity which strengthen on the tight characterization shown in [J., Klauck, Nayak 08].
Edit intent: fluency
Original:  We show new tight characterizations of public coin one-way communication complexity which strengthen on the tight characterization shown in [J., Klauck, Nayak 08].
Revised:  We show new tight characterizations of public coin one-way communication complexity which strengthens on the tight characterization shown in [J., Klauck, Nayak 08].
Edit intent: fluency
Original:  We use the new characterizations to show our direct product result and these may also be of independent interest.
Revised:  We use the new characterization to show our direct product result and these may also be of independent interest.
Edit intent: fluency
Original:  We use the new characterizations to show our direct product result and these may also be of independent interest.
Revised:  We use the new characterizations to show our direct product result and this may also be of independent interest.
Edit intent: fluency
Original: The paper explores the ideology behind the concept of inside a simple or self intersecting polygon by presenting new definitions on Inaccessibility and Inside for a point S related to a  polygon P.
Revised: The paper explores the ideology behind the concept of inside a simple or self intersecting polygon by presenting new definitions on Inaccessibility and Inside for a point S related to a simple or self intersecting polygon P.
Edit intent: fluency
Original:  It further goes on to give a theoretical proof to establish a relation as to when a point is inaccessible and inside a polygon.
Edit intent: coherence
Original:  The proposed analytical solution depicts a novel way of tackling the well known point in polygon problem by employing the properties of epigraphs and hypographs, explicitly.
Revised:  The proposed analytical solution depicts a novel way of solving the point in polygon problem by employing the properties of epigraphs and hypographs, explicitly.
Edit intent: clarity
Original:  Contrary to the ambiguous solutions given by the cross over for the simple and self intersecting polygons and the solution of a point being multi-ply inside a self intersecting polygon given by the winding number rule, the current solution gives unambiguous and singular result for both kinds of polygons.
Revised:  Contrary to the ambiguous solutions given by the cross over for the simple and self intersecting polygons and the solution of a point being multiply inside a self intersecting polygon given by the winding number rule, the current solution gives unambiguous and singular result for both kinds of polygons.
Edit intent: clarity
Original:  The solution also deals with the rare and subtle issues of ray crossing a odd or even number of vertices, an edge as well as analytically questions the idea of a point being multi-ply inside a polygon.
Edit intent: coherence
Original:  We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectations values of functions of the terminal segment number  do not depend on the distribution of the total branching probability over the terminal segments.
Revised:  We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectation values of functions of the terminal segment number do not depend on the distribution of the total branching probability over the terminal segments.
Edit intent: fluency
Original:  For the continuous BES-model, this system of differential equations also gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the developement of the mean and standard deviation of the number of terminal segments at a time t.
Revised:  For the continuous BES-model, this system of differential equations gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the developement of the mean and standard deviation of the number of terminal segments at a time t.
Edit intent: clarity