The Learning with Errors (LWE) problem is a versatile basis for building various purpose post-quantum schemes. Goldwasser et al. [ISC 2010] initialized the study of a variant of this problem called the Entropic LWE problem, where the LWE secret is generated from a distribution with a certain min-entropy. Brakerski and Döttling recently further extended the study in this field, and first proved the hardness of the Entropic LWE problem with unbounded secret [Eurocrypt 2020], then gave a similar result for the Entropic Ring-LWE problem [TCC 2020]. In this work, we systematically study the hardness of the Entropic Module-LWE problem. Adapting the “lossiness approach” to the module setting, we give lower entropy bounds for the secret distributions that guarantee the hardness of the Entropic Module-LWE problem in both search and decision cases, where results are divided into two settings: bounded and unbounded norm. We also present that our search entropy lower bound in the unbounded case is essentially tight. An application of our bounded result is to deduce the hardness for the Binary Module-LWE problem. One of our central techniques is a new generalized leftover hash lemma over rings, which might be of independent interest.@en

In stratified porous media, non-uniform velocity between layers combined with thermal conduction across layers causes spreading of the thermal front: thermal Taylor dispersion. Conventional upscaling not accounting for this heterogeneity within simulation grid blocks underestimates thermal dispersion, leading to overestimation of thermal breakthrough time. We derive a model for effective longitudinal thermal diffusivity in the direction of flow, αeff, to represent the effective thermal dispersion in two-layer media. αeff, accounting for thermal Taylor dispersion, is much greater than the thermal diffusivity of the rock itself. We define a dimensionless number, NTC, a ratio of times for longitudinal convection to transverse conduction, as an indicator of transverse thermal equilibration of the system during cold- or hot-water injection. For NTC > 5, thermal dispersion in the two-layer system closely approximates a single layer with αeff. This suggests a two-layer medium satisfying NTC > 5 can be combined into a single layer with an effective longitudinal thermal diffusivity αeff. In application to a geothermal reservoir, one can apply the model to perform upscaling in stages, i.e. combining two layers satisfying the NTC criterion in each stage. The αeff model accounting for the fine-scale heterogeneity within simulation grid blocks would enhance the prediction accuracy of thermal breakthrough time and thus thermal lifetime.@en

Satellite retrieval of vertical column densities (VCDs) of tropospheric nitrogen dioxide (NO₂) is critical for NO_x pollution and impact evaluation. For regions with high aerosol loadings, the retrieval accuracy is greatly affected by whether aerosol optical effects are treated implicitly (as additional effective clouds) or explicitly, among other factors. Our previous POMINO algorithm explicitly accounts for aerosol effects to improve the retrieval, especially in polluted situations over China, by using aerosol information from GEOS-Chem simulations with further monthly constraints by MODIS/Aqua aerosol optical depth (AOD) data. Here we present a major algorithm update, POMINO v1.1, by constructing a monthly climatological dataset of aerosol extinction profiles, based on level 2 CALIOP/CALIPSO data over 2007-2015, to better constrain the modeled aerosol vertical profiles. We find that GEOS-Chem captures the month-to-month variation in CALIOP aerosol layer height (ALH) but with a systematic underestimate by about 300-600 m (season and location dependent), due to a too strong negative vertical gradient of extinction above 1 km. Correcting the model aerosol extinction profiles results in small changes in retrieved cloud fraction, increases in cloud-top pressure (within 2 %-6 % in most cases), and increases in tropospheric NO₂ VCD by 4 %-16 % over China on a monthly basis in 2012. The improved NO₂ VCDs (in POMINO v1.1) are more consistent with independent ground-based MAX-DOAS observations (R²=0.80, NMB =-3.4 %, for 162 pixels in 49 days) than POMINO (R²=0.80, NMB =-9.6 %), DOMINO v2 (R²=0.68, NMB =-2.1 %), and QA4ECV (R²=0.75, NMB =-22.0 %) are. Especially on haze days, R² reaches 0.76 for POMINO v1.1, much higher than that for POMINO (0.68), DOMINO v2 (0.38), and QA4ECV (0.34). Furthermore, the increase in cloud pressure likely reveals a more realistic vertical relationship between cloud and aerosol layers, with aerosols situated above the clouds in certain months span id=page2 instead of always below the clouds. The POMINO v1.1 algorithm is a core step towards our next public release of the data product (POMINO v2), and it will also be applied to the recently launched S5P-TROPOMI sensor.

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Knowledge of the field of view (FOV) of a remote sensing instrument is particularly important when interpreting their data and merging them with other spatially referenced data. Especially for instruments in space, information on the actual FOV, which may change during operation, may be difficult to obtain. Also, the FOV of ground-based devices may change during transportation to the field site, where appropriate equipment for the FOV determination may be unavailable. This paper presents an independent, simple and robust method to retrieve the FOV of an instrument during operation, i.e. the two-dimensional sensitivity distribution, sampled on a discrete grid. The method relies on correlated measurements featuring a significantly higher spatial resolution, e.g. by an imaging instrument accompanying a spectrometer. The method was applied to two satellite instruments, GOME-2 and OMI, and a ground-based differential optical absorption spectroscopy (DOAS) instrument integrated in an SO2 camera. For GOME-2, quadrangular FOVs could be retrieved, which almost perfectly match the provided FOV edges after applying a correction for spatial aliasing inherent to GOME-type instruments. More complex sensitivity distributions were found at certain scanner angles, which are probably caused by degradation of the moving parts within the instrument. For OMI, which does not feature any moving parts, retrieved sensitivity distributions were much smoother compared to GOME-2. A 2-D super-Gaussian with six parameters was found to be an appropriate model to describe the retrieved OMI FOV. The comparison with operationally provided FOV dimensions revealed small differences, which could be mostly explained by the limitations of our IFR implementation. For the ground-based DOAS instrument, the FOV retrieved using SO2-camera data was slightly smaller than the flat-disc distribution, which is assumed by the state-of-the-art correlation technique. Differences between both methods may be attributed to spatial inhomogeneities. In general, our results confirm the already deduced FOV distributions of OMI, GOME-2, and the ground-based DOAS. It is certainly applicable for degradation monitoring and verification exercises. For satellite instruments, the gained information is expected to increase the accuracy of combined products, where measurements of different instruments are integrated, e.g. mapping of high-resolution cloud information, incorporation of surface climatologies. For the SO2-camera community, the method presents a new and efficient tool to monitor the DOAS FOV in the field.@en

We present a concealing method in which an anti-point spread function (APSF) is generated using binary optics, which produces a large-scale dark area in the focal region that can hide any object located within it. This result is achieved by generating two identical PSFs of opposite signs, one consisting of positive electromagnetic waves from the zero-phase region of the binary optical element and the other consisting of negative electromagnetic waves from the pi-phase region of the binary optical element.

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Systematic physical experiments examining the packing densification of mono-sized cylindrical particles subject to 3D mechanical vibration were carried out. The influence of vibration conditions such as vibration time, frequency, amplitude, vibration strength, container size, and the aspect ratio and sphericity of the particle on the packing density were analyzed and discussed. For each initial packing density with a certain aspect ratio, operating parameters were optimized to achieve much denser packing. The results indicate that the packing density initially increases with vibration time and then remains constant. The effects of vibration frequency and amplitude on the packing densification have similar trends, i.e. the packing density first increases with the vibration frequency or amplitude to a high value and then decreases; too large or small frequency or amplitude does not enhance densification. Increasing the container size can reduce container wall effects and help achieve a high packing density. Varying the particle aspect ratio and sphericity can lead to different dense random packing structures. Overall, based on results of the examined systems, the highest random packing density obtained in an infinite sized container can reach 0.73, which agrees well with corresponding numerical and analytical results in the literature.

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