Hasil untuk "Earthwork. Foundations"

N. Wildmann, L. Györy

<p>This study demonstrates the feasibility of measuring temperature variance and heat flux with self-calibrated fine-wire platinum resistance thermometers (FWPRT) on multicopter drones. The sensors are especially designed for light weight, fast response-times and to be carried on miniature drones for turbulence measurements. A significant improvement was found in vertical profiling of temperature gradients compared to slower solid-state sensors, demonstrating reduced hysteresis between ascent and descent phases and accurate representation of strong gradients. More than 100 single flights with the sensors attached to drones of the SWUF-3D fleet were carried out in vicinity to a meteorological mast array at the WiValdi wind energy research park in Northern Germany. The comparison to sonic anemometers shows that temperature variance can be accurately measured within the background flow variability. The same applies for heat flux, which was measured for the first time with multicopter UAS and the eddy covariance method without external sensors. Heat flux is a crucial parameter to understand the energy balance of the atmospheric boundary layer and turbulent mixing. An uncertainty below 50 W m<span class="inline-formula">⁻²</span> was determined with the constraint that only low to moderate wind speed conditions (3–8 m s<span class="inline-formula">⁻¹</span>) could be used to allow vertical wind speed measurements with the current algorithm. The results indicate that the temperature sensors are suited for heat flux measurements, but further improvements are necessary with regard to vertical wind speed estimates to decrease the overall uncertainty.</p>

Sayan Sadhukhan, Warren Hare, Yves Lucet

The vertical alignment optimization problem in road design seeks the optimal vertical alignment of a road at minimal cost, taking into account earthwork while meeting all safety and design requirements. In recent years, modelling techniques have been advanced to incorporate: side slopes, multiple material types, multiple hauling types, and road networks. However, the advancements were created disjointly with implementations that only made a single advancement to the basic model. Herein, we present a mixed-integer linear programming optimization model that unifies all previous advancements. The model further improves on previous work by maintaining convexity even in the multi-material setting. We compare our new model to previous models, validate it numerically, and demonstrate its capability in approximating material volumes. Our new model performs particularly well for determining the optimal vertical alignment for large road networks.

Z. Yuan, Z. Yuan, G. Fu et al.

<p>This paper describes a neural network cloud masking scheme from PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Science coupled with Observations from a Lidar) multi-angle polarimetric measurements. The algorithm has been trained on synthetic measurements and has been applied to the processing of 1 year of PARASOL data. Comparisons of the retrieved cloud fraction with MODIS (Moderate Resolution Imaging Spectroradiometer) products show overall agreement in spatial and temporal patterns, but the PARASOL neural network (PARASOL-NN) retrieves lower cloud fractions. Comparisons with a goodness-of-fit mask from aerosol retrievals suggest that the NN cloud mask flags fewer clear pixels as cloudy than MODIS (<span class="inline-formula">∼</span> 3 % of the clear pixels versus <span class="inline-formula">∼</span> 15 % by MODIS). On the other hand the NN classifies more pixels incorrectly as clear than MODIS (<span class="inline-formula">∼</span> 20 % by NN, versus <span class="inline-formula">∼</span> 15 % by MODIS). Additionally, the NN and MODIS cloud mask have been applied to the aerosol retrievals from PARASOL using the Remote Sensing of Trace Gas and Aerosol Products (RemoTAP) algorithm. Validation with AERONET shows that the NN cloud mask performs comparably with MODIS in screening residual cloud contamination in retrieved aerosol properties. Our study demonstrates that cloud masking from multi-angle polarimeter (MAP) aerosol retrievals can be performed based on the MAP measurements themselves, making the retrievals independent of the availability of a cloud imager.</p>

Hanwen Xu, Mark Randall, Lei Li et al.

The escalating risk of urban inundation has drawn increased attention to urban stormwater management. This study proposes a multi-objective optimization for terrain modification, combining the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with digital elevation model (DEM)-based hydrological cost factor analysis. To reduce the precipitation erosive forces and runoff kinetic energy, the resulting framework offers the possibility of efficiently searching numerous solutions for trade-off sets that meet three conflicting objectives: minimizing maximum flow velocity, maximizing runoff path length and minimizing earthwork costs. Our application case study in Høje Taastrup, Denmark, demonstrates the ability of the optimization framework to iteratively generate diversified modification scenarios, which form the reference for topography planning. The three individual objective preferred solutions, a balanced solution, and twenty solutions under regular ordering are selected and visualized to determine the limits of the optimization and the cost-effectiveness tendency. Integrating genetic algorithms with DEM-based hydrological analysis demonstrates the potential to consider more complicated hydrological benefit objectives with open-ended characteristics. It provides a novel and efficient way to optimize topographic characteristics for improving holistic stormwater management strategies.

Ilan Shomorony, Reinhard Heckel

Due to its longevity and enormous information density, DNA is an attractive medium for archival data storage. Thanks to rapid technological advances, DNA storage is becoming practically feasible, as demonstrated by a number of experimental storage systems, making it a promising solution for our society's increasing need of data storage. While in living things, DNA molecules can consist of millions of nucleotides, due to technological constraints, in practice, data is stored on many short DNA molecules, which are preserved in a DNA pool and cannot be spatially ordered. Moreover, imperfections in sequencing, synthesis, and handling, as well as DNA decay during storage, introduce random noise into the system, making the task of reliably storing and retrieving information in DNA challenging. This unique setup raises a natural information-theoretic question: how much information can be reliably stored on and reconstructed from millions of short noisy sequences? The goal of this monograph is to address this question by discussing the fundamental limits of storing information on DNA. Motivated by current technological constraints on DNA synthesis and sequencing, we propose a probabilistic channel model that captures three key distinctive aspects of the DNA storage systems: (1) the data is written onto many short DNA molecules that are stored in an unordered fashion; (2) the molecules are corrupted by noise and (3) the data is read by randomly sampling from the DNA pool. Our goal is to investigate the impact of each of these key aspects on the capacity of the DNA storage system. Rather than focusing on coding-theoretic considerations and computationally efficient encoding and decoding, we aim to build an information-theoretic foundation for the analysis of these channels, developing tools for achievability and converse arguments.

Carlo Rovelli, Francesca Vidotto

Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual structure appropriate to make sense of the quantum aspects of space and time. In the course of the last decades, an extensive discussion on this problem has led to a clear conceptual picture, that provides a coherent conceptual foundation of today's Loop Quantum Gravity. We review this foundation, addressing issues such as the sense in which space and time are emergent, the notion of locality, the role of truncation that enables physical computations on finite graphs, the problem of time, and the characterization of the observable quantities in quantum gravity.

Benedikt Ahrens, Paige Randall North

In this paper, we explore the 'equivalence principle' (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the kinds of objects under consideration. In set theoretic foundations, EP may not always hold: for instance, the statement '1 \in N' is not invariant under isomorphism of sets. In univalent foundations, on the other hand, EP has been proven for many mathematical structures. We first give an overview of earlier attempts at designing foundations that satisfy EP. We then describe how univalent foundations validates EP.

B. Vansevenant, B. Vansevenant, B. Vansevenant et al.

<p>Atmospheric particles have several impacts on health and the environment, especially in urban areas. Parts of those particles are not fresh and have undergone atmospheric chemical and physical processes. Due to a lack of representativeness of experimental conditions and experimental artifacts such as particle wall losses in chambers, there are uncertainties on the effects of physical processes (condensation, nucleation and coagulation) and their role in particle evolution from modern vehicles. This study develops a new method to correct wall losses, accounting for size dependence and experiment-to-experiment variations. It is applied to the evolution of fresh diesel exhaust particles to characterize the physical processes which they undergo. The correction method is based on the black carbon decay and a size-dependent coefficient to correct particle distributions. Six diesel passenger cars, Euro 3 to Euro 6, were driven on a chassis dynamometer with Artemis Urban cold start and Artemis Motorway cycles. Exhaust was injected in an 8 m<span class="inline-formula">³</span> chamber with Teflon walls. The physical evolution of particles was characterized during 6 to 10 h. Increase in particle mass is observed even without photochemical reactions due to the presence of intermediate-volatility organic compounds and semi-volatile organic compounds. These compounds were quantified at emission and induce a particle mass increase up to 17 % h<span class="inline-formula">⁻¹</span>, mainly for the older vehicles (Euro 3 and Euro 4). Condensation is 4 times faster when the available particle surface is multiplied by 6.5. If initial particle number concentration is below [8–9] <span class="inline-formula">×</span> 10<span class="inline-formula">⁴</span> cm<span class="inline-formula">⁻³</span>, a nucleation mode seems to be present but not measured by a scanning mobility particle sizer (SMPS). The growth of nucleation-mode particles results in an increase in measured [PN]. Above this threshold, particle number concentration decreases due to coagulation, up to <span class="inline-formula">−</span>27 % h<span class="inline-formula">⁻¹</span>. Under those conditions, the chamber and experimental setup are well suited to characterizing and quantifying the process of coagulation.</p>

Özlem Tuğfe Demir, Emil Björnson, Luca Sanguinetti

Imagine a coverage area where each mobile device is communicating with a preferred set of wireless access points (among many) that are selected based on its needs and cooperate to jointly serve it, instead of creating autonomous cells. This effectively leads to a user-centric post-cellular network architecture, which can resolve many of the interference issues and service-quality variations that appear in cellular networks. This concept is called User-centric Cell-free Massive MIMO (multiple-input multiple-output) and has its roots in the intersection between three technology components: Massive MIMO, coordinated multipoint processing, and ultra-dense networks. The main challenge is to achieve the benefits of cell-free operation in a practically feasible way, with computational complexity and fronthaul requirements that are scalable to enable massively large networks with many mobile devices. This monograph covers the foundations of User-centric Cell-free Massive MIMO, starting from the motivation and mathematical definition. It continues by describing the state-of-the-art signal processing algorithms for channel estimation, uplink data reception, and downlink data transmission with either centralized or distributed implementation. The achievable spectral efficiency is mathematically derived and evaluated numerically using a running example that exposes the impact of various system parameters and algorithmic choices. The fundamental tradeoffs between communication performance, computational complexity, and fronthaul signaling requirements are thoroughly analyzed. Finally, the basic algorithms for pilot assignment, dynamic cooperation cluster formation, and power optimization are provided, while open problems related to these and other resource allocation problems are reviewed. All the numerical examples can be reproduced using the accompanying Matlab code.

P. Eriksson, B. Rydberg, V. Mattioli et al.

<p>The second generation of the EUMETSAT Polar System (EPS-SG) will include the Ice Cloud Imager (ICI), the first operational sensor covering sub-millimetre wavelengths. Three copies of ICI will be launched that together will give a measurement time series exceeding 20 years. Due to the novelty of ICI, preparing the data processing is especially important and challenging. This paper focuses on activities related to the operational product planned, but also presents basic technical characteristics of the instrument. A retrieval algorithm based on Bayesian Monte Carlo integration has been developed. The main retrieval quantities are ice water path (IWP), mean mass height (<span class="inline-formula"><i>Z</i>_m</span>) and mean mass diameter (<span class="inline-formula"><i>D</i>_m</span>). A novel part of the algorithm is that it fully presents the inversion as a description of the posterior probability distribution. This is preferred for ICI as its retrieval errors do not always follow Gaussian statistics. A state-of-the-art retrieval database is used to test the algorithm and to give an updated estimate of the retrieval performance. The degrees of freedom in measured radiances, and consequently the retrieval precision, vary with cloud situation. According to present simulations, IWP, <span class="inline-formula"><i>Z</i>_m</span> and <span class="inline-formula"><i>D</i>_m</span> can be determined with 90&thinsp;% confidence at best inside 50&thinsp;%, 700&thinsp;<span class="inline-formula">m</span> and 50&thinsp;<span class="inline-formula">µm</span>, respectively. The retrieval requires that the data from the 13 channels of ICI are remapped to a common footprint. First estimates of the errors introduced by this remapping are also presented.</p>

T. Hilbig, K. Bramstedt, M. Weber et al.

<p>SCIAMACHY (SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY) on-board the European Environmental Satellite (Envisat) provided spectrally resolved measurements in the wavelength range from 0.24 to 2.4&thinsp;<span class="inline-formula">µm</span> by looking into the Earth's atmosphere using different viewing geometries (limb, nadir, solar, and lunar occultation). These observations were used to derive a multitude of parameters, in particular atmospheric trace gas amounts. In addition to radiance measurements solar spectral irradiances (SSIs) were measured on a daily basis. The instrument was operating for nearly a decade, from August 2002 to April 2012. Due to the harsh space environment, it suffered from continuous optical degradation. As part of recent radiometric calibration activities an optical (physical) model was introduced that describes the behaviour of the scanner unit of SCIAMACHY with time <span class="cit" id="xref_paren.1">(<a href="#bib1.bibx30">Krijger et al.</a>, <a href="#bib1.bibx30">2014</a>)</span>. This model approach accounts for optical degradation by assuming contamination layers on optical surfaces in the scanner unit. The variation in layer thicknesses of the various optical components is determined from the combination of solar measurements from different monitoring light paths available for SCIAMACHY. In this paper, we present an optimisation of this degradation correction approach, which in particular improves the solar spectral data. An essential part of the modification is the use of measurements from SCIAMACHY's internal white light source (WLS) in combination with direct solar measurements. The WLS, as an independent light source, therefore, gives an opportunity to better separate instrument variations and natural solar variability. However, the WLS emission depends on its burning time and changes with time as well. To use these measurements in the optimised degradation correction, the change in the WLS emission in space needs to be characterised first. The changes in the WLS with accumulated burning time are in good agreement with detailed laboratory lamp studies by <span class="cit" id="xref_text.2"><a href="#bib1.bibx58">Sperling et al.</a> (<a href="#bib1.bibx58">1996</a>)</span>. Although the optimised degradation-corrected SCIAMACHY SSIs still show some instrumental issues when compared to SSI measurements from other instruments and model reconstructions, our study demonstrates the potential for the use of an internal WLS for degradation monitoring.</p>

Ingrid Hotz, Roxana Bujack, Christoph Garth et al.

Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to provide a taxonomy of the usage of mathematics in visualization, and to identify a fundamental set of mathematics that should be taught to students as part of an introduction to contemporary visualization research. Within the scope of this chapter, we are unable to provide a full review of all mathematical foundations of visualization; rather, we identify a number of concepts that are useful in visualization, explain their significance, and provide references for further reading.

X. Zhang, X. Zhang, J. Ortega et al.

Experiments performed in laboratory chambers have contributed significantly to the understanding of the fundamental kinetics and mechanisms of the chemical reactions occurring in the atmosphere. Two chemical regimes, classified as <q>high-NO</q> vs. <q>zero-NO</q> conditions, have been extensively studied in previous chamber experiments. Results derived from these two chemical scenarios are widely parameterized in chemical transport models to represent key atmospheric processes in urban and pristine environments. As the anthropogenic NO_<i>x</i> emissions in the United States have decreased remarkably in the past few decades, the classic <q>high-NO</q> and <q>zero-NO</q> conditions are no longer applicable to many regions that are constantly impacted by both polluted and background air masses. We present here the development and characterization of the NCAR Atmospheric Simulation Chamber, which is operated in steady-state continuous flow mode for the study of atmospheric chemistry under <q>intermediate NO</q> conditions. This particular chemical regime is characterized by constant sub-ppb levels of NO and can be created in the chamber by precise control of the inflow NO concentration and the ratio of chamber mixing to residence timescales. Over the range of conditions achievable in the chamber, the lifetime of peroxy radicals (RO₂), a key intermediate from the atmospheric degradation of volatile organic compounds (VOCs), can be extended to several minutes, and a diverse array of reaction pathways, including unimolecular pathways and bimolecular reactions with NO and HO₂, can thus be explored. Characterization experiments under photolytic and dark conditions were performed and, in conjunction with model predictions, provide a basis for interpretation of prevailing atmospheric processes in environments with intertwined biogenic and anthropogenic activities. We demonstrate the proof of concept of the steady-state continuous flow chamber operation through measurements of major first-generation products, methacrolein (MACR) and methyl vinyl ketone (MVK), from OH- and NO₃-initiated oxidation of isoprene.

C. D. Christopoulos, S. Garimella, S. Garimella et al.

<p>Compositional analysis of atmospheric and laboratory aerosols is often conducted via single-particle mass spectrometry (SPMS), an in situ and real-time analytical technique that produces mass spectra on a single-particle basis. In this study, classifiers are created using a data set of SPMS spectra to automatically differentiate particles on the basis of chemistry and size. Machine learning algorithms build a predictive model from a training set for which the aerosol type associated with each mass spectrum is known a priori. Our primary focus surrounds the growing of random forests using feature selection to reduce dimensionality and the evaluation of trained models with confusion matrices. In addition to classifying  ∼ 20 unique, but chemically similar, aerosol types, models were also created to differentiate aerosol within four broader categories: fertile soils, mineral/metallic particles, biological particles, and all other aerosols. Differentiation was accomplished using  ∼ 40 positive and negative spectral features. For the broad categorization, machine learning resulted in a classification accuracy of  ∼ 93&thinsp;%. Classification of aerosols by specific type resulted in a classification accuracy of  ∼ 87&thinsp;%. The <q>trained</q> model was then applied to a <q>blind</q> mixture of aerosols which was known to be a subset of the training set. Model agreement was found on the presence of secondary organic aerosol, coated and uncoated mineral dust, and fertile soil.</p>

J. Schwarz, J. Schwarz, G. Kirchengast et al.

Global Navigation Satellite System (GNSS) radio occultation (RO) observations are highly accurate, long-term stable data sets and are globally available as a continuous record from 2001. Essential climate variables for the thermodynamic state of the free atmosphere – such as pressure, temperature, and tropospheric water vapor profiles (involving background information) – can be derived from these records, which therefore have the potential to serve as climate benchmark data. However, to exploit this potential, atmospheric profile retrievals need to be very accurate and the remaining uncertainties quantified and traced throughout the retrieval chain from raw observations to essential climate variables. The new Reference Occultation Processing System (rOPS) at the Wegener Center aims to deliver such an accurate RO retrieval chain with integrated uncertainty propagation. Here we introduce and demonstrate the algorithms implemented in the rOPS for uncertainty propagation from excess phase to atmospheric bending angle profiles, for estimated systematic and random uncertainties, including vertical error correlations and resolution estimates. We estimated systematic uncertainty profiles with the same operators as used for the basic state profiles retrieval. The random uncertainty is traced through covariance propagation and validated using Monte Carlo ensemble methods. The algorithm performance is demonstrated using test day ensembles of simulated data as well as real RO event data from the satellite missions CHAllenging Minisatellite Payload (CHAMP); Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC); and Meteorological Operational Satellite A (MetOp). The results of the Monte Carlo validation show that our covariance propagation delivers correct uncertainty quantification from excess phase to bending angle profiles. The results from the real RO event ensembles demonstrate that the new uncertainty estimation chain performs robustly. Together with the other parts of the rOPS processing chain this part is thus ready to provide integrated uncertainty propagation through the whole RO retrieval chain for the benefit of climate monitoring and other applications.

Giulio Chiribella, Robert W. Spekkens

We present here our introduction to the contributed volume "Quantum Theory: Informational Foundations and Foils", Springer Netherlands (2016). It highlights recent trends in quantum foundations and offers an overview of the contributions appearing in the book.

Jochen Szangolies

In-principle restrictions on the amount of information that can be gathered about a system have been proposed as a foundational principle in several recent reconstructions of the formalism of quantum mechanics. However, it seems unclear precisely why one should be thus restricted. We investigate the notion of paradoxical self-reference as a possible origin of such epistemic horizons by means of a fixed-point theorem in Cartesian closed categories due to F. W. Lawvere that illuminates and unifies the different perspectives on self-reference.

J. Stutz, B. Werner, M. Spolaor et al.

Observations of atmospheric trace gases in the tropical upper troposphere (UT), tropical tropopause layer (TTL), and lower stratosphere (LS) require dedicated measurement platforms and instrumentation. Here we present a new limb-scanning Differential Optical Absorption Spectroscopy (DOAS) instrument developed for NASA's Global Hawk (GH) unmanned aerial system and deployed during the Airborne Tropical TRopopause EXperiment (ATTREX). The mini-DOAS system is designed for automatic operation under unpressurized and unheated conditions at 14–18 km altitude, collecting scattered sunlight in three wavelength windows: UV (301–387 nm), visible (410–525 nm), and near infrared (900–1700 nm). A telescope scanning unit allows selection of a viewing angle around the limb, as well as real-time correction of the aircraft pitch. Due to the high altitude, solar reference spectra are measured using diffusors and direct sunlight. The DOAS approach allows retrieval of slant column densities (SCDs) of O₃, O₄, NO₂, and BrO with relative errors similar to other aircraft DOAS systems. Radiative transfer considerations show that the retrieval of trace gas mixing ratios from the observed SCD based on O₄ observations, the most common approach for DOAS measurements, is inadequate for high-altitude observations. This is due to the frequent presence of low-altitude clouds, which shift the sensitivity of the O₄ SCD into the lower atmosphere and make it highly dependent on cloud coverage. A newly developed technique that constrains the radiative transfer by comparing in situ and DOAS O₃ observations overcomes this issue. Extensive sensitivity calculations show that the novel O₃-scaling technique allows the retrieval of BrO and NO₂ mixing ratios at high accuracies of 0.5 and 15 ppt, respectively. The BrO and NO₂ mixing ratios and vertical profiles observed during ATTREX thus provide new insights into ozone and halogen chemistry in the UT, TTL, and LS.

K. S. Olsen, K. Strong, K. A. Walker et al.

The primary instrument on the Greenhouse gases Observing SATellite (GOSAT) is the Thermal And Near infrared Sensor for carbon Observations (TANSO) Fourier transform spectrometer (FTS). TANSO-FTS uses three short-wave infrared (SWIR) bands to retrieve total columns of CO₂ and CH₄ along its optical line of sight and one thermal infrared (TIR) channel to retrieve vertical profiles of CO₂ and CH₄ volume mixing ratios (VMRs) in the troposphere. We examine version 1 of the TANSO-FTS TIR CH₄ product by comparing co-located CH₄ VMR vertical profiles from two other remote-sensing FTS systems: the Canadian Space Agency's Atmospheric Chemistry Experiment FTS (ACE-FTS) on SCISAT (version 3.5) and the European Space Agency's Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on Envisat (ESA ML2PP version 6 and IMK-IAA reduced-resolution version V5R_CH4_224/225), as well as 16 ground stations with the Network for the Detection of Atmospheric Composition Change (NDACC). This work follows an initial inter-comparison study over the Arctic, which incorporated a ground-based FTS at the Polar Environment Atmospheric Research Laboratory (PEARL) at Eureka, Canada, and focuses on tropospheric and lower-stratospheric measurements made at middle and tropical latitudes between 2009 and 2013 (mid-2012 for MIPAS). For comparison, vertical profiles from all instruments are interpolated onto a common pressure grid, and smoothing is applied to ACE-FTS, MIPAS, and NDACC vertical profiles. Smoothing is needed to account for differences between the vertical resolution of each instrument and differences in the dependence on a priori profiles. The smoothing operators use the TANSO-FTS a priori and averaging kernels in all cases. We present zonally averaged mean CH₄ differences between each instrument and TANSO-FTS with and without smoothing, and we examine their information content, their sensitive altitude range, their correlation, their a priori dependence, and the variability within each data set. Partial columns are calculated from the VMR vertical profiles, and their correlations are examined. We find that the TANSO-FTS vertical profiles agree with the ACE-FTS and both MIPAS retrievals' vertical profiles within 4 % (± ∼  40 ppbv) below 15 km when smoothing is applied to the profiles from instruments with finer vertical resolution but that the relative differences can increase to on the order of 25 % when no smoothing is applied. Computed partial columns are tightly correlated for each pair of data sets. We investigate whether the difference between TANSO-FTS and other CH₄ VMR data products varies with latitude. Our study reveals a small dependence of around 0.1 % per 10 degrees latitude, with smaller differences over the tropics and greater differences towards the poles.

Tiziana Bascelli, Piotr Blaszczyk, Alexandre Borovik et al.

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.