wanyu/IteraTeR_v2 huggingface dataset:
Original:  As a results , we show that the same  holds if (i_k,j_k) are the starting and ending positions of the k'th maximal zero block, and, more generally, of the k'th maximal x-block, where x is an arbitrary word.
Revised:  As a result , we show that the same holds if (i_k,j_k) are the starting and ending positions of the k'th maximal zero block, and, more generally, of the k'th maximal x-block, where x is an arbitrary word.
Edit intent: fluency
Original:  As a results , we show that the same  holds if (i_k,j_k) are the starting and ending positions of the k'th maximal zero block, and, more generally, of the k'th maximal x-block, where x is an arbitrary word.
Revised:  As a results , we show that the same conclusion holds if (i_k,j_k) are the starting and ending positions of the k'th maximal zero block, and, more generally, of the k'th maximal x-block, where x is an arbitrary word.
Edit intent: clarity
Original:  A fast convergent iterative method is introduced in this paper to find the intrinsic mode function (IMF ) components of time series data, which is faster and more predictable than the Empirical Mode Decomposition method devised by the author of Hilbert Huang Transform.
Revised:  A fast convergent iterative method is introduced in this paper to find the IMF components of the data, the method is faster and more predictable than the Empirical Mode Decomposition method devised by the author of Hilbert Huang Transform.
Edit intent: clarity
Original:  The method iteratively adjust the control points on the data function corresponding to the extrema of the refining IMF, the control points of the residue function are calculated as the median of the straight line segments passing through the data control points, the residue function is then constructed as the cubic spline function of the median points.
Revised:  The approach is to iteratively adjust the control points on the data function corresponding to the extrema of the refining IMF, the control points of the residue function are calculated as the median of the straight line segments passing through the data control points, the residue function is then constructed as the cubic spline function of the median points.
Edit intent: clarity
Original:  The IMF found can also reveal the riding waves on the steep edge of the data .
Revised:  The IMF found reveals all the riding waves on the steep edge of the data .
Edit intent: clarity
Original: This paper is an exploration in a functional programming framework of isomorphisms {\em  between elementary data types (natural numbers, sets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals  etc.) and their extension to hereditarily finite universes through hylomorphisms derived from {\em  {\em ranking/unranking and{\em pairing/unpairing operations.
Revised: This paper is an exploration in a functional programming framework of {\em between elementary data types (natural numbers, sets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals etc.) and their extension to hereditarily finite universes through hylomorphisms derived from {\em {\em ranking/unranking and{\em pairing/unpairing operations.
Edit intent: fluency
Original: This paper is an exploration in a functional programming framework of isomorphisms {\em  between elementary data types (natural numbers, sets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals  etc.) and their extension to hereditarily finite universes through hylomorphisms derived from {\em  {\em ranking/unranking and{\em pairing/unpairing operations.
Revised: This paper is an exploration in a functional programming framework of isomorphisms {\em between elementary data types (natural numbers, sets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals etc.) and their extension to hereditarily finite universes through hylomorphisms derived from {\em hylomorphisms {\em ranking/unranking and{\em pairing/unpairing operations.
Edit intent: clarity
Original: This paper is an exploration in a functional programming framework of isomorphisms {\em  between elementary data types (natural numbers, sets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals  etc.) and their extension to hereditarily finite universes through hylomorphisms derived from {\em  {\em ranking/unranking and{\em pairing/unpairing operations.
Revised: This paper is an exploration in a functional programming framework of isomorphisms {\em between elementary data types (natural numbers, sets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals etc.) and their extension to hereditarily finite universes through hylomorphisms derived from {\em {\em ranking/unranking and{\em pairing/unpairing operations.
Edit intent: fluency
Original:  An embedded higher order combinator language {\em  provides any-to-any encodings automatically.
Revised:  An embedded higher order {\em provides any-to-any encodings automatically.
Edit intent: clarity
Original:  The paper is part of a larger effort to cover in a declarative programming paradigm some fundamental combinatorial generation algorithms along the lines of Knuth's recent work \mbox{ knuth06draft data types and, through the use of the embedded combinator language, provide 380 distinct bijective encodings between them.
Revised:  The paper covers 26 data types and, through the use of the embedded combinator language, provide 380 distinct bijective encodings between them.
Edit intent: clarity
Original:  The paper is part of a larger effort to cover in a declarative programming paradigm some fundamental combinatorial generation algorithms along the lines of Knuth's recent work \mbox{ knuth06draft data types and, through the use of the embedded combinator language, provide 380 distinct bijective encodings between them.
Revised:  The paper is part of a larger effort to cover in a declarative programming paradigm some fundamental combinatorial generation algorithms along the lines of Knuth's recent work \mbox{ knuth06draft data types and, through the use of the embedded combinator language, provides 650 distinct bijective transformations between them.
Edit intent: fluency
Original:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL  Keywords: Haskell data representations,  computational mathematics,  ranking/unranking, Ackermann encoding, hereditarily finite sets, hereditarily finite functions , permutations, factoradics, BDDs
Revised:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . Keywords: Haskell data representations, computational mathematics, ranking/unranking, Ackermann encoding, hereditarily finite sets, hereditarily finite functions , permutations, factoradics, BDDs
Edit intent: fluency
Original:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . Keywords: {\bf  {\em Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Revised:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . {\bf {\em Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Edit intent: coherence
Original:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . Keywords: {\bf  {\em Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Revised:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . Keywords: {\bf Keywords {\em Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Edit intent: fluency
Original:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . Keywords: {\bf  {\em Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Revised:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . Keywords: {\bf :{\em Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Edit intent: fluency
Original: This paper is an exploration in a functional programming framework of {\em isomorphisms} between elementary data types (natural numbers, sets, multisets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals,  DNA sequences etc.) and their extension to hereditarily finite universes through {\em hylomorphisms} derived from {\em ranking/unranking} and {\em pairing/unpairing} operations.
Revised: This paper is an exploration in a functional programming framework of {\em isomorphisms} between elementary data types (natural numbers, sets, multisets, finite functions, permutations binary decision diagrams, graphs, hypergraphs, parenthesis languages, dyadic rationals, primes, DNA sequences etc.) and their extension to hereditarily finite universes through {\em hylomorphisms} derived from {\em ranking/unranking} and {\em pairing/unpairing} operations.
Edit intent: clarity
Original:  Besides applications to experimental mathematics, a few examples of "free algorithms" obtained by transferring operations between data types are shown.
Revised:  Besides applications to experimental mathematics, a few examples of ``free algorithms'' obtained by transferring operations between data types are shown.
Edit intent: fluency
Original:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL . {\bf Keywords}: %DIFDELCMD < {\em %%% Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Revised:  The self-contained source code of the paper, as generated from a literate Haskell program, is available at URL {\bf Keywords}: %DIFDELCMD < {\em %%% Haskell data representations, data type isomorphisms, declarative combinatorics, computational mathematics, Ackermann encoding, G\"{o}del numberings, arithmetization, ranking/unranking, hereditarily finite sets, functions and permutations, encodings of binary decision diagrams, dyadic rationals, DNA encodings
Edit intent: fluency
Original: By analyzing ] financial time series of exceptional events such as bubbles and crashes, we confirm the existence of nonlinear potential forces in the markets.
Revised: By analyzing ] financial time series of exceptional events such as bubbles and crashes, we confirm the appearance of nonlinear potential forces in the markets.
Edit intent: clarity
Original: By analyzing ] financial time series of exceptional events such as bubbles and crashes, we confirm the existence of nonlinear potential forces in the markets.
Revised: By analyzing ] financial time series of exceptional events such as bubbles and crashes, we confirm the existence of nonlinear potential force in the markets.
Edit intent: fluency
Original:  These patterns are characterized by an ordered sequences of spikes from different neurons with specific delays between spikes.
Revised:  These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes.
Edit intent: fluency
Original: "Cognizing" ( i.e. , thinking, understanding, knowing, and having the capacity to do what cognizers can do ) is a mental state.
Revised: "Cognizing" ( e.g. , thinking, understanding, knowing, and having the capacity to do what cognizers can do ) is a mental state.
Edit intent: coherence
Original: "Cognizing" ( i.e. , thinking, understanding, knowing, and having the capacity to do what cognizers can do ) is a mental state.
Revised: "Cognizing" ( i.e. , thinking, understanding, and knowing ) is a mental state.
Edit intent: clarity
Original:  Systems without mental states, such as cognitive technology, can sometimes also do some of what cognizers can do , but that does not make them cognizers.
Revised:  Systems without mental states, such as cognitive technology, can sometimes contribute to human cognition , but that does not make them cognizers.
Edit intent: clarity
Original:  Cognitive technology allows cognizers to offload some of the functions they would otherwise have had to execute with their own brains and bodies alone;
Revised:  Cognizers can offload some of the functions they would otherwise have had to execute with their own brains and bodies alone;
Edit intent: clarity
Original:  it also extends cognizers' performance powers beyond those of brains and bodies alone . Language itself is a form of cognitive technology that allows cognizers to offload some of their brain functions onto the brains of other cognizers.
Revised:  it also extends cognizers' performance powers beyond those of brains and bodies alone . Language itself is a form of cognitive technology that allows cognizers to offload some of their cognitive functions onto the brains of other cognizers.
Edit intent: fluency
Original:  And now the web, with its distributed network of cognizers, digital databases and sofware agents, has become the Cognitive Commonsin which cognizers and cognitive technology can interact globally with a speed, scope and degree of interactivity that yield performance powers inconceivable with unaided individual cognition alone  .
Revised:  And now the web, with its network of cognizers, digital databases and sofware agents, has become the Cognitive Commonsin which cognizers and cognitive technology can interact globally with a speed, scope and degree of interactivity that yield performance powers inconceivable with unaided individual cognition alone .
Edit intent: clarity
Original:  And now the web, with its distributed network of cognizers, digital databases and sofware agents, has become the Cognitive Commonsin which cognizers and cognitive technology can interact globally with a speed, scope and degree of interactivity that yield performance powers inconceivable with unaided individual cognition alone  .
Revised:  And now the web, with its distributed network of cognizers, digital databases and software agents, all accessible anytime, anywhere, has become our 'Cognitive Commons,' in which distributed cognizers and cognitive technology can interact globally with a speed, scope and degree of interactivity that yield performance powers inconceivable with unaided individual cognition alone .
Edit intent: clarity
Original:  And now the web, with its distributed network of cognizers, digital databases and sofware agents, has become the Cognitive Commonsin which cognizers and cognitive technology can interact globally with a speed, scope and degree of interactivity that yield performance powers inconceivable with unaided individual cognition alone  .
Revised:  And now the web, with its distributed network of cognizers, digital databases and sofware agents, has become the Cognitive Commonsin which cognizers and cognitive technology can interoperate globally with a speed, scope and degree of interactivity that yield performance powers inconceivable with unaided individual cognition alone .
Edit intent: fluency
Original:  And now the web, with its distributed network of cognizers, digital databases and sofware agents, has become the Cognitive Commonsin which cognizers and cognitive technology can interact globally with a speed, scope and degree of interactivity that yield performance powers inconceivable with unaided individual cognition alone  .
Revised:  And now the web, with its distributed network of cognizers, digital databases and sofware agents, has become the Cognitive Commonsin which cognizers and cognitive technology can interact globally with a speed, scope and degree of interactivity inconceivable through local individual cognition alone .
Edit intent: clarity
Original: Tuffley and Steel (1997) proved that maximum likelihood and maximum parsimony methods in phylogenetics are equivalent  under a simple symmetric model of substitution for sequences of characters with no common mechanism.
Revised: Tuffley and Steel (1997) proved that Maximum Likelihood and Maximum Parsimony methods in phylogenetics are equivalent under a simple symmetric model of substitution for sequences of characters with no common mechanism.
Edit intent: fluency
Original: Tuffley and Steel (1997) proved that maximum likelihood and maximum parsimony methods in phylogenetics are equivalent  under a simple symmetric model of substitution for sequences of characters with no common mechanism.
Revised: Tuffley and Steel (1997) proved that maximum likelihood and maximum parsimony methods in phylogenetics are equivalent for sequences of characters under a simple symmetric model of substitution for sequences of characters with no common mechanism.
Edit intent: fluency
Original: Tuffley and Steel (1997) proved that maximum likelihood and maximum parsimony methods in phylogenetics are equivalent  under a simple symmetric model of substitution for sequences of characters with no common mechanism.
Revised: Tuffley and Steel (1997) proved that maximum likelihood and maximum parsimony methods in phylogenetics are equivalent under a simple symmetric model of substitution with no common mechanism.
Edit intent: clarity
Original:  We present a very short and elementary proof of their result and show that small changes to the model assumptions suffice to make the two methods inequivalent.
Revised:  We show that small changes to the model assumptions suffice to make the two methods inequivalent.
Edit intent: coherence
Original:  In particular, we analyze the case of small transition probabilities as well as the setting under a molecular clock .
Revised:  In particular, we analyze the case of small transition probabilities as well as the molecular clock assumption .
Edit intent: clarity
Original: We show that the Blokh-Zyablov ]  error exponent can be arbitrarily approached by concatenated block codes over general discrete-time memoryless channels  with linear encoding/decoding complexity in the block length .
Revised: We show that the Blokh-Zyablov ] error exponent can be arbitrarily approached by concatenated block codes over general discrete-time memoryless channels with linear encoding/decoding complexity .
Edit intent: clarity
Original:  The key result is an extension to Justesen 's general minimum distance decoding algorithm, which enables a low complexity integration of Guruswami-Indyk's outer code into Forney's and Blokh-Zyablov's concatenated coding schemes.
Revised:  The key result is a revision to Forney 's general minimum distance decoding algorithm, which enables a low complexity integration of Guruswami-Indyk's outer code into Forney's and Blokh-Zyablov's concatenated coding schemes.
Edit intent: clarity
Original:  The key result is an extension to Justesen 's general minimum distance decoding algorithm, which enables a low complexity integration of Guruswami-Indyk's outer code into Forney's and Blokh-Zyablov's concatenated coding schemes.
Revised:  The key result is an extension to Justesen 's general minimum distance decoding algorithm, which enables a low complexity integration of Guruswami-Indyk's outer codes into the concatenated coding schemes.
Edit intent: clarity
Original:  We develop a theory of this phenomenon on the example of a stochastic birth-death process which includes binary reproduction, immigration and death.
Revised:  We study this effect on the example of a stochastic birth-death process which includes binary reproduction, immigration and death.
Edit intent: clarity
Original:  We develop a theory of this phenomenon on the example of a stochastic birth-death process which includes binary reproduction, immigration and death.
Revised:  We develop a theory of this phenomenon on the example of a stochastic birth-death model which includes immigration, binary reproduction and death.
Edit intent: clarity
Original:  The unlimited population growth proceeds as an exponentially slow decay of a long-lived metastable probability distribution (MPD) of the population.
Revised:  The unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution (MPD) of the population.
Edit intent: clarity
Original:  An important signature of the MPD is a power-law tail  such that all the distribution moments, except the zeroth one, diverge  .
Revised:  Important signatures of the MPD is a power-law tail such that all the distribution moments, except the zeroth one, diverge .
Edit intent: clarity
Original:  An important signature of the MPD is a power-law tail  such that all the distribution moments, except the zeroth one, diverge  .
Revised:  An important signature of the MPD is a power-law tail ( such that all the distribution moments, except the zeroth one, diverge .
Edit intent: fluency
Original: We present a quantitative model for the biological evolution of species body masses within large groups of related species, e.g., terrestrial mammals, in which body mass M evolves according to branching ( speciating)multiplicative diffusion and an extinction probability that increases logarithmically with mass.
Revised: We present a quantitative model for the biological evolution of species body masses within large groups of related species, e.g., terrestrial mammals, in which body mass M evolves according to branching ( speciation), multiplicative diffusion, and an extinction probability that increases logarithmically with mass.
Edit intent: fluency
Original:  A standard pumping lemma in formal language theory is, however, of no use in order to prove that a given language is not regular with advice.
Revised:  A standard pumping lemma encounters difficulty in proving that a given language is not regular with advice.
Edit intent: clarity
Original:  A standard pumping lemma in formal language theory is, however, of no use in order to prove that a given language is not regular with advice.
Revised:  A standard pumping lemma in formal language theory is, however, of no use in order to prove that a given language is not regular in the presence of advice.
Edit intent: clarity
Original:  We develop its substitution, called a swapping lemma for regular languages, to prove the non-regularity of the language with advice.
Revised:  We develop its substitution, called a swapping lemma for regular languages, to demonstrate the non-regularity of the language with advice.
Edit intent: clarity