wanyu/IteraTeR_v2 huggingface dataset:
Original:  As an application , we improve the running time of an algorithm of Edmonds for embedding finite metrics into the Manhattan-metric plane , from O(n^2 \log^2 n)to O(n ^2 ).
Revised:  As an application , we improve the running time of an algorithm of Edmonds for embedding finite metrics into the Manhattan-metric plane , from O(n^2 \log^2 n)to O(n ).
Edit intent: fluency
Original:  Although two of these network reconstruction algorithms , Sessak-Monasson approximation and inversion of Thouless-Anderson-Palmer equations, were found to do a good job when applied to analyze the data from a simulated network of spiking neurons (Roudi Y, Tyrcha J and Hertz J 2009 Phys.
Revised:  Although performances of these network reconstruction algorithms , Sessak-Monasson approximation and inversion of Thouless-Anderson-Palmer equations, were found to do a good job when applied to analyze the data from a simulated network of spiking neurons (Roudi Y, Tyrcha J and Hertz J 2009 Phys.
Edit intent: clarity
Original:  Although two of these network reconstruction algorithms , Sessak-Monasson approximation and inversion of Thouless-Anderson-Palmer equations, were found to do a good job when applied to analyze the data from a simulated network of spiking neurons (Roudi Y, Tyrcha J and Hertz J 2009 Phys.
Revised:  Although two of these network reconstruction algorithms on the simulated network of spiking neurons (Roudi Y, Tyrcha J and Hertz J 2009 Phys.
Edit intent: clarity
Original:  In the retrieval phase favored when the network wants to memory one of stored patterns, all the reconstruction algorithms fail to extract interactions within a desired accuracy, while in the paramagnetic or high temperature spin glass phase , albeit unfavored during the retrieval dynamics, the algorithms work well to reconstruct the network itself.
Revised:  In the retrieval phase favored when the network wants to memory one of stored patterns, all the reconstruction algorithms fail to extract interactions within a desired accuracy, and the same failure occurs in the spin glass phase , albeit unfavored during the retrieval dynamics, the algorithms work well to reconstruct the network itself.
Edit intent: coherence
Original: In this study, an efficient method to immunize modular networks ( i.e. , networks with community structure) is proposed.
Revised: In this study, an efficient method to immunize modular networks ( i.e. , networks with community structure) is proposed.
Edit intent: fluency
Original:  We verify the effectiveness of the proposed method by applying it  model and real networks with modular structure.
Revised:  We verify the effectiveness of the proposed method by applying it to model and real networks with modular structure.
Edit intent: fluency
Original:  This new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modeling ), econometrics of financial bubbles and crashes .
Revised:  This new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distributions), microstructure of financial markets (order book modelling ), econometrics of financial bubbles and crashes .
Edit intent: fluency
Original:  We begin the presentation with the widely acknowledged "stylized facts " describing the distribution of the returns of financial assets: fat-tails , volatility clustering, etc.
Revised:  We begin the presentation with the widely acknowledged stylized facts which describe the returns of financial assets: fat-tails , volatility clustering, etc.
Edit intent: clarity
Original:  We begin the presentation with the widely acknowledged "stylized facts " describing the distribution of the returns of financial assets: fat-tails , volatility clustering, etc.
Revised:  We begin the presentation with the widely acknowledged "stylized facts " describing the distribution of the returns of financial assets- fat tails , volatility clustering, etc.
Edit intent: fluency
Original:  Then we show that some of these properties are directly linked to the way "time " is taken into account.
Revised:  Then we show that some of these properties are directly linked to the way time is taken into account.
Edit intent: fluency
Original:  We then turn to models of wealth distribution where an agent-based approach also prevails: kinetic theory models , and continue with game theory models and review the now classic minority games.
Revised:  We then turn to models of wealth distribution where an agent-based approach also prevails: kinetic theory models , and continue with game theory models by reviewing the now classic minority games.
Edit intent: coherence
Original: This paper resolves the main open question left by Gottlob, Lee, and Valiant (PODS 2009)[ GLV09 ], establishing tight worst-case bounds for the size of the result Q(D) of a conjunctive query Q to a database D given an arbitrary set of functional dependencies.
Revised: This paper extends the work of Gottlob, Lee, and Valiant (PODS 2009)[ GLV09 ], establishing tight worst-case bounds for the size of the result Q(D) of a conjunctive query Q to a database D given an arbitrary set of functional dependencies.
Edit intent: clarity
Original: This paper resolves the main open question left by Gottlob, Lee, and Valiant (PODS 2009)[ GLV09 ], establishing tight worst-case bounds for the size of the result Q(D) of a conjunctive query Q to a database D given an arbitrary set of functional dependencies.
Revised: This paper resolves the main open question left by Gottlob, Lee, and Valiant (PODS 2009)[ GLV ], establishing tight worst-case bounds for the size of the result Q(D) of a conjunctive query Q to a database D given an arbitrary set of functional dependencies.
Edit intent: clarity
Original: This paper resolves the main open question left by Gottlob, Lee, and Valiant (PODS 2009)[ GLV09 ], establishing tight worst-case bounds for the size of the result Q(D) of a conjunctive query Q to a database D given an arbitrary set of functional dependencies.
Revised: This paper resolves the main open question left by Gottlob, Lee, and Valiant (PODS 2009)[ GLV09 ], and considers worst-case bounds for the size of the result Q(D) of a conjunctive query Q to a database D given an arbitrary set of functional dependencies.
Edit intent: clarity
Original:  We show that the lower bound presented in [ GLV09 ] in which the variables of the query are " colored" so as to yield a coloring number C(Q) for each query Q is, in fact, also an upper bound.
Revised:  The bounds in [ GLV09 ] in which the variables of the query are " colored" so as to yield a coloring number C(Q) for each query Q is, in fact, also an upper bound.
Edit intent: clarity
Original:  We show that the lower bound presented in [ GLV09 ] in which the variables of the query are " colored" so as to yield a coloring number C(Q) for each query Q is, in fact, also an upper bound.
Revised:  We show that the lower bound presented in [ GLV09 ] are based on a "coloring " colored" so as to yield a coloring number C(Q) for each query Q is, in fact, also an upper bound.
Edit intent: clarity
Original:  To show this, we formalize the original intuition that each color used represents some possible entropy of that variable, and express the maximum possible size increase as a linear program that seeks to maximize how much more entropy is in the result of the query than the input.
Revised:  To show this, we formalize the original intuition that each color used represents some possible entropy of that variable, and bound the maximum possible size increase as a linear program that seeks to maximize how much more entropy is in the result of the query than the input.
Edit intent: clarity
Original:  To show this, we formalize the original intuition that each color used represents some possible entropy of that variable, and express the maximum possible size increase as a linear program that seeks to maximize how much more entropy is in the result of the query than the input.
Revised:  To show this, we formalize the original intuition that each color used represents some possible entropy of that variable, and express the maximum possible size increase via a linear program that seeks to maximize how much more entropy is in the result of the query than the input.
Edit intent: clarity
Original:  On the other hand  the species with fitness less than the critical disappear after a finite (random) time.
Revised:  On the other hand all the species with fitness less than the critical disappear after a finite (random) time.
Edit intent: clarity
Original: We model intermittently-connected mobile networks (ICMN) in terms of Markovian random temporal graphs.
Revised: Connectivity patterns in intermittently-connected mobile networks (ICMN) in terms of Markovian random temporal graphs.
Edit intent: clarity
Original:  The numerical results for the trigonometric signal, the square wave, and the Gaussian-modulated sinusoidal pulse  were demonstrated and discussed.
Revised:  The numerical results for the trigonometric signal, the Gaussian-modulated sinusoidal pulse were demonstrated and discussed.
Edit intent: clarity
Original:  And in switching of fractals from one base to another, the increment of fractal dimension is constant, which is 1.58, its quite surprising.
Edit intent: coherence
Original:  The bundle size distribution for filaments emerging from an ordered array yield a distribution that is peaked at a particular bundle size, which is qualitatively different from the random initial conditions motivated by the experiments.
Edit intent: coherence
Original:  We then use the fact that the maximum volume is \Omega(1{n}) in our design of the first efficient (1-\eps)-approximation algorithm for the following problem: Given an axis-parallel d-dimensional box R in \RR^d containing n points, compute the maximum-volume empty axis-parallel d-dimensional box contained in R.
Revised:  We then use the fact that the maximum volume is \Omega(1{n}) in our design of the first efficient (1-\eps)-approximation algorithm for the following problem: Given an axis-parallel d-dimensional box R in \RR^d containing n points, compute a maximum-volume empty axis-parallel d-dimensional box contained in R.
Edit intent: fluency
Original:  The running time of our algorithm is nearly linear in n, for small d  . No previous efficient exact or approximation algorithms were known for this problem for d \geq 4. Confirming our intuition and this status quo, recently Backer and Keil \mbox{ BK09b NP-hard in arbitrary high dimensions (i.e., when d is part of the input) \RR).
Revised:  The running time of our algorithm is nearly linear in n, for small d . No previous efficient exact or approximation algorithms were known for this problem for d \geq 4. As the problem has been recently shown to be NP-hard in arbitrary high dimensions (i.e., when d is part of the input) \RR).
Edit intent: coherence
Original:  An explicit formula for the dynamic risk indifference price is given as the solution of a one-dimensional linear BSDE with stochastic Lipschitz coefficient .
Revised:  An explicit formula for the dynamic risk indifference price is given as the solution of a one-dimensional BSDEs with stochastic Lipschitz coefficient .
Edit intent: clarity
Original:  An explicit formula for the dynamic risk indifference price is given as the solution of a one-dimensional linear BSDE with stochastic Lipschitz coefficient .
Revised:  An explicit formula for the dynamic risk indifference price is given as the solution of a one-dimensional linear BSDE with stochastic Lipschitz coefficients .
Edit intent: fluency
Original:  More generally, we make a structural conjecture about the Fourier spectra of boolean functions which, if true, would imply that the quantum and classical deterministic communication complexities of all XOR functions are asymptotically equivalent.
Revised:  More generally, we make a structural conjecture about the Fourier spectra of boolean functions which, if true, would imply that the quantum and classical exact communication complexities of all XOR functions are asymptotically equivalent.
Edit intent: clarity
Original:  We investigate the impact of epistasis  on adaptive evolution in a multiplicative NK model, by evolving a population of asexual haploid organisms with circular binary genomes of length N , where each locus interacts with K neighbors .
Revised:  We investigate the impact of epistasis on adaptive evolution by simulating the evolution of a population of asexual haploid organisms with circular binary genomes of length N , where each locus interacts with K neighbors .
Edit intent: clarity
Original:  We use a quantitative measure of epistasis and find that epistasis is a monotonically increasing function of K.
Revised:  We use a quantitative measure of the magnitude of epistatic interactions and find that epistasis is a monotonically increasing function of K.
Edit intent: clarity
Original:  We use a quantitative measure of epistasis and find that epistasis is a monotonically increasing function of K.
Revised:  We use a quantitative measure of epistasis and find that it is a monotonically increasing function of K.
Edit intent: fluency
Original:  Higher fitness is attained when more epistatic interactions are possible, with an optimum at an intermediate amount of epistasis.
Revised:  Higher fitness is attained in landscapes with an intermediate amount of epistasis.
Edit intent: clarity
Original: Evolutionary adaptation is a process that increases a population's "fit" to the world it inhabits, and is often likened to climbing a hill or peak.
Revised: Evolutionary adaptation is often likened to climbing a hill or peak.
Edit intent: clarity
Original:  While this process is simple for fitness landscapes where each mutation provides an advantage (or disadvantage) to the organism that is independentof the fitness effect of a mutation on a different locus , the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes.
Revised:  While this process is simple for fitness landscapes where mutations are independent , the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes.
Edit intent: clarity
Original:  We investigate the impact of epistasis and pleiotropy on adaptive evolution by simulating the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci.
Revised:  We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci.
Edit intent: clarity
Original:  We use a quantitative measure of the magnitude of epistatic interactions  and find that it is a monotonically increasing function of K.
Revised:  We use a quantitative measure of the magnitude of epistatic interactions and find that it is an increasing function of K.
Edit intent: clarity
Original:  When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected , whereas at low mutation rates epistatic interactions are avoided .
Revised:  When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected .
Edit intent: clarity
Original:  The highest fitness is attained in landscapes with an intermediate amount of ruggedness (K~5) because while both the height of the global peak and the average selection coefficient per beneficial mutation increase with K, interacting with too many other loci leads to untraversable landscapes .
Revised:  The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability .
Edit intent: clarity
Original:  More precisely, for a contamination probability p, the number of agents required by the probabilistic and explicit designs for identification of up to k infected members is bounded by m = O(k^2 log(n/k)/ ( 1-p) )  and m = O(k^2 log^2(n)/ ( 1-p) ^2), respectively.
Revised:  More precisely, for a contamination probability p, the number of agents required by the probabilistic and explicit designs for identification of up to k infected members is bounded by m = O(k^2 ( 1-p) ) and m = O(k^2 log^2(n)/ ( 1-p) ^2), respectively.
Edit intent: clarity
Original:  More precisely, for a contamination probability p, the number of agents required by the probabilistic and explicit designs for identification of up to k infected members is bounded by m = O(k^2 log(n/k)/ ( 1-p) )  and m = O(k^2 log^2(n)/ ( 1-p) ^2), respectively.
Revised:  More precisely, for a contamination probability p, the number of agents required by the probabilistic and explicit designs for identification of up to k infected members is bounded by m = O(k^2 log(n/k)/ ( 1-p) ) and m = O(k^2 ( 1-p) ^2), respectively.
Edit intent: coherence
Original:  More precisely, for a contamination probability p, the number of agents required by the probabilistic and explicit designs for identification of up to k infected members is bounded by m = O(k^2 log(n/k)/ ( 1-p) )  and m = O(k^2 log^2(n)/ ( 1-p) ^2), respectively.
Revised:  More precisely, for a contamination probability p, the number of agents required by the probabilistic and explicit designs for identification of up to k infected members is bounded by m = O(k^2 log(n/k)/ ( 1-p) ) and m = O(k^2 log^2(n)/ ( log n)^2 /p ^2), respectively.
Edit intent: clarity
Original:  Two eminent examples of web-fraudulent activities are phishing and typosquatting.
Revised:  Two eminent examples of webfraudulent activities are phishing and typosquatting.
Edit intent: fluency
Original:  We validate our methodology with large amounts of data collected from the Internet.
Revised:  We validate our methodology with different data sets collected from the Internet.
Edit intent: clarity
Original:  Two eminent examples of webfraudulent activities are phishing and typosquatting.
Revised:  Two well-known examples of fraudulent activities on the web are phishing and typosquatting.
Edit intent: clarity
Original:  Their effects range from relatively benign (such as unwanted or unexpected ads) to downright sinister (especially, when typosquatting is combined with phishing).
Revised:  Their effects range from relatively benign (such as unwanted ads) to downright sinister (especially, when typosquatting is combined with phishing).
Edit intent: clarity
Original:  To achieve this , we conduct the first comprehensive study of SSL certificates for legitimate and popular domains , as opposed to those used for web-fraud . Drawing from extensive measurements, we build a classifier that detects  malicious domains with high accuracy .
Revised:  To this end , we conduct the first comprehensive study of SSL certificates for legitimate and popular domains , as opposed to those used for web-fraud . Drawing from extensive measurements, we build a classifier that detects malicious domains with high accuracy .
Edit intent: coherence
Original:  To achieve this , we conduct the first comprehensive study of SSL certificates for legitimate and popular domains , as opposed to those used for web-fraud . Drawing from extensive measurements, we build a classifier that detects  malicious domains with high accuracy .
Revised:  To achieve this , we conduct the first comprehensive study of SSL certificates . We analyze certificates of legitimate and popular domains , as opposed to those used for web-fraud . Drawing from extensive measurements, we build a classifier that detects malicious domains with high accuracy .
Edit intent: coherence
Original:  To achieve this , we conduct the first comprehensive study of SSL certificates for legitimate and popular domains , as opposed to those used for web-fraud . Drawing from extensive measurements, we build a classifier that detects  malicious domains with high accuracy .
Revised:  To achieve this , we conduct the first comprehensive study of SSL certificates for legitimate and popular domains and those used by fraudulent ones . Drawing from extensive measurements, we build a classifier that detects malicious domains with high accuracy .
Edit intent: clarity
Original:  To achieve this , we conduct the first comprehensive study of SSL certificates for legitimate and popular domains , as opposed to those used for web-fraud . Drawing from extensive measurements, we build a classifier that detects  malicious domains with high accuracy .
Revised:  To achieve this , we conduct the first comprehensive study of SSL certificates for legitimate and popular domains , as opposed to those used for web-fraud . Drawing from extensive measurements, we build a classifier that detects such malicious domains with high accuracy .
Edit intent: clarity
Original: The famous \v{Cern\'y conjecture claims thateach n-state synchronizing automaton A has a reset word of length at most (n-1)^2.
Revised: ern\'y conjecture claims thateach n-state synchronizing automaton A has a reset word of length at most (n-1)^2.
Edit intent: clarity
Original:  The best upper bound for }  the minimum length of reset word for \mathrsfs{A \sws \san  .
Revised:  The best upper bound for } the minimum length of \sws \san .
Edit intent: clarity
Original: Let \mathrsfs{A Cern\'y conjecture claims that \mathrsfs{A\san  a \sw of length at most (n-1)^2.
Revised: Let \mathrsfs{A Cern\'y conjecture states that each\san a \sw of length at most (n-1)^2.
Edit intent: clarity
Original:  The best upper bound for the minimum length of%DIFDELCMD < \sws %%% for \mathrsfs{A of n.
Revised:  %DIFDELCMD < \sws %%% for \mathrsfs{A of n.
Edit intent: clarity
Original:  The Extension conjecture claims that each proper subset of states can be extended to a larger subset using anexpanding word of length at most n. Cern\'y conjecture easily follows from this one statement.
Revised:  The Extension expanding word of length at most n. Cern\'y conjecture easily follows from this one statement.
Edit intent: clarity
Original:  The Extension conjecture claims that each proper subset of states can be extended to a larger subset using anexpanding word of length at most n. Cern\'y conjecture easily follows from this one statement.
Revised:  The Extension conjecture claims that each proper subset of states can be extended to a larger subset using an word of length at most n. Cern\'y conjecture easily follows from this one statement.
Edit intent: clarity
Original:  We also consider the related conjectures and disprove one of them, introduced in the paper \mbox{ \cite{CARPI1 }\hspace{0pt} of Alessandro and Carpi}  .
Revised:  We also consider the }\hspace{0pt} of Alessandro and Carpi} .
Edit intent: coherence
Original:  Is thus proved (if I am not mistaken yet) that the problem 3Sat is fully resolved in polynomial time and therefore that it is in P, by the work of Cook and Levin, and can transform a SAT problem in a 3Sat in polynomial time (ref. Karp), it follows that P = NP. Open Source program is available at URL
Revised:  Is thus proved that the problem 3Sat is fully resolved in polynomial time and therefore that it is in P, by the work of Cook and Levin, and can transform a SAT problem in a 3Sat in polynomial time (ref. Karp), it follows that P = NP. Open Source program is available at URL
Edit intent: coherence
Original: Confidence is an essential ingredient of success in a wide range of domains including job performance , mental health,  sports, business, and combat.
Revised: Confidence is an essential ingredient of success in a wide range of domains ranging from job performance and mental health, sports, business, and combat.
Edit intent: clarity
Original: Confidence is an essential ingredient of success in a wide range of domains including job performance , mental health,  sports, business, and combat.
Revised: Confidence is an essential ingredient of success in a wide range of domains including job performance , mental health, to sports, business, and combat.
Edit intent: fluency