wanyu/IteraTeR_full_sent huggingface dataset:
Original: Given a set S of n d-dimensional points  , the k-nearest neighbors ( KNN) is the problem of quickly finding k points in S that are nearest to a query point q. The k-nearest neighbors problem has applications in machine learning for classification and regression and also in searching. The secure version of KNN where either q or S are encrypted, has applications such as providing services over sensitive (such as medical or localization) data .
Revised: Given a set S of n d-dimensional points , the k-nearest neighbors ( kNN) classifier assigns q with the majority class of its k nearest neighbors in S. In the secure version of KNN where either q or S are encrypted, has applications such as providing services over sensitive (such as medical or localization) data .
Edit intent: meaning-changed
Original:  In this work we present the first scalable and efficient algorithm for solving KNN with Fully Homomorphic Encryption (FHE)that is realized by a polynomial whose degree is independent of n, the number of points. We implemented our algorithm in an open source library based on HELib implementation for the Brakerski-Gentry-Vakuntanthan's FHE scheme, and ran experiments on MIT's OpenStack cloud. Our experiments show that given a query point q, we can find the set of 20 nearest points out of more than 1000 points in less than an hour. Our result introduces a statistical coreset, which is a data summarization technique that allows statistical functions, such as moments, to be efficiently and scalably computed. As a central tool, we design a new coin toss technique which we use to build the coreset. This coin toss technique and computation of statistical functions may be of independent interest.
Revised:  In this work we present a classifier based on kNN, that can be implemented efficiently with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make on kNN, where we allow it to consider kappa nearest neighbors for kappa ~ k with some probability. We therefore call our classifier k-ish Nearest Neighbors (k-ish NN). The success probability of our solution depends on the distribution of the distances from q to S and increase as its statistical distance to Gaussian decrease. To implement our classifier we introduce the concept of double-blinded coin-toss. In a doubly-blinded coin-toss the success probability as well as the output of the toss are encrypted. We use this coin-toss to efficiently approximate the average and variance of the distances from q to S. We believe these two techniques may be of independent interest.
Edit intent: meaning-changed
Original:  \\%DIF > and classification took less than 3 hours compared to (estimated) weeks in current HE implementations.
Revised:  When implemented with HE, the k-ish NN has a circuit depth that is independent of n, therefore making it scalable. We also implemented our classifier in an open source library based on HELib and tested it on a breast tumor database. The accuracy of our classifier (F_1 score) were 98\\%DIF > and classification took less than 3 hours compared to (estimated) weeks in current HE implementations.
Edit intent: meaning-changed
Original:  Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate predictors that are not just marginally important, but whose associations also stem from significant covarying relationships with other variables in the data.
Revised:  Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate genetic variants that are not just marginally important, but whose associations also stem from significant covarying relationships with other variables in the data.
Edit intent: clarity
Original:  Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate predictors that are not just marginally important, but whose associations also stem from significant covarying relationships with other variables in the data.
Revised:  Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate predictors that are not just marginally important, but whose associations also stem from significant covarying relationships with other variants in the data.
Edit intent: clarity
Original: The Fundamental Review of Trading Book (FRTB) from the Basel Committee overhauls the regulatory framework for minimum capital requirements for market risk. Facing the tightened regulation , banks need to allocate their capital to each of their risk positions to evaluate the capital efficiency of their strategies.
Revised: Facing the FRTB , banks need to allocate their capital to each of their risk positions to evaluate the capital efficiency of their strategies.
Edit intent: clarity
Original:  This paper proposes two computational efficient allocation methods under the FRTB framework. Simulation analysis shows that both these two methods provide more liquidity horizon weighted, more stable , and less negative allocations than the standard methods under the current regulatory framework.
Revised:  This paper proposes two computational efficient allocation methods which are weighted according to liquidity horizon. Both methods provide more liquidity horizon weighted, more stable , and less negative allocations than the standard methods under the current regulatory framework.
Edit intent: meaning-changed
Original:  The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute both the finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
Revised:  The main goal of the article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute both the finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
Edit intent: fluency
Original:  The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute both the finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
Revised:  The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem and to compute both the finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
Edit intent: clarity
Original:  The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute both the finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
Revised:  The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute the ruin probability in finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
Edit intent: meaning-changed
Original:  The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute both the finite-time and infinite-time horizonruin probabilities . Numerical results will also be given.
Revised:  The main goal of this article is to establish a diffusion approximation by verifying a functional central limit theorem of this model and to compute both the finite-time horizon . Numerical results will also be given.
Edit intent: clarity
Original:  for example %DIFDELCMD < \xcal%%%  =C( %DIFDELCMD < \rbb%%% ,%DIFDELCMD < \rbb%%%  ), the class of continuous functions of one real (spatial) variable.
Revised:  for example %DIFDELCMD < \xcal%%% X =C( %DIFDELCMD < \rbb%%% ,%DIFDELCMD < \rbb%%% ), the class of continuous functions of one real (spatial) variable.
Edit intent: meaning-changed
Original:  for example %DIFDELCMD < \xcal%%%  =C( %DIFDELCMD < \rbb%%% ,%DIFDELCMD < \rbb%%%  ), the class of continuous functions of one real (spatial) variable.
Revised:  for example %DIFDELCMD < \xcal%%% =C( %DIFDELCMD < \rbb%%% %DIFDELCMD < \rbb%%% ), the class of continuous functions of one real (spatial) variable.
Edit intent: coherence
Original:  for example %DIFDELCMD < \xcal%%%  =C( %DIFDELCMD < \rbb%%% ,%DIFDELCMD < \rbb%%%  ), the class of continuous functions of one real (spatial) variable.
Revised:  for example %DIFDELCMD < \xcal%%% =C( %DIFDELCMD < \rbb%%% ,%DIFDELCMD < \rbb%%% R,R ), the class of continuous functions of one real (spatial) variable.
Edit intent: meaning-changed
Original:  We study these analog systems and their associated operators, and show how some classically non-generable functions, such as the gamma function and the Riemann zeta function, can be captured with the L-GPAC.
Revised:  We study these analog systems and their associated operators, and show how some classically non-generable functions, such as the gamma function and the zeta function, can be captured with the L-GPAC.
Edit intent: clarity
Original: Inspired by the matching of supply to demand in logistical problems, the optimal transportation (or Monge-Kantorovich ) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.
Revised: Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich ) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.
Edit intent: fluency
Original:  After discretization, optimal transportation becomes a large-scale linear program, which typically is infeasible to solve efficiently on triangle meshes, graphs, point clouds, and other domains encountered in graphics and machine learning.
Revised:  In its most obvious discretization, optimal transportation becomes a large-scale linear program, which typically is infeasible to solve efficiently on triangle meshes, graphs, point clouds, and other domains encountered in graphics and machine learning.
Edit intent: meaning-changed
Original: We consider a stochastic game between a trader and the central bank on target zone markets. In this type of markets the price process is modeled as a diffusion which is reflected at one or more barriers. Such models arise when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider a trader who wishes to liquidate a large amount of currency, where for whom prices are optimal at the barrier.
Revised: We consider a stochastic control problem for a trader who wishes to liquidate a large amount of currency, where for whom prices are optimal at the barrier.
Edit intent: clarity
Original:  We consider a trader who wishes to liquidate a large amount of currency, where for whom prices are optimal at the barrier. The central bank, who wishes to keep the currency exchange rate above this barrier, therefore needs to buy its own currency. The permanent price impact, which is created by the transactions of both sides, turns the optimal trading problems of the trader and the central bank into coupled singular control problems, where the common singularity arises from a local time along a random curve. We first solve the central bank's control problem by means of the Skorokhod map and then derive the trader's optimal strategy by solving a sequence of approximated control problems, thus establishing a Stackelberg equilibrium in our model .
Revised:  We consider a trader who wishes to maximize the expected local time through generating price impact. The local time can be regarded as a proxy for the inventory of a central bank whose aim is to maintain a target zone .
Edit intent: clarity
Original: We consider a stochastic control problem for a trader who wishes to maximize the expected local time through generating price impact. The local time can be regarded as a proxy for the inventory of a central bank whose aim is to maintain a target zone .
Revised: We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever increasing risky position in foreign reserves. We describe this situation mathematically by means of two coupled singular control problems, where the common singularity arises from a local time along a random curve. Our first result identifies a certain local time as that central bank strategy for which this risk position is minimized. We then consider the worst-case situation the central bank may face by identifying that strategy of the strategic investor that maximizes the expected inventory of the central bank under a cost criterion, thus establishing a Stackelberg equilibrium in our model .
Edit intent: meaning-changed
Original:  Our main result is a linear-time algorithm for deciding whether a polygonal curve is threadable, and if so, finding a sequence of rigid motions to thread it through a hole.
Revised:  Our main result is a linear-time algorithm for deciding whether a polygonal curve is threadable---O(n) for a curve of n vertices---and if threadable, finding a sequence of rigid motions to thread it through a hole.
Edit intent: meaning-changed
Original:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time.
Revised:  We also sketch an argument that shows that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time.
Edit intent: coherence
Original:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time.
Revised:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve . The second main result is an O(n polylog n)-time algorithm for deciding whether a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time.
Edit intent: meaning-changed
Original:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time.
Revised:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve can thread through hole in a plane can be decided in quadratic time.
Edit intent: clarity
Original:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane can be decided in quadratic time. Finally, we connect threadable curves to the problem known as "moving a chair through a doorway."
Revised:  In addition, we sketch arguments that show that the threadability of algebraic curves can be decided in time polynomial in the degree of the curve , and that threading a 3D polygonal curve through a point-hole in a plane in R^3, and if so, providing a description of the rigid motions that achieve the threading.
Edit intent: meaning-changed
Original:  We find that the Variance Gamma model generates the highest out-of-sample likelihood of observed prices and the lowest predictive errors, whereas the ARCH-based GRJ-FHS delivers the most consistent forecasts across the entire density range.
Revised:  We find that the Variance Gamma model generates the highest out-of-sample likelihood of observed prices and the lowest predictive errors, whereas the ARCH-based GJR-FHS delivers the most consistent forecasts across the entire density range.
Edit intent: fluency
Original:  We describe the maximum entropy problem and give an overview of the algorithms that are implemented as part of ConIII URL including Monte Carlo histogram, pseudolikelihood, minimum probability flow, a regularized mean field method, and a cluster expansion method . We briefly explain how one should approach and validate maxent models from the perspective of model selection .
Revised:  We describe the maximum entropy problem and give an overview of the algorithms that are implemented as part of ConIII URL including Monte Carlo histogram, pseudolikelihood, minimum probability flow, a regularized mean field method, and a cluster expansion method .
Edit intent: coherence
Original: We consider the approximability of maximization and minimization variants of the Morse matching problem, posed as open problems by Joswig and Pfetsch.
Revised: Discrete Morse theory has emerged as a powerful tool for a wide range of problems, including the computation of (persistent) homology. In this context, discrete Morse theory is used to reduce the problem of computing a topological invariant of an input simplicial complex to computing the same topological invariant of a (significantly smaller) collapsed cell or chain complex. Consequently, devising methods for obtaining gradient vector fields on complexes to reduce the size of the problem instance has become an emerging theme over the last decade. While computing the optimal gradient vector field on a simplicial complex is NP-hard, several heuristics have been observed to compute near-optimal gradient vector fields on a wide variety of datasets. Understanding the theoretical limits of these strategies is therefore a fundamental problem in computational topology. In this paper, we consider the approximability of maximization and minimization variants of the Morse matching problem, posed as open problems by Joswig and Pfetsch.
Edit intent: meaning-changed
Original:  JointDNN not only provides an energy and performance efficient method of querying DNNs for the mobile side , but also benefits the cloud server by reducing the amount of its workload and communications compared to the cloud-only approach.
Revised:  JointDNN not only provides an energy and performance efficient method of querying DNNs for the mobile side but also benefits the cloud server by reducing the amount of its workload and communications compared to the cloud-only approach.
Edit intent: fluency
Original:  The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, caps and floors, year-on-year swaps, caps and floors, and the exotic limited price index swap.
Revised:  The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, year-on-year swaps, caps and floors, and the exotic limited price index swap.
Edit intent: fluency
Original:  The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, caps and floors, year-on-year swaps, caps and floors, and the exotic limited price index swap. The model retains the attractive features of a nominal multi-curve interest rate model  such as closed-form pricing of nominal swaptions  .
Revised:  The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, caps and floors, year-on-year swaps, caps and floors, and the exotic limited-price-index swap. We study the conditions necessary for the multiplicative nominal pricing kernel to give rise to short rate models for the nominal interest rate process. The proposed class of pricing kernel models retains the attractive features of a nominal multi-curve interest rate model such as closed-form pricing of nominal swaptions .
Edit intent: meaning-changed
Original:  The model retains the attractive features of a nominal multi-curve interest rate model  such as closed-form pricing of nominal swaptions  .
Revised:  The model retains the attractive features of a nominal multi-curve interest rate model such as closed-form pricing of nominal swaptions , and it isolates the so-called inflation convexity-adjustment term arising from the covariance between the underlying stochastic drivers .
Edit intent: meaning-changed
Original:  We also find that the weak variance-alpha-gamma process exhibits a wider range of dependence and produces a significantly better fit than the variance-alpha-gamma process on a S&P500-FTSE100 data set, and that DME produces the best fit in this situation.
Revised:  We also find that the weak variance-alpha-gamma process exhibits a wider range of dependence and produces a significantly better fit than the variance-alpha-gamma process on an S&P500-FTSE100 data set, and that DME produces the best fit in this situation.
Edit intent: fluency
Original:  Left-lateralized enhancement in upper alpha EEG coherence also exhibited a significant positive correlation with initial CAPS ratings . Reduction in PTSD severity between the first and last rtfMRI-nf sessions significantly correlated with enhancement in functional connectivity between the LA and the left DLPFC.
Revised:  Left-lateralized enhancement in upper alpha EEG coherence also exhibited a significant positive correlation with the initial CAPS . Reduction in PTSD severity between the first and last rtfMRI-nf sessions significantly correlated with enhancement in functional connectivity between the LA and the left DLPFC.
Edit intent: clarity
Original:  We model the information propagation on a brain graph by the generalized Markov system associated to a new edge transition matrix. The volume entropy is estimated by the stationary equation of the generalized Markov system.
Revised:  We model the information propagation on a brain graph by the generalized Markov system associated to the weighted edge-transition matrix. We estimate the volume entropy using the stationary equation of the generalized Markov system.
Edit intent: meaning-changed
Original:  Our model suggests that the receptor distribution is tuned to maximize the amount of information about the olfactory environment , in accordance with the efficient coding hypothesis. The optimal receptor distribution depends on natural odor statistics, implying that a change in environment should lead to changes in receptor abundances.
Revised:  Our model suggests that the receptor distribution is tuned to maximize the amount of information about the olfactory environment . This adaptation occurs before olfactory signals are decorrelated, leading to a new regime of efficient coding in which the optimal receptor distribution depends on natural odor statistics, implying that a change in environment should lead to changes in receptor abundances.
Edit intent: meaning-changed
Original:  The optimal receptor distribution depends on natural odor statistics, implying that a change in environment should lead to changes in receptor abundances. The effect is more pronounced when olfactory receptors respond strongly to a smaller number of odors. Our model also predicts that, between closely-related species, those with more neurons in the olfactory epithelium should express more receptor types . We show that simple dynamical rules for neural birth and death processes converge to the predicted optimum .
Revised:  The optimal receptor distribution is sensitive to the global context of the correlated responses of all receptor types in the population. We demonstrate how this effect reproduces the context-dependence seen in experiments. We also show that the optimal receptor distribution can be achieved by following simple dynamical rules for neural birth and death processes converge to the predicted optimum .
Edit intent: clarity