wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper, we give a new construction of such a HSG assuming that we have an explicit polynomial of sufficient hardness in the sense of approximative or border complexity .
Revised:  In this paper, we give a new construction of such a HSG assuming that we have an explicit polynomial of sufficient hardness .
Edit intent: clarity
Original:  Formally, we prove the following result over any characteristic zero field \mathbb{F : Suppose P(z_1,\ldots, z_k) is an explicit k-variate degree d polynomial that is not in the border of circuits of size s.
Revised:  Formally, we prove the following result over any characteristic zero field \mathbb{F : Suppose P(z_1,\ldots, z_k) is an explicit k-variate degree d polynomial that is not computable by circuits of size s.
Edit intent: clarity
Original:  Then, there is an explicit hitting-set generator Gen _P:F^{2k} \rightarrow \mathbb{F}^n such that every non-zero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies Q \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s'  < s.
Revised:  Then, there is an explicit HSG G _P:F^{2k} \rightarrow \mathbb{F}^n such that every non-zero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies Q \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s' < s.
Edit intent: clarity
Original:  Then, there is an explicit hitting-set generator Gen _P:F^{2k} \rightarrow \mathbb{F}^n such that every non-zero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies Q \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s'  < s.
Revised:  Then, there is an explicit hitting-set generator Gen _P:F^{2k} \rightarrow \mathbb{F}^n such that every nonzero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies Q \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s' < s.
Edit intent: coherence
Original:  Then, there is an explicit hitting-set generator Gen _P:F^{2k} \rightarrow \mathbb{F}^n such that every non-zero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies Q \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s'  < s.
Revised:  Then, there is an explicit hitting-set generator Gen _P:F^{2k} \rightarrow \mathbb{F}^n such that every non-zero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies C \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s' < s.
Edit intent: coherence
Original:  Then, there is an explicit hitting-set generator Gen _P:F^{2k} \rightarrow \mathbb{F}^n such that every non-zero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies Q \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s'  < s.
Revised:  Then, there is an explicit hitting-set generator Gen _P:F^{2k} \rightarrow \mathbb{F}^n such that every non-zero n-variate degree D polynomial Q(x_1, x_2, \ldots, x_n) in the border of size s' circuits satisfies Q \neq 0 \Rightarrow Q \circ \mathsf{Gen _P \neq 0, provided n^{10k}d ^2 D s' ) < s.
Edit intent: coherence
Original:  Suppose , for every s \geq k , there is an explicit hitting set of size s^{k-\delta of k-variate size s algebraic circuits.
Revised:  Suppose for every s \geq k , there is an explicit hitting set of size s^{k-\delta of k-variate size s algebraic circuits.
Edit intent: fluency
Original:  Then , there is an explicit hitting set of size poly(s) for the border s-variate algebraic circuits of size s and degree s.
Revised:  Then there is an explicit hitting set of size poly(s) for the border s-variate algebraic circuits of size s and degree s.
Edit intent: fluency
Original:  Formally, we prove the following result over any field \mathbb{F of characteristic zero: Suppose P(z_1,\ldots, z_k) and \delta > 0 be arbitrary constants.
Revised:  Formally, we prove the following over any field \mathbb{F of characteristic zero: Suppose P(z_1,\ldots, z_k) and \delta > 0 be arbitrary constants.
Edit intent: clarity
Original:  Formally, we prove the following result over any field \mathbb{F of characteristic zero: Suppose P(z_1,\ldots, z_k) and \delta > 0 be arbitrary constants.
Revised:  Formally, we prove the following result over any field of characteristic zero: Suppose P(z_1,\ldots, z_k) and \delta > 0 be arbitrary constants.
Edit intent: clarity
Original:  Suppose \{P_d\}_{d\in N} } is an explicit  k-variate degree d polynomial that is not computable by  circuits of size s . Then, there is an explicit HSG G_P:
Revised:  Suppose \{P_d\}_{d\in N} } is an explicit k-variate polynomials such that circuits of size s . Then, there is an explicit HSG G_P:
Edit intent: clarity
Original:  Unlike the prior constructions of such maps, our construction is purely algebraic and does not rely on the notion of combinatorial designs.
Edit intent: coherence
Original:  As a direct consequence, we show that even saving a single point from the "trivial" explicit, exponential sized hitting sets for constant-variate polynomials of low individual-degree which are computable by small circuits, implies a deterministic polynomial time algorithm for PIT.
Revised:  As a direct consequence, we show that even saving a single point from the "trivial" explicit, exponential sized hitting sets for constant-variate polynomials of low individual degree which are computable by small circuits, implies a deterministic polynomial time algorithm for PIT.
Edit intent: fluency
Original: We introduce a measurement tool for  performance evaluation of wireless communications with drones over cellular networks.
Revised: We introduce a measurement tool for the performance evaluation of wireless communications with drones over cellular networks.
Edit intent: fluency
Original: In this paper, we present a cyber-physical testbed created to enable a human-robot team to preform a shared task in a shared workspace.
Revised: In this paper, we present a cyber-physical testbed created to enable a human-robot team to perform a shared task in a shared workspace.
Edit intent: fluency
Original:  The testbed integrates elements that exists in the physical and virtual world.
Revised:  The testbed integrates elements that exist in the physical and virtual world.
Edit intent: fluency
Original:  In this work, we report the insights we gathered through out our exploration in understanding and implementing task planning and execution for human-robot team.
Revised:  In this work, we report the insights we gathered throughout our exploration in understanding and implementing task planning and execution for human-robot team.
Edit intent: fluency
Original: In future transportation systems, the charging behavior of electric Autonomous Mobility on Demand (AMoD) fleets, i.e., fleets of  self-driving cars that service on-demand trip requests, will likely challenge power distribution networks (PDNs), causing overloads or voltage drops.
Revised: In future transportation systems, the charging behavior of electric Autonomous Mobility on Demand (AMoD) fleets, i.e., fleets of electric self-driving cars that service on-demand trip requests, will likely challenge power distribution networks (PDNs), causing overloads or voltage drops.
Edit intent: fluency
Original:  In this paper, we show that these challenges can be significantly attenuated if the PDNs' operational constraints and exogenous loads (e.g., from homes or businesses) are considered when operating the electric AMoD fleet.
Revised:  In this paper, we show that these challenges can be significantly attenuated if the PDNs' operational constraints and exogenous loads (e.g., from homes or businesses) are accounted for when operating an electric AMoD fleet.
Edit intent: clarity
Original:  We focus on a system-level perspective, assuming full cooperation between the AMoD and the PDN operators.
Revised:  We focus on a system-level perspective, assuming full coordination between the AMoD and the PDN operators.
Edit intent: fluency
Original:  Through this single entity perspective, we derive an upper bound on the benefits of coordination .
Revised:  From this single entity perspective, we derive an upper bound on the benefits of coordination .
Edit intent: fluency
Original:  We present an optimization-based modeling approach  to jointly control an electric AMoD fleet and a series of PDNs, and analyze the benefit of coordination under load balancing constraints.
Revised:  We present an optimization-based modeling approach for electric AMoD systems to jointly control an electric AMoD fleet and a series of PDNs, and analyze the benefit of coordination under load balancing constraints.
Edit intent: clarity
Original:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of  overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Revised:  For a case study of Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Edit intent: clarity
Original:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of  overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Revised:  For a case study in Orange County, CA, we show that the coordination between the electric AMoD fleet and the PDNs helps to reduce 99\% of overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Edit intent: clarity
Original:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of  overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Revised:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs eliminates 99\% of overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Edit intent: clarity
Original:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of  overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Revised:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of the overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Edit intent: fluency
Original:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of  overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Revised:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of overloads and 50\% of the voltage drops that the electric AMoD fleet causes without coordination .
Edit intent: fluency
Original:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of  overloads and 50\% of voltage drops which the electric AMoD fleet causes without coordination .
Revised:  For a case study in Orange County, CA, we show that coordinating the electric AMoD fleet and the PDNs helps to reduce 99\% of overloads and 50\% of voltage drops which the electric AMoD fleet would cause in an uncoordinated setting .
Edit intent: clarity
Original:  Our results show that coordinating electric AMoD and PDNs helps to level loads and can significantly postpone the point at which upgrading the network's capacity to a larger scale becomes inevitable to preserve stability .
Revised:  Our results show that coordinating electric AMoD and PDNs can help maintain the reliability of PDNs under added electric AMoD charging load, thus significantly mitigating or deferring the need for PDN capacity upgrades .
Edit intent: clarity
Original: Industrial automation has received a considerable attention for last few years with the rise of Internet of Things (IoT).
Revised: Industrial automation has received a considerable attention in the last few years with the rise of Internet of Things (IoT).
Edit intent: clarity
Original:  Specifically, industrial communication network technology such as Profinet has played the role of a major game changer for such automation.
Revised:  Specifically, industrial communication network technology such as Profinet has proved to be a major game changer for such automation.
Edit intent: clarity
Original:  However, industrial automation devices often have to exhibit robustness under dynamically changing network conditions and thus, demands a rigorous testing environment to avoid any safety-critical failures.
Revised:  However, industrial automation devices often have to exhibit robustness to dynamically changing network conditions and thus, demands a rigorous testing environment to avoid any safety-critical failures.
Edit intent: clarity
Original:  However, industrial automation devices often have to exhibit robustness under dynamically changing network conditions and thus, demands a rigorous testing environment to avoid any safety-critical failures.
Revised:  However, industrial automation devices often have to exhibit robustness under dynamically changing network conditions and thus, demand a rigorous testing environment to avoid any safety-critical failures.
Edit intent: fluency
Original:  Hence, in this paper, we have proposed an FPGA-based novel framework called " Profi-Load " to generate Profinet traffic with specific intensities for a specified duration of time.
Revised:  Hence, in this paper, we have proposed an FPGA-based novel framework called Profi-Load " to generate Profinet traffic with specific intensities for a specified duration of time.
Edit intent: fluency
Original:  Hence, in this paper, we have proposed an FPGA-based novel framework called " Profi-Load " to generate Profinet traffic with specific intensities for a specified duration of time.
Revised:  Hence, in this paper, we have proposed an FPGA-based novel framework called " Profi-Load to generate Profinet traffic with specific intensities for a specified duration of time.
Edit intent: fluency
Original:  The proposed Profi-Load will facilitate the testing of the performance of automated devices under various network conditions.
Revised:  The proposed Profi-Load intends to facilitate the performance testing of the performance of automated devices under various network conditions.
Edit intent: clarity
Original:  The proposed Profi-Load will facilitate the testing of the performance of automated devices under various network conditions.
Revised:  The proposed Profi-Load will facilitate the testing of the industrial automated devices under various network conditions.
Edit intent: clarity
Original:  We have developed our proposed " Profi-Load " framework by employing the Xilinx based "NetJury " device which is based on Zynq-7000 FPGA family.
Revised:  We have developed our proposed Profi-Load " framework by employing the Xilinx based "NetJury " device which is based on Zynq-7000 FPGA family.
Edit intent: fluency
Original:  We have developed our proposed " Profi-Load " framework by employing the Xilinx based "NetJury " device which is based on Zynq-7000 FPGA family.
Revised:  We have developed our proposed " Profi-Load framework by employing the Xilinx based "NetJury " device which is based on Zynq-7000 FPGA family.
Edit intent: fluency
Original:  We have developed our proposed " Profi-Load " framework by employing the Xilinx based "NetJury " device which is based on Zynq-7000 FPGA family.
Revised:  We have developed our proposed " Profi-Load " framework by employing the Xilinx-based NetJury device which belongs to Zynq-7000 FPGA family.
Edit intent: clarity
Original:  A series of experiments have been conducted to evaluate the effectiveness of Profi-Load and it has been observed that Profi-Load is able to generate precise Load at a constant rate for stringent timing requirements.
Revised:  A series of experiments have been conducted to evaluate the effectiveness of Profi-Load and it has been observed that Profi-Load is able to generate precise load at a constant rate for stringent timing requirements.
Edit intent: fluency
Original:  Further, s suitable Human Machine Interface (HMI) has also been developed for quick access to our framework.
Revised:  Furthermore, a suitable Human Machine Interface (HMI) has also been developed for quick access to our framework.
Edit intent: fluency
Original:  The HMI at the client side can directly communicate with the NetJury device and parameters such as, required Load amount, number of packet(s) to be sent or desired time duration can be selected using the HMI.
Revised:  The HMI at the client side can directly communicate with the NetJury device and parameters such as, required load amount, number of packet(s) to be sent or desired time duration can be selected using the HMI.
Edit intent: fluency
Original: We propose and analyse the properties of a new class of models for the electromechanics of the cardiac tissue.
Revised: We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue.
Edit intent: fluency
Original:  The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so for  active stress and active strain formulation of active mechanics) coupled with a four-variable phenomenological model for human  action potential.
Revised:  The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so for both active stress and active strain formulation of active mechanics) coupled with a four-variable phenomenological model for human action potential.
Edit intent: clarity
Original:  The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so for  active stress and active strain formulation of active mechanics) coupled with a four-variable phenomenological model for human  action potential.
Revised:  The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law (this is so for active stress and active strain formulations of active mechanics) coupled with a four-variable phenomenological model for human action potential.
Edit intent: fluency
Original:  and the activation model assumes a simplified stretch-calcium interaction generating active tension and active strain.
Revised:  and the activation model assumes a simplified stretch-calcium interaction generating active tension or active strain.
Edit intent: fluency
Original:  Finally, combining these two schemes, we provide a computationally efficient and almost optimal scheme to solve the MG channel allocation problem, and various results and insights on the variation of the optimal system performance with respect to different system parameters .
Revised:  Finally, combining these two schemes, we provide a computationally efficient and almost optimal scheme to solve the channel allocation problem, and various results and insights on the variation of the optimal system performance with respect to different system parameters .
Edit intent: clarity
Original:  Finally, combining these two schemes, we provide a computationally efficient and almost optimal scheme to solve the MG channel allocation problem, and various results and insights on the variation of the optimal system performance with respect to different system parameters .
Revised:  Finally, combining these two schemes, we provide a computationally efficient and almost optimal scheme to solve the MG channel allocation problem, and various results and insights on the variation of the optimal system performance with respect to different system parameters 
Edit intent: fluency
Original: In this paper we present a sub-system to convert audio information from low-power MEMS microphones with pulse density modulation (PDM) output into rate coded spike streams .
Revised: In this paper we present a sub-system to convert audio information from low-power pulse density modulation (PDM) output into rate coded spike streams .
Edit intent: clarity
Original: In this paper we present a sub-system to convert audio information from low-power MEMS microphones with pulse density modulation (PDM) output into rate coded spike streams .
Revised: In this paper we present a sub-system to convert audio information from low-power MEMS microphones with pulse density modulation (PDM) output into rate coded spike frequencies .
Edit intent: clarity
Original:  For this conversion, we have designed a HDL component for FPGA able to interface with PDM microphonesand converts their pulses to temporal distributed spikes following a pulse frequency modulation (PFM) scheme with an accurate configurable Inter-Spike-Interval .
Revised:  For this conversion, we have designed a HDL component for FPGA able to interface with PDM microphonesand converts their pulses to temporal distributed spikes following a pulse frequency modulation (PFM) scheme with an accurate Inter-Spike-Interval .
Edit intent: clarity
Original:  The new FPGA component has been tested in two scenarios, first as a stand-alone circuit for its characterization, and then it has been integrated with a full NAS design to verify its behavior.
Revised:  The new FPGA component has been tested in two scenarios, first as a stand-alone circuit for its characterization, and then integrated with a full NAS design to verify its behavior.
Edit intent: fluency
Original:  This PDM interface demands less than 1 \% of a Spartan 6 FPGA resources and has a power \\%DIF > of the resources of a Spartan-6 FPGA and has a power consumption below 5mW.
Revised:  This PDM interface demands less than 1 \\%DIF > of the resources of a Spartan-6 FPGA and has a power consumption below 5mW.
Edit intent: fluency
Original: Noisy Intermediate-Scale Quantum (NISQ) computers aim to perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires comparison with a state-of-the-art classical simulator.
Revised: Noisy Intermediate-Scale Quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires comparison with a state-of-the-art classical simulator.
Edit intent: clarity
Original:  In addition, we propose a standard benchmark for NISQ computers based on qFlex , a tensor-network-based classical high-performance simulator of RQC, which are considered the leading proposal for Quantum Supremacy .
Revised:  In addition, we propose a standard benchmark for NISQ computers based on qFlex .
Edit intent: coherence
Original:  Examples are Steiner trees ( minimal-weight trees spanning T) and subsetwise spanners ( subgraphs G'(V',E')such that for given \alpha,\beta%DIFDELCMD < \geq1%%% , d_{G'(u,v)\leq \alpha d_{G}(u,v)+\beta for u,v\in T)}  . Multi-level subsetwise sparsifiers are generalizations in which terminal vertices require different levels or grades of service  .
Revised:  Examples are Steiner trees ( minimal-weight trees spanning T) and subsetwise spanners ( %DIFDELCMD < \geq1%%% , d_{G'(u,v)\leq \alpha d_{G}(u,v)+\beta for u,v\in T)} . Multi-level subsetwise sparsifiers are generalizations in which terminal vertices require different levels or grades of service .
Edit intent: clarity