The Lunar Fossil Figure in a Cassini State

The present ellipsoidal figure of the Moon requires a deformation that is significantly larger than the hydrostatic deformation in response to the present rotational and tidal potentials. This has long been explained as due to a fossil rotational and tidal deformation from a time when the Moon was closer to Earth. Previous studies constraining the orbital parameters at the time the fossil deformation was established find that high orbit eccentricities (e ≳ 0.2) are required at this ancient time, which is difficult to reconcile with the freezing of a fossil figure owing to the expected large tidal heating. We extend previous fossil deformation studies in several ways. First, we consider the effect of removing South Pole−Aitken (SPA) contributions from the present observed deformation using a nonaxially symmetric SPA model. Second, we use the assumption of an equilibrium Cassini state as an additional constraint, which allows us to consider the fossil deformation due to nonzero obliquity self-consistently. A fossil deformation established during Cassini state 1, 2, or 4 is consistent with the SPA-corrected present deformation. However, a fossil deformation established during Cassini state 2 or 4 requires large obliquity and orbit eccentricity (ϵ ∼ 68° and e ∼ 0.65), which are difficult to reconcile with the corresponding strong tidal heating. The most likely explanation is a fossil deformation established during Cassini state 1, with a small obliquity (ϵ ∼ −0.2°) and an orbit eccentricity range that includes zero eccentricity (0 ≤ e ≲ 0.3).

REDUCING THE CLOCKWISE-ALGORITHM TO k LENGTH CLASSES

In the present paper, we consider an optimization problem related to the extension in k-dimensions of the well known 3x3 points problem by Sam Loyd. In particular, thanks to a variation of the so called “clockwise-algorithm”, we show how it is possible to visit all the 3^k points of the k-dimensional grid given by the Cartesian product of (0, 1, 2) using covering trails formed by h(k)=(3^k-1)/2 links who belong to k (Euclidean) length classes. We can do this under the additional constraint of allowing only turning points which belong to the set B(k):={(0, 3) x (0, 3) x ... x (0, 3)}.

Learning to Approximate Industrial Problems by Operations Research Classic Problems

Operations research (OR) practitioners are accustomed to dealing with variants of classic OR problems. Indeed, an industrial problem often looks like a traveling salesman problem, a vehicle routing problem, a shortest path problem, etc., but has an additional constraint or a different objective that prevent the use of the powerful algorithms produced by decades of research on the classic OR problems. This situation can be frustrating, notably when we realize that the classic problem catches most of the structure of the variant. In “Learning to approximate industrial problems by operations research classic problems,” Axel Parmentier introduces a machine learning approach to use the algorithms for the classic OR problems on the variant. The idea is to leverage structured learning to obtain a mapping that approximates an instance of the variant by an instance of the classic problem.

Sedimentological responses to initial continental collision: Triggering of sand injection and onset of mass movement in a syn-collisional trench basin, Saga, southern Tibet

A continuous Late Cretaceous-Paleocene sedimentary succession within the India-Asia collision suture zone in Xigaze, Tibet, contains a c. 80 m thick sand injection complex immediately overlain by a c. 60 m thick mass transport deposit (MTD, the first of several) with the first evidence of Asian provenance, and immediately followed by a ∼61 Ma tuff. The youngest in situ strata with unequivocal Indian provenance are probably the source beds of the sand intrusions, separated from the first MTD by c. 50 m of pelagic deposits that potentially represent an interval of several million years; the collision could thus have occurred at any time within this interval. However, the uppermost limit of the sand intrusions closely coinciding with the MTD suggests that they occurred penecontemporaneously, possibly associated with initial continental collision. This may provide additional constraint of initial collision onset at c. 61 Ma. Co-occurrence of MTDs and sand injections are possibly good sedimentary indicators of continental collision onset and characteristic of syn-collisional trench basins. Since neither the youngest Indian nor the oldest Asian provenance sediments are in their original stratigraphic position, this study shows that detailed sedimentological work combined with provenance study can better constrain the timing of continental collision.

To Conserve, or Not to Conserve: A Review of Nonconservative Theories of Gravity

Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy–momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity allowing departures from the usual conservative framework. Many of these theories became popular in the last few years, aiming to describe the phenomenology behind dark matter and dark energy. However, within these scenarios, it is common to see attempts to preserve the conservative property of the energy–momentum tensor. Most of the time, it is done by means of some additional constraint that ensures the validity of the standard conservation law, as long as this option is available in the theory. However, if no such extra constraint is available, the theory will inevitably carry a non-trivial conservation law as part of its structure. In this work, we review some of such proposals discussing the theoretical construction leading to the non-conservation of the energy–momentum tensor.

Modification of Algorithm of Directed Graph Paths Decomposition with Schedule

This study aims to refinement of the oriented graph paths decomposition algorithm. An additional constraint on the balance parameter is considered to take into account the locomotive departure schedule. Also new rule to compute Ns parameters is given. An example of the operation of the oriented graph paths decomposition algorithm with the schedule is given. The scientific and practical novelty of the work lies in a significant reduction in the dimension of the original problem, which is especially important in the conditions of transport networks of complex topology.

High-Accuracy 3-D Sensor for Rivet Inspection Using Fringe Projection Profilometry with Texture Constraint

Riveted workpieces are widely used in manufacturing; however, current inspection sensors are mainly limited in nondestructive testing and obtaining the high-accuracy dimension automatically is difficult. We developed a 3-D sensor for rivet inspection using fringe projection profilometry (FPP) with texture constraint. We used multi-intensity high dynamic range (HDR) FPP method to address the varying reflectance of the metal surface then utilized an additional constraint calculated from the fused HDR texture to compensate for the artifacts caused by phase mixture around the stepwise edge. By combining the 2-D contours and 3-D FPP data, rivets can be easily segmented, and the edge points can be further refined for diameter measurement. We tested the performance on a sample of riveted aluminum frame and evaluated the accuracy using standard objects. Experiments show that denser 3-D data of a riveted metal workpiece can be acquired with high accuracy. Compared with the traditional FPP method, the diameter measurement accuracy can be improved by 50%.

Smooth adversarial examples

This paper investigates the visual quality of the adversarial examples. Recent papers propose to smooth the perturbations to get rid of high frequency artifacts. In this work, smoothing has a different meaning as it perceptually shapes the perturbation according to the visual content of the image to be attacked. The perturbation becomes locally smooth on the flat areas of the input image, but it may be noisy on its textured areas and sharp across its edges.This operation relies on Laplacian smoothing, well-known in graph signal processing, which we integrate in the attack pipeline. We benchmark several attacks with and without smoothing under a white box scenario and evaluate their transferability. Despite the additional constraint of smoothness, our attack has the same probability of success at lower distortion.

Resolving color differences of comet 41P/Tuttle-Giacobini-Kresák

Three different measurement campaigns have resulted in three drastically different sets of color measurements of Comet 41P/Tuttle-Giacobini-Kresák, ranging from a strongly red to a strongly blue color. Although the color slope is normalized to the wavelength range between the filters used, this only serves to partially normalize the resulting color, as the reflectance of cometary dust has a very strong dependence on particle absorption, which may change significantly over the wavelength range of measurement. We demonstrate that the different measurements are physical and are consistent with real materials; for example, we are able to reproduce the color measured during one epoch in which both strong blue and red color slopes were measured almost simultaneously in different filter sets with the mineral dust pyroxene. Such measurements with different filter sets serve as an additional constraint in modeling dust properties.