wanyu/IteraTeR_v2 huggingface dataset:
Original:  In addition, the author discusses the limitation of this method to show that it can strengthen the hardness for approximating Minimum Unique Game to 2-\kappa where \kappa is a small absolute positive, but is short of proving \omega_k(1) hardness for Minimum Unique Game  or Small Set Expansion  , by assuming a generalization of this hypothesis on Unbalanced Max k-CSP with balanced pairwise independent predicate.
Revised:  In addition, the author discusses the limitation of this method to show that it can strengthen the hardness for approximating Minimum Unique Game to 2-\kappa where \kappa is a small absolute positive, but is short of proving \omega_k(1) hardness for Minimum Unique Game ( or Small Set Expansion , by assuming a generalization of this hypothesis on Unbalanced Max k-CSP with balanced pairwise independent predicate.
Edit intent: fluency
Original:  In addition, the author discusses the limitation of this method to show that it can strengthen the hardness for approximating Minimum Unique Game to 2-\kappa where \kappa is a small absolute positive, but is short of proving \omega_k(1) hardness for Minimum Unique Game  or Small Set Expansion  , by assuming a generalization of this hypothesis on Unbalanced Max k-CSP with balanced pairwise independent predicate.
Revised:  In addition, the author discusses the limitation of this method to show that it can strengthen the hardness for approximating Minimum Unique Game to 2-\kappa where \kappa is a small absolute positive, but is short of proving \omega_k(1) hardness for Minimum Unique Game or Small Set Expansion ) , by assuming a generalization of this hypothesis on Unbalanced Max k-CSP with balanced pairwise independent predicate.
Edit intent: fluency
Original: This paper deals with dependence across marginally-exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory.
Revised: This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory.
Edit intent: fluency
Original:  We present a homogeneity characterization of the self chaining condition.
Edit intent: coherence
Original:  We find that the random walk statistics of irreducible boundaries exhibit surprising regularities and suggest a threshold separating two distinct classes.
Revised:  We find that the random walk statistics of irreducible boundaries exhibit surprising regularities and suggest that a threshold separates two classes.
Edit intent: clarity
Original: Critical-like characteristics in open living systems at each organizational level (from bio-molecules to ecosystems) indicate that non-equilibrium phase transitions into absorbing states lead to self-organized states comprising autonomous components.
Revised: Critical-like characteristics in open living systems at each organizational level (from bio-molecules to ecosystems) indicate that non-equilibrium phase-transitions into absorbing states lead to self-organized states comprising autonomous components.
Edit intent: fluency
Original:  Here, we recall Langton's hypothesis of the spontaneous emergence of computation in the vicinity of a critical phase-transition, which points to the importance of conservative redistribution rules, threshold, meta-stability, and so on.
Revised:  Also Langton's hypothesis of the spontaneous emergence of computation in the vicinity of a critical phase-transition, which points to the importance of conservative redistribution rules, threshold, meta-stability, and so on.
Edit intent: coherence
Original:  Here, we recall Langton's hypothesis of the spontaneous emergence of computation in the vicinity of a critical phase-transition, which points to the importance of conservative redistribution rules, threshold, meta-stability, and so on.
Revised:  Here, we recall Langton's hypothesis of the spontaneous emergence of computation in the vicinity of a critical phase-transition, points to the importance of conservative redistribution rules, threshold, meta-stability, and so on.
Edit intent: coherence
Original:  But extrapolating these features to the origins of life, brings up a paradox: how could simple organics - lacking the 'soft matter' response properties of today's complex bio-molecules-have dissipated energy from primordial reactions ( for eventual reduction of CO2) in a controlled manner for their 'ordering'?
Revised:  But extrapolating these features to the origins of life, brings up a paradox: how could simple organics-- lacking the 'soft matter' response properties of today's complex bio-molecules-have dissipated energy from primordial reactions ( for eventual reduction of CO2) in a controlled manner for their 'ordering'?
Edit intent: fluency
Original:  But extrapolating these features to the origins of life, brings up a paradox: how could simple organics - lacking the 'soft matter' response properties of today's complex bio-molecules-have dissipated energy from primordial reactions ( for eventual reduction of CO2) in a controlled manner for their 'ordering'?
Revised:  But extrapolating these features to the origins of life, brings up a paradox: how could simple organics - lacking the 'soft matter' response properties of today's complex bio-molecules--have dissipated energy from primordial reactions ( for eventual reduction of CO2) in a controlled manner for their 'ordering'?
Edit intent: fluency
Original:  But extrapolating these features to the origins of life, brings up a paradox: how could simple organics - lacking the 'soft matter' response properties of today's complex bio-molecules-have dissipated energy from primordial reactions ( for eventual reduction of CO2) in a controlled manner for their 'ordering'?
Revised:  But extrapolating these features to the origins of life, brings up a paradox: how could simple organics - lacking the 'soft matter' response properties of today's complex bio-molecules-have dissipated energy from primordial reactions ( eventually reducing CO2) in a controlled manner for their 'ordering'?
Edit intent: fluency
Original:  Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the ' functional takeover ' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's "crystal-scaffold").
Revised:  Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the ' functional-takeover ' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's "crystal-scaffold").
Edit intent: fluency
Original:  Field-structured colloids offer a mechanism for bootstrapping - bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry.
Revised:  A field-controlled structure offers a mechanism for bootstrapping - bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry.
Edit intent: clarity
Original:  Field-structured colloids offer a mechanism for bootstrapping - bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry.
Revised:  Field-structured colloids offer a mechanism for bootstrapping-- bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry.
Edit intent: fluency
Original:  Field-structured colloids offer a mechanism for bootstrapping - bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry.
Revised:  Field-structured colloids offer a mechanism for bootstrapping - bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of magnetic (H)-field energy for aggregation breaks time-reversal symmetry.
Edit intent: clarity
Original: Critical-like characteristics in open living systems at each organizational level (from bio-molecules to ecosystems) indicate that non-equilibrium phase-transitions into absorbing states lead to self-organized states comprising autonomous components.
Revised: Instances of critical-like characteristics in living systems at each organizational level (from bio-molecules to ecosystems) indicate that non-equilibrium phase-transitions into absorbing states lead to self-organized states comprising autonomous components.
Edit intent: clarity
Original:  Also Langton's hypothesis of the spontaneous emergence of computation in the vicinity of a critical phase-transition, points to the importance of conservative redistribution rules, threshold, meta-stability, and so on . But extrapolating these features to the origins of life , brings up a paradox:
Revised:  Also Langton's hypothesis of the spontaneous emergence of computation in the vicinity of a critical phase-transition, points to the importance of conservative redistribution rules, threshold, meta-stability, and so on . But extrapolating complex bio-systems to life's origins , brings up a paradox:
Edit intent: clarity
Original:  how could simple organics-- lacking the 'soft matter' response properties of today's complex bio-molecules--have dissipated energy from primordial reactions (eventually reducing CO2) in a controlled manner for their 'ordering'?
Revised:  how could simple organics--lacking the 'soft matter' response properties of today's complex bio-molecules--have dissipated energy from primordial reactions (eventually reducing CO2) in a controlled manner for their 'ordering'?
Edit intent: fluency
Original:  how could simple organics-- lacking the 'soft matter' response properties of today's complex bio-molecules--have dissipated energy from primordial reactions (eventually reducing CO2) in a controlled manner for their 'ordering'?
Revised:  how could simple organics-- lacking the 'soft matter' response properties of today's bio-molecules--have dissipated energy from primordial reactions (eventually reducing CO2) in a controlled manner for their 'ordering'?
Edit intent: clarity
Original:  how could simple organics-- lacking the 'soft matter' response properties of today's complex bio-molecules--have dissipated energy from primordial reactions (eventually reducing CO2) in a controlled manner for their 'ordering'?
Revised:  how could simple organics-- lacking the 'soft matter' response properties of today's complex bio-molecules--have dissipated energy from primordial reactions in a controlled manner for their 'ordering'?
Edit intent: clarity
Original:  Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's " crystal-scaffold " ).
Revised:  Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's ' crystal-scaffold " ).
Edit intent: fluency
Original:  Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's " crystal-scaffold " ).
Revised:  Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's " crystal-scaffold ' ).
Edit intent: fluency
Original:  A field-controlled structure offers a mechanism for bootstrapping-- bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of magnetic (H)-field energy for aggregation breaks time-reversal symmetry.
Revised:  A field-controlled structure offers a mechanism for bootstrapping--bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of magnetic (H)-field energy for aggregation breaks time-reversal symmetry.
Edit intent: fluency
Original:  A field-controlled structure offers a mechanism for bootstrapping-- bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of magnetic (H)-field energy for aggregation breaks time-reversal symmetry.
Revised:  A field-controlled structure offers a mechanism for bootstrapping-- bottom-up assembly with top-down control: its super-paramagnetic components obey reversible dynamics, but its dissipation of magnetic (H)-field energy for aggregation breaks time-reversal symmetry.
Edit intent: clarity
Original:  A field-controlled structure offers a mechanism for bootstrapping-- bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of magnetic (H)-field energy for aggregation breaks time-reversal symmetry.
Revised:  A field-controlled structure offers a mechanism for bootstrapping-- bottom-up assembly with top-down control: its super-paramagnetic colloidal components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry.
Edit intent: clarity
Original:  Further, these adjustments of a cooperative networkcould alter its capacity to assist a spontaneous process , thus enabling the selection of the functional configuration .
Revised:  Further, these adjustments of a cooperative networkcould alter its capacity to assist a spontaneous process .
Edit intent: clarity
Original:  A non-equilibrium dynamics could now drive the kinetically-oriented system (trimming the phase-space of sterically-coupled organics) towards a series of phase-transitions with appropriate replacements " taking-over " its functions.
Revised:  A non-equilibrium dynamics could now drive the kinetically-oriented system towards a series of phase-transitions with appropriate replacements " taking-over " its functions.
Edit intent: clarity
Original:  A non-equilibrium dynamics could now drive the kinetically-oriented system (trimming the phase-space of sterically-coupled organics) towards a series of phase-transitions with appropriate replacements " taking-over " its functions.
Revised:  A non-equilibrium dynamics could now drive the kinetically-oriented system (trimming the phase-space of sterically-coupled organics) towards a series of phase-transitions with appropriate organic replacements ' taking-over " its functions.
Edit intent: clarity
Original:  A non-equilibrium dynamics could now drive the kinetically-oriented system (trimming the phase-space of sterically-coupled organics) towards a series of phase-transitions with appropriate replacements " taking-over " its functions.
Revised:  A non-equilibrium dynamics could now drive the kinetically-oriented system (trimming the phase-space of sterically-coupled organics) towards a series of phase-transitions with appropriate replacements " taking-over ' its functions.
Edit intent: fluency
Original: In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles by developing a variant of marked branching diffusion method.
Revised: In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method.
Edit intent: clarity
Original: An integer polynomial p of n variables is called a threshold gate for the Boolean function f of n variables if for all x \in \{0,1\} \zoon f(x)=1 if and only if p(x)\geq 0.
Revised: An integer polynomial p of n variables is called a threshold gate for a Boolean function f of n variables if for all x \in \{0,1\} \zoon f(x)=1 if and only if p(x)\geq 0.
Edit intent: fluency
Original:  In this paper we study how large  weight might be needed if we fix some function and some threshold degree.
Revised:  In this paper we study how large a weight might be needed if we fix some function and some threshold degree.
Edit intent: fluency
Original:  Each individual is assigned a mass of 1/N and the total mass in the system is called population density .
Revised:  Each individual is assigned a mass of 1/N and the total mass in the system is called population density .
Edit intent: fluency
Original:  We show that under a timescale separation between the slow migration mechanism and the fast density regulation mechanism, the population dynamics converges to a Fleming-Viot process as the scaling parameter N %DIFDELCMD < \to %%%  \infty.
Revised:  We show that under a timescale separation between the slow migration mechanism and the fast density regulation mechanism, the population dynamics converges to a Fleming-Viot process as the scaling parameter N %DIFDELCMD < \to %%% \infty.
Edit intent: fluency
Original:  We show that under a timescale separation between the slow migration mechanism and the fast density regulation mechanism, the population dynamics converges to a Fleming-Viot process as the scaling parameter N %DIFDELCMD < \to %%%  \infty.
Revised:  We show that under a timescale separation between the slow migration mechanism and the fast density regulation mechanism, the population dynamics converges to a Fleming-Viot process as the scaling parameter N %DIFDELCMD < \to %%% approaches \infty.
Edit intent: fluency
Original:  In this case we obtain a neutral Fleming-Viot process.
Revised:  In this case we obtain a neutral Fleming-Viot process.
Edit intent: fluency
Original:  We show how these extensions add mutation and selection  to the limiting Fleming-Viot process.
Revised:  We show how these extensions add mutation to the limiting Fleming-Viot process.
Edit intent: clarity
Original:  We show how these extensions add mutation and selection  to the limiting Fleming-Viot process.
Revised:  We show how these extensions add mutation and selection selection to the limiting Fleming-Viot process.
Edit intent: clarity
Original:  All the results are proved in a multi-type setting, where there are q types of individuals reproducing each other.
Revised:  All the results are proved in a multi-type setting, where there are q types of individuals interacting with each other.
Edit intent: clarity
Original:  To illustrate the usefulness of our convergence result , we discuss certain applications in ecology and cell biology.
Revised:  We illustrate the usefulness of our convergence result , we discuss certain applications in ecology and cell biology.
Edit intent: fluency
Original:  We obtain a simple expression for the length scale controlling the spatial variation of stresses in the cellular material in terms of cell and substrate parameters  .
Revised:  We obtain a simple expression for the length scale controlling the spatial variation of stresses in terms of cell and substrate parameters .
Edit intent: clarity
Original:  All problems that we consider are solvable in polynomial time, but not expressible in fixed-point logic with counting.
Revised:  All problems that we consider are decidable in polynomial time, but not expressible in fixed-point logic with counting.
Edit intent: clarity
Original:  Further , we prove closure properties for classes of queries that reduce to solvability over rings .
Revised:  Moreover , we prove closure properties for classes of queries that reduce to solvability over rings .
Edit intent: coherence
Original: Biochemical reaction networks are subjected to large fluctuations due to small molecule numbers, yet underlie reliable biological functions.
Revised: Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions.
Edit intent: fluency
Original:  Here, we investigate the dynamics of a self-repressing gene using an intermediate approach based on a moment expansion of the master equation, taking into account the binary character of gene activity.
Revised:  Here, we investigate the dynamics of a self-repressing gene using an intermediate approach based on a moment expansion of the master equation, which allows us to take into account the binary character of gene activity.
Edit intent: coherence
Original:  We thereby obtain deterministic equations which describe how nonlinearity feeds back fluctuations into the mean-field equations, providing insight into the interplay of determinism and stochasticity.
Revised:  We thereby obtain deterministic equations that describe how nonlinearity feeds back fluctuations into the mean-field equations, providing insight into the interplay of determinism and stochasticity.
Edit intent: fluency
Original:  This allows us to identify a region of parameter space where fluctuations induce relatively regular oscillations.
Revised:  This allows us to identify regions of parameter space where fluctuations induce relatively regular oscillations.
Edit intent: fluency
Original:  With a parallel encoding structure, the proposed Progressive Rateless codes ( Pro-Rateless ) assign unequal redundancy to each layer in accordance with their importance.
Revised:  With a parallel encoding structure, the proposed Progressive Rateless codes ( PRC ) assign unequal redundancy to each layer in accordance with their importance.
Edit intent: clarity
Original: We study the query complexity of testing for properties defined by read once formulae , as instances of {\em massively parametrized properties}, and prove several testability and non-testability results.
Revised: We study the query complexity of testing for properties defined by read once formulas , as instances of {\em massively parametrized properties}, and prove several testability and non-testability results.
Edit intent: fluency
Original:  For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasipolynomial in \epsilon.
Revised:  For formulas only involving And/Or gates, we provide a more efficient test whose query complexity is only quasipolynomial in \epsilon.
Edit intent: fluency
Original:  On the other hand  we show that such testability results do not hold in general for formulae over non-Boolean alphabets;
Revised:  On the other hand , we show that such testability results do not hold in general for formulae over non-Boolean alphabets;
Edit intent: fluency
Original:  On the other hand  we show that such testability results do not hold in general for formulae over non-Boolean alphabets;
Revised:  On the other hand we show that such testability results do not hold in general for formulas over non-Boolean alphabets;
Edit intent: fluency
Original:  specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size  .
Revised:  specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over an alphabet of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size .
Edit intent: fluency
Original:  In order to do that, we develop a technique, which we believe can have further applications, of approximating Chase(D, T), for a database instance D and some sets of tuple generating dependencies T, by an in?nite sequence of finite structures, all of them being models of T.
Revised:  In order to do that, we develop a technique, which we believe can have further applications, of approximating Chase(D, T), for a database instance D and some sets of tuple generating dependencies T, by an infinite sequence of finite structures, all of them being models of T.
Edit intent: fluency