wanyu/IteraTeR_v2 huggingface dataset:
Original:  We predict that any land mass (such as part of north China  ) which then lay about 20 degrees or more north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.
Revised:  We predict that any land mass (such as part of north China ) which then lay about 20 degrees or more north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if induced by such a radiation event.
Edit intent: clarity
Original: The concept of evolutionary development of structures constituted a real revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system.
Revised: The concept of evolutionary development of structures constituted a real revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system.
Edit intent: fluency
Original: The tuning function that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained.
Revised: The sigmoidal tuning curve that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained.
Edit intent: clarity
Original:  The optimal tuning function is found to have a discrete structure that results in a quantization of the input signal.
Revised:  The optimal tuning curve is found to have a discrete structure that results in a quantization of the input signal.
Edit intent: clarity
Original:  The number of quantization levels undergoes a hierarchy of phase transitions as the length of the decoding window is varied.
Revised:  The number of quantization levels undergoes a hierarchy of phase transitions as the length of the coding window is varied.
Edit intent: clarity
Original:  The concept of %DIFDELCMD < {\em %%% codivergence , the divergence of one lineage (species or gene) as a result of the divergence of another, has fascinated researchers for a long time.
Revised:  The concept of %DIFDELCMD < {\em %%% codivergence , the divergence of one lineage (species or gene) as a result of the divergence of another, has fascinated researchers for a long time.
Edit intent: fluency
Original:  In this paper we focus on its underlying algebraic and polyhedral geometric structures . Specifically, we define a notion of the spaces of cophylogenetic trees .
Revised:  In this paper we focus on its underlying algebraic and polyhedral geometric structures .
Edit intent: coherence
Original: Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytic tractability and statistical flexibility.
Revised: Affine term structure models have gained significant attention in the finance literature, which is due to their analytic tractability and statistical flexibility.
Edit intent: clarity
Original: Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytic tractability and statistical flexibility.
Revised: Affine term structure models have gained a lot of attention in the finance literature, mainly due to their analytic tractability and statistical flexibility.
Edit intent: coherence
Original: Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytic tractability and statistical flexibility.
Revised: Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytical tractability and statistical flexibility.
Edit intent: fluency
Original:  Pricing and estimation techniques are eventually mentioned, showing how the analytic tractability of affine models can be exploited for practical purposes.
Revised:  Methods for securities pricing and for parameter estimation are also discussed, demonstrating how the analytical tractability of affine models can be exploited for practical purposes.
Edit intent: clarity
Original:  SWIM shows both experimentally and theoretically the presence of the power law and exponential decay dichotomy of inter-contact times , and, most importantly, our experiments show that it can predict very accurately the performance of forwarding protocols.
Revised:  SWIM shows experimentally and theoretically the presence of the power law and exponential decay dichotomy of inter-contact times , and, most importantly, our experiments show that it can predict very accurately the performance of forwarding protocols.
Edit intent: coherence
Original:  SWIM shows both experimentally and theoretically the presence of the power law and exponential decay dichotomy of inter-contact times , and, most importantly, our experiments show that it can predict very accurately the performance of forwarding protocols.
Revised:  SWIM shows both experimentally and theoretically the presence of the power law and exponential decay dichotomy of inter-contact time , and, most importantly, our experiments show that it can predict very accurately the performance of forwarding protocols.
Edit intent: fluency
Original:  The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power ), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification.
Revised:  The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power ), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification.
Edit intent: fluency
Original:  We thereby answer an open problem first mentioned by Dom, Guo, H\"uffner and Niedermeier \mbox{ DGH05 .
Revised:  We thereby answer an open problem first mentioned by Dom, Guo, Huffner and Niedermeier (2005) .
Edit intent: clarity
Original:  This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular  operations to the original matrix row by row (or column by column) .
Revised:  This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular operations to the original matrix .
Edit intent: coherence
Original: Scale-free networks are ultra-small worlds.
Revised: Random scale-free networks are ultrasmall worlds.
Edit intent: clarity
Original:  The average length of  shortest paths in networks of size N scales as \ln \ln N . Here we show that these ultra-small worlds can be navigated in ultra-short time.
Revised:  The average length of the shortest paths in networks of size N scales as \ln \ln N . Here we show that these ultra-small worlds can be navigated in ultra-short time.
Edit intent: fluency
Original:  The average length of  shortest paths in networks of size N scales as \ln \ln N . Here we show that these ultra-small worlds can be navigated in ultra-short time.
Revised:  The average length of shortest paths in networks of size N scales as lnlnN . Here we show that these ultra-small worlds can be navigated in ultra-short time.
Edit intent: clarity
Original:  The average length of  shortest paths in networks of size N scales as \ln \ln N . Here we show that these ultra-small worlds can be navigated in ultra-short time.
Revised:  The average length of shortest paths in networks of size N scales as \ln \ln N . Here we show that these ultrasmall worlds can be navigated in ultra-short time.
Edit intent: fluency
Original:  The average length of  shortest paths in networks of size N scales as \ln \ln N . Here we show that these ultra-small worlds can be navigated in ultra-short time.
Revised:  The average length of shortest paths in networks of size N scales as \ln \ln N . Here we show that these ultra-small worlds can be navigated in ultrashort time.
Edit intent: fluency
Original:  Greedy routing on scale-free networks embedded in metric spaces finds paths with the average length scaling also as \ln \ln N . Greedy routing uses only local information to navigate a network.
Revised:  Greedy routing on scale-free networks embedded in metric spaces finds paths with the average length scaling also as lnlnN . Greedy routing uses only local information to navigate a network.
Edit intent: coherence
Original:  Nevertheless, it finds asymptotically  shortest paths,  direct computation of which requires global topology knowledge.
Revised:  Nevertheless, it finds asymptotically the shortest paths, direct computation of which requires global topology knowledge.
Edit intent: fluency
Original:  Nevertheless, it finds asymptotically  shortest paths,  direct computation of which requires global topology knowledge.
Revised:  Nevertheless, it finds asymptotically shortest paths, a direct computation of which requires global topology knowledge.
Edit intent: fluency
Original:  Our findings imply that the peculiar structure of complex networks insures that the lack of global topological awareness has asymptotically no impact on the length of communication paths.
Revised:  Our findings imply that the peculiar structure of complex networks ensures that the lack of global topological awareness has asymptotically no impact on the length of communication paths.
Edit intent: fluency
Original:  Together, G,T and S are said to form a network ( Eulerian network if all nodes in N\T have even degrees ).
Revised:  Together, G,T and S form a network ( Eulerian network if all nodes in N\T have even degrees ).
Edit intent: clarity
Original:  Together, G,T and S are said to form a network ( Eulerian network if all nodes in N\T have even degrees ).
Revised:  Together, G,T and S are said to form a network . A network is an Eulerian network if all nodes in N\T have even degrees ).
Edit intent: clarity
Original:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S,  D is infinite , while in that class, D can be 1,2 or 4.
Revised:  Fractionality of this path packing problem by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S, D is infinite , while in that class, D can be 1,2 or 4.
Edit intent: clarity
Original:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S,  D is infinite , while in that class, D can be 1,2 or 4.
Revised:  Fractionality of this path packing problem , first defined by A. Karzanov as the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S, D is infinite , while in that class, D can be 1,2 or 4.
Edit intent: coherence
Original:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S,  D is infinite , while in that class, D can be 1,2 or 4.
Revised:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S, D is infinite , while in that class, D can be 1,2 or 4.
Edit intent: clarity
Original:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S,  D is infinite , while in that class, D can be 1,2 or 4.
Revised:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, D is infinite , while in that class, D can be 1,2 or 4.
Edit intent: clarity
Original:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S,  D is infinite , while in that class, D can be 1,2 or 4.
Revised:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S, outside which D is infinite , while in that class, D can be 1,2 or 4.
Edit intent: clarity
Original:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S,  D is infinite , while in that class, D can be 1,2 or 4.
Revised:  Fractionality of this path packing problem , first defined by A. Karzanov , is the smallest natural number D so that there exists a solution to the fractional path packing problem that becomes integer-valued when multiplied by D. A. Karzanov proved that for Eulerian networks not having specific structure to T and S, D is infinite and proved that whithin this class D can be 1,2 or 4.
Edit intent: coherence
Original:  He conjectured that in this case, D should be 1 or 2 only.
Revised:  He conjectured that D should be 1 or 2 only.
Edit intent: clarity
Original:  The model is developed using Feynman's action--amplitude (partition function) formalism.
Revised:  The model is developed using Feynman's action-amplitude (partition function) formalism.
Edit intent: fluency
Original: This work is a proceeding of the CANUM 2008 conference.
Edit intent: coherence
Original:  This has applications in the theory of Adaptive Dynamics.
Revised:  This has applications to the theory of Adaptive Dynamics.
Edit intent: fluency
Original: Minority game is generalized to more than one market  .
Revised: Generalization of the minority game to more than one market .
Edit intent: clarity
Original: Minority game is generalized to more than one market  .
Revised: Minority game is generalized to more than one market is considered .
Edit intent: clarity
Original:  Bouchaud and Mezard have proposed an interesting model of economy [Bouchaud and Mezard (2000)] based on trade and investments of agents.
Revised:  Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and Mezard (2000)] based on trade and investments of agents.
Edit intent: fluency
Original:  Bouchaud and Mezard have proposed an interesting model of economy [Bouchaud and Mezard (2000)] based on trade and investments of agents.
Revised:  Bouchaud and Mezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents.
Edit intent: fluency
Original:  An ideal quantum addition circuit shows that the depth lower bound is \Omega(\log n%DIFDELCMD < }%%% )where n is the length of numbers to be added, in qubits.
Revised:  An ideal quantum addition circuit shows that the depth lower bound is \Omega(\log %DIFDELCMD < }%%% )where n is the length of numbers to be added, in qubits.
Edit intent: fluency
Original:  However, we find that if the allowable quantum interaction distance is only one (only neighboring qubits can interact), then the quantum depth lower bound of the quantum addition is no longer \Omega (\log {n}) .
Revised:  However, we find that if the allowable quantum interaction distance is only one (only neighboring qubits can interact), then the quantum depth lower bound of the quantum adder is no longer \Omega (\log {n}) .
Edit intent: clarity
Original:  However, we find that if the allowable quantum interaction distance is only one (only neighboring qubits can interact), then the quantum depth lower bound of the quantum addition is no longer \Omega (\log {n}) .
Revised:  However, we find that if the allowable quantum interaction distance is only one (only neighboring qubits can interact), then the quantum depth lower bound of the quantum addition is no longer the O (\log {n}) .
Edit intent: clarity
Original:  For the 1D, 2D, 3D and in general kD structures, the quantum depth lower bounds are \Omega(n), \Omega(n), \Omega(\sqrt[3 ]{n}) , and \Omega(\sqrt[k n%DIFDELCMD < }%%% ), respectively .
Revised:  For the 1D, 2D, 3D and in general kD structures, the quantum depth lower bounds are \Omega(n), \Omega(n), \Omega(\sqrt[3 ]{n}) , and \Omega(\sqrt[k %DIFDELCMD < }%%% ), respectively .
Edit intent: clarity
Original: We investigate the theoretical limits of the effect of the quantum interaction distance on the fastest quantum addition circuit by embedding the circuit graph into the physical interaction graph .
Revised: We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis .
Edit intent: clarity
Original:  We study a logical mapping of qubits and gates of any O(\log  n)-depth quantum adder circuit into the NTC architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates.
Revised:  We study a logical mapping of qubits and gates of any \Omega n)-depth quantum adder circuit into the NTC architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates.
Edit intent: clarity
Original:  Unfortunately, on the k-dimensional NTC architecture,  the depth of the quantum adder is no longer the O(\log { n }  ) that is possible on an ideal machine, but \Omega(\sqrt[k n  ).
Revised:  Unfortunately, on the k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the O(\log { n } ) that is possible on an ideal machine, but \Omega(\sqrt[k n ).
Edit intent: coherence
Original:  We study a logical mapping of qubits and gates of any \Omega (log n)-depth quantum adder circuit for two n-qubit registers onto the NTC architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates.
Revised:  We study a logical mapping of qubits and gates of any (log n)-depth quantum adder circuit for two n-qubit registers onto the NTC architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates.
Edit intent: clarity
Original:  We study a logical mapping of qubits and gates of any \Omega (log n)-depth quantum adder circuit for two n-qubit registers onto the NTC architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates.
Revised:  We study a logical mapping of qubits and gates of any \Omega (log n)-depth quantum adder circuit for two n-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates.
Edit intent: clarity
Original:  Unfortunately, on the  k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n }  ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Revised:  Unfortunately, on the chosen k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n } ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Edit intent: clarity
Original:  Unfortunately, on the  k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n }  ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Revised:  Unfortunately, on the k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer \Omega%DIFDELCMD < }%%% (log n } ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Edit intent: coherence
Original:  Unfortunately, on the  k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n }  ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Revised:  Unfortunately, on the k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the %DIFDELCMD < }%%% (log n } ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Edit intent: coherence
Original:  Unfortunately, on the  k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n }  ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Revised:  Unfortunately, on the k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n n} ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Edit intent: coherence
Original:  Unfortunately, on the  k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n }  ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Revised:  Unfortunately, on the k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n } n ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Edit intent: fluency
Original:  Unfortunately, on the  k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n }  ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Revised:  Unfortunately, on the k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n } ) \Omega%DIFDELCMD < }%%% (k\surd n) .
Edit intent: coherence
Original:  Unfortunately, on the  k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n }  ) that is possible on an ideal machine, but \Omega%DIFDELCMD < }%%% (k\surd n) .
Revised:  Unfortunately, on the k-dimensional NTC architecture, we prove that the depth of the quantum adder is no longer the \Omega%DIFDELCMD < }%%% (log n } ) that is possible on an ideal machine, but %DIFDELCMD < }%%% (k\surd n) .
Edit intent: coherence