wanyu/IteraTeR_full_sent huggingface dataset:
Original:  If only insertions are considered, our algorithm is also able to achieve optimal packing density as defined in our paper , with an amortized reallocation cost of O(c\log 1{c}) for squares, and O(c(1+s^2)1+s^21{c}) for right angled triangles, where s is the ratio of the lengths of the second shortest side to the shortest, when inserting a circle of area c.
Revised:  If only insertions are considered, our algorithm is also able to achieve optimal packing density as defined in our paper , with an amortised reallocation cost of O(c\log 1{c}) for squares, and O(c(1+s^2)1+s^21{c}) for right angled triangles, where s is the ratio of the lengths of the second shortest side to the shortest, when inserting a circle of area c.
Edit intent: fluency
Original:  When insertions and deletions are considered, we achieve a packing density of (1-\epsilon) of the optimal, where \epsilon>0 can be made arbitrarily small, for an additional amortized reallocation cost of O(  c1{\epsilon}).
Revised:  When insertions and deletions are considered, we achieve a packing density of (1-\epsilon) of the optimal, where \epsilon>0 can be made arbitrarily small, with an amortised reallocation cost of O( c1{\epsilon}).
Edit intent: clarity
Original:  When insertions and deletions are considered, we achieve a packing density of (1-\epsilon) of the optimal, where \epsilon>0 can be made arbitrarily small, for an additional amortized reallocation cost of O(  c1{\epsilon}).
Revised:  When insertions and deletions are considered, we achieve a packing density of (1-\epsilon) of the optimal, where \epsilon>0 can be made arbitrarily small, for an additional amortized reallocation cost of O( c(1+s^2)\log_{1+s^2 c1{\epsilon}).
Edit intent: meaning-changed
Original: The Split Packing algorithm \mbox{%DIFAUXCMD splitpacking_ws, splitpacking is an offline algorithm that packs a set of circles into shapes ( triangles and squares ) at an optimal packing density.
Revised: The Split Packing algorithm \mbox{%DIFAUXCMD splitpacking_ws, splitpackingsoda, splitpacking is an offline algorithm that packs a set of circles into shapes ( triangles and squares ) at an optimal packing density.
Edit intent: meaning-changed
Original: The Split Packing algorithm \mbox{%DIFAUXCMD splitpacking_ws, splitpacking is an offline algorithm that packs a set of circles into shapes ( triangles and squares ) at an optimal packing density.
Revised: The Split Packing algorithm \mbox{%DIFAUXCMD splitpacking_ws, splitpacking is an offline algorithm that packs a set of circles into triangles and squares ) at an optimal packing density.
Edit intent: clarity
Original: The Split Packing algorithm \mbox{%DIFAUXCMD splitpacking_ws, splitpacking is an offline algorithm that packs a set of circles into shapes ( triangles and squares ) at an optimal packing density.
Revised: The Split Packing algorithm \mbox{%DIFAUXCMD splitpacking_ws, splitpacking is an offline algorithm that packs a set of circles into shapes ( triangles and squares up to critical density.
Edit intent: clarity
Original:  If only insertions are considered, our algorithm is also able to achieve optimal packing density, with an amortised reallocation cost of O(c\log 1{c}) for squares, and O(c(1+s^2)1+s^21{c}) for right angled triangles, where s is the ratio of the lengths of the second shortest side to the shortest  , when inserting a circle of area c.
Revised:  If only insertions are considered, our algorithm is also able to pack to critical density, with an amortised reallocation cost of O(c\log 1{c}) for squares, and O(c(1+s^2)1+s^21{c}) for right angled triangles, where s is the ratio of the lengths of the second shortest side to the shortest , when inserting a circle of area c.
Edit intent: clarity
Original:  If only insertions are considered, our algorithm is also able to achieve optimal packing density, with an amortised reallocation cost of O(c\log 1{c}) for squares, and O(c(1+s^2)1+s^21{c}) for right angled triangles, where s is the ratio of the lengths of the second shortest side to the shortest  , when inserting a circle of area c.
Revised:  If only insertions are considered, our algorithm is also able to achieve optimal packing density, with an amortised reallocation cost of O(c\log 1{c}) for squares, and O(c(1+s^2)1+s^21{c}) for right angled triangles, where s is the ratio of the lengths of the second shortest side to the shortest side of the triangle , when inserting a circle of area c.
Edit intent: clarity
Original:  When insertions and deletions are considered, we achieve a packing density of (1-\epsilon) of the optimal , where \epsilon>0 can be made arbitrarily small, with an amortised reallocation cost of O(c(1+s^2)1+s^2\frac{1}{c} + c\frac{1}{\epsilon}).
Revised:  When insertions and deletions are considered, we achieve a packing density of (1-\epsilon) of the critical density , where \epsilon>0 can be made arbitrarily small, with an amortised reallocation cost of O(c(1+s^2)1+s^2\frac{1}{c} + c\frac{1}{\epsilon}).
Edit intent: meaning-changed
Original: We revisit the classical problem of market impact through the lens of a new agent-based model. Drawing from the mean-field approach in Statistical Mechanics and Physics, we assume a large number of agents interacting in the order book .
Revised: We revisit the classical problem of market impact through the lens of a new agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field approach in Statistical Mechanics and Physics, we assume a large number of agents interacting in the order book .
Edit intent: meaning-changed
Original:  Drawing from the mean-field approach in Statistical Mechanics and Physics, we assume a large number of agents interacting in the order book . By taking the 'continuum' limit we obtain a set of nonlinear differential equations, the core of our dynamical theory of price formation. And we explicitly solve them using Fourier analysis. One could talk as well of a "micro-macro" approach of equilibrium, where the market price is the consequence of each ("microscopic") agent behaving with respect to his preferences and to global ("macroscopic") information. When a large market order (or metaorder) perturbs the market, our model recovers the square-root law of impact , providing new insights on the price formation process. In addition, we give various limiting cases, examples and possible extensions .
Revised:  Drawing from the mean-field assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book .
Edit intent: meaning-changed
Original: In order to understand the formation of social conventions we need to know the specific role of control and learning in multi-agent systems. To advance in this direction, we propose, within the framework of the Distributed Adaptive Control (DAC) theory , a novel Control-based Reinforcement Learning architecture (CRL) that can account for the acquisition of social conventions in multi-agent populations that are solving a benchmark social decision-making problem.
Revised: In order to understand the formation of social conventions ? To answer this question, we propose a computational model that matches human behavioral data in a social decision-making game that was analyzed both in discrete-time and continuous-time setups. Furthermore, unlike previous approaches, our model takes into account the role of sensorimotor control loops in embodied decision-making scenarios. For this purpose, we introduce the Control-based Reinforcement Learning (CRL) model. CRL is grounded in the Distributed Adaptive Control (DAC) theory , a novel Control-based Reinforcement Learning architecture (CRL) that can account for the acquisition of social conventions in multi-agent populations that are solving a benchmark social decision-making problem.
Edit intent: meaning-changed
Original:  To advance in this direction, we propose, within the framework of the Distributed Adaptive Control (DAC) theory , a novel Control-based Reinforcement Learning architecture (CRL) that can account for the acquisition of social conventions in multi-agent populations that are solving a benchmark social decision-making problem. Our new CRL architecture, as a concrete realization of DAC multi-agent theory, implements a low-level sensorimotor control loop handling the agent's reactive behaviors (pre-wired reflexes), along with a layer based on model-free reinforcement learning that maximizes long-term reward.
Revised:  To advance in this direction, we propose, within the framework of the Distributed Adaptive Control (DAC) theory of mind and brain, where low-level sensorimotor control loop handling the agent's reactive behaviors (pre-wired reflexes), along with a layer based on model-free reinforcement learning that maximizes long-term reward.
Edit intent: clarity
Original:  Our new CRL architecture, as a concrete realization of DAC multi-agent theory, implements a low-level sensorimotor control loop handling the agent's reactive behaviors (pre-wired reflexes), along with a layer based on model-free reinforcement learning that maximizes long-term reward.
Revised:  Our new CRL architecture, as a concrete realization of DAC multi-agent theory, implements a low-level sensorimotor control is modulated through perceptual and behavioral learning in a layered structure. CRL follows these principles by implementing a feedback control loop handling the agent's reactive behaviors (pre-wired reflexes), along with a layer based on model-free reinforcement learning that maximizes long-term reward.
Edit intent: meaning-changed
Original:  Our new CRL architecture, as a concrete realization of DAC multi-agent theory, implements a low-level sensorimotor control loop handling the agent's reactive behaviors (pre-wired reflexes), along with a layer based on model-free reinforcement learning that maximizes long-term reward.
Revised:  Our new CRL architecture, as a concrete realization of DAC multi-agent theory, implements a low-level sensorimotor control loop handling the agent's reactive behaviors (pre-wired reflexes), along with an adaptive layer that uses reinforcement learning to maximize long-term reward.
Edit intent: clarity
Original:  We show that our CRL architecture is able to both find optimal solutions in discrete and continuous time and reproduce human experimental data on standard game-theoretic metrics such as efficiency in acquiring rewards , fairness in reward distribution and stability of convention formation .
Revised:  We show that CRL is able to both find optimal solutions in discrete and continuous time and reproduce human experimental data on standard game-theoretic metrics such as efficiency in acquiring rewards , fairness in reward distribution and stability of convention formation .
Edit intent: clarity
Original:  We show that our CRL architecture is able to both find optimal solutions in discrete and continuous time and reproduce human experimental data on standard game-theoretic metrics such as efficiency in acquiring rewards , fairness in reward distribution and stability of convention formation .
Revised:  We show that our CRL architecture is able to reach human-level performance on standard game-theoretic metrics such as efficiency in acquiring rewards , fairness in reward distribution and stability of convention formation .
Edit intent: clarity
Original:  We show that our CRL architecture is able to both find optimal solutions in discrete and continuous time and reproduce human experimental data on standard game-theoretic metrics such as efficiency in acquiring rewards , fairness in reward distribution and stability of convention formation .
Revised:  We show that our CRL architecture is able to both find optimal solutions in discrete and continuous time and reproduce human experimental data on standard game-theoretic metrics such as efficiency in acquiring rewards and fairness in reward distribution and stability of convention formation .
Edit intent: fluency
Original:  We show that our CRL architecture is able to both find optimal solutions in discrete and continuous time and reproduce human experimental data on standard game-theoretic metrics such as efficiency in acquiring rewards , fairness in reward distribution and stability of convention formation .
Revised:  We show that our CRL architecture is able to both find optimal solutions in discrete and continuous time and reproduce human experimental data on standard game-theoretic metrics such as efficiency in acquiring rewards , fairness in reward distribution .
Edit intent: clarity
Original:  The trial-shuffle method, for spike train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons , rather than globally comparing all neuron transfer entropy values .
Revised:  The trial-shuffle method, for spike train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons by comparing to a created baseline distribution using a rigorous statistical test. This is in contrast to either globally comparing all neuron transfer entropy values .
Edit intent: meaning-changed
Original:  The trial-shuffle method, for spike train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons , rather than globally comparing all neuron transfer entropy values . We establish the viability of this method by showing that it performs comparably or better to a previous approach in the literature based on the false positive detection rate .
Revised:  The trial-shuffle method, for spike train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons , rather than globally comparing all neuron transfer entropy values or comparing pairwise values to a single baseline value. In establishing the viability of this method by showing that it performs comparably or better to a previous approach in the literature based on the false positive detection rate .
Edit intent: meaning-changed
Original: Let R and B be sets of n red and n blue points in the plane, respectively, with P = R \cup B. Let M be a perfect matching between points from R and B, using n straight line segments to match the points, that is, each point is an endpoint of exactly one line segment, and each line segment has one red and one blue endpoint.
Revised: Let R and B be sets of n red and n blue points in the plane, we are interested in matching red points with blue points by straight line segments to match the points, that is, each point is an endpoint of exactly one line segment, and each line segment has one red and one blue endpoint.
Edit intent: clarity
Original:  Let M be a perfect matching between points from R and B, using n straight line segments to match the points, that is, each point is an endpoint of exactly one line segment, and each line segment has one red and one blue endpoint. We forbid line segments to cross. Denote the length of a longest line segmentin M with bn(M), which we also call the%DIFDELCMD < \intro[~]{value, bn} %%% of M.
Revised:  Let M be a perfect matching between points from R and B, using n straight line segments so that the segments do not cross. Bottleneck matching is such a matching that minimizes the length of a longest line segmentin M with bn(M), which we also call the%DIFDELCMD < \intro[~]{value, bn} %%% of M.
Edit intent: clarity
Original:  Denote the length of a longest line segmentin M with bn(M), which we also call the%DIFDELCMD < \intro[~]{value, bn} %%% of M. We aim to find a matching under given constraints that minimizes bn(M). Any such matching is called a%DIFDELCMD < \intro[~]{bottleneck matching} %%% of P .
Revised:  Denote the length of a longest line segmentin M with bn(M), which we also call the%DIFDELCMD < \intro[~]{value, bn} %%% %DIFDELCMD < \intro[~]{bottleneck matching} %%% of P .
Edit intent: coherence
Original:  Any such matching is called a%DIFDELCMD < \intro[~]{bottleneck matching} %%% of P .
Revised:  Any such matching is called a%DIFDELCMD < \intro[~]{bottleneck matching} %%% the longest segment. We develop a range of tools for dealing with non-crossing matchings of points in convex position, which enable us to solve the problem of finding bottleneck matchings of points in convex position in O(n^2) time. Combining the same set of tools with a geometric analysis, we design an O(n)-time algorithm for the case where the given points lie on a circle. Previously best known results were O(n^3) for points in convex position, and O(n \log n) for points on a circle .
Edit intent: meaning-changed
Original:   Bottleneck matching is such a matching that minimizes the length of the longest segment.
Revised:  We develop a range of tools for dealing with the non-crossing matchings of points in convex position. It turns out that the points naturally partition into groups that we refer to as orbits, with a number of properties that prove useful for studying and efficiently processing the non-crossing matchings. Bottleneck matching is such a matching that minimizes the length of the longest segment.
Edit intent: meaning-changed
Original:  Widely used reinforcement learning algorithms discretize continuous time and use the Bellman equation to estimate exponentially-discounted future reward . However, exponential discounting introduces a time scale to the computation of value. Scaling is a serious problem in continuous time: efficient learning with scaled algorithms requires prior knowledge of the relevant scale. That is, with scaled algorithms one must know at least part of the solution to a problem prior to attempting a solution .
Revised:  Widely used reinforcement learning algorithms discretize continuous time and use the Bellman equation to estimate exponentially-discounted future reward using the Bellman equation (model-free algorithms). An important drawback of model-based algorithms is that computational cost grows linearly with the solution to a problem prior to attempting a solution .
Edit intent: meaning-changed
Original:  This mechanism efficiently computes a model for future time on a logarithmically-compressed scale, and can be used to generate a scale-invariant power-law-discounted estimate of expected future reward.
Revised:  This mechanism efficiently computes an estimate of inputs as a function of future time on a logarithmically-compressed scale, and can be used to generate a scale-invariant power-law-discounted estimate of expected future reward.
Edit intent: clarity
Original: The stability of sequence replication was crucial for the emergence of molecular evolution and early life. Exponential replication with a first-order growth dynamics show inherent instabilities such as the error catastrophe and the dominance by the fastest replicators. This favors less structured and short sequences. The theoretical concept of hypercycles has been proposed to solve these problems. Their higher-order growth kinetics leads to frequency-dependent selection and stabilizes the replication of majority molecules. However, many implementations of hypercycles are unstable or require special sequenceswith catalytic activity .
Revised: Each living species carries a complex DNA sequence that determines their unique features and functionalities. It is generally assumed that life started from a random pool of oligonucleotides sequences, generated by a prebiotic polymerization of nucleotides. The mechanism that initially facilitated the emergence of sequences that code for the function of the first species from such a random pool of sequences remains unknown. It is a central problem of the origin of life. An interesting option would be a self-selection mechanism by spontaneous symmetry breaking. Initial concentration fluctuations of specific sequence motifs would have been amplified and outcompeted less abundant sequences, enhancing the signal to noise to replicate and select functional sequences .
Edit intent: meaning-changed
Original:  Here, we demonstrate the spontaneous emergence of higher-order cooperative replication from a network of simple ligationchain reactions (LCR). We performed long-term LCR experiments from a mixture of sequences under molecule degrading conditions with a ligase protein. At the chosen temperature cycling, a network of positive feedback loops arose from both the cooperative ligation of matching sequences and the emerging increase in sequence length.
Revised:  Here, we demonstrate with experimental and theoretical findings that templated ligation would provide such a self-selection. In templated ligation, two adjacent single sequences strands are chemically joined when a third complementary strand sequence brought them in close proximity. This simple mechanism was a likely side-product of a network of positive feedback loops arose from both the cooperative ligation of matching sequences and the emerging increase in sequence length.
Edit intent: meaning-changed
Original:  At the chosen temperature cycling, a network of positive feedback loops arose from both the cooperative ligation of matching sequences and the emerging increase in sequence length.
Revised:  At the chosen temperature cycling, a prebiotic polymerization chemistry once the strands reach the length to form double stranded species. As shown here, the ligation gave rise to a nonlinear replication process by the cooperative ligation of matching sequences and the emerging increase in sequence length.
Edit intent: meaning-changed
Original:  At the chosen temperature cycling, a network of positive feedback loops arose from both the cooperative ligation of matching sequences and the emerging increase in sequence length. It generated higher-order replication with frequency-dependent selection. The experiments matched a complete simulation using experimentally determined ligation rates and the hypercycle mechanism was also confirmed by abstracted modeling. Since templated ligation is a most basic reaction of oligonucleotides, the described mechanism could have been implemented under microthermal convection on early Earth .
Revised:  At the chosen temperature cycling, a network of positive feedback loops arose from both the cooperative ligation of matching sequences which self-promoted their own elongation. This led to a cascade of enhanced template binding and faster ligation reactions. A requirement was the reshuffling of the strands by thermal cycling, enabled for example by microscale convection. Assuming that templated ligation was driven by the same chemical mechanism that generated prebiotic polymerization of oligonucleotides, the described mechanism could have been implemented under microthermal convection on early Earth .
Edit intent: clarity
Original:  Since templated ligation is a most basic reaction of oligonucleotides, the described mechanism could have been implemented under microthermal convection on early Earth .
Revised:  Since templated ligation is a most basic reaction of oligonucleotides, the mechanism could function as a missing link between polymerization and the self-stabilized replication, offering a pathway to the autonomous emergence of Darwinian evolution for the origin of life .
Edit intent: meaning-changed