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One of the common challenges faced by researchers in recent data analysis is missing values. In the context of penalized linear regression, which has been extensively explored over several decades, missing values introduce bias and yield a non-positive definite covariance matrix of the covariates, rendering the least square loss function non-convex. In this paper, we propose a novel procedure called the linear shrinkage positive definite (LPD) modification to address this issue. The LPD modification aims to modify the covariance matrix of the covariates in order to ensure consistency and positive definiteness. Employing the new covariance estimator, we are able to transform the penalized regression problem into a convex one, thereby facilitating the identification of sparse solutions. Notably, the LPD modification is computationally efficient and can be expressed analytically. In the presence of missing values, we establish the selection consistency and prove the convergence rate of the $\ell_1$-penalized regression estimator with LPD, showing an $\ell_2$-error convergence rate of square-root of $\log p$ over $n$ by a factor of $(s_0)^{3/2}$ ($s_0$: the number of non-zero coefficients). To further evaluate the effectiveness of our approach, we analyze real data from the Genomics of Drug Sensitivity in Cancer (GDSC) dataset. This dataset provides incomplete measurements of drug sensitivities of cell lines and their protein expressions. We conduct a series of penalized linear regression models with each sensitivity value serving as a response variable and protein expressions as explanatory variables.

Quantum information processing comprises physical processes, which obey the quantum speed limit (QSL): high speed requires strong driving. Single-qubit gates using Rabi oscillation, which is based on the rotating wave approximation (RWA), satisfy this bound in the form that the gate time $T$ is inversely proportional to the Rabi frequency $\Omega$, characterizing the driving strength. However, if the gate time is comparable or shorter than the qubit period $T_{0} \equiv 2\pi / \omega_{0}$, the RWA actually breaks down since the Rabi frequency has to be large compared to the qubit frequency $\omega_{0}$ due to the QSL, which is given as $T \gtrsim \pi/\Omega$. We show that it is possible to construct a universal set of single-qubit gates at this strong-coupling and ultrafast regime, by adjusting the central frequency $\omega$ and the Rabi frequency $\Omega$ of the driving pulse. We observe a transition in the scaling behavior of the central frequency from the long-gate time regime ($T \gg T_{0}$) to the short-gate time ($T \ll T_{0}$) regime. In the former, the central frequency is nearly resonant to the qubit, i.e., $\omega \simeq \omega_{0}$, whereas in the latter, the central frequency is inversely proportional to the gate time, i.e., $\omega \sim \pi/T$. We identify the transition gate time at which the scaling exponent $n$ of the optimal central frequency $\omega \sim T^{n}$ changes from $n=0$ to $n=-1$., Comment: 11 pages, 4 figures

Large Language Models (LLMs) have recently demonstrated significant potential in the field of time series forecasting, offering impressive capabilities in handling complex temporal data. However, their robustness and reliability in real-world applications remain under-explored, particularly concerning their susceptibility to adversarial attacks. In this paper, we introduce a targeted adversarial attack framework for LLM-based time series forecasting. By employing both gradient-free and black-box optimization methods, we generate minimal yet highly effective perturbations that significantly degrade the forecasting accuracy across multiple datasets and LLM architectures. Our experiments, which include models like TimeGPT and LLM-Time with GPT-3.5, GPT-4, LLaMa, and Mistral, show that adversarial attacks lead to much more severe performance degradation than random noise, and demonstrate the broad effectiveness of our attacks across different LLMs. The results underscore the critical vulnerabilities of LLMs in time series forecasting, highlighting the need for robust defense mechanisms to ensure their reliable deployment in practical applications., Comment: 11 pages, 5 figures

Timely detection and treatment are essential for maintaining eye health. Visual acuity (VA), which measures the clarity of vision at a distance, is a crucial metric for managing eye health. Machine learning (ML) techniques have been introduced to assist in VA measurement, potentially alleviating clinicians' workloads. However, the inherent uncertainties in ML models make relying solely on them for VA prediction less than ideal. The VA prediction task involves multiple sources of uncertainty, requiring more robust approaches. A promising method is to build prediction sets or intervals rather than point estimates, offering coverage guarantees through techniques like conformal prediction and Probably Approximately Correct (PAC) prediction sets. Despite the potential, to date, these approaches have not been applied to the VA prediction task.To address this, we propose a method for deriving prediction intervals for estimating visual acuity from fundus images with a PAC guarantee. Our experimental results demonstrate that the PAC guarantees are upheld, with performance comparable to or better than that of two prior works that do not provide such guarantees., Comment: To be published in ML4H 2024

We generalize cellular sheaf Laplacians on an ordered finite abstract simplicial complex to the set of simplices of a symmetric simplicial set. We construct a functor from the category of hypergraphs to the category of finite symmetric simplicial sets and define cellular sheaf Laplacians on the set of simplices of finite symmetric simplicial set induced by hypergraph. We provide formulas for cellular sheaf Laplacians and show that cellular sheaf Laplacian on an ordered finite abstract simplicial complex is exactly the ordered cellular sheaf Laplacian on the set of simplices induced by abstract simplicial complex., Comment: 20 pages, 1 figure

Deep Generative Models (DGMs) have rapidly advanced in recent years, becoming essential tools in various fields due to their ability to learn complex data distributions and generate synthetic data. Their importance in transportation research is increasingly recognized, particularly for applications like traffic data generation, prediction, and feature extraction. This paper offers a comprehensive introduction and tutorial on DGMs, with a focus on their applications in transportation. It begins with an overview of generative models, followed by detailed explanations of fundamental models, a systematic review of the literature, and practical tutorial code to aid implementation. The paper also discusses current challenges and opportunities, highlighting how these models can be effectively utilized and further developed in transportation research. This paper serves as a valuable reference, guiding researchers and practitioners from foundational knowledge to advanced applications of DGMs in transportation research., Comment: 64 pages, 21 figures, 4 tables

In this work, we present a quantum theory for pulsed photon pair generation in a single ring resonator. Our approach combines the Heisenberg picture input-output formalism with the Ikeda mapping from classical nonlinear optics. In doing so, we address the high-gain regime by incorporating non-perturbative effects, including self-phase modulation, cross-phase modulation, and time-ordering, which are roots for significantly different behaviors in the low-gain regime. We also account for optical losses by introducing an auxiliary waveguide, allowing for a more accurate representation of experimentally viable scenarios. Numerical simulations reveal that non-perturbative effects significantly distort transfer functions, making desirable operations challenging without careful optimization. We show that appropriate detuning of the pump frequency can mitigate these issues, leading to enhanced brightness and higher spectral purity in the high-gain regime. We further investigate the performance of a single ring resonator as a two-mode squeezer by analyzing various performance metrics under experimentally relevant optical loss conditions., Comment: 22 pages, 11 figures

This paper investigates the security vulnerabilities of adversarial-example-based image encryption by executing data reconstruction (DR) attacks on encrypted images. A representative image encryption method is the adversarial visual information hiding (AVIH), which uses type-I adversarial example training to protect gallery datasets used in image recognition tasks. In the AVIH method, the type-I adversarial example approach creates images that appear completely different but are still recognized by machines as the original ones. Additionally, the AVIH method can restore encrypted images to their original forms using a predefined private key generative model. For the best security, assigning a unique key to each image is recommended; however, storage limitations may necessitate some images sharing the same key model. This raises a crucial security question for AVIH: How many images can safely share the same key model without being compromised by a DR attack? To address this question, we introduce a dual-strategy DR attack against the AVIH encryption method by incorporating (1) generative-adversarial loss and (2) augmented identity loss, which prevent DR from overfitting -- an issue akin to that in machine learning. Our numerical results validate this approach through image recognition and re-identification benchmarks, demonstrating that our strategy can significantly enhance the quality of reconstructed images, thereby requiring fewer key-sharing encrypted images. Our source code to reproduce our results will be available soon., Comment: 12 pages

We introduce HyperCLOVA X, a family of large language models (LLMs) tailored to the Korean language and culture, along with competitive capabilities in English, math, and coding. HyperCLOVA X was trained on a balanced mix of Korean, English, and code data, followed by instruction-tuning with high-quality human-annotated datasets while abiding by strict safety guidelines reflecting our commitment to responsible AI. The model is evaluated across various benchmarks, including comprehensive reasoning, knowledge, commonsense, factuality, coding, math, chatting, instruction-following, and harmlessness, in both Korean and English. HyperCLOVA X exhibits strong reasoning capabilities in Korean backed by a deep understanding of the language and cultural nuances. Further analysis of the inherent bilingual nature and its extension to multilingualism highlights the model's cross-lingual proficiency and strong generalization ability to untargeted languages, including machine translation between several language pairs and cross-lingual inference tasks. We believe that HyperCLOVA X can provide helpful guidance for regions or countries in developing their sovereign LLMs., Comment: 44 pages; updated authors list and fixed author names

Multiple-phase estimation exploiting quantum states has broad applications in novel sensing and imaging technologies. However, the unavoidable presence of lossy environments in practical settings often diminishes the precision of phase estimations. To address this challenge, we propose an optimal multiple-phase estimation scheme that is inherently robust against photon loss, ensuring a persistent quantum advantage across all levels of photon loss. The scheme employs a multi-mode definite photon-number (DPN) state with weights optimized for given levels of photon loss. We theoretically demonstrate that the DPN state can sustain quantum enhancement in estimation precision under all levels of photon loss, compared to the classical benchmark that employs a coherent state input. The proposed scheme using DPN states generalizes earlier studies employing NOON states, which are only optimal when photon loss is small. We believe that our study, demonstrating persistent robustness to photon loss, paves the way for significant advancements in quantum-enhanced sensing technologies, enabling practical applications and quantum advantages in real-world scenarios., Comment: 11 pages, 5 figures, supplementary note

Cooperative Adaptive Cruise Control (CACC) plays a pivotal role in enhancing traffic efficiency and safety in Connected and Autonomous Vehicles (CAVs). Reinforcement Learning (RL) has proven effective in optimizing complex decision-making processes in CACC, leading to improved system performance and adaptability. Among RL approaches, Multi-Agent Reinforcement Learning (MARL) has shown remarkable potential by enabling coordinated actions among multiple CAVs through Centralized Training with Decentralized Execution (CTDE). However, MARL often faces scalability issues, particularly when CACC vehicles suddenly join or leave the platoon, resulting in performance degradation. To address these challenges, we propose Communication-Aware Reinforcement Learning (CA-RL). CA-RL includes a communication-aware module that extracts and compresses vehicle communication information through forward and backward information transmission modules. This enables efficient cyclic information propagation within the CACC traffic flow, ensuring policy consistency and mitigating the scalability problems of MARL in CACC. Experimental results demonstrate that CA-RL significantly outperforms baseline methods in various traffic scenarios, achieving superior scalability, robustness, and overall system performance while maintaining reliable performance despite changes in the number of participating vehicles.

Threefold Hopf semimetals are a novel type of topological semimetals that possess an internal anisotropy characterized by a dipolar structure of the Berry curvature and an isotropic energy band structure consisting of a Dirac cone and a flat band. In this study, we theoretically investigate the impact of internal anisotropy on plasmons in threefold Hopf semimetals using random-phase approximation. In contrast to the classical intuition that isotropy of the energy band dispersion leads to isotropic plasmons in the classical regime (i.e., in the wavelength limit), we find that plasmons in threefold Hopf semimetals exhibit notable anisotropy even in the long-wavelength limit. We derive an explicit analytical form of the long-wavelength plasmon frequency, and numerically demonstrate the validity of our results in a wide range of situations. Our work reveals that the anisotropy of long-wavelength plasmons can reach 25%, making it experimentally observable., Comment: 7 pages, 5 figures

Recently, remote-controlled quantum information processing has been proposed for its applications in secure quantum processing protocols and distributed quantum networks. For remote-controlled quantum gates, the experimental realization of controlled unitary (CU) gates between any quantum gates is an essential task. Here, we propose and experimentally demonstrate a scheme for implementing CU gates between arbitrary pairs of unitary gates using the polarization and time-bin degrees of freedom of single-photons. Then, we experimentally implement remote-controlled single-qubit unitary gates by controlling either the state preparation or measurement of the control qubit with high process fidelities. We believe that the proposed remote-controlled quantum gate model can pave the way for secure and efficient quantum information processing., Comment: 7 pages, 4 figures

A new scheme of a highly efficient hybrid laser cavity is proposed and experimentally demonstrated utilizing a hot cesium (Cs) vapor cell as an optical gain medium. The laser cavity consists of a macroscopic concave reflecting mirror (>99% reflectivity) and a 4% Fresnel-reflecting perpendicularly cleaved facet of a single mode fiber (SMF). The cylindrical cesium gain cell is located between these two reflectors. The SMF serves multiple roles: 1) a passive mode-matching component to approximate the pump beam diameter to that of the laser cavity mode within the cesium cell, 2) an output coupler with low reflectivity, and 3) a high beam-quality laser delivery with a low loss. Optimizing the pump beam waist diameter and the cesium vapor cell temperature, a high slope efficiency of 86% and continuous wave power of 419 mW were obtained in the pump power range of 400 to 600 mW, with an optical-to-optical conversion efficiency of 71%. The unique multi-functional role of the SMF in the hybrid cavity is fully described, and it can also be applied to other phases of high optical gain media., Comment: 15 pages, 4 figures

Addressing pedestrian safety at intersections is one of the paramount concerns in the field of transportation research, driven by the urgency of reducing traffic-related injuries and fatalities. With advances in computer vision technologies and predictive models, the pursuit of developing real-time proactive protection systems is increasingly recognized as vital to improving pedestrian safety at intersections. The core of these protection systems lies in the prediction-based evaluation of pedestrian's potential risks, which plays a significant role in preventing the occurrence of accidents. The major challenges in the current prediction-based potential risk evaluation research can be summarized into three aspects: the inadequate progress in creating a real-time framework for the evaluation of pedestrian's potential risks, the absence of accurate and explainable safety indicators that can represent the potential risk, and the lack of tailor-made evaluation criteria specifically for each category of pedestrians. To address these research challenges, in this study, a framework with computer vision technologies and predictive models is developed to evaluate the potential risk of pedestrians in real time. Integral to this framework is a novel surrogate safety measure, the Predicted Post-Encroachment Time (P-PET), derived from deep learning models capable to predict the arrival time of pedestrians and vehicles at intersections. To further improve the effectiveness and reliability of pedestrian risk evaluation, we classify pedestrians into distinct categories and apply specific evaluation criteria for each group. The results demonstrate the framework's ability to effectively identify potential risks through the use of P-PET, indicating its feasibility for real-time applications and its improved performance in risk evaluation across different categories of pedestrians.

In recent years, distributed quantum sensing has gained interest for a range of applications requiring networks of sensors, from global-scale clock synchronization to high energy physics. In particular, a network of entangled sensors can improve not only the sensitivity beyond the shot noise limit, but also enable a Heisenberg scaling with the number of sensors. Here, using bright entangled twin beams, we theoretically and experimentally demonstrate the detection of a linear combination of two distributed phases beyond the shot noise limit with a truncated SU(1,1) interferometer. We experimentally demonstrate a quantum noise reduction of 1.7 dB and a classical 3 dB signal-to-noise ratio improvement over the separable sensing approach involving two truncated SU(1,1) interferometers. Additionally, we theoretically extend the use of a truncated SU(1,1) interferometer to a multi-phase-distributed sensing scheme that leverages entanglement as a resource to achieve a quantum improvement in the scaling with the number of sensors in the network. Our results pave the way for developing quantum enhanced sensor networks that can achieve an entanglement-enhanced sensitivity.

Nonlinear quantum photonics serves as a cornerstone in photonic quantum technologies, such as universal quantum computing and quantum communications. The emergence of integrated photonics platform not only offers the advantage of large-scale manufacturing but also provides a variety of engineering methods. Given the complexity of integrated photonics engineering, a comprehensive simulation framework is essential to fully harness the potential of the platform. In this context, we introduce a nonlinear quantum photonics simulation framework which can accurately model a variety of features such as adiabatic waveguide, material anisotropy, linear optics components, photon losses, and detectors. Furthermore, utilizing the framework, we have developed a device scheme, chip-scale temporal walk-off compensation, that is useful for various quantum information processing tasks. Applying the simulation framework, we show that the proposed device scheme can enhance the squeezing parameter of photon-pair sources and the conversion efficiency of quantum frequency converters without relying on higher pump power., Comment: 35 pages, 33 figures, 4 tables

A novel method is presented for generating radiation using the beat wave associated with a bi-frequency laser pulse, to excite plasma oscillations in a plasma slab with a density gradient. By resonantly exciting a plasma wave, it can be localised and transformed into a plasma oscillator that produces a beam of radially polarised terahertz radiation. Particle-in-cell simulations and analytic theory are used to demonstrate its main characteristics, which includes narrow bandwidth. The radiator should have useful applications such as terahertz-band particle accelerators and pump-probe experiments.

Multi-mode NOON states can quantum-enhance multiple-phase estimation in the absence of photon loss. However, a multi-mode NOON state is known to be vulnerable to photon loss, and its quantum-enhancement can be dissipated by lossy environment. In this work, we demonstrate that a quantum advantage in estimate precision can still be achieved in the presence of photon loss. This is accomplished by optimizing the weights of the multi-mode NOON states according to photon loss rates in the multiple modes, including the reference mode which defines the other phases. For practical relevance, we also show that photon-number counting via a multi-mode beam-splitter achieves the useful, albeit sub-optimal, quantum advantage. We expect this work to provide valuable guidance for developing quantum-enhanced multiple-phase estimation techniques in lossy environments., Comment: 10 pages, 7 figures

Recently, using a powerful proprietary Large Language Model (LLM) (e.g., GPT-4) as an evaluator for long-form responses has become the de facto standard. However, for practitioners with large-scale evaluation tasks and custom criteria in consideration (e.g., child-readability), using proprietary LLMs as an evaluator is unreliable due to the closed-source nature, uncontrolled versioning, and prohibitive costs. In this work, we propose Prometheus, a fully open-source LLM that is on par with GPT-4's evaluation capabilities when the appropriate reference materials (reference answer, score rubric) are accompanied. We first construct the Feedback Collection, a new dataset that consists of 1K fine-grained score rubrics, 20K instructions, and 100K responses and language feedback generated by GPT-4. Using the Feedback Collection, we train Prometheus, a 13B evaluator LLM that can assess any given long-form text based on customized score rubric provided by the user. Experimental results show that Prometheus scores a Pearson correlation of 0.897 with human evaluators when evaluating with 45 customized score rubrics, which is on par with GPT-4 (0.882), and greatly outperforms ChatGPT (0.392). Furthermore, measuring correlation with GPT-4 with 1222 customized score rubrics across four benchmarks (MT Bench, Vicuna Bench, Feedback Bench, Flask Eval) shows similar trends, bolstering Prometheus's capability as an evaluator LLM. Lastly, Prometheus achieves the highest accuracy on two human preference benchmarks (HHH Alignment & MT Bench Human Judgment) compared to open-sourced reward models explicitly trained on human preference datasets, highlighting its potential as an universal reward model. We open-source our code, dataset, and model at https://kaistai.github.io/prometheus/., Comment: ICLR 2024

We study the generation of entanglement between two qubits which communicate through a single cavity mode of quantum light but have no direct interaction. We show that such entanglement can be generated simply by exchanging quanta with a third party, which is in our case the cavity mode. Exchanging only a single quantum creates maximal entanglement. A single quantum can be provided by an external quantum light source. However, we use a classical light source to pump quanta which are used for the exchange, and investigate the degree of two-qubit entanglement. We first identify a characteristic timescale of the interaction between the cavity mode and each qubit. We investigate two regimes of the driving pulse length, one is short and the other is long compared to the characteristic timescale of the interaction. In the first regime, it is known that the pulse can pump the system by generating a displacement of the cavity mode. We show that, by using a specific pulse shape, one can make the displacement to essentially vanish after the pulse finishes interaction with the cavity mode. In this case, a rotation of the qubits can be invoked. In addition, higher-order effects of the pulse including a non-local operation on the joint system of the cavity mode and the qubits are found, and we present a formalism to compute each term up to a given order. An explicit condition on the pulse shape for each term to be nonzero or suppressed is derived to enable an experimental design for verifying the entanglement generation using a classical light source. In the opposite regime where the driving is sufficiently long, we utilize a squeezed state which may be obtained adiabatically. We study how the squeezing and the accompanied rotation of qubits affect the generated two-qubit entanglement.

Deep probabilistic time series forecasting has gained attention for its ability to provide nonlinear approximation and valuable uncertainty quantification for decision-making. However, existing models often oversimplify the problem by assuming a time-independent error process and overlooking serial correlation. To overcome this limitation, we propose an innovative training method that incorporates error autocorrelation to enhance probabilistic forecasting accuracy. Our method constructs a mini-batch as a collection of $D$ consecutive time series segments for model training. It explicitly learns a time-varying covariance matrix over each mini-batch, encoding error correlation among adjacent time steps. The learned covariance matrix can be used to improve prediction accuracy and enhance uncertainty quantification. We evaluate our method on two different neural forecasting models and multiple public datasets. Experimental results confirm the effectiveness of the proposed approach in improving the performance of both models across a range of datasets, resulting in notable improvements in predictive accuracy., Comment: The 27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024); We corrected a misleading notation in the published version and added a link to the code

Magneto-optical microscopies, including optical measurements of magnetic circular dichroism, are increasingly ubiquitous tools for probing spin-orbit coupling, charge-carrier g-factors, and chiral excitations in matter, but the minimum detectable signal in classical magnetic circular dichroism measurements is fundamentally limited by the shot-noise limit of the optical readout field. Here, we use a two-mode squeezed light source to improve the minimum detectable signal in magnetic circular dichroism measurements by 3 dB compared with state-of-the-art classical measurements, even with relatively lossy samples like terbium gallium garnet. We also identify additional opportunities for improvement in quantum-enhanced magneto-optical microscopies, and we demonstrate the importance of these approaches for environmentally sensitive materials and for low temperature measurements where increased optical power can introduce unacceptable thermal perturbations.

Deep learning models for traffic forecasting often assume the residual is independent and isotropic across time and space. This assumption simplifies loss functions such as mean absolute error, but real-world residual processes often exhibit significant autocorrelation and structured spatiotemporal correlation. This paper introduces a dynamic regression (DR) framework to enhance existing spatiotemporal traffic forecasting models by incorporating structured learning for the residual process. We assume the residual of the base model (i.e., a well-developed traffic forecasting model) follows a matrix-variate seasonal autoregressive (AR) model, which is seamlessly integrated into the training process through the redesign of the loss function. Importantly, the parameters of the DR framework are jointly optimized alongside the base model. We evaluate the effectiveness of the proposed framework on state-of-the-art (SOTA) deep traffic forecasting models using both speed and flow datasets, demonstrating improved performance and providing interpretable AR coefficients and spatiotemporal covariance matrices.

Deep learning-based multivariate and multistep-ahead traffic forecasting models are typically trained with the mean squared error (MSE) or mean absolute error (MAE) as the loss function in a sequence-to-sequence setting, simply assuming that the errors follow an independent and isotropic Gaussian or Laplacian distributions. However, such assumptions are often unrealistic for real-world traffic forecasting tasks, where the probabilistic distribution of spatiotemporal forecasting is very complex with strong concurrent correlations across both sensors and forecasting horizons in a time-varying manner. In this paper, we model the time-varying distribution for the matrix-variate error process as a dynamic mixture of zero-mean Gaussian distributions. To achieve efficiency, flexibility, and scalability, we parameterize each mixture component using a matrix normal distribution and allow the mixture weight to change and be predictable over time. The proposed method can be seamlessly integrated into existing deep-learning frameworks with only a few additional parameters to be learned. We evaluate the performance of the proposed method on a traffic speed forecasting task and find that our method not only improves model performance but also provides interpretable spatiotemporal correlation structures., Comment: 11 pages, 4 figures, 2 table

Optomechanical sensors are capable of transducing external perturbations to resolvable optical signals. A particular regime of interest is that of high-bandwidth force detection, where an impulse is delivered to the system over a short period of time. Exceedingly sensitive impulse detection has been proposed to observe very weak signals like those for long range interactions with dark matter requiring much higher sensitivities than current sensors can provide. Quantum resources to go beyond the standard quantum limit of noise in these sensors include squeezing of the light used to transduce the signal, backaction evasion by measuring the optimum quadrature, and quantum nondemolition (QND) measurements which reduce backaction directly. However, it has been extremely difficult to determine a scheme where all these quantum resources contribute to noise reduction thereby exceeding the benefit of using only one quantum resource alone. We provide the theoretical limits to noise reduction while combining quantum enhanced readout techniques such as squeezing and QND measurements for these optomechanical sensors. We demonstrate that backaction evasion through QND techniques dramatically reduces the technical challenges presented when using squeezed light for broadband force detection, paving the way for combining multiple quantum noise reduction techniques for enhanced sensitivity in the context of impulse metrology., Comment: 14 pages, 7 figures