wanyu/IteraTeR_full_sent huggingface dataset:
Original:  This paper deals with the following separability problem in 3D space: Given a rigid polyhedron P with n vertices , does a semi-rigid polyhedron G exist, such that both polyhedra can be transformed into an inseparable assembled state, where the fixture snaps on to P, by applying a linear force and exploiting the mild flexibility of G? If such a flexible snapping polyhedron exists, devise an efficient and robust algorithm that constructs it. In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending  G on the way  , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Revised:  This paper deals with the following separability problem in 3D space: Given a rigid polyhedron P with n vertices , does a semi-rigid polyhedron G , made of a palm and several fingers, such that when P and G are separate , we can push G towards P , slightly bending G on the way , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Edit intent: meaning-changed
Original:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending  G on the way  , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Revised:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are well separated , we can push G towards P , slightly bending G on the way , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Edit intent: clarity
Original:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending  G on the way  , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Revised:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push P toward G , slightly bending G on the way , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Edit intent: fluency
Original:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending  G on the way  , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Revised:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending the fingers of G on the way , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Edit intent: meaning-changed
Original:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending  G on the way  , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Revised:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending G on the way (exploiting its mild flexibility) , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Edit intent: meaning-changed
Original:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending  G on the way  , and obtain a configuration, where G is back in its original shape , and both P and G are inseparable as rigid bodies.
Revised:  In simple words, we are looking for s semi-rigid polyhedron G, such that when P and G are separate , we can push G towards P , slightly bending G on the way , and obtain a configuration, where G is back in its original shape and P and G are inseparable as rigid bodies.
Edit intent: clarity
Original:  We define certain properties such a pair of polyhedron and its snapping fixture may possess, and prove two theorems related to the pair. We introduce an algorithm that produces a snapping fixture with such properties in O(n ^5) time , if a snapping fixture exists , and an efficient and robust implementation of this algorithm .
Revised:  We prove the minimal closure conditions under which such fixtures can hold parts, using Helly's theorem. We then introduce an algorithm that produces a snapping fixture with such properties in O(n ^5) time , if a snapping fixture exists , and an efficient and robust implementation of this algorithm .
Edit intent: meaning-changed
Original:  We introduce an algorithm that produces a snapping fixture with such properties in O(n ^5) time , if a snapping fixture exists , and an efficient and robust implementation of this algorithm .
Revised:  We introduce an algorithm that produces a snapping fixture with such properties in O(n ^3) time that produces a snapping fixture, minimizing the number of fingers and optimizing additional objectives, if a snapping fixture exists , and an efficient and robust implementation of this algorithm .
Edit intent: meaning-changed
Original:  We introduce an algorithm that produces a snapping fixture with such properties in O(n ^5) time , if a snapping fixture exists , and an efficient and robust implementation of this algorithm .
Revised:  We introduce an algorithm that produces a snapping fixture with such properties in O(n ^5) time , if a snapping fixture exists , and an efficient and robust implementation of a simpler version of the algorithm, which produces the fixture model to be 3D printed and runs in O(n^4) time. We describe two applications with different optimization criteria: Fixtures to hold add-ons for drones, where we aim to make the fixture as lightweight as possible, and small-scale fixtures to hold precious stones in jewelry, where we aim to maximize the exposure of the stones, namely minimize the obscuring of the workpiece by the fixture .
Edit intent: meaning-changed
Original:  In this paper, we show that self-reported data from menstrual trackers can reveal statistically significant relationships between per-person variability of cycle length and self-reported qualitative symptoms.
Revised:  By exploring a database of user-tracked observations from the Clue app by BioWink of over 378,000 users and 4.9 million natural cycles, we show that self-reported data from menstrual trackers can reveal statistically significant relationships between per-person variability of cycle length and self-reported qualitative symptoms.
Edit intent: meaning-changed
Original:  We find that women located at different ends of the spectrum of menstrual patterns , based on the consistency of their cycle length statistics, exhibit statistically significant differences in  cycle characteristics and symptom tracking .
Revised:  We find that women located at different ends of the spectrum of menstrual patterns , based on the consistency of their cycle length statistics, exhibit statistically significant differences in cycle characteristics and symptom tracking patterns. We also find that cycle and period length statistics are stationary over the app usage timeline across the variability spectrum. The symptoms that we identify as showing statistically significant association with timing data can be useful to clinicians and users for predicting cycle variability from symptoms or as potential health indicators for conditions like endometriosis.
Edit intent: meaning-changed
Original: Feedback of calcium signaling through calcium-activated potassium channels of a dendritic spine is investigated. To simulate such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine , we applythe immersed boundary method with electrodiffusion .
Revised: Feedback of calcium signaling through calcium-activated potassium channels of a dendritic spine by applying the immersed boundary method with electrodiffusion. We simulate the stochastic gating of such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine , we applythe immersed boundary method with electrodiffusion .
Edit intent: meaning-changed
Original:  As already pointed out by Karatzas \& Shreve \mbox{%DIFAUXCMD KS0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )}  }  this allows for arbitrages in the market.
Revised:  As already pointed out by Karatzas 0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )} } this allows for arbitrages in the market.
Edit intent: clarity
Original:  As already pointed out by Karatzas \& Shreve \mbox{%DIFAUXCMD KS0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )}  }  this allows for arbitrages in the market.
Revised:  As already pointed out by Karatzas \& Shreve \mbox{%DIFAUXCMD KS0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )} Shreve } this allows for arbitrages in the market.
Edit intent: meaning-changed
Original:  As already pointed out by Karatzas \& Shreve \mbox{%DIFAUXCMD KS0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )}  }  this allows for arbitrages in the market.
Revised:  As already pointed out by Karatzas \& Shreve \mbox{%DIFAUXCMD KS0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )} KS} this allows for arbitrages in the market.
Edit intent: fluency
Original:  As already pointed out by Karatzas \& Shreve \mbox{%DIFAUXCMD KS0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )}  }  this allows for arbitrages in the market.
Revised:  As already pointed out by Karatzas \& Shreve \mbox{%DIFAUXCMD KS0pt%DIFAUXCMD (see also Jarrow \& Protter \mbox{%DIFAUXCMD JP }0pt%DIFAUXCMD )} } (in the Brownian motion case), this allows for arbitrages in the market.
Edit intent: meaning-changed
Original:  The model is also relevant for high frequency trading issues. See e.g. Lachapelle\textit{et al \mbox{%DIFAUXCMD \cite{LLLL }\hspace{0pt}%DIFAUXCMD and the references therein}  .
Revised:  \textit{et al \mbox{%DIFAUXCMD \cite{LLLL }\hspace{0pt}%DIFAUXCMD and the references therein} .
Edit intent: coherence
Original:  See e.g. Lachapelle\textit{et al \mbox{%DIFAUXCMD \cite{LLLL }\hspace{0pt}%DIFAUXCMD and the references therein}  .
Revised:  See e.g. Lachapelle\textit{ \mbox{%DIFAUXCMD \cite{LLLL }\hspace{0pt}%DIFAUXCMD and the references therein} .
Edit intent: clarity
Original:  See e.g. Lachapelle\textit{et al \mbox{%DIFAUXCMD \cite{LLLL }\hspace{0pt}%DIFAUXCMD and the references therein}  .
Revised:  See e.g. Lachapelle\textit{et al }\hspace{0pt}%DIFAUXCMD and the references therein} .
Edit intent: meaning-changed
Original:  See e.g. Lachapelle\textit{et al \mbox{%DIFAUXCMD \cite{LLLL }\hspace{0pt}%DIFAUXCMD and the references therein}  .
Revised:  See e.g. Lachapelle\textit{et al \mbox{%DIFAUXCMD \cite{LLLL }\hspace{0pt}%DIFAUXCMD and the references therein} However, the situation in the case of jumps is not clear. Moreover, it is not clear what happens if there is a delay in the system .
Edit intent: meaning-changed
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised: The mathematical theory of neural networks is ``meant to tell us what is possible and, sometimes equally importantly, what is not." This paper contributes a case that fits into this principle. We propose that "option price or time value" is a natural hyperparameter in the design of neural network option models. Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: coherence
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio asked the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: fluency
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning networks can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: clarity
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they studied the network ( S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: clarity
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K , \tau)\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: fluency
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to C_t/K where S_t, K, \tau, C_t are the underlying price, strike, time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: meaning-changed
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity and option price . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: clarity
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel decision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: fluency
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network ( S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: fluency
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K %DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Edit intent: fluency
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values'
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% , \tau)\to V_t/K . Time values'
Edit intent: clarity
Original:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to  time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K . Time values' appearance in artificial intelligence fits into traders' natural intelligence.
Revised:  Hutchinson, Lo and Poggio raised the question that if learning works can learn the Black-Scholes formula, and they proposed the network mapping the ratio of underlying price to strike S_t/K and the\to time to maturity \tau directly into the ratio of option priceto strike C_t/K . In this paper we propose a novel descision function and study the network mapping S_t/K and%DIFDELCMD < \tauinto %%% the ratio of time value to strike\to V_t/K where V_t is the time value.
Edit intent: meaning-changed
Original:  In order to take a conceptual viewpoint and to prove that V_t/K but not C_t/K can be approximated by superpositions of logistic functions on its domain of definition, we work on the theory of universal approximation on unbounded domains. We prove some general results which imply that an artificial neural network with a single hidden layer and sigmoid activation represents no function in L^{p(}%DIFDELCMD < \RR%%% ^2 \times 0, 1%DIFDELCMD < ]%%% ^{n neural network with a single hidden layer and logistic activation is a universal approximator of L^{2}( %DIFDELCMD < \RR %%%  \times [0, 1] ^{n^+ \times } [0, 1] ^{n .
Revised:  (}%DIFDELCMD < \RR%%% ^2 \times 0, 1%DIFDELCMD < ]%%% ^{n neural network with a single hidden layer and logistic activation is a universal approximator of L^{2}( %DIFDELCMD < \RR %%% \times [0, 1] ^{n^+ \times } [0, 1] ^{n .
Edit intent: coherence