wanyu/IteraTeR_v2 huggingface dataset:
Original: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf  . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Revised: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not\subset{\sf . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Edit intent: clarity
Original: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf  . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Revised: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf TC^0 . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Edit intent: fluency
Original: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf  . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Revised: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf . Natural Proofs have three properties: they are constructive (an efficient algorithm A is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Edit intent: clarity
Original: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf  . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Revised: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( A accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Edit intent: fluency
Original: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf  . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( ALG rejects all strings which are truth tables of small circuits).
Revised: We study connections between Natural Proofs, derandomization, and the problem of proving weak circuit lower bounds such as 'NEXPis not contained in TC^0' which are still wide open {\sf } \not{\sf . Natural Proofs have three properties: they are constructive (an efficient algorithm ALG is embedded in them), have largeness ( ALG accepts a large fraction of strings), and are useful ( A rejects all strings which are truth tables of small circuits).
Edit intent: fluency
Original:  Strong circuit lower bounds that are "naturalizing" would contradict present cryptographic understanding, yet the vast majority of known circuit lower bound proofs are naturalizing.
Revised:  Strong circuit lower bounds that are ``naturalizing'' would contradict present cryptographic understanding, yet the vast majority of known circuit lower bound proofs are naturalizing.
Edit intent: fluency
Original:  Some heuristic arguments say constructivity should be circumventable . Largeness is inherent in many proof techniques, and it is probably our presently weak techniques that yield constructivity.
Revised:  Some heuristic arguments say constructivity should be circumventable : largeness is inherent in many proof techniques, and it is probably our presently weak techniques that yield constructivity.
Edit intent: fluency
Original:  Informally, we prove for all "typical" non-uniform circuit classes C, NEXP is not contained in C {\cal  {\sf } \not{\cal  if and only if there exists a constructive property that is nontrivially useful against C-circuits.
Revised:  Informally, we prove for all ``typical'' non-uniform circuit classes C, NEXP is not contained in C {\cal {\sf } \not{\cal if and only if there exists a constructive property that is nontrivially useful against C-circuits.
Edit intent: fluency
Original:  Informally, we prove for all "typical" non-uniform circuit classes C, NEXP is not contained in C {\cal  {\sf } \not{\cal  if and only if there exists a constructive property that is nontrivially useful against C-circuits.
Revised:  Informally, we prove for all "typical" non-uniform circuit classes {\cal {\sf } \not{\cal if and only if there exists a constructive property that is nontrivially useful against C-circuits.
Edit intent: coherence
Original:  Informally, we prove for all "typical" non-uniform circuit classes C, NEXP is not contained in C {\cal  {\sf } \not{\cal  if and only if there exists a constructive property that is nontrivially useful against C-circuits.
Revised:  Informally, we prove for all "typical" non-uniform circuit classes C, NEXP is not contained in C {\cal ,{\sf } \not{\cal if and only if there exists a constructive property that is nontrivially useful against C-circuits.
Edit intent: fluency
Original:  *{\cal  {\sf } \not{\cal  {\cal   There are no \sf P-natural properties useful against C {\cal  if and only if randomized exponential time can be "derandomized" using truth tables of circuits from C {\cal  as random seeds.
Revised:  *{\cal {\sf } \not{\cal {\cal C There are no \sf P-natural properties useful against C {\cal if and only if randomized exponential time can be "derandomized" using truth tables of circuits from C {\cal as random seeds.
Edit intent: clarity
Original:  *{\cal  {\sf } \not{\cal  {\cal   There are no \sf P-natural properties useful against C {\cal  if and only if randomized exponential time can be "derandomized" using truth tables of circuits from C {\cal  as random seeds.
Revised:  *{\cal {\sf } \not{\cal {\cal There are no \sf P-natural properties useful against {\cal if and only if randomized exponential time can be "derandomized" using truth tables of circuits from C {\cal as random seeds.
Edit intent: fluency
Original:  *{\cal  {\sf } \not{\cal  {\cal   There are no \sf P-natural properties useful against C {\cal  if and only if randomized exponential time can be "derandomized" using truth tables of circuits from C {\cal  as random seeds.
Revised:  *{\cal {\sf } \not{\cal {\cal There are no \sf P-natural properties useful against C {\cal if and only if randomized exponential time can be ``derandomized'' using truth tables of circuits from C {\cal as random seeds.
Edit intent: fluency
Original:  *{\cal  {\sf } \not{\cal  {\cal   There are no \sf P-natural properties useful against C {\cal  if and only if randomized exponential time can be "derandomized" using truth tables of circuits from C {\cal  as random seeds.
Revised:  *{\cal {\sf } \not{\cal {\cal There are no \sf P-natural properties useful against C {\cal if and only if randomized exponential time can be "derandomized" using truth tables of circuits from {\cal as random seeds.
Edit intent: fluency
Original: We study connections between Natural Proofs, derandomization, and the problem of proving ``weak'' circuit lower bounds such as {\sf NEXP} \not\subset {\sf TC^0}.
Revised: We study connections between Natural Proofs, derandomization, and the problem of proving "weak" circuit lower bounds such as {\sf NEXP} \not\subset {\sf TC^0}.
Edit intent: fluency
Original:  Strong circuit lower bounds that are ``naturalizing'' would contradict present cryptographic understanding, yet the vast majority of known circuit lower bound proofs are naturalizing.
Revised:  Strong circuit lower bounds that are "naturalizing" would contradict present cryptographic understanding, yet the vast majority of known circuit lower bound proofs are naturalizing.
Edit intent: fluency
Original:  Informally, we prove for all ``typical'' non-uniform circuit classes {\cal C}, {\sf NEXP} \not\subset {\cal C} if and only if there is a polynomial-time algorithm distinguishing some function from all functions computable by {\cal C}-circuits.
Revised:  Informally, we prove for all "typical" non-uniform circuit classes {\cal C}, {\sf NEXP} \not\subset {\cal C} if and only if there is a polynomial-time algorithm distinguishing some function from all functions computable by {\cal C}-circuits.
Edit intent: fluency
Original:  \bullet There are no \sf P-natural properties useful against {\cal C} if and only if randomized exponential time can be ``derandomized'' using truth tables of circuits from {\cal C} as random seeds.
Revised:  \bullet There are no \sf P-natural properties useful against {\cal C} if and only if randomized exponential time can be "derandomized" using truth tables of circuits from {\cal C} as random seeds.
Edit intent: fluency
Original:  We provide a general construction that for any arcwise connected compact set X in R ^2 that is not an axis-aligned rectangle and for any positive integer k produces a family F of sets, each obtained by an independent horizontal and vertical scaling and translation of X, such that no three sets in F pairwise intersect and chi(F )>k.
Revised:  We provide a general construction that for any arc-connected compact set X in R ^2 that is not an axis-aligned rectangle and for any positive integer k produces a family F of sets, each obtained by an independent horizontal and vertical scaling and translation of X, such that no three sets in F pairwise intersect and chi(F )>k.
Edit intent: fluency
Original:  This provides a negative answer to a question of Gy\'arf\'asrf\'{a}s } and Lehel for L-shapes.
Revised:  This provides a negative answer to a question of Gy\'{arf\'{a}s } and Lehel for L-shapes.
Edit intent: fluency
Original: Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number.
Revised: Several classical constructions illustrate the fact that the chromatic number of a graph can be arbitrarily large compared to its clique number.
Edit intent: fluency
Original:  However, until very recently  no such construction was known for intersection graphs of geometric objects in the plane.
Revised:  However, until very recently , no such construction was known for intersection graphs of geometric objects in the plane.
Edit intent: fluency
Original:  This provides a negative answer to a question of Gy\'{arf\'{a}s }  and Lehel for L-shapes.
Revised:  This provides a negative answer to a question of rf\'{a}s } and Lehel for L-shapes.
Edit intent: coherence
Original:  With extra conditions  we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number.
Revised:  With extra conditions , we also show how to construct a triangle-free family of homothetic (uniformly scaled) copies of a set with arbitrarily large chromatic number.
Edit intent: fluency
Original:  This applies to many common shapes, like circles, square boundaries or equilateral L-shapes.
Revised:  This applies to many common shapes, like circles, square boundaries , and equilateral L-shapes.
Edit intent: fluency
Original: On-line portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining, etc.
Revised: Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining, etc.
Edit intent: fluency
Original:  This article aims to provide a comprehensive survey and a structural understanding of existing on-line portfolio selection techniques in literature .
Revised:  This article aims to provide a comprehensive survey and a structural understanding of published online portfolio selection techniques in literature .
Edit intent: clarity
Original:  This article aims to provide a comprehensive survey and a structural understanding of existing on-line portfolio selection techniques in literature .
Revised:  This article aims to provide a comprehensive survey and a structural understanding of existing on-line portfolio selection techniques .
Edit intent: coherence
Original:  In addition to the problem formulation and related algorithms, we also discuss the relationship of these algorithms with the Capital Growth theory in order to better understand the commons and differences of their underlying trading ideas.
Revised:  In addition to the problem formulation and related algorithms, we also discuss the relationship of these algorithms with the Capital Growth theory in order to better understand the similarities and differences of their underlying trading ideas.
Edit intent: fluency
Original:  This is the first exact deterministic representation of a complex heterogeneous and finite epidemic system which can be numerically evaluated.
Revised:  This is an exact deterministic representation of a complex heterogeneous and finite epidemic system which can be numerically evaluated.
Edit intent: clarity
Original:  This is the first exact deterministic representation of a complex heterogeneous and finite epidemic system which can be numerically evaluated.
Revised:  This is the first exact deterministic representation of a complex heterogeneous and finite epidemic system which can been numerically evaluated.
Edit intent: fluency
Original: We consider a class of deterministic susceptible-infectious-removed (SIR) models on time-independent weighted contact networks where the infection and removal processes are Poisson  .
Revised: We consider a class of deterministic susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson .
Edit intent: clarity
Original:  We prove that a particular closed form of these models generates an exact representation of the expected infectious time series for networks with no closed loops.
Revised:  We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no closed loops.
Edit intent: clarity
Original: Modern massive graphs such as the web and communication networks are trulydynamic graphs .
Revised: dynamic graphs .
Edit intent: clarity
Original: Modern massive graphs such as the web and communication networks are trulydynamic graphs .
Revised: Modern massive graphs such as the web and communication networks are truly .
Edit intent: clarity
Original:  The graph is not a static object, but is most accurately characterized as astream of edges .
Revised:  The graph is not a static object, but is most accurately characterized as a .
Edit intent: clarity
Original:  Being a single pass streaming algorithm, our procedure also maintains a real-time estimate of the clustering coefficient /number of triangles of a graph, by storing a miniscule fraction of edges.
Revised:  Being a single pass streaming algorithm, our procedure also maintains of the clustering coefficient /number of triangles of a graph, by storing a miniscule fraction of edges.
Edit intent: clarity
Original:  Being a single pass streaming algorithm, our procedure also maintains a real-time estimate of the transitivity/number of triangles of a graph, by storing a miniscule fraction of edges.
Revised:  Being a single pass streaming algorithm, our procedure also maintains a real-time estimate of the transitivity/number of triangles of a graph, by storing a minuscule fraction of edges.
Edit intent: fluency
Original:  In particular, we reduce the problem of evaluating the Tutte polynomial  at the point (3,3) to counting the number of Eulerian orientations over planar 4-regular graphs to show the latter is #P-hard.
Revised:  In particular, we reduce the problem of evaluating the Tutte polynomial of a planar graph at the point (3,3) to counting the number of Eulerian orientations over planar 4-regular graphs to show the latter is #P-hard.
Edit intent: clarity
Original:  Our work represents the first instance of an architecture-conscious runtime implementation of tree-based models that we are aware of .
Revised:  Our work contributes to the exploration of architecture-conscious runtime implementation of tree-based models that we are aware of .
Edit intent: clarity
Original:  Our work represents the first instance of an architecture-conscious runtime implementation of tree-based models that we are aware of .
Revised:  Our work represents the first instance of an architecture-conscious runtime implementations of machine learning algorithms .
Edit intent: clarity
Original: We consider the problem of inferring the topology of  an M-by-N network  by sending probes between M sources and N receivers.
Revised: We consider the problem of inferring the topology of an M-by-N network ), by sending probes between M sources and N receivers.
Edit intent: fluency
Original: We consider the problem of inferring the topology of  an M-by-N network  by sending probes between M sources and N receivers.
Revised: We consider the problem of inferring the topology of an M-by-N network by sending probes between the sources and receivers.
Edit intent: fluency
Original:  The problem is which 2-by-2's to query and how to merge them with the  1-by-N, so as to exactly identify the 2-by-N topology, and optimize a number of performance metrics including measurement traffic , time complexity, and memory usage.
Revised:  The problem is which 2-by-2's to query and how to merge them with the given 1-by-N, so as to exactly identify the 2-by-N topology, and optimize a number of performance metrics including measurement traffic , time complexity, and memory usage.
Edit intent: clarity
Original:  The second algorithm follows the framework of multiple hypothesis testing, in particular Generalized Binary Search (GBS).
Edit intent: coherence
Original:  Simulation results over synthetic and realistic topologies demonstrate that both algorithms correctly identify the 2-by-N topology and are near-optimal, but the bottom-up approach is more efficient in practice.
Revised:  Simulation results over synthetic and realistic topologies demonstrate that both algorithms correctly identify the 2-by-N topology and are near-optimal, but REA is more efficient in practice.
Edit intent: clarity
Original:  Importantly, all features of the tree , including topology, sources of gene flow, branch lengths, and mixture proportions, are optimized automatically from the data and include estimates of statistical uncertainty.
Revised:  Importantly, all features of the model , including topology, sources of gene flow, branch lengths, and mixture proportions, are optimized automatically from the data and include estimates of statistical uncertainty.
Edit intent: clarity
Original:  Notably, we confirm a signal of ancient admixture in European populations---including previously undetected admixture in Sardinians and Basques---involving a proportion of 20-40 \% ancient northern Eurasian ancestry.
Revised:  Notably, we confirm a signal of ancient admixture in European populations---including previously undetected admixture in Sardinians and Basques---involving a proportion of 20--40 \% ancient northern Eurasian ancestry.
Edit intent: fluency
Original: The large volumes of sequencing data required to deeply sample complex environments  pose new challenges to sequence analysis approaches.
Revised: The large volumes of sequencing data required to sample complex environments pose new challenges to sequence analysis approaches.
Edit intent: clarity
Original:  We apply two data reduction approaches, digital normalization and partitioning, to this challenge .
Revised:  We apply two data reduction approaches, digital normalization and partitioning, to make large metagenome assemblies more comput\ ationaly tractable .
Edit intent: clarity
Original: In this paper, the concept of sparse difference resultant for a  transformally essential system of difference polynomials is introduced and its properties are proved.
Revised: In this paper, the concept of sparse difference resultant for a Laurent transformally essential system of difference polynomials is introduced and its properties are proved.
Edit intent: fluency
Original:  Based on these bounds, an algorithm to compute the sparse difference resultant is proposed, which is single exponential in terms of the number of variables, the Jacobi number, and the size of the  transformally essential system.
Revised:  Based on these bounds, an algorithm to compute the sparse difference resultant is proposed, which is single exponential in terms of the number of variables, the Jacobi number, and the size of the Laurent transformally essential system.
Edit intent: fluency
Original:  Also , the precise order , degree, a determinant representation, and a Poisson-type product formula for difference resultants are given.
Revised:  Furthermore , the precise order , degree, a determinant representation, and a Poisson-type product formula for difference resultants are given.
Edit intent: coherence
Original:  Also , the precise order , degree, a determinant representation, and a Poisson-type product formula for difference resultants are given.
Revised:  Also , the precise order and degree, a determinant representation, and a Poisson-type product formula for difference resultants are given.
Edit intent: fluency
Original:  Also , the precise order , degree, a determinant representation, and a Poisson-type product formula for difference resultants are given.
Revised:  Also , the precise order , degree, a determinant representation, and a Poisson-type product formula for the difference resultant are given.
Edit intent: fluency
Original:  Numerical tests show that the lower bound approximation is fast and accurate in comparison with the Monte Carlo method, the partial-exact approximation method and the asymptotic expansion method .
Revised:  Numerical tests show that the suggested approximation is fast and accurate in comparison with the Monte Carlo method, the partial-exact approximation method and the asymptotic expansion method .
Edit intent: clarity
Original:  The methods and results that we present are general , and relevant beyond protein structures .
Revised:  The methods and results are general and relevant beyond protein structures .
Edit intent: clarity