wanyu/IteraTeR_v2 huggingface dataset:
Original:  Furthermore, we relate the existence of such a coupling with sampling k-colourings of sparse random graphs, with expected degree d , for k<d.
Revised:  Furthermore, we relate the existence of such a coupling with sampling k-colourings of sparse random graphs, with expected degree d and k<d.
Edit intent: clarity
Original: We study the spread of epidemics in large networks  when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\'a-vis the underlying network a topology.
Revised: We study epidemic spreading processes in large networks when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\'a-vis the underlying network a topology.
Edit intent: clarity
Original: We study the spread of epidemics in large networks  when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\'a-vis the underlying network a topology.
Revised: We study the spread of epidemics in large networks , when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\'a-vis the underlying network a topology.
Edit intent: fluency
Original: We study the spread of epidemics in large networks  when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\'a-vis the underlying network a topology.
Revised: We study the spread of epidemics in large networks when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\`a-vis the underlying network a topology.
Edit intent: fluency
Original: We study the spread of epidemics in large networks  when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\'a-vis the underlying network a topology.
Revised: We study the spread of epidemics in large networks when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\'a-vis the underlying network topology.
Edit intent: fluency
Original:  For networks which are ' spatially constrained', we show that the spread of infection can be significantly speeded up even by a few such  agents infecting randomly.
Revised:  For networks which are ` spatially constrained', we show that the spread of infection can be significantly speeded up even by a few such agents infecting randomly.
Edit intent: fluency
Original:  More specifically , for general networks with bounded external virulence (e.g., a single or finite number of random mobile agents), we derive upper-bounds on the order of the infection time as a function of network size . Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external infection-spreading policies;
Revised:  Moreover , for general networks with bounded external virulence (e.g., a single or finite number of random mobile agents), we derive upper-bounds on the order of the infection time as a function of network size . Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external infection-spreading policies;
Edit intent: coherence
Original:  More specifically , for general networks with bounded external virulence (e.g., a single or finite number of random mobile agents), we derive upper-bounds on the order of the infection time as a function of network size . Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external infection-spreading policies;
Revised:  More specifically , for general networks , we derive upper-bounds on the order of the infection time as a function of network size . Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external infection-spreading policies;
Edit intent: clarity
Original:  More specifically , for general networks with bounded external virulence (e.g., a single or finite number of random mobile agents), we derive upper-bounds on the order of the infection time as a function of network size . Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external infection-spreading policies;
Revised:  More specifically , for general networks with bounded external virulence (e.g., a single or finite number of random mobile agents), we derive upper-bounds on the order of the infection time as a function of network size . Conversely, for certain common classes of networks such as line graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) external-spreading policies;
Edit intent: clarity
Original:  these adversarial lower bounds match (up to logarithmic factors) the spreading time achieved by an external agent with random mobility .
Revised:  these adversarial lower bounds match (up to logarithmic factors) the spreading time achieved by an external agent with a random spreading policy .
Edit intent: clarity
Original:  This demonstrates that random, state-oblivious infection-spreading by an external agent is in fact order-wise optimal for dissemination in such spatially constrained networks.
Revised:  This demonstrates that random, state-oblivious infection-spreading by an external agent is in fact order-wise optimal for spreading in such spatially constrained networks.
Edit intent: fluency
Original:  In these graphs, the interval [0,x] is the vertex set, while links are generated at random according to the following procedure: From each point yin the interval [0,x], directed links are drawn to points y' in the interval (y,x] which are chosen uniformly with density one.
Revised:  In these graphs, the interval [0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to points y' in the interval (y,x] which are chosen uniformly with density one.
Edit intent: coherence
Original:  In these graphs, the interval [0,x] is the vertex set, while links are generated at random according to the following procedure: From each point yin the interval [0,x], directed links are drawn to points y' in the interval (y,x] which are chosen uniformly with density one.
Revised:  In these graphs, the interval [0,x] is the vertex set, while links are generated at random according to the following procedure: From each point yin the interval [0,x], directed links are drawn to points in the interval (y,x] which are chosen uniformly with density one.
Edit intent: fluency
Original: In some Density Functional Theory based simulations each self-consistent cycle comprises dozens of large dense generalized eigenproblems.
Revised: In Density Functional Theory based simulations each self-consistent cycle comprises dozens of large dense generalized eigenproblems.
Edit intent: clarity
Original:  It was then demonstrated that successive eigenproblems in a sequence are strongly correlated to one another.
Revised:  It was then demonstrated that successive eigenproblems in a sequence are strongly correlated with one another.
Edit intent: fluency
Original:  This last result suggests that we could manipulate the eigenvectors, solving for a specific eigenproblem in a sequence, as an approximate solution for the following eigenproblem.
Revised:  This last result suggests that we can manipulate the eigenvectors, solving for a specific eigenproblem in a sequence, as an approximate solution for the following eigenproblem.
Edit intent: fluency
Original:  In the present work we present a set of preliminary results confirming this initial intuition.
Revised:  In this work we present a set of preliminary results confirming this initial intuition.
Edit intent: clarity
Original:   All the numerical tests are run employing sequences of eigenproblems extracted from simulations of real-world materials .
Revised:  All the numerical tests are carried out employing sequences of eigenproblems extracted from simulations of real-world materials .
Edit intent: clarity
Original:   All the numerical tests are run employing sequences of eigenproblems extracted from simulations of real-world materials .
Revised:  All the numerical tests are run employing sequences of eigenproblems extracted from simulations of solid-state physics crystals .
Edit intent: clarity
Original:  each sequence groups together eigenproblems with equal%DIFDELCMD < {\bf %%% k -vectors and an increasing outer-iteration cycle index \ell.
Revised:  each sequence groups together eigenproblems with equal%DIFDELCMD < {\bf %%% -vectors and an increasing outer-iteration cycle index \ell.
Edit intent: clarity
Original:  First, we provide numerical examples where opportunely selected block iterative solvers benefit from the reuse of eigenvectors by achieving a substantial speed-up.
Revised:  We provide numerical examples where opportunely selected block iterative solvers benefit from the reuse of eigenvectors by achieving a substantial speed-up.
Edit intent: coherence
Original:  First, we provide numerical examples where opportunely selected block iterative solvers benefit from the reuse of eigenvectors by achieving a substantial speed-up.
Revised:  First, we provide numerical examples where opportunely selected block iterative eigensolvers benefit from the reuse of eigenvectors by achieving a substantial speed-up.
Edit intent: fluency
Original:  The results presented here could eventually open the way to a widespread use of block iterative solvers in ab initio electronic structure codes based on the LAPW approach.
Revised:  The results presented will eventually open the way to a widespread use of block iterative solvers in ab initio electronic structure codes based on the LAPW approach.
Edit intent: clarity
Original: One main challenge in the design of distributed storage codes is the%DIFDELCMD < {\it %DIFDELCMD < %%% Exact Repair Problem : if a node storing encoded information fails, to maintain the same level of reliability, we need to exactly regenerate what was lost in a new node .
Revised: %DIFDELCMD < {\it %DIFDELCMD < %%% Exact Repair Problem : if a node storing encoded information fails, to maintain the same level of reliability, we need to exactly regenerate what was lost in a new node .
Edit intent: clarity
Original: One main challenge in the design of distributed storage codes is the%DIFDELCMD < {\it %DIFDELCMD < %%% Exact Repair Problem : if a node storing encoded information fails, to maintain the same level of reliability, we need to exactly regenerate what was lost in a new node .
Revised: One main challenge in the design of distributed storage codes is the%DIFDELCMD < {\it %DIFDELCMD < %%% : if a node storing encoded information fails, to maintain the same level of reliability, we need to exactly regenerate what was lost in a new node .
Edit intent: coherence
Original:  A major open problem in this area has been the design of codes that {\it i)} admit exact and low cost repair of nodes and {\it ii)} have arbitrarily high data rates.
Revised:  A major open problem in this area has been the design of codes that {\it i)} are repair efficient and {\it ii)} have arbitrarily high data rates.
Edit intent: clarity
Original:  A major open problem in this area has been the design of codes that {\it i)} admit exact and low cost repair of nodes and {\it ii)} have arbitrarily high data rates.
Revised:  A major open problem in this area has been the design of codes that {\it i)} admit exact and low cost repair of nodes and {\it ii)} achieve arbitrarily high data rates.
Edit intent: clarity
Original:  In this paper, we are interested in the metric of {\it repair locality}, which corresponds to the the number of disk accesses required during a  node repair.
Revised:  In this paper, we explore the repair metric of {\it repair locality}, which corresponds to the the number of disk accesses required during a node repair.
Edit intent: clarity
Original:  In this paper, we are interested in the metric of {\it repair locality}, which corresponds to the the number of disk accesses required during a  node repair.
Revised:  In this paper, we are interested in the metric of {\it locality}, which corresponds to the the number of disk accesses required during a node repair.
Edit intent: fluency
Original:  In this paper, we are interested in the metric of {\it repair locality}, which corresponds to the the number of disk accesses required during a  node repair.
Revised:  In this paper, we are interested in the metric of {\it repair locality}, which corresponds to the number of disk accesses required during a node repair.
Edit intent: fluency
Original:  In this paper, we are interested in the metric of {\it repair locality}, which corresponds to the the number of disk accesses required during a  node repair.
Revised:  In this paper, we are interested in the metric of {\it repair locality}, which corresponds to the the number of disk accesses required during a single node repair.
Edit intent: clarity
Original:  Under this metric we characterize an information theoretic trade-off that binds together locality, code distance, and storage cost per node.
Revised:  Under this metric we characterize an information theoretic trade-off that binds together locality, code distance, and the storage capacity of each node.
Edit intent: clarity
Original:  We introduce {\it Locally repairable codes} (LRCs) which are shown to achieve this tradeoff .
Revised:  We introduce {\it locally repairable codes} (LRCs) which are shown to achieve this tradeoff .
Edit intent: fluency
Original:  We introduce {\it Locally repairable codes} (LRCs) which are shown to achieve this tradeoff .
Revised:  We introduce {\it Locally repairable codes} (LRCs) that achieve this trade-off .
Edit intent: coherence
Original:  The achievability proof uses a "locality aware " flow graph gadget which leads to a randomized code construction.
Revised:  The achievability proof uses a locality aware flow-graph gadget which leads to a randomized code construction.
Edit intent: fluency
Original:  We then present the%DIFDELCMD < {\it %%% first explicit construction of LRCs that can achieve arbitrarily high data-rates  .
Revised:  %DIFDELCMD < {\it %%% first explicit construction of LRCs that can achieve arbitrarily high data-rates .
Edit intent: coherence
Original:  We then present the%DIFDELCMD < {\it %%% first explicit construction of LRCs that can achieve arbitrarily high data-rates  .
Revised:  We then present the%DIFDELCMD < {\it %%% explicit construction of LRCs that can achieve arbitrarily high data-rates .
Edit intent: clarity
Original:  We then present the%DIFDELCMD < {\it %%% first explicit construction of LRCs that can achieve arbitrarily high data-rates  .
Revised:  We then present the%DIFDELCMD < {\it %%% first Finally, we present an optimal and explicit LRC that achieves arbitrarily high data-rates .
Edit intent: clarity
Original: A fully adaptive system for the suppression of vibration transmission using a single piezoelectric actuator shunted by a negative capacitance circuit is presented.
Revised: An adaptive system for the suppression of vibration transmission using a single piezoelectric actuator shunted by a negative capacitance circuit is presented.
Edit intent: clarity
Original:  The problem of high sensitivity of the vibration control system  is resolved by applying the adaptive control to the circuit parameters of the negative capacitor.
Revised:  The problem of high sensitivity of the vibration control system is resolved by applying an adaptive control to the circuit parameters of the negative capacitor.
Edit intent: fluency
Original:  It is shown that such an arrangement allows a realization of a simple electronic system, which, however, offers a great vibration isolation efficiency in variable vibration conditions.
Revised:  It is shown that such an arrangement allows a design of a simple electronic system, which, however, offers a great vibration isolation efficiency in variable vibration conditions.
Edit intent: clarity
Original:   In this paper, we prove the Total Coloring Conjecture (TCC ) holds for the 1-toroidal graphs with maximum degree at least 11 and some restrictions on the triangles  has a vertex of degree at most four, then G admits a total-(\Delta + 2)-coloring} .
Revised:  In this paper, we prove TCC holds for the 1-toroidal graphs with maximum degree at least 11 and some restrictions on the triangles has a vertex of degree at most four, then G admits a total-(\Delta + 2)-coloring} .
Edit intent: clarity
Original:  Consequently, if G is a diamon-free 1-toroidal graph with maximum degree at most \Delta , where \Delta \geq 11 , and every subgraph K_{4 , then G admits a total-( \Delta + 2 )-coloring .
Revised:  Consequently, if G is a 1-toroidal graph with maximum degree at most \Delta , where \Delta \geq 11 , and every subgraph K_{4 , then G admits a total-( \Delta + 2 )-coloring .
Edit intent: clarity
Original:  Consequently, if G is a diamon-free 1-toroidal graph with maximum degree at most \Delta , where \Delta \geq 11 , and every subgraph K_{4 , then G admits a total-( \Delta + 2 )-coloring .
Revised:  Consequently, if G is a diamon-free 1-toroidal graph with maximum degree \Delta at least 11 , and every subgraph K_{4 , then G admits a total-( \Delta + 2 )-coloring .
Edit intent: clarity
Original:  Consequently, if G is a diamon-free 1-toroidal graph with maximum degree at most \Delta , where \Delta \geq 11 , and every subgraph K_{4 , then G admits a total-( \Delta + 2 )-coloring .
Revised:  Consequently, if G is a diamon-free 1-toroidal graph with maximum degree at most \Delta , where \Delta \geq 11 , and every subgraph K_{4 , then G admits a total coloring with at most \Delta + 2 )-coloring .
Edit intent: coherence
Original:  Consequently, if G is a diamon-free 1-toroidal graph with maximum degree at most \Delta , where \Delta \geq 11 , and every subgraph K_{4 , then G admits a total-( \Delta + 2 )-coloring .
Revised:  Consequently, if G is a diamon-free 1-toroidal graph with maximum degree at most \Delta , where \Delta \geq 11 , and every subgraph K_{4 , then G admits a total-( \Delta + 2 colors .
Edit intent: fluency
Original:  The {\em total chromatic number} of a graph G, denoted by \chiup''(G), is the minimum number of colors needed in a total coloring of G. The most well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree \Delta admits a total coloring with at most \Delta + 2 colors.
Revised:  The {\em total chromatic number} of a graph G, denoted by \chiup''(G), is the minimum number of colors in a total coloring of G. The most well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree \Delta admits a total coloring with at most \Delta + 2 colors.
Edit intent: clarity
Original:  The {\em total chromatic number} of a graph G, denoted by \chiup''(G), is the minimum number of colors needed in a total coloring of G. The most well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree \Delta admits a total coloring with at most \Delta + 2 colors.
Revised:  The {\em total chromatic number} of a graph G, denoted by \chiup''(G), is the minimum number of colors needed in a total coloring of G. The well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree \Delta admits a total coloring with at most \Delta + 2 colors.
Edit intent: coherence
Original:  A graph is {\em 1-toroidal} if it can be drawn on torus such that every edge crosses at most one other edge.
Revised:  A graph is {\em 1-toroidal} if it can be drawn in torus such that every edge crosses at most one other edge.
Edit intent: clarity
Original:  In this paper, we investigate the total coloring of 1-toroidal graphs, and prove that the TCC holds for the 1-toroidal graphs with maximum degree at least  11 and some restrictions on the triangles.
Revised:  In this paper, we investigate the total coloring of 1-toroidal graphs, and prove that the TCC holds for the 1-toroidal graphs with maximum degree at least ~ 11 and some restrictions on the triangles.
Edit intent: fluency
Original: The nonlinear elastic properties of fibrin networks are crucial for normal blood clotting .
Revised: Bundles of polymer filaments are responsible for the rich and unique mechanical behaviors of many biomaterials, including cells and extracellular matrices. In fibrin biopolymers, whose nonlinear elastic properties of fibrin networks are crucial for normal blood clotting .
Edit intent: coherence
Original: The nonlinear elastic properties of fibrin networks are crucial for normal blood clotting .
Revised: The nonlinear elastic properties are crucial for normal blood clotting .
Edit intent: clarity
Original:  Here, we show that the extraordinary strain-stiffening response of fibrin clots reflects the hierarchical architecture of the fibrin fibers , which are bundles of wormlike protofibrils .
Revised:  Here, we show that the extraordinary strain-stiffening response of fibrin clots reflects the hierarchical architecture of the fibrin fibers .
Edit intent: coherence
Original:  We measure the rheology of networks of unbundled protofibrils , and find excellent agreement with an affine model of extensible wormlike polymers.
Revised:  We measure the rheology of networks of unbundled protofibrils and find excellent agreement with an affine model of extensible wormlike polymers.
Edit intent: fluency
Original:  By direct comparison with these data, we show that physiological clots of thick fibers can be modeled as networks of tight protofibril bundles.
Revised:  By direct comparison with these data, we show that physiological fibrin networks composed of thick fibers can be modeled as networks of tight protofibril bundles.
Edit intent: clarity
Original:  We give a general theorem that , for different representations of structures, reduces this classification question to the corresponding question for primitive positive logic  .
Revised:  We give a general theorem that reduces this classification question to the corresponding question for primitive positive logic .
Edit intent: clarity
Original: A weak odd dominated (WOD) set is a set B of vertices for which there exists a subset C of V%DIFDELCMD < \B %%%  }  such that every vertex in B has an odd number of neighbors in C. Given a graph G of order n, \kappa(G) denotes the size of the greatest WOD set, and \kappa'(G) the size of the smallest non-WOD set.
Revised: A weak odd dominated (WOD) set %DIFDELCMD < \B %%% } such that every vertex in B has an odd number of neighbors in C. Given a graph G of order n, \kappa(G) denotes the size of the greatest WOD set, and \kappa'(G) the size of the smallest non-WOD set.
Edit intent: clarity