wanyu/IteraTeR_v2 huggingface dataset:
Original:  For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time  .
Revised:  For simple polygons (i.e., h = 0), the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time .
Edit intent: coherence
Original:  In this paper, we present  first algorithms that compute the geodesic diameter of a given polygonal domain in worst-case time O(n ^{7.73 ) or O(n^7 (log n + h)).
Revised:  In this paper, we present the first algorithms that compute the geodesic diameter of a given polygonal domain in worst-case time O(n ^{7.73 ) or O(n^7 (log n + h)).
Edit intent: fluency
Original:  In this paper, we present  first algorithms that compute the geodesic diameter of a given polygonal domain in worst-case time O(n ^{7.73 ) or O(n^7 (log n + h)).
Revised:  In this paper, we present first algorithms that compute the geodesic diameter of a given polygonal domain in worst-case time O(n ^7.73 ) or O(n^7 (log n + h)).
Edit intent: fluency
Original:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there are at least five  shortest paths between the two points .
Revised:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter and in that case there are at least five shortest paths between the two points .
Edit intent: clarity
Original:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there are at least five  shortest paths between the two points .
Revised:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there exist at least five shortest paths between the two points .
Edit intent: clarity
Original:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there are at least five  shortest paths between the two points .
Revised:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there are at least five distinct shortest paths between the two points .
Edit intent: clarity
Original:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there are at least five  shortest paths between the two points .
Revised:  The algorithms are based on our new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there are at least five shortest paths between the two .
Edit intent: fluency
Original: Recent advances in Micro-Electro-Mechanical Systems (MEMS) technology, integrated circuits, and wire-less communication have allowed the realization of Wireless Body Area Networks (WBANs).
Revised: Recent advances in Micro-Electro-Mechanical Systems (MEMS) technology, integrated circuits, and wireless communication have allowed the realization of Wireless Body Area Networks (WBANs).
Edit intent: clarity
Original:  WBANs promise unobtrusive ambulatory health monitoring for a long period of time , and provide real-time updates of the patients status to the physician.
Revised:  WBANs promise unobtrusive ambulatory health monitoring for a long period of time and provide real-time updates of the patients status to the physician.
Edit intent: fluency
Original:  WBANs promise unobtrusive ambulatory health monitoring for a long period of time , and provide real-time updates of the patients status to the physician.
Revised:  WBANs promise unobtrusive ambulatory health monitoring for a long period of time , and provide real-time updates of the patient's status to the physician.
Edit intent: fluency
Original:  We further discuss in-body antenna design and low-power MAC protocol for a WBAN.
Revised:  We further discuss in-body antenna design and low-power MAC protocol for WBAN.
Edit intent: fluency
Original:  More precisely, by encoding sets using their distance functions, we prove that the multidimensional matching distance between rank invariants of persistent homology groups is always upperly bounded by the Hausdorff distance between sets.
Revised:  More precisely, by encoding sets using the distance function, the multidimensional matching distance between rank invariants of persistent homology groups is always upperly bounded by the Hausdorff distance between sets.
Edit intent: clarity
Original:  Moreover we prove that our construction fully maintains information about the original set.
Revised:  Moreover we prove that our construction maintains information about the original set.
Edit intent: clarity
Original:  Some experiments showing the potential of our approach conclude the paper.
Revised:  Some experiments showing the potential of our approach concludes the paper.
Edit intent: fluency
Original:  Our results show that function, diversity and interspecific interactions of locally linked communities undergo a sharp phase transition with changes in the rate of species dispersal.
Revised:  Our results show that function, diversity and interspecific interactions of locally linked communities undergo a phase transition with changes in the rate of species dispersal.
Edit intent: clarity
Original:  On the other hand, high spatial interconnectedness promotes local biodiversity at the expense of local stability and supports communities with a wide diversity of weak interspecific interactions.
Revised:  On the other hand, high spatial interconnectedness promotes local biodiversity at the expense of local stability and supports communities with a wide range of interspecific interactions.
Edit intent: clarity
Original: The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighbouring sites are allowed.
Revised: The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed.
Edit intent: fluency
Original: We present an efficient algorithm for computing a function that minimizes the number of critical points among all functions  within a prescribed distance d from a given input function.
Revised: We solve the problem of minimizing the number of critical points among all functions within a prescribed distance d from a given input function.
Edit intent: clarity
Original:  Our method completely removes homological noise with persistence less than 2d  , constructively proving that the lower bound on the number of critical points given by the stability theorem of persistent homology is tight in dimension two for any input function  .
Revised:  Our method completely removes homological noise with persistence less than 2 , constructively proving that the lower bound on the number of critical points given by the stability theorem of persistent homology is tight in dimension two for any input function .
Edit intent: clarity
Original:  Our method completely removes homological noise with persistence less than 2d  , constructively proving that the lower bound on the number of critical points given by the stability theorem of persistent homology is tight in dimension two for any input function  .
Revised:  Our method completely removes homological noise with persistence less than 2d , constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology is tight in dimension two for any input function .
Edit intent: clarity
Original:  Our method completely removes homological noise with persistence less than 2d  , constructively proving that the lower bound on the number of critical points given by the stability theorem of persistent homology is tight in dimension two for any input function  .
Revised:  Our method completely removes homological noise with persistence less than 2d , constructively proving that the lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function .
Edit intent: clarity
Original:  Motivated by applications in network tomography, sensor networks and infection propagation we formulate group testing problems on graphs  . Unlike conventional group testing problems  each group here must conform to the constraints imposed by a graph.
Revised:  Motivated by applications in network tomography, sensor networks and infection propagation , a variation of group testing problems on graphs . Unlike conventional group testing problems each group here must conform to the constraints imposed by a graph.
Edit intent: clarity
Original:  Motivated by applications in network tomography, sensor networks and infection propagation we formulate group testing problems on graphs  . Unlike conventional group testing problems  each group here must conform to the constraints imposed by a graph.
Revised:  Motivated by applications in network tomography, sensor networks and infection propagation we formulate group testing problems on graphs is formulated . Unlike conventional group testing problems each group here must conform to the constraints imposed by a graph.
Edit intent: clarity
Original:  Motivated by applications in network tomography, sensor networks and infection propagation we formulate group testing problems on graphs  . Unlike conventional group testing problems  each group here must conform to the constraints imposed by a graph.
Revised:  Motivated by applications in network tomography, sensor networks and infection propagation we formulate group testing problems on graphs . Unlike conventional group testing problems , each group here must conform to the constraints imposed by a graph.
Edit intent: fluency
Original:  In this paper we associate a test with a random walk.
Revised:  In this paper , a test is associated with a random walk.
Edit intent: clarity
Original:  In this context  conventional group testing corresponds to the special case of a complete graph on n vertices.
Revised:  In this context , conventional group testing corresponds to the special case of a complete graph on n vertices.
Edit intent: fluency
Original:  For interesting classes of graphs we arrive at a rather surprising result  , namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed.
Revised:  For interesting classes of graphs a rather surprising result , namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed.
Edit intent: clarity
Original:  For interesting classes of graphs we arrive at a rather surprising result  , namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed.
Revised:  For interesting classes of graphs we arrive at a rather surprising result is obtained , namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed.
Edit intent: clarity
Original:  For interesting classes of graphs we arrive at a rather surprising result  , namely, that the number of tests required to identify d defective items is substantially similar to that required in conventional group testing problems, where no such constraints on pooling is imposed.
Revised:  For interesting classes of graphs we arrive at a rather surprising result , namely, that the number of tests required to identify d defective items is substantially similar to what is required in conventional group testing problems, where no such constraints on pooling is imposed.
Edit intent: fluency
Original:  Specifically, if T(n) corresponds to the mixing time of the graph G, we show that with m=O(d^2T^2(n) log (n/d)) non-adaptive tests, one can identify the defective items.
Revised:  Specifically, if T(n) corresponds to the mixing time of the graph G, it is shown that with m=O(d^2T^2(n) log (n/d)) non-adaptive tests, one can identify the defective items.
Edit intent: clarity
Original:  We next consider a specific scenario  that arises in network tomography and show that m=O(d^3 log^3(n) ) non-adaptive tests are sufficient to identify d defective items.
Revised:  Next, a specific scenario that arises in network tomography and show that m=O(d^3 log^3(n) ) non-adaptive tests are sufficient to identify d defective items.
Edit intent: clarity
Original:  We next consider a specific scenario  that arises in network tomography and show that m=O(d^3 log^3(n) ) non-adaptive tests are sufficient to identify d defective items.
Revised:  We next consider a specific scenario is considered that arises in network tomography and show that m=O(d^3 log^3(n) ) non-adaptive tests are sufficient to identify d defective items.
Edit intent: clarity
Original:  We next consider a specific scenario  that arises in network tomography and show that m=O(d^3 log^3(n) ) non-adaptive tests are sufficient to identify d defective items.
Revised:  We next consider a specific scenario that arises in network tomography , for which it is shown that m=O(d^3 log^3(n) ) non-adaptive tests are sufficient to identify d defective items.
Edit intent: clarity
Original:  We also consider noisy counterparts of the graph constrained group testing problem and develop parallel results for these cases .
Revised:  Noisy counterparts of the graph constrained group testing problem and develop parallel results for these cases .
Edit intent: clarity
Original:   Our approach is valid over a commutative integral domain D and for a sequence of n terms, the resulting algorithm requires at most 3n^2/4-multiplications\lfloor{4}}\rfloor in D.
Revised:  Our approach is valid over a commutative integral domain D and for a sequence of n terms, the resulting algorithm requires at most 3\lfloor{4}}\rfloor in D.
Edit intent: clarity
Original:   Our approach is valid over a commutative integral domain D and for a sequence of n terms, the resulting algorithm requires at most 3n^2/4-multiplications\lfloor{4}}\rfloor in D.
Revised:  Our approach is valid over a commutative integral domain D and for a sequence of n terms, the resulting algorithm requires at most 3n^2/4-multiplications\lfloor{4}}\rfloor-multiplications in D.
Edit intent: fluency
Original:  Our approach is valid over a commutative integral domain D and for a sequence of n terms, the resulting algorithm requires at most 3 \lfloor \frac{(n+1)^2 \rfloor -multiplications in D .
Revised:  Our approach is valid over a commutative integral domain D and for a sequence of n terms, the resulting algorithm requires at most 3 \lfloor \frac{(n+1)^2 \rfloor multiplications .
Edit intent: clarity
Original:  The guaranteed stability of a class of single input, single output metabolic cycles is established . Next, parameter regimes for the stability of a small autocatalytic cycle are determined.
Revised:  The guaranteed stability of a class of single input, single output metabolic cycles is established . Next, we extend our analysis to a small autocatalytic cycle are determined.
Edit intent: clarity
Original:  Results suggest that elevated metabolite concentrations and certain crucial saturation parameters can strongly affect the stability of the entire metabolic cycle.
Revised:  In addition, our results suggest that elevated metabolite concentrations and certain crucial saturation parameters can strongly affect the stability of the entire metabolic cycle.
Edit intent: coherence
Original: Despite considerable effort to date, DNA transcription factor binding sites prediction in whole genome remains a challenge for the researchers.
Revised: In computational molecular biology, gene regulatory binding sites prediction in whole genome remains a challenge for the researchers.
Edit intent: clarity
Original:  Currently the genome wide transcription factor binding sites prediction tools required either direct pattern sequence or weight matrix.
Revised:  Now a days, the genome wide transcription factor binding sites prediction tools required either direct pattern sequence or weight matrix.
Edit intent: coherence
Original:  Currently the genome wide transcription factor binding sites prediction tools required either direct pattern sequence or weight matrix.
Revised:  Currently the genome wide regulatory binding site prediction tools required either direct pattern sequence or weight matrix.
Edit intent: clarity
Original:  Although there are known transcription factor binding sites pattern databases and tools for genome level prediction but no tool for weight matrix construction . Considering this, we developed a DNA MATRIX tool for searching putative transcription factor binding sites in genomic sequences.
Revised:  Although there are known transcription factor binding sites databases available for genome wide prediction but no tool for weight matrix construction . Considering this, we developed a DNA MATRIX tool for searching putative transcription factor binding sites in genomic sequences.
Edit intent: clarity
Original:  Although there are known transcription factor binding sites pattern databases and tools for genome level prediction but no tool for weight matrix construction . Considering this, we developed a DNA MATRIX tool for searching putative transcription factor binding sites in genomic sequences.
Revised:  Although there are known transcription factor binding sites pattern databases and tools for genome level prediction but no tool for weight matrix construction . Considering this, we developed a DNA MATRIX tool for searching putative regulatory binding sites in genomic sequences.
Edit intent: clarity
Original:  DNA MATRIX uses the simple heuristic approach for weight matrix construction, which can be transformed into different formats as per the requirement of researchers for further genome wide prediction and therefore provides the possibility to identify the conserved known DNA binding sites in the coregulated genesand also to search for a great variety of different regulatory binding patterns .
Revised:  DNA MATRIX uses the simple heuristic approach for weight matrix construction, which can be transformed into different formats after motif alignment and therefore provides the possibility to identify the conserved known DNA binding sites in the coregulated genesand also to search for a great variety of different regulatory binding patterns .
Edit intent: clarity
Original:  DNA MATRIX uses the simple heuristic approach for weight matrix construction, which can be transformed into different formats as per the requirement of researchers for further genome wide prediction and therefore provides the possibility to identify the conserved known DNA binding sites in the coregulated genesand also to search for a great variety of different regulatory binding patterns .
Revised:  DNA MATRIX uses the simple heuristic approach for weight matrix construction, which can be transformed into different formats as per the requirement of researchers for further genome wide prediction and therefore provides the possibility to identify the most potential conserved binding sites in the coregulated genesand also to search for a great variety of different regulatory binding patterns .
Edit intent: clarity
Original:  DNA MATRIX uses the simple heuristic approach for weight matrix construction, which can be transformed into different formats as per the requirement of researchers for further genome wide prediction and therefore provides the possibility to identify the conserved known DNA binding sites in the coregulated genesand also to search for a great variety of different regulatory binding patterns .
Revised:  DNA MATRIX uses the simple heuristic approach for weight matrix construction, which can be transformed into different formats as per the requirement of researchers for further genome wide prediction and therefore provides the possibility to identify the conserved known DNA binding sites in the regulated genes .
Edit intent: clarity
Original:  The user may construct and save specific weight or frequency matrices in different formats derived through user selected set of known motif sequences .
Revised:  The user may construct and save specific weight or frequency matrices in different form and file formats based on user based selection of conserved aligned block of short sequences ranges from 6 to 20 base pairs and prior nucleotide frequency before weight scoring .
Edit intent: clarity
Original: This paper proposes a general framework for the optimal scheduling problem in wireless networks with certain types of uncertain parameters,  under the assumption that the Strong Law of Large Numbers (SLLN) applies to the random processes which generate these parameters in the limit.
Revised: This paper proposes a general framework for the optimal scheduling problem in wireless networks subject to uncertain parameters, under the assumption that the Strong Law of Large Numbers (SLLN) applies to the random processes which generate these parameters in the limit.
Edit intent: clarity
Original:  The method may potentially be applied to other applications where  convex problems with uncertain parameters are to be solved .
Revised:  The method may potentially be applied to other applications where convex problems with uncertain parameters are needed .
Edit intent: clarity
Original:  Several phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework.
Revised:  Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework.
Edit intent: fluency
Original:  Available Bayesian phylogenetic softwarehas privileged so far the simplicity of the harmonic mean estimator (HM) and the arithmetic mean estimator (AM). However it is known that the resulting estimates of the Bayesian evidence in favor of one model are often biased and inaccurate up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful.
Revised:  Practitioners and researchers, often led by available software, have privileged so far the simplicity of the harmonic mean estimator (HM) and the arithmetic mean estimator (AM). However it is known that the resulting estimates of the Bayesian evidence in favor of one model are often biased and inaccurate up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful.
Edit intent: clarity
Original:  Available Bayesian phylogenetic softwarehas privileged so far the simplicity of the harmonic mean estimator (HM) and the arithmetic mean estimator (AM). However it is known that the resulting estimates of the Bayesian evidence in favor of one model are often biased and inaccurate up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful.
Revised:  Available Bayesian phylogenetic softwarehas privileged so far the simplicity of the harmonic mean estimator (HM) and the arithmetic mean estimator (AM). However it is known that the resulting estimates of the Bayesian evidence in favor of one model are biased and often inaccurate up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful.
Edit intent: fluency