wanyu/IteraTeR_v2 huggingface dataset:
Original:  We exploit the mathematical equivalence between HMMs for TF binding and the ``inverse'' statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low.
Revised:  We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low.
Edit intent: fluency
Original:  We address the problem of optimal relay location and power allocations at source and relay, so as to maximize the multicast rate  to all destinations , which in a generic sense boils down to a network planning problem .
Revised:  We address the problem of optimal relay positioning and power allocations at source and relay, so as to maximize the multicast rate to all destinations , which in a generic sense boils down to a network planning problem .
Edit intent: clarity
Original:  We address the problem of optimal relay location and power allocations at source and relay, so as to maximize the multicast rate  to all destinations , which in a generic sense boils down to a network planning problem .
Revised:  We address the problem of optimal relay location and power allocations at source and relay, to maximize the multicast rate to all destinations , which in a generic sense boils down to a network planning problem .
Edit intent: coherence
Original:  We address the problem of optimal relay location and power allocations at source and relay, so as to maximize the multicast rate  to all destinations , which in a generic sense boils down to a network planning problem .
Revised:  We address the problem of optimal relay location and power allocations at source and relay, so as to maximize the multicast rate from source to all destinations , which in a generic sense boils down to a network planning problem .
Edit intent: clarity
Original:  We address the problem of optimal relay location and power allocations at source and relay, so as to maximize the multicast rate  to all destinations , which in a generic sense boils down to a network planning problem .
Revised:  We address the problem of optimal relay location and power allocations at source and relay, so as to maximize the multicast rate to all destinations . To solve such a network planning problem .
Edit intent: coherence
Original:  We propose an  efficient algorithm to compute all hyperarcs , and prove that their total number is polynomially upper-bounded.
Revised:  We propose an easy and efficient algorithm to compute all hyperarcs , and prove that their total number is polynomially upper-bounded.
Edit intent: clarity
Original:  Ultimately, relying on techniques of geometric programming and p-th norm surrogation , we derive a convex approximation of the problem .
Revised:  Ultimately, availing on the techniques of geometric programming and p-th norm surrogation , we derive a convex approximation of the problem .
Edit intent: clarity
Original:  Ultimately, relying on techniques of geometric programming and p-th norm surrogation , we derive a convex approximation of the problem .
Revised:  Ultimately, relying on techniques of geometric programming and p-norm surrogate approximation , we derive a convex approximation of the problem .
Edit intent: clarity
Original:  Ultimately, relying on techniques of geometric programming and p-th norm surrogation , we derive a convex approximation of the problem .
Revised:  Ultimately, relying on techniques of geometric programming and p-th norm surrogation , we derive a good convex approximation .
Edit intent: clarity
Original:  We provide a detailed characterization of the problem for collinearly located destinations, and then give a generalization for arbitrarily located destinations and multiple sessions .
Revised:  We provide a detailed characterization of the problem for collinearly located destinations, and then give a generalization for arbitrarily located destinations .
Edit intent: clarity
Original:  Finally, we show that optimizing the relay location yields strong gains of the order of hundred percent in rate .
Revised:  Finally, we show strong gains for the optimal relay positioning compared to seemingly interesting positions .
Edit intent: clarity
Original: An (r,w;d) cover-free family (CFF) is a family of subsets of a finite set such that  intersection of any r members of the family contains at least d points that are not in the union of w other members.
Revised: An (r,w;d) cover-free family (CFF) is a family of subsets of a finite set such that the intersection of any r members of the family contains at least d points that are not in the union of w other members.
Edit intent: fluency
Original: An (r,w;d) cover-free family (CFF) is a family of subsets of a finite set such that  intersection of any r members of the family contains at least d points that are not in the union of w other members.
Revised: An (r,w;d) cover-free family (CFF) is a family of subsets of a finite set such that intersection of any r members of the family contains at least d points that are not in the union of any other w members.
Edit intent: fluency
Original:  The minimum number of points such that there exists an (r,w;d)-CFF with t blocks is denoted by N((r,w;d),t).
Revised:  The minimum number of elements for which there exists an (r,w;d)-CFF with t blocks is denoted by N((r,w;d),t).
Edit intent: clarity
Original:  In this paper  we show that the value of N((r,w;d),t) is equal to  d-biclique covering number of the  graph I_t(r,w) whose vertices are the w- and r-subsets of a t-element set where two vertices are adjacent if their intersection is empty.
Revised:  In this paper , we show that the value of N((r,w;d),t) is equal to d-biclique covering number of the graph I_t(r,w) whose vertices are the w- and r-subsets of a t-element set where two vertices are adjacent if their intersection is empty.
Edit intent: fluency
Original:  In this paper  we show that the value of N((r,w;d),t) is equal to  d-biclique covering number of the  graph I_t(r,w) whose vertices are the w- and r-subsets of a t-element set where two vertices are adjacent if their intersection is empty.
Revised:  In this paper we show that the value of N((r,w;d),t) is equal to the d-biclique covering number of the graph I_t(r,w) whose vertices are the w- and r-subsets of a t-element set where two vertices are adjacent if their intersection is empty.
Edit intent: fluency
Original:  In this paper  we show that the value of N((r,w;d),t) is equal to  d-biclique covering number of the  graph I_t(r,w) whose vertices are the w- and r-subsets of a t-element set where two vertices are adjacent if their intersection is empty.
Revised:  In this paper we show that the value of N((r,w;d),t) is equal to d-biclique covering number of the graph I_t(r,w) whose vertices are all w- and r-subsets of a t-element set where two vertices are adjacent if their intersection is empty.
Edit intent: clarity
Original:  In this paper  we show that the value of N((r,w;d),t) is equal to  d-biclique covering number of the  graph I_t(r,w) whose vertices are the w- and r-subsets of a t-element set where two vertices are adjacent if their intersection is empty.
Revised:  In this paper we show that the value of N((r,w;d),t) is equal to d-biclique covering number of the graph I_t(r,w) whose vertices are the w- and r-subsets of a t-element set , where a w-subset is adjacent to an r-subset if their intersection is empty.
Edit intent: clarity
Original:  We introduce some bounds for N((r,w;d),t).
Revised:  Next, we introduce some new bounds for N((r,w;d),t).
Edit intent: clarity
Original:   \choose  {\choose  {\choose } \over  {\log r}\log t. } Also, we determine the exact value of N((r,w;d),t) for some values of d.
Revised:  \choose {\choose {\choose } \over \log r {\log r}\log t. } Also, we determine the exact value of N((r,w;d),t) for some values of d.
Edit intent: coherence
Original:  Moreover , we show that there is a tight relationship between N(( r,r ;d), t)and the d-biclique covering number of the Kneser graph%DIFDELCMD < {\rm %%% KG (t,r) .
Revised:  Finally , we show that there is a tight relationship between N(( r,r ;d), t)and the d-biclique covering number of the Kneser graph%DIFDELCMD < {\rm %%% KG (t,r) .
Edit intent: fluency
Original:  Moreover , we show that there is a tight relationship between N(( r,r ;d), t)and the d-biclique covering number of the Kneser graph%DIFDELCMD < {\rm %%% KG (t,r) .
Revised:  Moreover , we show that N(( r,r ;d), t)and the d-biclique covering number of the Kneser graph%DIFDELCMD < {\rm %%% KG (t,r) .
Edit intent: clarity
Original:  Moreover , we show that there is a tight relationship between N(( r,r ;d), t)and the d-biclique covering number of the Kneser graph%DIFDELCMD < {\rm %%% KG (t,r) .
Revised:  Moreover , we show that there is a tight relationship between N(( r,r ;d), %DIFDELCMD < {\rm %%% KG (t,r) .
Edit intent: coherence
Original:  Moreover , we show that there is a tight relationship between N(( r,r ;d), t)and the d-biclique covering number of the Kneser graph%DIFDELCMD < {\rm %%% KG (t,r) .
Revised:  Moreover , we show that there is a tight relationship between N(( r,r ;d), t)and the d-biclique covering number of the Kneser graph%DIFDELCMD < {\rm %%% (t,r) .
Edit intent: clarity
Original:  This seems to be a natural step forward in the study of BSDEs.
Edit intent: coherence
Original:  We derive explicit solutions to the corresponding time-delayed BSDEs and we investigate in detail some properties of the solutions.
Revised:  We derive explicit solutions to the corresponding time-delayed BSDEs and we investigate in detail main properties of the solutions.
Edit intent: clarity
Original:  A motivation for dealing with generators of a moving average type in the context of dynamic pricing and recursive utilities is given.
Revised:  A motivation for dealing with generators of a moving average type is given.
Edit intent: clarity
Original: This paper includes supplementary material for the paper A.N. Gorban, A. Zinovyev, Principal manifolds and graphs in practice: from molecular biology to dynamical systems, International Journal of Neural Systems 20 (3) (2010), 219-232.
Revised:  A.N. Gorban, A. Zinovyev, Principal manifolds and graphs in practice: from molecular biology to dynamical systems, International Journal of Neural Systems 20 (3) (2010), 219-232.
Edit intent: coherence
Original: NE . We present details of the analysis of the nonlinear quality of life index for 162 countries.
Revised: NE We present details of the analysis of the nonlinear quality of life index for 162 countries.
Edit intent: fluency
Original:  We analyze the structure of the data in order to find the optimal and independent on any expert's opinion way to map several numerical indicators from a multidimensional space onto the one-dimensional space of the quality of life.
Revised:  We analyze the structure of the data in order to find the optimal and independent on expert's opinion way to map several numerical indicators from a multidimensional space onto the one-dimensional space of the quality of life.
Edit intent: clarity
Original:  The order along this principal curve gives us the rating of countries.
Revised:  The order along this principal curve gives us the ranking of countries.
Edit intent: clarity
Original:  In this paper, we study a particular natural class of linear-invariant properties , called matroid freeness properties.
Revised:  In this paper, we study the fundamental class of linear-invariant properties , called matroid freeness properties.
Edit intent: clarity
Original:  In this paper, we study a particular natural class of linear-invariant properties , called matroid freeness properties.
Revised:  In this paper, we study a particular natural class of linear-invariant properties called matroid freeness properties.
Edit intent: fluency
Original:  These properties have all been conjectured to be testable , and a recent sequence of works have established testability for increasingly larger subclasses.
Revised:  These properties have been conjectured to be testable , and a recent sequence of works have established testability for increasingly larger subclasses.
Edit intent: clarity
Original:  These properties have all been conjectured to be testable , and a recent sequence of works have established testability for increasingly larger subclasses.
Revised:  These properties have all been conjectured to be testable , and a recent sequence of works has established testability for increasingly larger subclasses.
Edit intent: fluency
Original:  One question left open, however, is whether the infinitely many syntactically different properties recently shown testable in fact correspond to new, semantically distinct properties .
Revised:  One question left open, however, is whether the infinitely many syntactically different properties recently shown testable in fact correspond to new, semantically distinct ones .
Edit intent: clarity
Original:  This is a crucial issue since it has also been shown that there exist subclasses of matroid freeness properties for which an infinite set of syntactically different representations collapse into one of a small, finite set of properties, all previously known to be testable.
Revised:  This is a crucial issue since it has also been shown that there exist subclasses of these properties for which an infinite set of syntactically different representations collapse into one of a small, finite set of properties, all previously known to be testable.
Edit intent: clarity
Original:  We shed light on this problem by developing a method for determining the relation between two matroid freeness properties P and Q. Furthermore, we show that there is a natural subclass of matroid freeness properties such that for any two properties P and Q from this subclass, a strong dichotomy must hold: either P is contained in Q or the two properties are "well separated  " from one another.
Revised:  We shed light on this problem by developing a method for determining the relation between two matroid freeness properties P and Q. Furthermore, we show that there is a natural subclass of matroid freeness properties such that for any two properties P and Q from this subclass, a strong dichotomy must hold: either P is contained in Q or the two properties are "well separated . " from one another.
Edit intent: fluency
Original:  We shed light on this problem by developing a method for determining the relation between two matroid freeness properties P and Q. Furthermore, we show that there is a natural subclass of matroid freeness properties such that for any two properties P and Q from this subclass, a strong dichotomy must hold: either P is contained in Q or the two properties are "well separated  " from one another.
Revised:  We shed light on this problem by developing a method for determining the relation between two matroid freeness properties P and Q. Furthermore, we show that there is a natural subclass of matroid freeness properties such that for any two properties P and Q from this subclass, a strong dichotomy must hold: either P is contained in Q or the two properties are "well separated " 
Edit intent: clarity
Original:  Our key technical tool is an apparently new notion of maps between linear matroids, which we call labeled matroid homomorphisms, that might be of independent interest.
Revised:  Our key technical tool is an apparently new notion of maps between linear matroids, called matroid homomorphisms, that might be of independent interest.
Edit intent: coherence
Original: In this paper, we thoroughly investigate the kinetic behavior of the general modifier mechanism of Botts and Morales at both equilibrium steady state assuming equilibrium substrate- and modifier-binding steps and non-equilibrium steady state (NESS) without assuming equilibrium binding steps.
Revised: In this paper, we perform a complete analysis of the kinetic behavior of the general modifier mechanism of Botts and Morales at both equilibrium steady state assuming equilibrium substrate- and modifier-binding steps and non-equilibrium steady state (NESS) without assuming equilibrium binding steps.
Edit intent: clarity
Original: In this paper, we thoroughly investigate the kinetic behavior of the general modifier mechanism of Botts and Morales at both equilibrium steady state assuming equilibrium substrate- and modifier-binding steps and non-equilibrium steady state (NESS) without assuming equilibrium binding steps.
Revised: In this paper, we thoroughly investigate the kinetic behavior of the general modifier mechanism of Botts and Morales in both equilibrium steady state assuming equilibrium substrate- and modifier-binding steps and non-equilibrium steady state (NESS) without assuming equilibrium binding steps.
Edit intent: clarity
Original: In this paper, we thoroughly investigate the kinetic behavior of the general modifier mechanism of Botts and Morales at both equilibrium steady state assuming equilibrium substrate- and modifier-binding steps and non-equilibrium steady state (NESS) without assuming equilibrium binding steps.
Revised: In this paper, we thoroughly investigate the kinetic behavior of the general modifier mechanism of Botts and Morales at both equilibrium steady states and non-equilibrium steady state (NESS) without assuming equilibrium binding steps.
Edit intent: clarity
Original: In this paper, we thoroughly investigate the kinetic behavior of the general modifier mechanism of Botts and Morales at both equilibrium steady state assuming equilibrium substrate- and modifier-binding steps and non-equilibrium steady state (NESS) without assuming equilibrium binding steps.
Revised: In this paper, we thoroughly investigate the kinetic behavior of the general modifier mechanism of Botts and Morales at both equilibrium steady state assuming equilibrium substrate- and modifier-binding steps and non-equilibrium steady states (NESS) without assuming equilibrium binding steps.
Edit intent: fluency
Original:  Using this new approach, the expression of product rate at NESSgives clear biophysical significance.
Revised:  Using this new approach, the expression of product rate in NESS, which has clear biophysical significance.
Edit intent: clarity
Original:  Moreover, we classify the kinetic behavior of the modifier into three categories, namely hyperbolic behavior, bell-shaped behavior, and switching behavior .
Revised:  Moreover, we classify the kinetic behavior of the modifier into three categories, which are named hyperbolic behavior, bell-shaped behavior, and switching behavior .
Edit intent: coherence
Original:  The switching-behaved modifier may convert between activator and inhibitor via the general modifier mechanism when the modifier concentration varies .
Revised:  The switching-behaved modifier may convert between an activator and an inhibitor when the modifier concentration varies .
Edit intent: clarity
Original:  Effects of drugs on  Pgp ATPase activity  where drugs may convert from activators to inhibitors with the increase of drug concentration typically exemplify the switching phenomenon.
Revised:  Effects of drugs on the Pgp ATPase activity where drugs may convert from activators to inhibitors with the increase of drug concentration typically exemplify the switching phenomenon.
Edit intent: fluency
Original:  Effects of drugs on  Pgp ATPase activity  where drugs may convert from activators to inhibitors with the increase of drug concentration typically exemplify the switching phenomenon.
Revised:  Effects of drugs on Pgp ATPase activity , where drugs may convert from activators to inhibitors with the increase of drug concentration typically exemplify the switching phenomenon.
Edit intent: fluency
Original:  However, both this assumption and its converse are possible if organic molecules and quantum circuits/protocols are considered as hardware and software of living systems that are co-optimized during evolution.
Revised:  However, both this assumption and its converse are possible if organic molecules and quantum circuits/protocols can be considered as hardware and software of living systems that are co-optimized during evolution.
Edit intent: clarity
Original:  In this paper, we try to model DNA replication as a multiparticle entanglement swapping with a reliable qubit representation of  nucleotides.
Revised:  We try to model DNA replication as a multiparticle entanglement swapping with a reliable qubit representation of nucleotides.
Edit intent: coherence
Original:  In this paper, we try to model DNA replication as a multiparticle entanglement swapping with a reliable qubit representation of  nucleotides.
Revised:  In this paper, we try to model DNA replication as a multiparticle entanglement swapping with a reliable qubit representation of the nucleotides.
Edit intent: fluency
Original:  In the model , molecular recognition of a nucleotide triggers an intrabase entanglement corresponding to a superposition state of different tautomer forms.
Revised:  In our model molecular recognition of a nucleotide triggers an intrabase entanglement corresponding to a superposition state of different tautomer forms.
Edit intent: fluency
Original: In this paper we analytically study the pricing of the arithmetically averaged Asian option in the path integral formalism.
Revised: In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism.
Edit intent: clarity
Original:  } The  theory of the generator, including the proof of periodic properties and the proof of statistical independence of bits on length up to \ell , is presented  .
Revised:  } The theory of the generator, including proofs of periodic properties and the proof of statistical independence of bits on length up to \ell , is presented .
Edit intent: fluency
Original:  } The  theory of the generator, including the proof of periodic properties and the proof of statistical independence of bits on length up to \ell , is presented  .
Revised:  } The theory of the generator, including the proof of periodic properties and of statistical independence of bits on length up to \ell , is presented .
Edit intent: fluency
Original:  New algorithm for generating uniform pseudorandom numbers is proposed.
Revised:  A new algorithm for generating uniform pseudorandom numbers is proposed.
Edit intent: clarity
Original:  The theory of the generator, including proofs of periodic properties and of statistical independence of bits on length up to logarithm of mesh size, is presented.
Revised:  The theory of the generator, which includes proofs of periodic properties and of statistical independence of bits on length up to logarithm of mesh size, is presented.
Edit intent: coherence
Original: Practical network coding systems for wireless networks employ network coding across unicast sessions to improve throughput.
Edit intent: clarity
Original:  Furthermore , redundancy allows intermediate nodes to operate without the knowledge of the decoding buffers at their neighbors.
Revised:  Furthermore , redundancy allows intermediate nodes to operate without knowledge of the decoding buffers at their neighbors.
Edit intent: fluency
Original:  Furthermore , redundancy allows intermediate nodes to operate without the knowledge of the decoding buffers at their neighbors.
Revised:  Furthermore , redundancy allows intermediate nodes to operate without the knowledge of the decoding buffers of their neighbors.
Edit intent: fluency