wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Our methods yield further results for regular triangulations. Among others, we show that there are arbitrarily large sets P with non-regular partial triangulations, while every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular partial triangulations (answering a question by F. Santos in the unexpected direction) .
Revised:  For the edge flip-graphs, the vertex connectivity can be shown to be at least as large as (and hence equal to) the minimum degree, provided n is large enough. Our methods yield several other results .
Edit intent: meaning-changed
Original:  Thermodynamic models that are used for secondary structure prediction report a large number of structures in a limited energy range, often failing in identifying the correct native structure unless complemented by auxiliary experimental data.
Revised:  Thermodynamic models that are used for secondary structure prediction rely on computing the partition function of folding ensembles, and can thus estimate minimum free-energy structures and ensemble populations. These models sometimes fail in identifying native structures in a limited energy range, often failing in identifying the correct native structure unless complemented by auxiliary experimental data.
Edit intent: meaning-changed
Original:  In this work we build an automatically trainable model that is based on a combination of thermodynamic parameters, chemical probing data ( Selective 2^\prime Hydroxyl Acylation analyzed via Primer Extension , SHAPE), and co-evolutionary data (Direct Coupling Analysis, DCA)
Revised:  Here, we build a set of models that combine thermodynamic parameters, chemical probing data ( Selective 2^\prime Hydroxyl Acylation analyzed via Primer Extension , SHAPE), and co-evolutionary data (Direct Coupling Analysis, DCA)
Edit intent: clarity
Original:  In this work we build an automatically trainable model that is based on a combination of thermodynamic parameters, chemical probing data ( Selective 2^\prime Hydroxyl Acylation analyzed via Primer Extension , SHAPE), and co-evolutionary data (Direct Coupling Analysis, DCA)
Revised:  In this work we build an automatically trainable model that is based on a combination of thermodynamic parameters, chemical probing data ( DMS , SHAPE), and co-evolutionary data (Direct Coupling Analysis, DCA)
Edit intent: meaning-changed
Original:   . Perturbations are trained on a suitable set of systems for which the native structure is known . A convolutional window is used to include neighboring reactivities in the SHAPE nodes of the network, and regularization terms limit overfitting improving transferability.
Revised:  through a network that outputs perturbations to the ensemble free energy . Perturbations are trained on a suitable set of systems for which the native structure is known . A convolutional window is used to include neighboring reactivities in the SHAPE nodes of the network, and regularization terms limit overfitting improving transferability.
Edit intent: meaning-changed
Original:   . Perturbations are trained on a suitable set of systems for which the native structure is known . A convolutional window is used to include neighboring reactivities in the SHAPE nodes of the network, and regularization terms limit overfitting improving transferability.
Revised:  . Perturbations are trained to increase the ensemble populations of a representative set of known native RNA structures. In the chemical probing nodes of the network, and regularization terms limit overfitting improving transferability.
Edit intent: clarity
Original:   . Perturbations are trained on a suitable set of systems for which the native structure is known . A convolutional window is used to include neighboring reactivities in the SHAPE nodes of the network, and regularization terms limit overfitting improving transferability.
Revised:  . Perturbations are trained on a suitable set of systems for which the native structure is known . A convolutional window is used to include neighboring reactivities in the SHAPE nodes of the network, a convolutional window combines neighboring reactivities, enlightening their structural information content and the contribution of local conformational ensembles. Regularization is used to limit overfitting and improve transferability.
Edit intent: meaning-changed
Original:  The most transferable model is chosen with a cross-validation strategy that allows to automatically optimize the relative importance of heterogenous input datasets. The model architecture enlightens the structural information content of SHAPE reactivities and their dependence on local conformational ensembles. By using the selected model , we obtain enhanced populations for reference native structures and more sensitive and precise predicted structures in an independent validation set not seen during training .
Revised:  The most transferable model is chosen with a cross-validation strategy that estimates the performance of models on systems on which they are not trained. With the selected model , we obtain enhanced populations for reference native structures and more sensitive and precise predicted structures in an independent validation set not seen during training .
Edit intent: clarity
Original:  In most cases it can be computed using either a recursion or a differential equation (for exponential job sizes with mean one). In this paper we study the value of the mean response time E[ R _\lambda] as the arrival rate \lambda approaches 1  (i.e. the system gets close to instability).
Revised:  In most cases it can be computed as the solution of a set of differential equations. Here we study the value of the mean response time E[ R _\lambda] as the arrival rate \lambda approaches 1 (i.e. the system gets close to instability).
Edit intent: clarity
Original:  In this paper we study the value of the mean response time E[ R _\lambda] as the arrival rate \lambda approaches 1  (i.e. the system gets close to instability).
Revised:  In this paper we study the value of the mean response time E[ R _\lambda] as the arrival rate \lambda approaches 1 for a number of load balancing policies when job sizes are exponential with mean 1 (i.e. the system gets close to instability).
Edit intent: meaning-changed
Original:  As E[ R _\lambda] diverges to infinity, we scale with -\log(1-\lambda) and present a method to compute the limit \lambda\rightarrow 1^--E[ R _\lambda]/\log(1-\lambda).
Revised:  As E[ W _\lambda] diverges to infinity, we scale with -\log(1-\lambda) and present a method to compute the limit \lambda\rightarrow 1^--E[ R _\lambda]/\log(1-\lambda).
Edit intent: meaning-changed
Original:  As E[ R _\lambda] diverges to infinity, we scale with -\log(1-\lambda) and present a method to compute the limit \lambda\rightarrow 1^--E[ R _\lambda]/\log(1-\lambda).
Revised:  As E[ R _\lambda] diverges to infinity, we scale with -\log(1-\lambda) and present a method to compute the limit \lambda\rightarrow 1^--E[ W _\lambda]/\log(1-\lambda).
Edit intent: fluency
Original:  This limit has been previously determined for SQ(d) and LL(d), two well-known policies that assign an incoming job to a server with either the shortest queue or least work left among d randomly selected servers. However, the derivation of the result for SQ(d) relied on the closed form representation of the mean response time and does not seem to generalize well, moreover the proof for LL(d) is incomplete. In contrast, we present a general result that holds for any policy for which the associated recursion or differential equation satisfies a list of criteria.
Revised:  This limit has a surprisingly simple form for the load balancing algorithms considered. We present a general result that holds for any policy for which the associated recursion or differential equation satisfies a list of criteria.
Edit intent: clarity
Original:  In contrast, we present a general result that holds for any policy for which the associated recursion or differential equation satisfies a list of criteria. For SQ(d) and LL(d) these criteria are trivially verified.
Revised:  In contrast, we present a general result that holds for any policy for which the associated recursion or differential equation satisfies a list of assumptions. For the LL(d) these criteria are trivially verified.
Edit intent: clarity
Original:  We apply our method to SQ(d,K) resp LL(d,K) with exponential job sizes of mean one. For these policies, jobs arrive in batches of size K and join the K servers with the shortest queue resp least amount of work left. For SQ(d ,K) we obtain \frac{1{\log(d/K)} as limiting value, while for LL(d,K) we find the limit to be }  equal to \frac{K}{d-K}.
Revised:  We apply our method to SQ(d,K) resp LL(d,K) {\log(d/K)} as limiting value, while for LL(d,K) we find the limit to be } equal to \frac{K}{d-K}.
Edit intent: meaning-changed
Original:  For SQ(d ,K) we obtain \frac{1{\log(d/K)} as limiting value, while for LL(d,K) we find the limit to be }  equal to \frac{K}{d-K}.
Revised:  For SQ(d ,K) we obtain \frac{1{\log(d/K)} as limiting value, while for LL(d,K) we find the limit to be } policy, which assigns batches of K jobs to the K least loaded servers among d randomly selected servers, satisfies the assumptions and the limit is equal to \frac{K}{d-K}.
Edit intent: meaning-changed
Original:  We further analyse a policy where SQ(d_i) resp LL(d_i) is used with probability p_i . For the shortest queue variant, we obtain the limit \frac{1{\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} {\sum_ip_id_i-1}.
Revised:  For a policy which applies LL(d_i) is used with probability p_i . For the shortest queue variant, we obtain the limit \frac{1{\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} {\sum_ip_id_i-1}.
Edit intent: clarity
Original:  We further analyse a policy where SQ(d_i) resp LL(d_i) is used with probability p_i . For the shortest queue variant, we obtain the limit \frac{1{\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} {\sum_ip_id_i-1}.
Revised:  We further analyse a policy where SQ(d_i) resp LL(d_i) with probability p_i . For the shortest queue variant, we obtain the limit \frac{1{\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} {\sum_ip_id_i-1}.
Edit intent: clarity
Original:  We further analyse a policy where SQ(d_i) resp LL(d_i) is used with probability p_i . For the shortest queue variant, we obtain the limit \frac{1{\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} {\sum_ip_id_i-1}.
Revised:  We further analyse a policy where SQ(d_i) resp LL(d_i) is used with probability p_i {\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} {\sum_ip_id_i-1}.
Edit intent: coherence
Original:  We further analyse a policy where SQ(d_i) resp LL(d_i) is used with probability p_i . For the shortest queue variant, we obtain the limit \frac{1{\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} {\sum_ip_id_i-1}.
Revised:  We further analyse a policy where SQ(d_i) resp LL(d_i) is used with probability p_i . For the shortest queue variant, we obtain the limit \frac{1{\log\left(\sum_{i=1}^np_id_i\right)}, while for the least loaded variant, we obtain \frac{1}{\sum_{i=1}^np_id_i-1}.} , we show that the limit is given by \frac{1{\sum_ip_id_i-1}.
Edit intent: meaning-changed
Original:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[ -E}[ \log(1-\lambda) / \log(p_\lambda)=1.}
Revised:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[W_\lambda -E}[ \log(1-\lambda) / \log(p_\lambda)=1.}
Edit intent: meaning-changed
Original:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[ -E}[ \log(1-\lambda) / \log(p_\lambda)=1.}
Revised:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[ /\log(p_\lambda) is well defined and non-zero (contrary to \lim_{\lambda\rightarrow 0^+-E}[ \log(1-\lambda) / \log(p_\lambda)=1.}
Edit intent: meaning-changed
Original:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[ -E}[ \log(1-\lambda) / \log(p_\lambda)=1.}
Revised:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[ -E}[W_\lambda \log(1-\lambda) / \log(p_\lambda)=1.}
Edit intent: meaning-changed
Original:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[ -E}[ \log(1-\lambda) / \log(p_\lambda)=1.}
Revised:  In addition, we propose an alternate scaling -\log(p_\lambda) instead of -\log(1-\lambda), for which the limit \lim_{\lambda\rightarrow 0^+}-E}[ -E}[ /\log(1-\lambda)), while \lim_{\lambda\rightarrow 1^-\log(1-\lambda) / \log(p_\lambda)=1.}
Edit intent: meaning-changed
Original: A compressed index is a data structure representing a text within compressed space and supporting fast count and locate queries: count/return all positions where a pattern occurs. The first compressed indexes operate within a space bounded by the text's entropy. Entropy, however, is insensitive to long repetitions. For this reason, in recent years more powerful compressed indexes have emerged; these are based on  the Lempel-Ziv factorization, the run-length BWT, context-free grammars and, more recently, string attractors.
Revised: In this paper, we consider the problem of compressing a trie while supporting the powerful the Lempel-Ziv factorization, the run-length BWT, context-free grammars and, more recently, string attractors.
Edit intent: clarity
Original:  these are based on  the Lempel-Ziv factorization, the run-length BWT, context-free grammars and, more recently, string attractors. Labeled trees add a whole new dimension to the problem: one needs not only to compress the labels, but also the tree 's topology. On this side, less is known. Jacobson showed how to represent the topology of a tree with n nodes in 2n+o(n) bits of space (succinct) while also supporting constant-time navigation queries.
Revised:  these are based on the pre-order identifiers of all nodes reached by a path labeled with a given query pattern. Our result builds on top of the XBWT tree transform of
Edit intent: clarity
Original:  Ferragina et al. presented the first entropy-compressed labeled tree representation (the XBWT) able to count, but not locate , paths labeled with a given pattern. Grammars and the Lempel-Ziv factorization have been extended to trees, but those representations do not support indexing queries. In this paper, we show for the first time how to support the powerful locate queries on compressed trees. We start by proposing suitable generalizations of  [  run-length  BWT , high-order entropy, and string attractors to cardinal trees (tries) .
Revised:  Ferragina et al. FOCS 2005 [ run-length BWT , high-order entropy, and string attractors to cardinal trees (tries) .
Edit intent: meaning-changed
Original:  We start by proposing suitable generalizations of  [  run-length  BWT , high-order entropy, and string attractors to cardinal trees (tries) .
Revised:  We start by proposing suitable generalizations of [ run-length encoded Burrows-Wheeler transform (BWT). Our first contribution is to propose a suitable generalization of the run-length BWT , high-order entropy, and string attractors to cardinal trees (tries) .
Edit intent: meaning-changed
Original:  We show that  the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's high-order worst-case entropyH.
Revised:  We show that this natural generalization enjoys several of the useful properties of its counterpart on strings: in particular, the transform natively supports counting occurrences of a query pattern on the trie's paths and its size r captures the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's high-order worst-case entropyH.
Edit intent: meaning-changed
Original:  We show that  the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's high-order worst-case entropyH. We finally present the first trie index able to locate in pre-order nodes reached by a path labeled with a given pattern. Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r log n) \leq 2n + o(n)  + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
Revised:  We show that the number r \leq n of XBWT-runs upper-bounds the size of the smallest tree attractor and lower-bounds the trie's repetitiveness and lower-bounds a natural notion of trie entropy. Our main contribution is a much deeper insight into the combinatorial structure of this object. In detail, we show that a data structure of O(r log n) \leq 2n + o(n) + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
Edit intent: meaning-changed
Original:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r log n) \leq 2n + o(n)  + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
Revised:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r \log n) + 2n + o(n) + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
Edit intent: clarity
Original:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r log n) \leq 2n + o(n)  + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
Revised:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r log n) \leq 2n + o(n) bits, where n is the number of nodes, allows locating the occ occurrences of a pattern of length m in nearly-optimal O(m\log\sigma + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
Edit intent: meaning-changed
Original:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r log n) \leq 2n + o(n)  + O(H log n) bitsof space: the reporting timeis optimal and the locate machinery fits within compressed space on top of the succinct topology .
Revised:  Our index locates path occurrences in constant time each and takes 2n + o(n) + O(r log n) \leq 2n + o(n) + occ) time, where \sigma is the alphabet's size. Our solution consists in sampling O(r) nodes that can be used as "anchor points" during the locate process. Once obtained the pre-order identifier of the first pattern occurrence (in co-lexicographic order), we show that a constant number of constant-time jumps between those anchor points lead to the identifier of the next pattern occurrence, thus enabling locating in optimal O(1) time per occurrence .
Edit intent: meaning-changed
Original:  Our conclusions are elaborated by a broad set of applications within macroeconomics and finance. These show that the inherent bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Revised:  Macroeconomic and financial applications show that the inherent bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Edit intent: clarity
Original:  These show that the inherent bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Revised:  These show that the bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Edit intent: clarity
Original:  These show that the inherent bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Revised:  These show that the inherent bias-variance tradeoff implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Edit intent: fluency
Original:  These show that the inherent bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Revised:  These show that the inherent bias-variance trade-off implied by targeting, due to increased correlation among trees in the forest , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Edit intent: meaning-changed
Original:  These show that the inherent bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium level , selecting the best 10-30\\%DIF < of commonly applied predictors.
Revised:  These show that the inherent bias-variance trade-off implied by targeting, due to increased tree correlation , is balanced at a medium degree of targeting , selecting the best 10-30\\%DIF < of commonly applied predictors.
Edit intent: clarity
Original:  The challenge is that selective isolation of the sick, an often viable and effective strategy, is insufficient against COVID-19 , due to its relatively long incubation period, in which exposed individuals experience no symptoms, but still contribute to the spread.
Revised:  The challenge is that selective isolation of the symptomatic patients is insufficient to control SARS-CoV-2 , due to its relatively long incubation period, in which exposed individuals experience no symptoms, but still contribute to the spread.
Edit intent: meaning-changed
Original:  The challenge is that selective isolation of the sick, an often viable and effective strategy, is insufficient against COVID-19 , due to its relatively long incubation period, in which exposed individuals experience no symptoms, but still contribute to the spread.
Revised:  The challenge is that selective isolation of the sick, an often viable and effective strategy, is insufficient against COVID-19 , due to its relatively long incubation period, in which individuals experience no symptoms, but still contribute to the spread.
Edit intent: clarity
Original:  The challenge is that selective isolation of the sick, an often viable and effective strategy, is insufficient against COVID-19 , due to its relatively long incubation period, in which exposed individuals experience no symptoms, but still contribute to the spread.
Revised:  The challenge is that selective isolation of the sick, an often viable and effective strategy, is insufficient against COVID-19 , due to its relatively long incubation period, in which exposed individuals experience no symptoms, but may already contribute to the spread.
Edit intent: clarity