wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Revised:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{coded shuffling reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Edit intent: meaning-changed
Original:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Revised:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor of (\alpha + \frac{1 \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Edit intent: meaning-changed
Original:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Revised:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Edit intent: fluency
Original:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to broadcasting a common message (of the same size) to n users.
Revised:  We show that when \alpha is the fraction of the data matrix that can be cached at each worker, and n is the number of workers, coded shuffling \emph{ reduces the communication cost by a factor \Theta(\alpha \gamma(n) ) compared to uncoded shuffling, where \gamma(n) is the ratio of the cost of unicasting n messages to n users to multicasting a common message (of the same size) to n users.
Edit intent: fluency
Original:  Our synthetic and Open MPI experiments on Amazon EC2 show that coded distributed algorithms can achieve significant speedups of up to 40\% compared to uncoded distributed algorithms.
Revised:  For instance, \gamma(n) \simeq n if multicasting a message to n users is as cheap as unicasting a message to one user. We also provide experiment results, corroborating our theoretical gains of the coded algorithms.
Edit intent: meaning-changed
Original:  While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP , theoretical studies of the fidelity issue are still lacking.
Revised:  While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP which consists of both a polymerase site and an exonuclease (proofreading) site, there were quite few theoretical studies on the fidelity issue are still lacking.
Edit intent: meaning-changed
Original:  While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP , theoretical studies of the fidelity issue are still lacking. Kinetic models which considered explicitly both the polymerase pathway and the exonuclease (proofreading ) pathway were proposed since 1970s', but so far there was no rigorous treatment of such models .
Revised:  While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP , theoretical studies of the fidelity issue . The first model which explicitly considered both sites was proposed in 1970s' and the basic idea was widely accepted by later models. However, all these models did not systematically and rigorously investigate the dominant factor on DNAP fidelity, i.e, the higher-order terminal effects through which the polymerization pathway and the exonuclease (proofreading ) pathway were proposed since 1970s', but so far there was no rigorous treatment of such models .
Edit intent: meaning-changed
Original:  We present a rigorous analytical treatment of the  steady-state kinetic equations including higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs .
Revised:  We present a rigorous analytical treatment of the steady-state kinetic equations of any-order terminal effects, and derive analytical expressions for fidelity in terms of kinetic parameters under bio-relevant conditions. These expressions offer new insights on how the the higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs .
Edit intent: meaning-changed
Original:  We present a rigorous analytical treatment of the  steady-state kinetic equations including higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs .
Revised:  We present a rigorous analytical treatment of the steady-state kinetic equations including higher-order terminal effects contribute substantially to the fidelity in an order-by-order way, and also show that the polymerization-and-proofreading mechanism is dominated only by very few key parameters. We then apply these results to calculate the fidelity of some real DNAPs .
Edit intent: meaning-changed
Original:  We present a rigorous analytical treatment of the  steady-state kinetic equations including higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs . Our results show good agreements with previous intuitive estimate of some DNAPs' fidelity under bio-relevant conditions .
Revised:  We present a rigorous analytical treatment of the steady-state kinetic equations including higher-order terminal effects , and then apply the results to the fidelity problem of some real DNAPs , which are in good agreements with previous intuitive estimate of some DNAPs' fidelity under bio-relevant conditions .
Edit intent: coherence
Original: Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization }  weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Revised: 0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization } weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Edit intent: clarity
Original: Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization }  weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Revised: Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization } Over the past half century, portfolio managers have carefully documented the advantages of the equally weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Edit intent: clarity
Original: Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization }  weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Revised: Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization } weighted S\&P 500 portfolio as well as the often overlooked disadvantages of the market capitalization weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Edit intent: clarity
Original: Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization }  weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Revised: Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization } weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio (see \mbox{%DIFAUXCMD Bloom0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ).
Edit intent: meaning-changed
Original:  } In this work, we find superior S\&P 500 portfolio weighting strategies to that of the MaxMedian rule, calculated over an updated 1958-2015 time horizon . The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  } In this work, we find superior S\&P 500 portfolio weighting strategies to that of the MaxMedian rule, calculated over an updated 1958-2015 time horizon weighted using John Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, 1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} , x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Edit intent: meaning-changed
Original:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, \,\, 1/x, 1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} , x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Edit intent: fluency
Original:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, \,\, 1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} , x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Edit intent: fluency
Original:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, 1/\sqrt{x}, \,\, \text{log (x), \sqrt{x,\,\, x,\,\, x^2} , x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Edit intent: meaning-changed
Original:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, 1/\sqrt{x}, \log (x), \,\, \sqrt{x,\,\, x,\,\, x^2} , x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Edit intent: coherence
Original:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, 1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} , where x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Edit intent: meaning-changed
Original:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, 1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} , x is the market capitalization weighted portfolio ) .
Edit intent: clarity
Original:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
Revised:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, 1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} , x , x^2 (in our setting, x is the market capitalization weighted portfolio .
Edit intent: fluency
Original:  We find that the 1/x^2 weighting strategy produces cumulative returns which significantly dominate all other portfolios, posting an annual geometric mean return of 20.889 \\%DIF < . In addition, we show that the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of Tukey's transformational ladder.
Revised:  We find that the 1/x^2 weighting strategy produces cumulative returns which significantly dominates all other portfolios, posting an annual geometric mean return of 20.889 \\%DIF < . In addition, we show that the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of Tukey's transformational ladder.
Edit intent: fluency
Original:  We find that the 1/x^2 weighting strategy produces cumulative returns which significantly dominate all other portfolios, posting an annual geometric mean return of 20.889 \\%DIF < . In addition, we show that the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of Tukey's transformational ladder.
Revised:  We find that the 1/x^2 weighting strategy produces cumulative returns which significantly dominate all other portfolios, achieving an annual geometric mean return of 20.889 \\%DIF < . In addition, we show that the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of Tukey's transformational ladder.
Edit intent: clarity
Original: One of the key factors in -1 programmed ribosomal frameshifting (PRF) is a pseudoknot (PK) RNA . A number of single molecule  experiments have been performed on PKs to decipher the mechanism of PRF.
Revised: Because of the potential link between -1 programmed ribosomal frameshifting (PRF) is a pseudoknot (PK) RNA . A number of single molecule experiments have been performed on PKs to decipher the mechanism of PRF.
Edit intent: clarity
Original: One of the key factors in -1 programmed ribosomal frameshifting (PRF) is a pseudoknot (PK) RNA . A number of single molecule  experiments have been performed on PKs to decipher the mechanism of PRF.
Revised: One of the key factors in -1 programmed ribosomal frameshifting (PRF) and response of a pseudoknot (PK) RNA . A number of single molecule experiments have been performed on PKs to decipher the mechanism of PRF.
Edit intent: meaning-changed
Original: One of the key factors in -1 programmed ribosomal frameshifting (PRF) is a pseudoknot (PK) RNA . A number of single molecule  experiments have been performed on PKs to decipher the mechanism of PRF.
Revised: One of the key factors in -1 programmed ribosomal frameshifting (PRF) is a pseudoknot (PK) RNA to force, a number of single molecule experiments have been performed on PKs to decipher the mechanism of PRF.
Edit intent: clarity
Original: One of the key factors in -1 programmed ribosomal frameshifting (PRF) is a pseudoknot (PK) RNA . A number of single molecule  experiments have been performed on PKs to decipher the mechanism of PRF.
Revised: One of the key factors in -1 programmed ribosomal frameshifting (PRF) is a pseudoknot (PK) RNA . A number of single molecule pulling experiments have been performed on PKs to decipher the mechanism of PRF.
Edit intent: meaning-changed
Original:  Motivated by the experiments, we performed simulations  to describe the response of a PK over a range of mechanical forces (fs) and monovalent salt concentrations (Cs).
Revised:  Motivated by the experiments, we performed simulations using a coarse-grained model of RNA to describe the response of a PK over a range of mechanical forces (fs) and monovalent salt concentrations (Cs).
Edit intent: meaning-changed
Original:  The free energy changes obtained in simulations are in excellent agreement with experiments , thus validating our model. The predicted phase diagram shows that a sequence of structural transitions, populating distinct intermediates, occur as f and C are changed .
Revised:  The free energy changes obtained in simulations are in excellent agreement with experiments . By varying f and C, we calculated the phase diagram that shows a sequence of structural transitions, populating distinct intermediates, occur as f and C are changed .
Edit intent: clarity
Original:  The predicted phase diagram shows that a sequence of structural transitions, populating distinct intermediates, occur as f and C are changed . The stem-loop tertiary interactions rupture first followed by unfolding of the 3^{\prime}-end hairpin (\textrm{ U-I } \textrm{ ).
Revised:  The predicted phase diagram shows that a sequence of structural transitions, populating distinct intermediates, occur as f and C are changed , the stem-loop tertiary interactions rupture first followed by unfolding of the 3^{\prime}-end hairpin (\textrm{ U-I } \textrm{ ).
Edit intent: fluency
Original:  The stem-loop tertiary interactions rupture first followed by unfolding of the 3^{\prime}-end hairpin (\textrm{ U-I } \textrm{ ).
Revised:  The stem-loop tertiary interactions rupture first followed by unfolding of the 3^{\prime}-end hairpin (\textrm{ U-I } \rightleftharpoons\textrm{ ).
Edit intent: meaning-changed
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ ( \textrm{ \textrm{ I-F } \textrm{ ) transition.
Edit intent: clarity
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I E \textrm{ \textrm{ I-F } \textrm{ ) transition.
Edit intent: meaning-changed
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I ( \rightleftharpoons\textrm{ \textrm{ I-F } \textrm{ ) transition.
Edit intent: meaning-changed
Original:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I ( \textrm{  \textrm{ I-F } \textrm{ ) transition.
Revised:  A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as \left(\log C_{\textrm{m}}\right)^{\alpha} with \alpha=1\,(0.5) for \textrm{ U-I ( \textrm{I \textrm{ I-F } \textrm{ ) transition.
Edit intent: fluency